The Investigation of Fluid Properties and Seismic Attributes for Reservoir Characterization

THE INVESTIGATION INVESTIGATION OF FLUID PROPERTIES AND SEISMIC ATTRIBUTES ATTRIBUTES FOR RESERVOIR CHARACTERIZATION

By TERRA E. BULLOCH

A THESIS Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN GEOLOGICAL ENGINEERING

MICHIGAN TECHNOLOGICAL UNIVERSITY 1999

This thesis, “THE INVESTIGATION OF FLUID PROPERTIES AND SEISMIC ATTRIBUTES FOR RESERVOIR CHARACTERIZATION”, is hereby approved in part pa rtia iall fulfi fulfill llme ment nt of the the requ requir irem emen ents ts for the the De Degr gree ee of MAST MASTER ER OF SC SCIE IENC NCE E IN GEOLOGICAL ENGINEERING.

DEPARTMENT: Geological Engineering and Sciences

Signatures: Thesis Advisor:____________________________________  Dr. Wayne D. Pennington Department Chair:___________________________________  Dr. Theodore J. Bornhorst Date:_________ Date:_________________ _______________ ______________ __________ ___ _ 

ABSTRACT Seis Se ismi mic c da data ta are are used used in pe petr trol oleu eum m explo xplora rati tion on to de defin fine e ge geol olog ogic ic fea eatu ture res s in the subsurface. Recent advancements in seismic exploration have examined the effect of fluid and rock properties on seismic attributes. These advancements may provide provide improv improved ed reservoi reservoirr charac characteriz terizatio ation n using using techniqu techniques es examin examined ed here. here. This This is acco accomp mpli lish shed ed two two pa part rts; s; first first,, a stud study y of fluid fluid prop proper erti ties es an and d thei theirr eff effect ect on seismic response; second, an attempt to relate the seismic attributes computed from a 2-D seismic line to the fluids and the rock framework in a particular reservoir in Michigan. To study the fluid properties and their seismic significance, a number of published predictors are used to model reservoir data. The models used in this study include the Batzle and Wang (1992) model to predict fluid properties, the Gassmann-Biot model to predict rock velocities as a function of the saturating fluids, and the amplitude variation with offset (AVO) model using Zoeppritz’ equations to predict seismic response from the layered rock properties. The The Ba Batz tzle le an and d Wan ang g (199 (1992) 2) mo mode dell resu result lts s are are comp compar ared ed to the the Ba Batz tzle le an and d Han Ha n (199 (1997) 7) labo labora rato tory ry da data ta to esta estab blish lish the the usef useful ulne ness ss of the the mo mode dell as a pred predic icto torr of fluid properties and found to perform reasonably well, although the model slig slight htly ly un unde derpr rpred edic icts ts the the veloc elocit ity y of liv live oils oils an and d overp overpre redi dict cts s the the veloc elocit ity y of de dead ad oils. As a result, this model can be used for specific reservoir cases. The Batzle and Wang, Gassmann-Biot, and Zoeppritz models are applied to a Gulf of Mexico field; the acoustic impedance and Poisson’s ratio are determin mined and it is shown tha that an AVO respo pon nse is pres resent as a resul sult of the fluid uid and roc rock prop propert ertie ies. s. The The mo mode deliling ng of Lo Lobs bste terr Fiel Field d illu illust stra rate tes s the the usef useful ulne ness ss of pred predic ic-tors described in this thesis for modeling the reservoir through time as it is produced and the pressure decreases. In an effort to apply these concepts to actual seismic data, 2-D seismic data da ta from from Cryst Crystal al Fiel Field, d, Mich Michig igan an wa was s evalua aluate ted d with with the the inte intent ntio ion n of iden identi tify fyin ing ga larg large e am amou ount nt of by-pa y-pass ssed ed oil oil that that ha has s be been en left left be betw twee een n ma man ny wells ells.. As a me mean ans s for identifying by-passed oil, efforts were made to enhance seismic imaging of

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fault faults s or karst karstic ic featu feature res s in Crysta Crystall Field Field based based on seism seismic ic att attrib ribute utes. s. Ka Karst rstific ificati ation on and an d incr increa ease sed d po poro rosi sity ty or frac fractu turi ring ng were ere no nott ob obse serv rvab able le on the the seis seismi mic c da data ta du due e to acquisition parameters that limit the usefulness of the data in the shallow section. Data acquired for shallow horizons may be very useful for evaluating the seis seismi mic c attr attrib ibut utes es in othe otherr field fields s in the the Mich Michig igan an Ba Basi sin n if the the fold old an and d offs offset et ran ange ges s are appropriate. Good quality seismic data for the horizons of interest is necessary to evaluate seismic attributes.

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ACKNOWLEDGMENTS First rst and foremo remos st, I would lik like to tha thank GOD for all tha that I have be bee en given. I thank my husband, John, for his support and friendship. If it weren’t for him I wouldn’t have made it this far. I thank my family for being there for me; especially my mother, Barbara, for all of her support and long talks and my sister, Jennifer, for being such a wonderful sister and friend. I thank my friend Lisa Stright for being my exercise buddy and for keeping me going through all of those stressful times with her motivation. I than thank k my ad advi viso sorr, Wayne yne D. Pen enni ning ngto ton, n, for all all of the the gu guid idan ance ce an and d op oppo porrtunities he has provided me. I thank my committee: Jackie Huntoon, Jim Wood, Randy McKnight, and Jaroslaw Drelich, for their time and input. A special thank you to Randy McKnight for his mentoring while I was a summer intern at Marathon Oil Company and his friendship since. I also thank Randy for his many ideas and input for this work. I thank all of my friends here at Michigan Tech that have given me support and an d frie friend ndsh ship ip thro throug ugho hout ut the the yea ears rs.. A spec specia iall than thanks ks to Mik Mike Do Dola lan n for his his frie friend nd-ship and all of his computer support. You are appreciated more than you know. Many thanks to those that have helped with this work: Josh Haataja, Bill Everham, Carol Asiala, Steve Chittick, Bill Harrison, Thomas Benz, and Dan Brugeman. I would like to acknowledge Marathon Oil Company and Texaco for providing the data for this work and thank them for their permission to publish it.

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I thank the following companies and organizations for their support of this project through funding, data, and software that I have used throughout: Marathon Oil Company Texaco Department of Energy: Recovery of Bypassed oil in the Dundee formation of the Michigan Basin Ba sin using using Ho Horiz rizont ontal al Drain Drains, s, Co Contr ntract act # DE DE-FC -FC22 22-94 -94BC BC14 1498 983 3 (PI: J.R. Wood) Calibration of Seismic Attributes for Reservoir Characterization, Contract # DE-AC26-98BC15135 (PI: W.D. .D. Pennington) Adva Ad vance nced d Ch Char arac acter teriza izatio tion n of Fractu racture red d Re Rese servo rvoirs irs in Sh Shall allow ow Sh Shelf elf Carbonate Rocks: The Michigan Basin, Contract # DE-AC2698BC15100 (PI: J.R. Wood) Michigan Basin Geological Society (MBGS) Society of Professional Well Log Analysts (SPWLA) Schlumberger GeoQuest Mercury International - iXL Seismic Unix (CSM) GeoGraphix Cronus Development (T ( Terra Energy) Maness Petroleum Aangstrom Precision

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TABLE OF CONTENTS SECTION

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ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i ACKNOWLEDGMEN ACKNOWLEDGMENTS TS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii LIST OF FIGURES FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1.0 Effects of of Fluid Properties Properties on Seismic Seismic Response Response . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Objectives Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Procedures. Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Batzle Batzle and Wang Fluid Fluid Property Property Model . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1.1 Gas Gas Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1.2 Live Live and Dead Oil Oil Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.1.3 Brine Brine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1.4 Mixture Mixture Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.1.5 Fluid Fluid Properties Properties Spreadsheet. Spreadsheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.2 Gassmann Gassmann - Biot Rock Rock and Fluid Fluid Model. . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.3 Equations Equations for Dry Dry Frame Effects Effects with Pressure Pressure . . . . . . . . . . . . . . . . . . 25 1.2.4 AVO Model - Zoeppritz Zoeppritz Equations Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3 Results Results and Discussion Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.1 Summary Summary of Batzle and and Han Data Data (1997 Fluid Fluid Study) . . . . . . . . . . . . . 30 1.3.2 Application Application to Lobster Lobster Field, Field, Well A-2 . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.3.2.1 Predicted Predicted Reservoir Reservoir Response Response to Production Production for Lobster Field . . . 58 1.4 Conclusions Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 1.5 References. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.0 A Search for Seismic Attributes for Reservoir Characterization, Crystal Field, Michigan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.1 Introduction Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.1.1 Objectives Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.2 Background Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.2.1 History History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.2.2 Location Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3 Background Background Geology Geology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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2.3.1 Michigan Michigan Basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.3.2 Crystal Crystal Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.3.2.1 Dundee Dundee Formation Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.3.2.2 Structure. Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.4 Procedures. Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.5 Results Results and Interpretation Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.5.1 Geophysical Geophysical Well Well Log Interpretations Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.5.2 Seismic Seismic Data Interpretatio Interpretations ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.6 Conclusions Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.7 Future Work Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2.8 References. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 APPENDIX APPENDIX A: Effects of Fluid Properties Properties on Seismic Response Response . . . . . . . . . . A-1 A.1 Figures from Chapter Chapter 1 in English English (Oil Field) Units . . . . . . . . . . . . . . . . A-1 A.2 Definition Definition of V Variables ariables for the Batzle and Wang Wang (1992) (1992) model. model . . . . . . . A-12 APPENDIX B: A Search for Seismic Attributes for Reservoir Characterization, Crystal Field, Field, Michigan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1 B.1 Work that Josh Haataja did processing a 2-D seismic line (MOC Line C-3) in iXL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1 B.2 Formation Data Data Used to Create Create the Contour Contour and Isopach Isopach Maps Maps . . . . . . B-7

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LIST OF FIGURES FIGURE

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1-1 1-1 Flow Flow char chartt show showin ing g the the rela relati tion onsh ship ip of flui fluid d prop proper erti ties es to seis seismi mic c resp respon onse se an and d the modeling modeling approach approach used in this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1-2 1-2 A typi typica call live live oil oil ph phas ase e diag diagra ram m de demo mons nstr trat atin ing g the the effe effect cts s of pres pressu sure re an and d temtemperature on fluids.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1-3 1-3 Plot Plot of refl reflec ecti tion on am ampl plit itud ude e vers versus us offs offset et show showin ing g the the diff differ eren entt clas classe ses s of AVO AVO response. response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1-4 1-4 Re Refl flec ecti tion on an and d tran transm smis issi sion on at a bo boun unda dary ry for for an inci incide dent nt P-wa P-wave ve (fro (from m Ma Mavk vko o et. al., 1998).. 1998).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1-5 Location of fluid samples studied in the Batzle and Han (1997) fluids project consortium. consortium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1-6 1-6 Hist Histog ogra ram m show showin ing g the the dist distri ribu buti tion on of API API grav gravit ity y valu values es for for the the samp sample les s in the the study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1-7 Histogram Histogram showing the distribution distribution of GOR for for the samples in the study. study. . . 33 1-8 1-8 Plot Plot show showin ing g the the calc calcul ulat ated ed live live oil oil velo veloci city ty (Bat (Batzl zle e an and d Wang Wang 19 1992 92 Mo Mode del) l) verversus the laboratory laboratory live oil velocity velocity (Batzle and Han Han 1997 Fluid Study). Study). . . . . 34 1-9 1-9 Plot lot of live live and dead oil densi nsitie ties for the the samp mple les s in the stud udy y and the the rel relatio ation nship ship to GOR GOR (the (the line lines s are are a leas leastt squa square res s regr regres essi sion on thro throug ugh h the the da data ta po poin ints ts)) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1-10 Plot of the calculated calculated velocity velocity versus GOR for the the samples in the study. study. . . 37 1-11 Plot of the calculated velocity versus API gravity for the samples in the study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1-12 Plot of calculated live oil modulus versus density for the samples in the study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1-13 Plot of live oil velocity velocity versus density density for the samples in the study. study. . . . . . . 39 1-14 Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and an d the the labo labora rato tory ry live live oil oil velo veloci city ty (Bat (Batzl zle e an and d Ha Han n 19 1997 97 Flui Fluid d Stud Study) y) vers versus us pressure for for a sample in the the study modeled modeled with constant constant GOR. GOR. . . . . . . . 40 1-15 The evolution of hydrocarbon phases with decreasing pressure. The liquid comp compon onen entt (oil (oil)) is be best st de desc scri ribe bed d as the the "liv "live" e" oil oil calc calcul ulat ated ed at the the spec specif ifie ied d GOR above the bubble point pressure, and by the maximum GOR at conditions below the bubble point point pressure.. pressure.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1-16 Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and an d the the labo labora rato tory ry live live oil oil velo veloci city ty (Bat (Batzl zle e an and d Ha Han n 19 1997 97 Flui Fluid d Stud Study) y) vers versus us pressure for for a sample in the the study modeled modeled with a variable variable GOR. GOR. . . . . . . 42 1-17 Lobster Lobster Field platform, platform, Ewing Bank Bank block 873.. 873.. . . . . . . . . . . . . . . . . . . . . . 44 1-18 Structure Structure and performance performance areas areas (from Petro Petro et.al., 1997). 1997). . . . . . . . . . . . . 45 1-19 1-19 Flow Flow char chartt show showin ing g the the ap appr proa oach ch to rese reserv rvoi oirr mo mode deliling ng with with chan changi ging ng satu satura ra-tion and pressure pressure conditions. conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1-20 1-20 Cros Crossp splo lott of flui fluid d mo modu dulu lus s an and d de dens nsit ity y as satu satura rati tion on valu values es chan change ge.. The The satsaturation change, change, in percent, are given given for (oil, gas, water) water) in the labels.. . . 50 1-21 Well log showing gamma ray, resistivity, compressional (P-wave) velocity, and bulk density density curves curves for Well A-2, Lobster Lobster Field. Field. . . . . . . . . . . . . . . . . . 52 vii

1-22 1-22 A) Ve Velo loci city ty an and d de dens nsit ity y vers versus us satu satura rati tion on B) impe impeda danc nce e an and d PR vers versus us satu satu-ration showing how water saturation affects a two phase mixture of live oil and brine in a sandstone sandstone matrix from water water to oil saturated saturated conditions. conditions. . . 54 1-23 A) Impedance versus PR B) Percent change in impedance versus percent change in PR showing how water saturation affects a two phase mixture of live live oil oil an and d brin brine e in a sand sandst ston one e ma matr trix ix from from wa wate terr satu satura rate ted d to oil oil satu satura rate ted d conditions. conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 1-24 P-wave velocity versus density showing how water saturation affects a two phas ph ase e mixt mixtur ure e of live live oil oil an and d brin brine e in a sand sandst ston one e ma matr trix ix from from wa wate terr satu satura rate ted d to oil saturated saturated conditions. conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1-25 1-25 Co Comp mpre ress ssio iona nall vs. vs. shea shearr velo veloci city ty for for a two two ph phas ase e mixt mixtur ure e of live live oil oil an and d brin brine e in a sandstone sandstone matrix from water water saturated saturated to oil saturated saturated conditions. conditions. . . 58 1-26 Modulus of the fluid mixture versus pressure showing changes in the fluid modu mo dulu lus s as the the pres pressu sure re an and d satu satura rati tion on in the the rese reserv rvoi oirr chan change ges. s. Sa Satu tura rati tion on valu values es are are show shown n as (% oil, oil,% % ga gas, s,% % wa wate ter) r).. The The Bu Bubb bble le-p -poi oint nt (PBP (PBP)) for for this this fluid mixture is is 29.3 MPa.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1-27 1-27 Flui Fluid d de dens nsit ity y vers versus us pres pressu sure re show showin ing g ho how w the the de dens nsit ity y chan change ges s as the the pres pres-sure sure an and d satur saturati ation on in the reserv reservoir oir chang changes. es.Sa Satur turat ation ion value values s are are show shown n as (% oil,% gas,% water). water)... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 1-28 Velocity and Poisson’s ratio versus pressure demonstrating that when the reservoir drops below the bubble point (at 29.3 MPa) it significantly effects the reservoir properties. A) Modeled with a constant dry frame modulus. B) Modeled with with a variable dry dry frame modulus modulus with pressure. pressure. . . . . . . . . . . . . 62 1-29 1-29 Re Refle flecti ction on am ampli plitud tude e versus versus off offse sett showi showing ng the amp amplit litud ude e varia variatio tion n with with off offset set as the pressure changes over time. Saturation values are shown in legend as (% oil,% gas,% gas,% water). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 1-30 1-30 Re Refle flecti ction on am ampli plitud tude e versus versus off offse sett showi showing ng the amp amplit litud ude e varia variatio tion n with with off offset set as the pressure changes over time including the effects on the dry frame. Saturation Saturation values are shown shown in legend legend as (% oil,% gas,% gas,% water). water). . . . . . . 64 2-1 2-1 Lo Loca cati tion on of the the proj projec ectt stud study y area area an and d surr surrou ound ndin ing g Du Dund ndee ee fiel fields ds (cou (court rtes esy y of C. Asiala and and S.D. Chittick).. Chittick).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2-2 Three-dimensional contour of top subsea of the Dundee formation, Michigan Basin (courtesy (courtesy of W.D. W.D. Everham). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2-3 Strati Stratigr graph aphic ic colum column n show showing ing the age of the the Du Dund ndee ee forma formatio tion, n, the the strat stratig igrap raphhic succ succes essi sion on of the the Mich Michig igan an Ba Basi sin, n, an and d the the oil oil an and d ga gas s prod produc ucin ing g form format atio ions ns (from Wood et. et. al., 1998). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2-4 Cross-section across the Michigan Basin showing the relationship of the two member members s and the Du Dund ndee ee forma formatio tion n an and d the de depos positi ition onal al en envir vironm onment ent in Crys Crys-tal Field (modified (modified from Montgomery Montgomery et. et. al., 1998). . . . . . . . . . . . . . . . . . . . 77 2-5 2-5 Stra Strati tigr grap aphi hic c colu column mn of the the De Devo voni nian an sect sectio ion n show showin ing g the the Du Dund ndee ee,, Be Bellll Sh Shal ale e and Lucas formations (from (from Montgomery Montgomery et. al., 1998). 1998). . . . . . . . . . . . . . . . 78 2-6 Structure contour map of top subsea of the Dundee formation over Crystal Field, Michigan (Contour Interval = 7.5 ft). Location of the seismic lines are shown in red. red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2-7 2-7 Isop Isopac ach h ma map p of the the lime limest ston one e cap cap at the the top top of the the Du Dund ndee ee form format atio ion n over over Crysrystal Field, Michigan Michigan (Contour (Contour Interval Interval = 5 ft). . . . . . . . . . . . . . . . . . . . . . . . . . 80 2-8 Structure contour map of top subsea of the top of the Dundee porosity over viii

Crystal Field, Field, Michigan Michigan (Contour (Contour Interval = 10 ft). ft). . . . . . . . . . . . . . . . . . . . . 81 2-9 Structure contour map of top subsea of the Bell Shale formation over Crystal Field, Michigan Michigan (Contour (Contour Interval Interval = 10 ft). . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2-10 2-10 Isop Isopac ach h ma map p of Be Bellll Sh Shal ale e form format atio ion n over over Crys Crysta tall Fiel Field, d, Mich Michig igan an (Con (Conto tour ur InInterval = 10 ft). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2-11 2-11 Co Cont ntou ourr ma map p of init initia iall prod produc ucti tion on in bb bbls ls/d /day ay of Crys Crysta tall Fiel Field, d, Mich Michig igan an (Con (Con-tour Interval Interval = 1000 bbls/day). bbls/day). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2-12 Cross-section through Crystal Field showing the location and geologic controls on production for the TOW 1-3 well (modified from Wood et. al, 1998, Montgomery et. et. al., 1998, and Pennington, Pennington, personal personal communication). communication)... . . 85 2-13 Basemap showing the location of the seismic lines and cross-sections over Crystal Field, Field, Michigan. Michigan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2-14 Cross-section A-A’ showing the Dundee formation and Bell Shale markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2-15 Cross-Section B-B’ showing the Dundee formation and Bell Shale markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2-16 2-16 Pick Picket ettt plot plot to show show ho how w the the ne neut utro ron n po poro rosi sity ty an and d resi resist stiv ivit ity y resp respon onse ses s can can be used to evaluate evaluate wells for for wet or residual residual oil zones. zones. . . . . . . . . . . . . . . . . . 89 2-17 Well log cross-section showing the log response for the residual oil and wet wells displayed on the Pickett plot, compared with the TOW 1-3 vertical well. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2-18 Well log cross-section showing the log response for the by-passed oil wells displayed on the the Pickett plot compared compared with the TOW 1-3 vertical vertical well. . . 90 2-19 Two-way Two-way travel time time for the Dundee Dundee formation. formation. . . . . . . . . . . . . . . . . . . . . . 93 2-20 Amplitude Amplitude variation variation of Dundee Dundee formation.. . . . . . . . . . . . . . . . . . . . . . . . . . 93 2-21 Three-dimensio Three-dimensional nal display of MOC seismic seismic lines in Crystal Crystal Field. . . . . . . . 95 2-22 2-22 Line Line C-3 C-3 show showin ing g inte interp rpre rete ted d ho hori rizo zons ns on an am ampl plit itud ude e disp displa lay y over over the the stud study y area.. area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2-23 Line C-3 showing showing the instantaneous instantaneous phase phase over Crystal Crystal Field. . . . . . . . . . 96 2-24 Line C-3 showing showing the reflection reflection character character over Crystal Field.. Field.. . . . . . . . . . . 96 2-25 Line C-3 showing the reflection character over Crystal Field after automatic gain control control has been applied. applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2-26 Three dimensional display of MOC seismic lines and top subsea structure contour of the the Dundee formation.. formation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

ix

LIST OF TABLES TABLE

PAGE

1-1 Coefficients Coefficients for velocity velocity of water water calculation calculation (Vw). . . . . . . . . . . . . . . . . . . . . 18 1-2 Spreadsheet Spreadsheet created created from Batzle and Wang (1992) (1992) equations. equations. . . . . . . . . . . 21 1-3 1-3 Sp Spre read adsh shee eett ba base sed d on Ba Batz tzle le an and d Wang Wang (199 (1992) 2) pred predic icto tors rs show showin ing g the the calc calcuulation of fluid fluid properties properties for Well A-2, Lobster Lobster Field. Field. . . . . . . . . . . . . . . . . . . 47 1-4 Mod Modulu ulus s an and d de dens nsity ity value values s for Lob Lobste sterr Field Field as fluid fluid satur saturati ation on chang changes es du durin ring g reservoi reservoirr producti production. on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1-5 Gassmann-Biot model to calculate velocity and density at various water saturati ration on cond condit itio ions ns (cor (core e samp sample les s me meas asur ured ed at 0.26 0.26,, 0.39 0.39.. an and d 0.53 0.53 satu satura rati tion on)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

x

1.0 Effects of Fluid Properties on Seismic Response 1.1 Introduction Seismic data are commonly used for interpretation of structural or stratigraphic features in the subsurface. The physical properties of pore fluids have an effect on the seismic response of a porous rock containing those fluids. It is necessa essary ry to ha hav ve an un unde ders rsta tand ndin ing g of the the chan change ges s in P-wa P-wav ve (com (compr pres essi sion onal al)) veloc eloc-ity, S-wave (shear) velocity, and density as fluid or rock properties change to recognize or predict the effect of changes in seismic amplitudes and traveltimes. Fluid properties are especially important in a type of seismic analysis call called ed am ampl plit itud ude e varia ariati tion on with with offs offset et (AV (AVO), O), wh wher ere e the the be beha havi vior or of a seis seismi mic c even entt as it varies with offset between source and receiver is studied from a common midpoint gather. For example, if a reservoir contains a very light oil with a high gasga s-oi oill rati ratio o (GOR (GOR), ), an am ampl plit itud ude e an anom omal aly y or AVO eff effect ect ma may y occu occurr in the the seis seismi mic c response of the reservoir. Thus, pore fluid properties can have significant implications for seismic exploration and production and an understanding of pore fluid properties enables seismic data to be used more effectively. Evaluation of fluid properties aids in determining the usefulness of time lapse seismic, in predicting AVO and amplitude response, and in making production and reservoir engineering decisions and forecasting. Figure 1-1 is a generalized flow chart for seismic reservoir modeling showing the relationship of fluid properties to seismic response, where AVO modeling is the end result of this work. Basic input values for modeling a field or area of interest are determined by testing a sample or using analog information from a

1

near ne arby by area area.. Ba Base sed d on thes these e inpu inputt value alues, s, the the fluid fluid prop propert ertie ies s of the the rese reserv rvoi oirr ma may y be calc calcul ulat ated ed usin using g the the Ba Batz tzle le an and d Wan ang g (199 (1992) 2) mo mode del. l. Once Once the the fluid fluid prop proper erti ties es (modulus, density, velocity) are known, a model must be used to determine the properties of the fluids within the reservoir rock matrix under differing conditions, such such as satu saturratio ation. n. The The Gassm assman annn-Bi Biot ot mo mode dell can can be used used for this this an and d it can can also also be used used to de dete term rmin ine e the the corr correc ecti tion on ne nece cess ssar ary y to con convert ert well ell log log value alues s from from loglogging ging condi conditio tions ns (inva (invade ded d condi conditio tions ns,, mostly mostly wa water ter or brine brine)) to reserv reservoir oir condi conditio tions ns.. The P- and S- wave velocities and density for the fluid saturated reservoir rock, predicted by the Gassmann-Biot model, may then be used along with the overlying rock property information (determined from logs or estimated) for AVO modeling, to compare a calculated response to seismic observations.

Figure 1-1: Flow chart showing the relationship of fluid properties to seismic response and the modeling approach used in this thesis. 2

In this chapter, this entire reservoir modeling process is explained (section 1.2) and then applied to Well A-2, Lobster Field (section 1.3.2). Determining the fluid properties from the Batzle and Wang (1992) model and comparing the results to laboratory data is the major focus of this work. If the fluid properties (such as modulus, density, and velocity) cannot be accurately determined, the entire reservoir model cannot be reliably modeled. One of the most important factors controlling seismic response of some hydrocarbon saturated rocks is whether the oil is live or dead. The gas-oil ratio is defined as the volume ratio of liberated gas to remaining oil at atmospheric pressure sure an and d 15 15.6 .6 oC (sur (surfface ace temp temper erat atur ure e an and d pres pressu sure re cond condit itio ions ns). ). A liv live oil oil is an oil oil containing hydrocarbon compounds that will occur in a gaseous state when brought to the surface (GOR > 0). A dead oil is an oil that has no gas in solution (GO (GOR = 0) and high igher den ens sity ity and veloc locity ity valu alues tha than a liv live oil. il. In this this the thesis sis, the the term "dead oil" is used for an oil from which all the hydrocarbon components that would be in gas phase at surface conditions have been removed. The maximum amount of gas that can be dissolved in solution for a live oil is a function of pressure, temperature, and the composition of both the gas and the oil (Mavko et. al., 199 19 98). It is imp mpo orta rtant to rec recogn gniize tha that neith ither term erm - liv live oil or de dea ad oil - ass assume mes s that there is any free gas (gas not in solution) present in the reservoir. Figur Figure e 1-2 shows shows a press pressure ure-te -tempe mpera ratu ture re ph phase ase diagr diagram am for for a fluid fluid mixtur mixture e as an example of fluid response to pressure and temperature changes in a reservoir oir. For examp xample le,, assu assume me a liv live oil oil samp sample le is at rese reserv rvoi oirr cond condit itio ions ns,, labe labele led d X in Figure 1-2; 1-2; these conditions are high pressure and high temperature conditions,

3

and no free gas is present. As the pressure drops, the oil properties change slightly through simple expansion, until the bubble point is reached. At the bubble point, gas comes out of solution, forming small gas bubbles in the oil (shown by the vertical dashed line). As the pressure continues to drop below the bubble point, additional gas comes out of solution. The pressure drop represents the primary effect of production on the reservoir.

Figur Figure e 1-2: 1-2: A typi typica call liv live oil oil ph phas ase e diag diagra ram m de demo mons nstr trat atin ing g the the eff effects ects of pres pressu sure re and temperature on fluids. As a sample of oil is produced through the wellbore to the surface, the pressure and temperature both drop (shown as the diagonal dashed line). Addition tional al ga gas s come comes s ou outt of solu soluti tion on as the the samp sample le is prod produc uced ed at pres pressu sure res s be belo low w the the

4

bubble point; surface temperature and pressure are reached only when the sample arrives at the stock tank or separator at the surface. Laboratory measurements of fluid density and bulk modulus are usually made at stock tank or surface temperature and pressure conditions. However, these fluid properties must also be known at reservoir conditions to accurately model mod el the reserv reservoir oir.. Resea Research rchers ers an and d oil compa companie nies s ha have ve reali realize zed d the importa importance nce of determining fluid properties at reservoir conditions and have formed a collaborative project to develop models and testing procedures for their prediction. A stud study y of oiloil-fie field ld fluid fluids s was comp comple lete ted d by Ba Batz tzle le an and d Ha Han n (199 (1997) 7) in wh whic ich h the the acou acoust stic ic veloc elocit ity y an and d de dens nsit ity y of oil oil samp sample les s we were re me meas asur ured ed at rese reserv rvoi oirr cond condiition tions s. From rom thes these e me meas asur urem emen ents ts,, the the bulk ulk mo modu dulu lus s of the the fluid fluids s are are comp comput uted ed.. In this this thes thesis is,, thes these e labo labora rato tory ry da data ta pres presen ente ted d by Ba Batz tzle le an and d Ha Han n (199 (1997) 7) are are used used to dete de termi rmine ne the the ap appr prop opri riat aten enes ess s of a set set of em empi piric rical al eq equa uati tion ons s ea earli rlier er pres presen ente ted d by Batz Ba tzle le an and d Wan ang g (199 (1992) 2) as pred predic icto tors rs of veloc elocit ity y, de dens nsit ity y, an and d bu bulk lk mo modu dulu lus s of flufluids. The Batzle and Wang (1992) model is also applied to a specific fluid sample, obtained from Well A-2 of Lobster Field, and the saturated-rock properties are modeled using the Gassmann-Biot approach for rocks from this field. The density and bulk modulus of the fluid mixture must be determined to correctly model the seismic response of the reservoir and the effects of production. These model results can be used to determine the usefulness of time lapse seismic studies in areas where hydrocarbons are produced. The velocity (V), bulk modulus (K), and density ( ρ) of fluids in a reservoir are related through an elastic theory for homogeneous, isotropic, media with a

5

basic basic mod modulu uluss-den densit sity-v y-velo elocit city y relat relation ionshi ship p. This This eq equat uation ion is used used throu through ghout out this this thesis: V  =

K  ----

ρ

1.1.1 Objectives The objectives of this thesis project are to: 1.) 1.) Co Compa mpare re tabu tabulat lated ed labor laborat atory ory result results s (velo (velocit cities ies an and d de dens nsiti ities) es) for for each each fluid under each study condition with calculations that are predicted from the Batzle and Wang (1992) relations for the same fluids at similar study conditions. The results are presented in graphical form with a concise summary describing the usefulness of the published predictors and an evaluation of the likely sources of significant error in their use. 2.) Apply the Batzle and Wang model to a specific fluid sample, obtained from Well A-2 of Lobster Field, model the saturated-rock properties in that field usin using g the the Gass Gassma mann nn-B -Bio iott ap appr proa oach ch,, an and d pred predic ictt the the AVO resp respon onse se usin using g the the AVO model (Zoeppritz equations).

1.2 Procedures The models used in this study are described below in section 1.2.1, 1.2.2, and 1.2.3, including all of the equations needed for their application. These models include the Batzle and Wang (1992) model to predict fluid properties, the Gassmann-Biot model to predict rock velocities as a function of the saturating fluids, and the amplitude variation with offset (AVO) model using Zoeppritz equations to predict seismic response from the layered rock properties.

6

First, data from laboratory studies (Batzle and Han, 1997) were organized into a useful format, where laboratory (ultrasonic) seismic velocities were measure sured d for samp sample les s of oils oils,, brin brines es,, cond conden ensa sate tes, s, an and d ga gase ses. s. This This labo labora rato tory ry da data ta is used used to de dete term rmin ine e the the ap appl plic icab abil ilit ity y of the the Ba Batz tzle le an and d Wan ang g (199 (1992) 2) mo mode del. l. The The Ba Battzle and Wang model results are compared to the Batzle and Han laboratory data to establish the usefulness of the model as a predictor of fluid properties (section 1.3.1). The Batzle and Wang model, the Gassmann-Biot model, and the AVO model (Zoeppritz equations) are then used to model a sample from the Gulf of Mexi Me xico co,, Well ell A-2, A-2, Lo Lobs bste terr Fiel Field d (sec (secti tion on 1.3. 1.3.2) 2).. The The rese reserv rvoi oirr cond condit itio ions ns are are inv invesestigated for the field where the fluid was sampled, including the geologic setting of the the rese reserv rvoi oirr (age (age,, roc rock type type,, de dept pth h of buria urial, l, therm thermal al hist history ory,, de depo posi siti tion onal al sett settin ing, g, fau ault ltin ing, g, etc. etc.). ). The The mo mode dels ls are are used used in conj conjun unct ctio ion n with with the the rese reserv rvoi oirr cond condit itio ions ns to predict the effects of reservoir production and saturation on seismic response in the reservoir (section 1.3.2.1). 1.2.1 Batzle and Wang Fluid Property Model The explanation that follows is a summary of a paper by Batzle and Wang (1992) (1992) publish published ed in G EOPHYSICS. This model combines thermodynamic relationships and empirical trends from published data to predict the effects of pressure, temperature, and composition on the seismic properties of fluids. Batzle and Wan ang g exami xamine ned d the the prop proper erti ties es of ga gase ses s, oils oils,, an and d brin brines es,, the the thre three e prim primar ary y type types s of pore fluids present in most reservoirs. The fluid properties predicted include dens de nsit ity y an and d bulk ulk mo modu dulu lus s (and (and ther theref efor ore e veloc elocit ity) y) as func functi tion ons s of fluid fluid temp temper erat atur ure e

7

and pressure, when the pore fluid composition is known or estimated. The complete fluid model development is discussed in Batzle and Wang (1992). A brief summary of the fluid model, including critical assumptions, and model equations will be discussed here. The models that are explained in the following pages include gas, live oil, dead oil, brine, and mixtures of these fluids. For this this ap appl plic icat atio ion n of the the Ba Batz tzle le an and d Wan ang g mo mode del, l, it is assu assume med d that that at an any y point below the bubble point, the gas that comes out of solution has the same propert properties ies/co /compo mposit sition ion as the tot total al gas foun found d to be liber liberate ated d at surf surfac ace e condit condition ions. s. This means that there is no compositional variation in the gas as it continues to come come ou outt of solu soluti tion on du durin ring g prod produc ucti tion on.. This This use use of the the mo mode dell also also assu assume mes s eith either er that the oil remaining as liquid after the gas begins to be liberated (below bubble poin po int) t) ha has s the the same same comp compos osit itio ion n as the the orig origin inal al liv live oil, oil, or that that it is satu saturrated ated by as much gas as possible for the given conditions. First, some basic input variables are necessary for all Batzle and Wang model calculations. The input variables are determined from pressure-volumetemperature (PVT) testing of an oil or fluid sample or estimated from analog information, if available for a nearby area.

Input Variables: T = T = Reservoir Reser voir Temperature, Temperature, oC P = P = Reservoir Pressure, MPa G = G = Specific Gravity of the Gas R g  = Gas - Oil Ratio (GOR), liter/liter (l/l) o 

API = API = Degree API Gravity of Oil

S = S = Salinity (ppm of NaCl)

8

Mixture Saturation Variables: S g  = Gas Saturation S o  = Oil Saturation S b  = Brine Saturation Constants:

ρair = Density of air, g/cm 3 = 0.00122 at 15.6 oC R = R = Gas Constant, m 3 * Pa/(mol - oK) = 8.3145 1.2.1.1 Gas Model Gases are simpler to model than oils because the composition and phase behavior of gases has been examined more thoroughly and is better understood. Hydr Hydroc ocar arbo bon n ga gase ses s usua usualllly y cons consis istt of alka alkane nes s such such as me meth than ane, e, etha ethane ne,, an and d propropane. Typical gases have specific gravity ( G ) values from 0.56 (nearly pure methane) to greater than 1.8 (compounds with high carbon number). The specific gravity of gases is measured relative to air, taken as 1.0. As an acoustic wave passes though a fluid, this process can be modeled as adiabatic, rather than isothermal, because of the large coefficient of thermal expansion in most fluids of interest here (Batzle and Wang,1992). Adiabatic compres pressi sibi bilility ty is rela relate ted d to isot isothe herma rmall comp compre ress ssib ibililit ity y thro throug ugh h the the rati ratio o of he heat at capa capaccity at constant pressure to heat capacity at constant volume ( γ ο). The gas deviation factor or compressibility factor ( z ) is important because the fluids in this stud study y cann cannot ot be mo mode dele led d as idea ideall ga gase ses s at rese reserv rvoi oirr temp temper erat atur ures es an and d pres pressu sure res. s. Both oth of the these term terms s ( γ ο and z ) are are inco incorpo rpora rate ted d in the the follo ollowi wing ng calc calcul ulat atio ions ns for the the adiabatic gas bulk modulus (K  ( K s ). The gas density equation ( ρg ) is an approximation that is adequate if the pseudoreduced temperature ( T pr ) and pressure (P  ( P pr )

9

are not within about 1 of unity (Thomas et al., 1970); most gases of interest can be modeled using the gas density equation. Using pseudoreduced values is preferable because mixtures can easily be incorporated, and components such as carbon dioxide and nitrogen can be combined by incorporating the pseudocritical temperature (T  (T pc ) and pressure (P  ( P pc ). The adiabatic gas modulus and the gas dens de nsit ity y are are bo both th stro strong ngly ly de depe pend nden entt on comp compos osit itio ion. n. The The ap appr proa oach ch used used ab abo ove is commonly found and described in detail in petroleum engineering literature such as Craft and Hawkins (1991) and McCain (1973). Natural gases have a variable composition which complicates calculations of the fluid properties. For pure compounds, the gas and liquid phases exist in equili equ ilibri brium um along along a specifi specific c press pressure ure-te -tempe mpera ratur ture e curve curve.. As press pressure ure an and d tem tempe perrature are increased, the properties of the two phases approach each other and merge at a critical point. For mixtures, there is a range of temperature and pressure sure for wh whic ich h bo both th ph phas ases es coe coexist xist,, bu butt ther there e is stil stilll on one e temp temper erat atur ure e an and d pres pressu sure re value at which all phases are indistinguishable, called the pseudocritical temperature (T  (T pc ) and pressure (P  ( P pc ). This pseudocritical point is a point of homogenization and depends on the composition. The properties of mixtures are made more systematic using as environmental conditions the pseudoreduced temperature (T pr ) and pressure (P  ( P pr ) which are normalized by the pseudocritical temperature and pressure. Using the equations listed below with the input variables previously listed allows calculation of the gas fluid properties. The terms that are not defined are listed in Appendix A.

10

The Gas Equations: Adiabatic Gas Modulus, K s, in MPa: P  K s  = ----------------------------------------- γ o  P pr  ∂z   1 – --------------------   z  ∂P pr  T  where: P  P pr  = --------P pc  P pc  = 4.892 – 0.4048 G 

∂z  2 1.2 0.2 ------------ = A + 0.13 0.1308 08( 3.85 3.85 – T pr ) exp ( D P pr  ) D P pr  ∂P pr  A = 0.03 + 0.00527 ( 3.5 T pr )

3

–1 1 2 D  =  ---------  0.45 + 8  0.56 – ---------     T pr    T pr    

T a  T pr  = --------T pc  o 

T a  = T ( C ) + 273.15

T pc  = 94.72 + 170.75 G 

γ o  =

5.6 27.1 0.85 + ------------------------ + ------------------------------2- – 8.7 8. 7 exp [ –0.65 0. 65 ( P pr  + 1 ) ] ( P pr  + 2 ) ( P  + 3.5 ) pr 

3

4

z  = [ 0.03 + 0.00527 ( 3.5 – T pr ) ] P pr  + ( 0.642T  0.642 T pr  – 0.007T  0.007 T pr  – 0.52 ) + E 

11

E  =

 0.10 0.109 9 ( 3.85 3.85 – T pr ) exp  –  2

1 2 0.45 + 8  0.56 – ---------   T pr  

1.2

P pr   ----------  T pr  

Gas Density, ρg , in g/cm3:

ρ g  =

28.8GP  28.8 GP  --------------------zR T a 

P-Wave Velocity Veloci ty,, V g , in m/s: V g  =

K s  -------

ρ g 

1.2.1.2 Live and Dead Oil Models Crud Crude e oils oils can can be mixt mixtur ures es of comp comple lex x orga organi nic c comp compou ound nds s an and d ma may y ran ange ge from from ligh lightt liqu liquid ids s (con (conde dens nsat ates es)) to very he heav avy y tars tars.. The The Amer Americ ican an Petro etrole leum um Inst Instiitute (API) gravity is a widely used classification for crude oils. An API gravity of abou ab outt 5 repr repres esen ents ts a very ery he hea avy, vy, tartar-li lik ke, oil oil an and d an API API gravity vity value alue ne near ar 80 reprepresents a very light condensate. Large quantities of hydrocarbon gases can be dissolved in oils under pressure, significantly decreasing the density and the bulk modulus for live oils. Under surface temperature and pressure conditions the liquid component (dead oil) will exhibit densities ( ρo ) from 0.5 g/cm3 to greater than 1 g/cm3. Variations in composition and the ability to absorb gases, produces variations in seismic properties for oil, particularly under reservoir pressures. The The de dens nsit ity y varia ariati tion on with with pres pressu sure re an and d temp temper erat atur ure e ha has s be been en exami xamine ned d in detail by McCain (1973). McCain found that the effects of pressure and temperature are largely independent from each other for oils of unchanging composition. The pressure dependence is relatively small and can be described by the polyno-

12

mial given below ( ρp ). The effect of temperature is greater and the expression use used to calc alcula ulate the the de den nsity ity of the dead oil ( ρd ), live oil (ρl ), an and d liv live oil oil satu satura rate ted d with as much gas as it can possibly dissolve ( ρlm , ignoring the specified gas-oil ratio) incorporates the density at pressure,

ρp (Dodson and Standing, 1945).

Wang (1988) and Wang et. al. (1988) developed a simplified velocity relationship for for ultr ultraso asonic nic veloc velociti ities es ( V d ) withi ithin n de dead ad oils oils.. This This veloc elocit ity y de depe pend nds s on the the temp temper er-ature and pressure of the reservoir and the API gravity of the oil. The dead oil mo mod del uses the densi nsity of a dea ead d oil oil at sur surface cond ndiitio tions ( ρo ) to calc calcul ulat ate e the the de dens nsit ity y at pres pressu sure re ( ρp ). The liv live oil mode dell uses ses the the density ity at sat saturat uratio ion n (ρgl ) calc calcul ulat ated ed from from the the de dens nsit ity y at surf surfac ace e cond condit itio ions ns,, spec specifi ific c gra gravity vity an and d gas-oil ratio (from PVT tests), and gas volume factor ( B ol ) (calculated from input values) to calculate the density at pressure, accounting for the effect of gas in solution. The live oil model also uses a pseudodensity ( ρdl ) based on the expansion of the oil caused by gas intake to calculate the live oil velocity ( V l , V lm ). Using the equations below with the input variables for a specific oil and a set of physical conditions allows calculation of the live and dead oil fluid properties. The terms that are not defined are listed in Appendix A. The Dead Oil Equations: Dead Oil Density, Density, ρd , in g/cm3:

ρ d  =

ρ p 

--------------------------------------------------------------------------------------------------1.175 –4 [ 0.972 + ( 3.81 x 10 ] x 10 ) ( T  + 17.78 )

where: 3 2 –7 –4 ρ p  = ρ o  + ( 0.00277P  0.00277 P – ( 1.71 1.71x  x 10 10 ) P  ) ( ρ o  – 1.15 ) + ( 3.49 3.49x  x 10 10 ) P 

13

ρ o  =

141.5 -------------------------------AP I  + 131.5

P-Wave Velocity Veloci ty,, V d , in m/s: V d  = 15 1545 450 0 ( 77 77.1 .1 + API  AP I )

– 0.5

–

0.5

3.7T  3.7 T  + 4.64 4.64P  P  + 0.01 0.0115 15( 0.36 0.36AP AP I 

–

1 ) TP 

Dead Oil Modulus, K d , in MPa: 2

K d  = V d ρ d 

The Live Oil Equations: Live Oil Density, Density, ρl , in g/cm3:

ρ l  =

ρ pl 

--------------------------------------------------------------------------------------------------1.175 –4 [ 0.972 + ( 3.81 x 10 ] x 10 ) ( T  + 17.78 )

where:

ρ pl 

=

3 2 –7 –4 ( ρ gl  + 0.00277P  0.00277 P – 1.71 1.71x  x 10 10 P  ) ( ρ gl  – 1.15 ) + ( 3.49 3.49x  x 10 10 ) P 

ρ gl 

( ρ o  + 0.0012G 0.0012 G R g ) = ------------------------------------------------B ol 

G  0.5 B ol  = 0.972 + 0.0003812 2.4955 R g  ------  + T  + 17.778

1.175

 ρ o  

P-Wave Velocity Veloci ty,, V l , in m/s: V l  =

ρ dl   0.5  2096 ---------------------3.7T  T  + 4.64 4.64P  P  + 0.01 0.0115 15  2.6 – ρ dl   – 3.7

ρ dl 

ρo 

= -------- ( 1 + 0.0 0.001 01R  R g ) B ol 

14

–1

0.5 1.08 4.12 4.12 ----------- – 1  – 1 TP 

 ρ dl 

 

Live Oil Modulus, K l , in MPa: 2

K l  = V l  ρ l 

The Equations for a Live Oil at its Maximum Gas-Oil Ratio: Live Oil Density, Density, ρlm , in g/cm3:

ρ lm  =

ρ pm 

--------------------------------------------------------------------------------------------------1.175 –4 [ 0.972 + ( 3.81 x 10 ] x 10 ) ( T  + 17.78 )

where: 3 2 –7 –4 ρ pm  = ( ρ gm  + 0.00277P  0.00277 P – 1.71 1.71x  x 10 10 P  ) ( ρ gm  – 1.15 ) + ( 3.49 3.49x  x 10 10 ) P 

ρgm  =

( ρ o  + 0.0012G 0.0012 G R gmax ) ---------------------------------------------------------B ol m 

G  0.5 B ol m  = 0.972 + 0.000381 812 2 2.4955 R gmax  ------  + T  + 17.778

1.175

 ρ o  

R gmax  = 2.028G 2.028 G [ P exp ( 0.02877AP 0.02877 API  I  – 0.003772T  0.003772 T ) ]

1.204

P-Wave Velocity Veloci ty,, V lm , in m/s: V lm  =

ρ pd m   0.5  2096 --------------------------3.7T  T  + 4.64 4.64P  P  + 0.01 0.0115 15  2.6 – ρ pd m   – 3.7

ρ pd m  =

ρ o 

---------- ( 1 + 0.001 R gmax ) B om 

Live Oil Modulus, K lm , in MPa: 2

K lm  = V lm ρ lm 

15

–1

1.08 4.12 4.12 ------------

 ρ pd m 

 0.5 – 1  

–1

TP 

1.2.1.3 Brine Model The most common pore fluid is brine; its composition can range from almost pure water to saturated saline solutions. Brine salinity is commonly one of the easiest variables to obtain because brine resistivities are routinely calculated during well log analysis. Simple relationships are available to convert brine resistivity to salinity (e.g., Western Atlas log interpretation charts, 1996). Waters and brin brines es are are un unus usua uall am amon ong g comm common on fluid fluids s in that that thei theirr veloc elocit itie ies s be begi gin n to de decr crea ease se at very high pressures. Incr Increa easi sing ng sali salini nity ty incr increa ease ses s the the de dens nsit ity y of the the brin brine. e. Usin Using g da data ta on sodi sodium um chloride solutions from Zarembo and Federov (1975) and Potter and Brown (1977), Batzle and Wang (1992) constructed a simple polynomial using salinity and reservoir temperature and pressure to calculate the density of sodium chloride solutions ( ρb ). This relationship is valid only for sodium chloride solutions. Wils Wilson on (195 (1959) 9) pro provide vided d a rela relati tion onsh ship ip for the the veloc elocit ity y of water ater for cond condit itio ions ns up to 100 oC an and d 10 100 0 MPa. MPa. This This eq equa uati tion on is used used to calc calcul ulat ate e the the veloc elocit ity y of water ater (V w ). Batzle and Wang (1992) extended the results of Millero et. al. (1977) and Chen et. al. (1978) for brines by using a simplified form of the velocity function prov provid ided ed an and d mo modi dify fyin ing g the the eq equa uati tion on cons consta tant nts. s. The The brin brine e veloc elocit ity y ( V b ) eq equa uati tion on is the modified equation (Batzle and Wang, 1992); the equation was modified to fit additional higher temperature and higher salinity data from Wyllie et. al. (1956). Gas can also be dissolved in a brine but the amount that can go into solution is significantly less than that of oils. The amount of gas that can go into the brine solution increases with pressure and decreases with salinity. R gb  is the gas-

16

water ratio and defines the amount of gas that can be in solution at surface temperature and pressure conditions. Dodson and Standing (1945) found that the isothermal bulk modulus ( K gb ) for the brine solution decreases nearly linearly with gas content. This also has a decreasing effect on the velocity. Using the equations below with the appropriate fluid state allows calculation tion of the the brin brine/ e/w water ater fluid fluid prop proper erti ties es.. The The term terms s that that are are no nott de defin fined ed are are list listed ed in Appendix A. The Brine/Water Equations: Density of Freshwater, Freshwater, ρw , in g/cm3: 2 3 ) ( – 80 80T  T  – 3.3 3.3T  T  + 0.00175T  0.00175 T  + 489 489P  P – 2 5 3 2 2 2 TP  + 0.016T  0.016 T  P – ( 1.3 1.3x  x 10 10 ) T  P – 0.333P  0.333 P  – 0.002T 0.002 T P  ) )

ρ w  =

1 + ( ( 1 x 10 x 10

–6

–

Density of Brine, ρb , in g/cm3: –6 ρ b  = ρ w  + S { 0.668 + 0.44 S + ( 1 x 10 x 10 ) [ 300 300P  P – 2400PS  2400 PS  +

T ( 80 + 3 T  – 3300S  3300 S – 13 13P  P  + 47 47PS  PS ) ] } Velocity of Water, V w , in m/s (constants w ij are provided in Table 1-1): 1-1 ): 4

V w  =

3

∑∑

i   j 

w ij T  P 

i  = 0 j  = 0

Velocity of Brine, V b , in m/s: 2

–5 3 ( 8.5 8.5x  x 10 10 ) T  + 2.6 2.6P  P – 2 1.5 2 2 0.0029TP  0.0029 TP  – 0.0476P  0.0476 P  ) + S  ( 780 – 10 P  + 0.16 0.16P  P  ) – 1820S  1820 S 

V b  = V w  + S ( 1170 – 9.6 T  + 0.055T  0.055 T 

Modulus of Gas Free Brine, K b , in MPa: 2

K b  = V b ρ b 

17

–

Modulus of Live Brine, K gb , in MPa: K gb 

K b  = -------------------------------------1 + 0.0494 R gb 

where: R gb  = 10

lo g 10 { 0.712P 0.712 P T  – 76.71

1.5

0.64

+ 3676P  3676 P 

7.786 S ( T  + 17.78 ) } – 4 – 7.786S

Table 1-1: Coefficients for velocity of water calculation ( V w ). w 00 =

1402.85

w 02 =

3.437 x 10 -3

w 10 =

4.871

w 12 =

1.739 x 10 -4

w 20 =

-0.04783

w 22 =

-2.135 x 10 -6

w 30 =

1.487 x 10 -4

w 32 =

-1.455 x 10 -8

w 40 =

-2.197 x 10 -7

w 42 =

5.230 x 10 -11

w 01 =

1.524

w 03 =

-1.197 x 10 -5

w 11 =

-0.0111

w 13 =

-1.628 x 10 -6

w 21 =

2.747 x 10 -4

w 23 =

1.237 x 10 -8

w 31 =

-6.503 x 10 -7

w 33 =

1.327 x 10 -10

w 41 =

7.987 x 10 -10

w 43 =

-4.614 x 10 -13

1.2.1.4 Mixture Model Properties of pore fluid mixtures containing liquid and gas phases in the rock pores are very important from an exploration standpoint. During production, gas may exsolve from the oil phase because of a pressure drop in the reservoir. Due to these effects, the seismic character of the reservoir can change significantly over time. For geophysical examinations of reservoirs, a method of determining the properties of mixed pore fluid phases is required.

18

–0

The density sity of a mix mixture ure ( ρml, ρmlm, ρmd ) is a mass ass balan lance tha that require uires s an arithmetic volume-weighted average of the separate pore fluid phases. The effective modulus of the mixed phase fluid can be calculated easily if the pressures in the two phases are equal. The equation used for the mixture modulus ( K ol ,K olm , K od ) is the the Re Reus uss s (iso (isost stre ress ss)) averag erage e of the the comp compos osit ite e solu soluti tion ons s. If the the prop proper erti ties es of the the indi indivi vidu dual al fluid fluids s an and d thei theirr volum olume e frac fracti tion on are are know known, n, the the mixt mixtur ure e prop propert ertie ies s can be calculated. The mixture velocities ( V ol , V olm , V od ) are then found from the Reuss average of the fluid moduli and the mixture densities (Mavko et. al., 1998). Using the equations below with the appropriate mixture saturation values allows calculation of the mixture fluid properties. The Fluid Mixture Equations: Live Oil Mixture Density, ρml , in g/cm3:

ρ ml 

= S g ρ g  + S o ρ l  + S b ρ b 

Max Live Oil Mixture Density, ρmlm , in g/cm3:

ρ ml m  =

S g ρ g  + S o ρ lm  + S b ρ b 

Dead Oil Mixture Density, ρmd , in g/cm3:

ρ md 

= S g ρg  + S o ρ d  + S b ρ b 

Live Oil Mixture Modulus, K ol , in MPa: 1 K ol  = ----------------------------------------S g  S o  S b   ------+ -------   K s  + ------K l  K g   Max Live Oil Mixture Modulus, K olm , in MPa: 1 K ol m  = -------------------------------------------S g  S o  S b   ------+ -------    K s  + ---------K lm  K g  

19

Dead Oil Mixture Modulus, K od , in MPa: 1 K od  = -----------------------------------------S g  S o  S b   ------- + -------   K s  + ------K d  K b   Velocity for Live Oil Mixture, V ol , in m/s: V ol  =

K ol ( 1000 ) ---------------------------

ρ ml 

Velocity for Max Live Oil Mixture, V olm , in m/s: V ol m  =

K ol m ( 1000 ) -------------------------------

ρ ml m 

Velocity for Dead Oil Mixture, V od , in m/s: V od  =

K od ( 1000 ) -----------------------------

ρ md 

1.2.1.5 Fluid Properties Spreadsheet Table 1-2 shows the spreadsheet created using the algorithms from the Batzle and Wang (1992) model. The spreadsheet allows calculation of the fluid properties for all of the models explained above, using the equations presented. The input values, in yellow, include the reservoir temperature and pressure, gasoil ratio, specific gravity of the gas, API oil gravity, and salinity of the water in the formation, as well as the relative concentrations of the fluids as a mixture. The results, in green, consist of the velocity, density, and modulus for live oil (at specified R g  and at maximum R g ), dead oil, gas, brine, and mixtures at the conditions entered as the input values, usually reservoir conditions.

20

Table 1-2: Spreadsheet created from Batzle and Wang (1992) equations.

Now that the algorithms required to predict the properties of pore fluids have been defined, a technique needs to be described to place them within a given rock matrix. In this project, the Gassmann-Biot model is used to combine rock and fluid properties and determine P- and S- wave velocity responses. 1.2.2 Gassmann - Biot Rock and Fluid Model Gassmann (1951) and Biot (1956) developed fundamental and relatively simple relationships to predict the velocities of porous media using global or bulk rock and fluid properties without referring to any specific pore geometry (Sheriff and Geldart, 1995). Gassmann’s equations are equivalent to Biot’s at low (seis-

21

mic) frequencies. The most significant unknown parameters are the bulk and shea shearr mo modu dulili of the the dry roc rock fram frame ewo work rk (sk (skelet eleton on). ). The The lowlow-fr freq eque uenc ncy y Gass Gassma mann nn-Biot theory predicts the resulting increase in effective bulk modulus of the saturated rock when the pore pressure changes as a seismic wave passes through the rock (Mavko et. al., 1998). These equations assume a homogeneous mineral modulus and isotropic pore space and the effects of pressure on the dry frame modulus are not addressed here. There are some input variables necessary for the Gassmann-Biot model calculations. The solid material grain bulk modulus and density are determined from from the the mine minera ralo logy gy of the the rese reserv rvoi oirr ma matri trix. x. The The water ater/b /brin rine e an and d hydro ydroca carb rbon on bulk ulk modu mo dulu lus s an and d de dens nsit ity y value alues s are are comp comput uted ed at rese reserv rvoi oirr temp temper erat atur ure e an and d pres pressu sure re conditions in the spreadsheet created for the Batzle and Wang (1992) model desc de scrib ribed ed ab abov ove e. The The P- an and d S- wa wav ve veloc elocit itie ies, s, an and d bu bulk lk de dens nsit ity y (V pi, Vsi, ρbi ) valalues ue s are are ob obta tain ined ed from from well ell logs logs an and d used used to calc calcul ulat ate e the the satu saturrated ated bulk ulk mo modu dulu lus s (K bs ) an and d the the dry frame she shear mo mod dulus lus ( G ). ) . Gass Gassma mann nn’’s rela relati tion ons s are are used used to calcalculate the dry frame bulk modulus (K  ( K df ) using the saturated bulk modulus ( K bs , determined from well log or laboratory tests). The bulk density ( ρb ) is calculated using a volume weighted average density for the reservoir. The fluid bulk modulus ( K f ) is computed using the Reuss (isostress) average is calculated using the water and hydrocarbon saturations. The The satu satura rate ted d bu bulk lk mo modu dulu lus s ( K b ) is comp comput uted ed at an any y de desi sire red d satu satura rati tion on cond condit itio ions ns usin using g the the dry fram frame e bulk ulk mo modu dulu lus, s, soli solid d ma mate teri rial al bu bulk lk mo modu dulu lus s, fluid fluid mo modu dulu lus, s, an and d porosity. The compressional and shear velocities ( V p , V s ) are calculated using a

22

velo velocit city y form form of Gass Gassman mann’ n’s s relati relation on sugge suggeste sted d by Murphy Murphy,, Schw Schwartz artz,, and Ho Hornb rnby y (1991). Input Variables:

φ = Porosity K s  = Solid Material Bulk Modulus, GPa

ρs = Solid Material Density, g/cm 3 K w  = Water Bulk Modulus, GPa

ρw = Water Density Densit y, g/cm 3 K hyd = Hydrocarbon Bulk Modulus, GPa

ρhyd = Hydrocarbon Density, g/cm 3 S w  = Water Saturation V pi  = Logged P-wave velocity, velocity, m/s V si  = Logged S-wave velocity, velocity, m/s

ρbi  = Logged Bulk Density, g/cm 3 K fi  = Fluid Bulk Modulus at logged conditions, GPa The Gassmann-Biot Equations: Saturated Bulk Modulus, K bs , in GPa: K bs  =

 ρ  V 2 –  -4- V 2    10–6  bi  pi   3 si    

Dry Frame Bulk Modulus, K df , in GPa:

K df  =

K s  K s    ( φ ) φ 1 + ---------------– –  K bs  K fi    K bs  ----------------------------------------------------    K bs  K fi    ( φ + 1 ) + ---------– φ -------  K s  K s   

Dry Frame Shear Modulus-Rigidity, G, in GPa: 2

G = ( V si ρ bi ) 10

–6

Bulk Density, ρb , in g/cm3:

ρ b  = ( 1 – φ )ρ s  + φ S w ρw  + ( 1 – S w ) ρhy d φ

23

Fluid Bulk Modulus, K f , in GPa: 1 K f  = ------------------------------------------( 1 – S w ) S w    --------------------- K hy d  + -------K w   Saturated Bulk Modulus, K b , in GPa: 2

K df  + ( K s  – K df ) K b  = ---------------------------------------------------------------K s  K s ( 1 – φ ) – K df  + φ  -------   K f   P-Wave Velocity Veloci ty,, V p , in m/s:

V p  =

 K  + -4- G    b  3   ---------------------------ρ b 

0.5

10

3

S-Wave Velocity Veloci ty,, V s , in m/s: V s  =

G  3 ------ 10

ρ b 

Two other useful parameters are given below: Poisson’s Ratio, σ: V p    ------ V s  

2

σ

–

2

= 0.5 ------------------------V p  2  ------ V s   – 1

Acoustic impedance, AI : AI = V p ρ b 

Using Using the these se equ equati ations ons with with the neces necessary sary input input varia variabl bles es allow allows s calcu calculat latio ion n of the the over overal alll rese reserv rvoi oirr prop propert ertie ies s taki taking ng into into acco accoun untt the the po poro rosi sity ty,, rock rock prop propert ertie ies, s, and fluid properties. An example of the Gassmann-Biot model applied to the Lobster Field data is provided in Figure 1-5 in the results and discussions section (section 1.3.1). 24

Now that a means for calculating the properties of the reservoir unit have been defined, dry frame property effects can be modeled with changing pressure and Zoeppritz equations can be applied to model the AVO response, if the overlying layer information is known. 1.2.3 Equations for Dry Frame Effects with Pressure The following equations are used for modeling the dry frame property effects with changing effective pressure. These equations were obtained from Laurence Bentley, University of Calgary, by personal communication with Wayne D. Pennington, 1999 and were derived from data presented in Han, 1986. The effective pressure (P  ( P eff  in MPa), is determined by subtracting the pore pressu pressure re (rese (reservo rvoir ir press pressure ure)) from from the confin confining ing press pressure ure.. An increa increase se in eff effect ectiv ive e confining stress (due to the decrease in pore pressure) results in more grain to grain contact and a stiffening of the frame. Dry Frame Bulk Modulus, K dp , in GPa: d K dp  – 0.0582 ( P ef f ) ------------- = 0.24 0. 2437 37 e  d P ef f  Dry Frame Shear Modulus, G dp , in GPa: d G dp  – 0.0549 ( P ef f ) ------------- = 0.27 0. 2794 94 e  d P ef f  The dry frame bulk and shear modulus at varying effective pressures are used as input values for Gassmann-Biot modeling. 1.2.4 AVO Model - Zoeppritz Equations Amplitude variation with offset, or more simply amplitude-versus-offset (AV (AVO), O), comp comput utes es the the seis seismi mic c resp respon onse se of an inte interf rfac ace e be betw twee een n two two be beds ds from from the the contrast in elastic properties between the overlying and underlying formations. A 25

normal incident, or zero offset, reflection (R o) is readily found from the contrast in acoustic impedance.

ρ 2 V p 2 – ρ 1 V p 1 R o  = ---------------------------------------ρ 2 V p 2 + ρ 1 V p 1 where: Ro = Reflection Coefficient

ρ1 = Density of medium 1 ρ2 = Density of medium 2 V1 = Velocity in medium 1 V2 = Velocity in medium 2 The The chan change ge in am ampl plit itud ude e of the the refle reflect ctio ion n coef coeffic ficie ient nt with with offs offset et is a func functi tion on of the contrast in elastic properties across the interface.

I

II R III

Offset Figure 1-3: Plot of reflection amplitude versus offset showing the different classes of AVO response. AVO response is divided into three classes, Figure 1-3: 1-3 : 1.) 1.) A Clas Class s I AVO resp respon onse se ha has s a larg large e po posi siti tiv ve refle reflect ctio ion n at zero ero offs offset et an and d becomes smaller with increasing offset. 2.) A Class II AVO response has a small positive reflection at zero offset and becomes very small or even negative with increasing offset. 26

3.) A Class III AVO response has a negative reflection at zero offset and increasingly large negative reflections at increasing offsets. This is the classical AVO behavior. For example, a sand-shale interface often displays a negative reflection response that is increasingly large with offset. Zoeppritz equations express the energy partitioning at a boundary when a plane wave impinges on an acoustic impedance contrast (Sheriff, 1991). At a boundary where the incident angle is zero (normal incidence) there is no mode conversion. For example, a downward moving P-wave only generates reflected and trans transmit mitted ted P-wa P-wave ves s an and d a no normal rmally ly incid incident ent S-wa S-wave ve only only ge gene nera rates tes reflect reflected ed and an d tran transm smit itte ted d S-w S-waves. es. At a bo boun unda dary ry wh wher ere e the the inci incide dent nt an angl gle e is no nott zero ero (non (non-normal incidence) the seismic energy typically generates four waves, at the boundary by splitting (mode conversion): reflected P-wave and S-wave and transmitted P-wave and S-wave (Figure ( Figure 1-4). 1-4). Most reflections are a superposition of even ents ts from from a seri series es of lay layers ers an and d will will ha hav ve a mo more re comp comple lex x be beha havi vior or than than wh what at is shown here.

Figure 1-4: Reflection and transmission at a boundary for an incident P-wave (from Mavko et. al., 1998). 27

Zoeppritz equations can be used to determine the amplitude of reflected and refracted waves at this boundary for an incident P-wave. The original equations are valid for any incident waves but only the P-wave is presented here and used in this study. The reflection and transmission coefficients depend on the angle of incidence and the material properties of the two layers. (Mavko et. al., 1998). The angles for incident, reflected, and transmitted rays at a boundary are related by Snell’s law (Castagna and Backus, 1993).

Snell’s law:

sin Θ1 sin Θ 2 sin Φ 1 sin Φ 2 p  = --------------- = --------------- = --------------- = --------------V p 1 V p 2 V s 1 V s 2

where: p = p = Ray parameter V p1 = P-wave velocity in medium 1 V p2  = P-wave velocity in medium 2 V s1 = S-wave velocity in medium 1 V s2  = S-wave velocity in medium 2

Θ1 = Incident and reflected P-wave angle Θ2  = Transmitted P-wave angle Φ1 = Reflected S-wave angle Φ2  = Transmitted S-wave angle The The varia ariati tion on of refle reflect ctio ion n an and d tran transm smis issi sion on coef coeffic ficie ient nts s with with inci incide dent nt an angl gle e and corresponding increasing offset is referred to as offset-dependant-reflectivity and is the fundamental basis for AVO (Castagna and Backus, 1993). Zoeppritz (1919) equations provide a complete solution for amplitudes of tran transm smit itte ted d an and d refle reflect cted ed P- an and d S- waves for bo both th inci incide dent nt P- an and d S- waves. es. The The equations are very complex and subject to troublesome sign, convention, or typographic errors (Hales and Roberts, 1974) and Aki and Richards (1980), Shuey

28

(1985), and Hilterman (1989) developed simplifications and approximations for Zoeppritz equations. Aki and Richards (1980) derived a simplified form of Zoeppritz equations by assuming small contrasts in properties between layers, where the results are expressed in terms of P-wave velocity, S-wave velocity, and density contrasts across the interface. Shuey (1985) presented another approximation to Zoeppritz equations were the AVO gradient is expressed in terms of Poisson’s ratio ( σ). Due to the complexity of Zoeppritz equations, approximations are extremely useful for application. The most commonly used form, due to Shuey (1985), is given below (valid for incidence angles less than 30 degrees): Zoeppritz Equation: R ( Θ ) = A + B sin2 ( Θ ) where: R( Θ ) = Reflection coefficient (function of

Θ)

Θ = Angle of incidence A = ZeroZero-off offset set reflec reflectio tion n coeffi coefficie cient nt (AV (AVO inter intercep cept) t) 1 ∆ V p  ∆ρ A = --  ----------- + -------  ρ   2  V p  B = B = Slope of amplitude (AVO Gradient)

∆σ

B = A o A + --------------------2 (1 – σ) A is the the no norma rmall inci incide denc nce e refle reflect ctio ion n coef coeffic ficie ient nt.. B de desc scri ribe bes s the the varia ariati tion on at intermediate offsets and is called the AVO gradient or slope factor where, A o is a func functi tion on of averag erage e value alues s of Poiss oisson on’’s rati ratio o ( σ), compress compressiona ionall veloci velocity ty (Vp), and

29

density( ρ) an and d the the chan change ges s of Poiss oisson on’’s rati ratio o, comp compre ress ssio iona nall veloc elocit ity y an and d de dens nsit ity y. A an and d B are are bo both th high highly ly de depe pend ndan antt on the the prop proper erti ties es of the the rese reserv rvoi oirr an and d the the overerlying formation. In general, P-wave velocity is dependant on both lithology (rock type type)) an and d fluid fluid cont conten ent. t. S-wa S-wav ve veloc elocit ity y is de depe pend ndan antt on lith lithol olog ogy y, but no nott sens sensit itiv ive e to fluid fluid cont conten ent. t. S-w S-wave ave veloc elocit itie ies s are are no nott ge gene nera ralllly y me meas asur ured ed dire direct ctly ly so the the V p /Vs ratio or Poisson’s ratio is used to determine the shear velocity from the compressional velocity. velocity. This This comm common only ly used used form orm of Zoep Zoeppr prit itz z eq equa uati tion ons s ha has s the the inte interpr rpret etat atio ion n that that the near-offset traces reveal the P-wave impedance, and the intermediate-offset traces image contrasts in Poisson’s ratio (Castagna, 1993). Another term can be added to account for far offsets near the critical angle, C(tan 2θ - sin2θ), where C=1/2(∆Vp /Vp) (Shuey, 1985). Assumptions and limitations for these equations are the rock is linear, isotropic, and elastic. A plane-wave propagation is assumed and most of the simplified fied forms orms assu assume me smal smalll cont contra rast sts s in ma mate teri rial al prop proper erti ties es an and d no spac space e or slip slippi ping ng across the boundary (Mavko et. al., 1998).

1.3 Results and Discussion 1.3.1 Summary of Batzle and Han Data (1997 Fluid Study) In 19 1997 97,, M. Ba Batz tzle le an and d D.H. .H. Ha Han n cond conduc ucte ted d a stud study y of fluid fluid prop proper erti ties es me meaasured on samples provided by a consortium of twenty-one supporting oil companies nies.. The The proj projec ectt was a join jointt eff effort ort led led by the the Ho Hous usto ton n Ad Adv van ance ced d Re Rese sear arch ch Ce Cent nter er (D.H. Han) and the Colorado School of Mines (M. Batzle), where laboratory tests and other work were completed.

30

The The pu purpo rpose se of the the cons consort ortiu ium m wa was s to de dete termi rmine ne the the eff effects ects of fluid fluid de dens nsit ity y, initial oil gravity, and gas in solution on seismic velocity of the fluid. The goals of the Batzle and Han (1997) project were to: 1) conduct measurements of velocity and density on 30 samples provided by industry sponsors, 2) make these data available to consortium members in spreadsheet format, 3) develop empirical relations to describe oil properties, 4) link static pressure-volume-temperature (PVT (PVT)) da data ta to seis seismi mic c prop proper erti ties es,, an and d 5) de dev velop elop a prog progra ram m to calc calcul ulat ate e fluid fluid prop prop-erties under realistic conditions. This summary will focus on the velocity and density measurements from the study and how they compare to values computed from from the the Ba Batz tzle le an and d Wan ang g (199 (1992) 2) mo mode del. l. So Some me samp sample les s were ere no nott an anal alyz yzed ed at the the presumed reservoir temperature and pressure conditions of 80-90 oC and 6000 psi that were used for calculations in this thesis study, and are not included in the plots or calculations. This laboratory data is used to determine the usefulness of the Batzle and Wang (1992) model as a predictive tool. The The samp sample les s used used in the the labo laborrator atory y test tests s incl includ uded ed liv live oils oils that that were ere reco reconnstit stitut uted ed from from de dead ad oils oils.. In ge gene nera ral, l, the the liv live oil oil was reco recons nsti titu tute ted d ba base sed d on the the comcomposition report from the PVT data. The samples were subjected to temperature and pressure conditions above the bubble point and different gases were added based on weight percent until the GOR reached the value reported for the reservoir and the fluid was in a single oil phase. Figure 1-5 shows the locations of most of the oil samples studied in the Batz Ba tzle le an and d Ha Han n (199 (1997) 7) fluid fluids s cons consort ortiu ium. m. The The samp sample les s are are from from the the Un Unit ited ed Stat States es (AK, WY, NM, TX), the Gulf of Mexico, the North Sea, and Indonesia. This

31

distribution provides a variety of depositional environments and reservoirs and gives a good overall sample set to study.

Figur Figure e 1-5: 1-5: Lo Loca cati tion on of fluid fluid samp sample les s stud studie ied d in the the Ba Batz tzle le an and d Ha Han n (199 (1997) 7) fluid fluids s project consortium. The distributions of API gravity and GOR values for the samples in the stud study y are are incl includ uded ed in Figur Figure e 1-6 and Figure Figure 1-7, 1-7, resp respec ecti tiv vely ely. The The oils oils in the the stud study y consist of mostly middle range API gravity values. Very few light or heavy oils were included in this study. The distribution of GOR is broad but oils with an extremely high GOR are missing. The API and GOR are indicated for an oil from the Lobster Field (Gulf of Mexico) for reference. The sample for the Lobster Field is analyzed in detail later in this thesis.

32

Figure 1-6: Histogram showing the distribution of API gravity values for the samples in the study.

Figure 1-7: Histogram showing the distribution of GOR for the samples in the study.

33

Figures 1-8 through 1-13 compare the summary data from the Batzle and Han (1997) fluids project and calculations based on the Batzle and Wang (1992) mode mo del. l. The The calc calcul ulat ated ed value alues s we were re comp comput uted ed usin using g the the spre spread adsh shee eett pres presen ente ted d in section 1.2.1, using the Batzle and Wang (1992) model, and are based on input values from reservoir conditions (given in the Batzle and Han (1997) fluid study). The measured values selected for plotting are those conducted under conditions most most simil similar ar to reserv reservoir oir condi conditio tions ns (appr (approx oxima imatel tely y 80-90 80-90 oC and 600 000 0 psi). i). Some samp sample les s we were re no nott an anal alyz yzed ed at thes these e rese reserv rvoi oirr cond condit itio ions ns used used for calc calcul ulat atio ions ns an and d are not included in the study.

Perfect Perfect Correlation

Figure 1-8: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) versus the laboratory live oil velocity (Batzle and Han 1997 Fluid Study).

34

Figure 1-8 shows the live oil laboratory velocities tested in the Batzle and Han Ha n (199 (1997) 7) fluid fluid stud study y plot plotte ted d versu ersus s the the calc calcul ulat ated ed liv live oil oil veloc elocit itie ies s from from the the Ba Battzle zle an and d Wan ang g (199 (1992) 2) mo mode del. l. The The diag diagon onal al da dash shed ed line line repr repres esen ents ts a pe perf rfec ectt corr correelation. This figure shows that the Batzle and Wang (1992) model is in general quit qu ite e go good od for pred predic icti ting ng the the veloc elocit ity y ob obse serv rved ed in the the labo labora rato tory ry,, alth althou ough gh it slig slight htly ly but consistently underestimates the live oil velocity compared to the measured laboratory live oil velocities. In order to investigate the dependence of live fluid velo velocit city y on the vario various us input input pa para ramet meters ers,, the calcu calculat lated ed veloc velocity ity,, de dens nsity ity,, an and d mod mod-ulus is plotted versus various parameters for the specific oils used in the Batzle and Han (1997) fluid study. Figure 1-9 shows the live and dead oil density and how these properties corr correl elat ate e with with the the ga gass-oi oill rati ratio o. The The comp comput uted ed de dead ad oil oil de dens nsit ity y is plot plotte ted d versu ersus s the the gasga s-oi oill rati ratio o for the the orig origin inal al oil oil in-s in-sit itu u (liv (live e oil) oil).. The The de dead ad oil oil de dens nsit ity y is calc calcul ulat ated ed at surface conditions and the live oil is calculated at reservoir conditions, from the same API gravity and GOR which were reported for the individual samples. The trend of data for live oil density demonstrates that as the gas-oil ratio increases, the density of the oil decreases. It is interesting to note that there is no obvious corr correl elat atio ion n be betw twee een n the the de dead ad oil oil de dens nsit ity y (or (or API API gra gravity vity)) an and d the the ga gas s in solu soluti tion on as found under reservoir conditions. Figure 1-10 shows that the solution gas-oil ratio has a large effect on the velocity for the samples in the study. As the gas-oil ratio increases, the velocity of the the liv live oil oil de decr crea ease ses s sign signifi ifica cant ntly ly.. This This de demo mons nstr trat ates es that that even a smal smalll am amou ount nt of gas in solution has a large effect on the fluid compressibility. The gas in solution

35

also decreases the density of the live oil (see Figure 1-9), 1-9), but not enough to overcome the effect of increased compressibility on the velocity. Figure 1-11 is a plot of calculated velocity versus API gravity for the live oil samp sample les s inv involv olved in the the stud study y. In ge gene nera ral, l, as the the API API grav gravit ity y incr increa ease ses, s, the the veloc elocit ity y of the the liv live oil oil de decr crea ease ses s, but the the eff effect ect is mu much ch smal smalle lerr than than for the the solu soluti tion on ga gass-oi oill ratio.

Figur Figure e 1-9: 1-9: Plot lot of live ive and dea ead d oil densiti sities es for the samp mplles in the the stud tudy and the the relationship to GOR (the lines are a least squares regression through the data points). Figure 1-12 is a cross plot of the calculated live oil modulus versus calculated live oil density for the samples in the study. Note that the data set has an exponential trend. This is apparently due to the high compressibility and low

36

Figure 1-10: Plot of the calculated velocity versus GOR for the samples in the study.

Figure 1-11: Plot of the calculated velocity versus API gravity for the samples in the study. 37

dens de nsit ity y of the the ligh lighte terr hydro ydroca carb rbon ons s that that are are in the the ga gas s ph phas ase e at surf surfac ace e cond condit itio ions ns yet are in solution under reservoir conditions. The live oil modulus decreases as the live oil density decreases due to the increasing compressibility in the system. Figure 1-13 is a plot of the calculated live oil velocity versus the calculated live oil density for the samples in the study, showing a strong correlation, where the velocity of the oil decreases as the density decreases. The modulus decreases so rapidly with density that the overall effect on velocity is a decrease in velocity with density.

Figure 1-12: Plot of calculated live oil modulus versus density for the samples in the study.

38

Figure 1-13: Plot of live oil velocity versus density for the samples in the study. Figure 1-14 is a plot of the laboratory velocity and calculated velocity data versus pressure for a specific sample (Marathon Oil Company, Well A-2) in the Batzle and Han (1997) fluid study. The calculated velocity data was modeled assu assumi ming ng a cons consta tant nt GOR of 11 112. 2.2 2 l/l l/l (630 (630 ft 3 /bbl). The data shows that the Batzle and Wang (1992) model, indicated by the solid symbols connected by lines, underestimates the laboratory data shown by the open unconnected symbols. The bub ubb ble po poiint for this this sam amp ple is at 29.3 MPa MPa (4250 psi) at 75 oC (res (reserv ervoi oirr temtemperature). Notice that at pressure below the bubble point the laboratory data and pred predic icte ted d da data ta div diverge erge sign signifi ifica cant ntly ly.. This This is du due e to the the fact act that that the the labo labora rato tory ry me meaasurements were made on only the oil fraction as the gas exsolved from solution

39

and the GOR in that oil fraction changes below the bubble point. However, the GOR GOR of the the oil oil frac fracti tion on is he held ld cons consta tant nt in the the calc calcul ulat atio ions ns.. Figur Figure e 1-14 1-14 also also show shows s that temperature affects the disagreement between the calculated and measured values above the bubble point pressure, with the disagreement becoming greater at lower temperature, and is very small at reservoir conditions.

Figure 1-14: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and the laboratory live oil velocity (Batzle and Han 1997 Fluid Study) versus pressure for a sample in the study modeled with constant GOR. Figur Figure e 1-15 1-15 helps helps to expla explain in the discre discrepa panc ncy y be betw twee een n the calcul calculate ated d value values s (assuming constant GOR) and the laboratory values below the bubble point pressure. The term "black oil" refers to reservoirs containing immiscible water, oil and gas phases with a simple pressure-dependant solubility of the gas component in the the oil phase. se. The com compo pos sitio ition n of the the oil oil an and d ga gas s comp mpo onents are assum sumed to be 40

cons consta tant nt at all all pres pressu sure re cond condit itio ions ns (Bra (Bradl dle ey, 19 1987 87). ). In such such a mo mode del, l, it is assu assume med d that at reservoir pressure conditions, the live oil has a specified GOR (normally dete de termi rmine ned d from from PVT PVT test testin ing) g),, an and d as pres pressu sure re de decr crea ease ses, s, bu butt rema remain ins s ab abov ove e the the bubble point, the GOR of the live oil remains constant. When the pressure rea reache hes s the the bubble po poiint, nt, fre free gas beg egiins to come out of soluti lution on and the the GOR of the the liqu liquid id oil oil de decr crea ease ses s. As the the pres pressu sure re drop drops s furt furthe herr, mo more re free free ga gas s come comes s ou outt of solution and the GOR of the liquid oil continues to decrease. The GOR of the liquid oil below the bubble point is referred to as the maximum GOR at specified temperature and pressure conditions.

Figure Figure 1-15: 1-15: The The evolu evolutio tion n of hydro hydroca carbo rbon n ph phase ases s with with de decre creas asing ing press pressure ure.. The The liqu liquid id comp compon onen entt (oil (oil)) is be best st de desc scri ribe bed d as the the "liv "live" e" oil oil calc calcul ulat ated ed at the the spec specifi ified ed GOR above the bubble point pressure, and by the maximum GOR at conditions below the bubble point pressure. Figur Figure e 1-16 1-16 is an anot othe herr plot plot of the the labo labora rato tory ry veloc elocit ity y an and d calc calcul ulat ated ed veloc elocit ity y data versus pressure for a specific sample (Marathon Oil Company, Well A-2) in

41

the Batzle and Han (1997) fluid study. In this case, the calculated velocity data was mo mod deled led with a con constan tant GOR of 112.2 l/l (63 (630 ft 3 /bbl) above above the bubble bubble point pressure and a variable GOR (the maximum GOR at the specified pressure and temperature conditions) below the bubble point. The data shows that the Batzle and an d Wan ang g (199 (1992) 2) mo mode dell stil stilll un unde dere rest stim imat ates es the the labo labora rato tory ry da data ta,, simi simila larr to Figure 1-14, 1-14, but fits much more closely below the bubble point where the GOR of the oil fraction fraction varies varies.. Figur Figure e 1-16 1-16 also also sho shows that that the the diff differ eren ence ce be betw twee een n the the labo labora rato tory ry and calcul calculate ated d value values s decre decrease ase with with increa increasin sing g tem temper peratu ature re at high high press pressure ures s bu butt at pressures near the bubble point the difference increases with increasing temperature. The error between the modeled data and the laboratory data increases

Figure 1-16: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and the laboratory live oil velocity (Batzle and Han 1997 Fluid Study) versus pressure for a sample in the study modeled with a variable GOR. 42

near ne ar the the bub ubb ble po poin intt be beca caus use e cons consta tant nt comp compos osit itio ion n of the the oil oil an and d ga gas s is assu assume med d yet compositional variations are, most likely, an important factor near the bubble point. The following section will focus on more in-depth modeling of Well A-2 usin using g the the Ba Batz tzle le an and d Wan ang g mo mode del, l, the the Gass Gassma mann nn-B -Bio iott mo mode del, l, an and d the the AVO mo mode dell desc de scrib ribed ed ab abov ove e in sect sectio ions ns 1.2. 1.2.1, 1, 1.2. 1.2.2, 2, an and d 1.2. 1.2.3, 3, resp respec ecti tiv vely ely. Be Beca caus use e the the Ba Battzle zle an and d Wan ang g mo mode dell ad adeq equa uate tely ly de desc scri ribe bes s the the oil oil veloc elocit itie ies s un unde derr rese reserv rvoi oirr cond condiitions, it is assumed that it can be used to model conditions of reservoir depletion during production. 1.3.2 Application to Lobster Field, Well A-2 The Lobster Field, located in Ewing Bank block 873 in the Gulf of Mexico, was disc disco overed ered in late late 19 1991 91.. The The field field is loca locate ted d ap appr pro oxima ximate tely ly 20 200 0 mile miles s sout south h of New Orleans, Louisiana and the platform (shown in Figure 1-17) 1-17) is in approximate ma tely ly 77 775 5 fee eett of water ater.. The The field field prod produc uces es from from an overpr erpres essu sure red d rese reserv rvoi oirr, in a formation marked by the Bulminella foraminifera (Bul-1 formation), of Pliocene age ag e, at a de dept pth h of ab abou outt 11 11,0 ,000 00 ft subs subsea ea (Pet (Petro ro et. et. al., al., 19 1997 97). ). The The Bu Bull-1 1 forma ormati tion on cons consis ists ts of po poor orly ly cons consol olid idat ated ed turb turbid idit ite e sand sands s with with a po poro rosi sity ty of ap appr pro oxima ximate tely ly 30 percent. The trapping mechanism is a combination stratigraphic and structural trap trap,, show shown n in Figur Figure e 1-18 1-18. It lies lies alon along g the the flexu flexure re tren trend d be betw twee een n the the curr curren entt shel shelff and an d cont contin inen enta tall slop slope e an and d at the the no north rth en end d of a semi semi-c -cir ircu cula larr salt salt with withdr dra awa wall ba basi sin. n. Hydrocarbon migration is believed to have occurred along faults from a deep, Jurassic age, high sulfur, carbonate source (Petro et. al., 1997).

43

Figure 1-17: Lobster Field platform, Ewing Bank block 873. A series of fan-shaped sand lobes are stacked over the west and central port po rtio ion n of the the field field an and d are are ref referre erred d to as the the weste estern rn pe perf rfor orma manc nce e area area,, sho shown in Figure 1-18. 1-18 . The lobes are in hydraulic communication, have the same oil-water contact, and pressure histories. These sands are well sorted and fine- to very fine- grained with quartz as the primary mineral and minor amounts of potassium and plagioclase feldspars and zeolite cement (Petro et. al., 1997). The horizontal and vertical permeability in this field is excellent. Two san and d lob lobes loc located ted on the the east ast sid side of the the field consi nsist of chann nne el an and d over overba bank nk de depo posi sits ts an and d are are ref referre erred d to as the the ea east stern ern pe perf rform orman ance ce area area,, show shown n in Figure Figure 1-18 1-18. Thes These e two two lobe lobes s are are in hydr ydrau auli lic c comm commun unic icat atio ion n with with ea each ch othe otherr an and d

44

are separated from the western performance area. The sands are fine- to very fine- grained with smectite, volcanic fragments, and zeolite cement present with quartz, the predominant mineral. Lamination is more prevalent here than the western performance area (Petro et. al., 1997). This This stud study y will will focus ocus on the the ea east stern ern pe perf rform orman ance ce area area,, spec specifi ifica calllly y Well ell A-2 A-2 (completed in October, 1994), located on Figure 1-18, 1-18, which contains an undersatu saturrated ated oil oil syst system em at a rese reserv rvoi oirr temp temper erat atur ure e of 75 oC (167 oF) an and d pres pressu sure re of 7400 psi (51 MPa). The height of the oil column is approximately 4350 feet and Well A-2 has a completion interval of 121 feet (Petro et. al., 1997).

Well used in study

Figure 1-18: Structure and performance areas (from Petro et.al., 1997).

45

Figure 1-19 is a flow chart showing the approach used in this thesis to model the reservoir with changing saturation and pressure conditions. First, the reservoir is modeled with varying saturation and constant pressure conditions using the Batzle and Wang and Gassmann-Biot models. The results from this appr ap proa oach ch are are sho shown in Figu Figure res s 1-20 1-20 an and d 1-22 1-22 thro throug ugh h 1-25 1-25.. The The rese reserv rvoi oirr is then then modeled varying both saturation and pressure conditions using the Batzle and Wang, Gassmann-Biot, and AVO (seismic) models. The dry frame changes with pressure are also modeled using an equation obtained from Laurence Bentley (University of Calgary, personal communication, July 1999). The results from this approach are shown in Figures 1-26 through 1-30 (section 1.3.2.1).

Figure 1-19: Flow chart showing the approach to reservoir modeling with changing saturation and pressure conditions. Essential input parameters for the Batzle and Wang (1992) model were obta ob tain ined ed from from PVT PVT test testin ing g on an oil oil samp sample le from from Well ell A-2 A-2 (tak (taken en at ap appr pro oxima ximate tely ly

46

12,000 feet depth). The gas specific gravity (G) is 0.70, the gas-oil ratio is 121 liter/ liter/lit liter er (630 (630 ft3 /bbl), the API gravity gravity is 22.3, and the salinity of the brine in the formati ma tion on is 75 75,0 ,000 00 pp ppm. m. Thes These e value alues s are are inpu inputt to the the spre spread adsh shee eett crea create ted d from from the the Batzle and Wang (1992) model, shown in Table 1-3. 1-3 . The values are then compute pu ted d for veloc elocit ity y, de dens nsit ity y, an and d mo modu dulu lus s for a ga gas s, liv live oil, oil, de dead ad oil, oil, an and d brin brine e usin using g the equations that are described above in the Batzle and Wang model. It is evident in Table 1-3 that the amount of gas in solution has a significant effect on the fluid properties. Table able 1-3: 1-3: Sp Spre read adsh shee eett ba base sed d on Ba Batz tzle le an and d Wan ang g (199 (1992) 2) pred predic icto tors rs show showin ing g the calculation of fluid properties for Well A-2, Lobster Field.

The densities for a live and dead oil are 0.7613 and 0.8991 g/cm 3, respectively, at reservoir conditions. The moduli for a live and dead oil are 1184.0 and

47

2131.4 213 1.4 MPa, MPa, respe respecti ctive vely ly,, at reserv reservoir oir condi conditio tions ns.. These These mod model el result results s yield yield veloc veloc-ities for live and dead oil of 1247.1 and 1539.7 m/s, respectively, at reservoir conditi dition ons. s. Ca Calc lcul ulat atio ions ns ha hav ve also also be been en ma made de for certa certain in fluid fluid mixt mixtur ures es,, wh whic ich h prov provid ide e more realistic views of this reservoir. The spreadsheet shown in Table 1-3 gives the the resu result lts s for a mixt mixtur ure e of 80 pe perc rcen entt oil oil an and d 20 pe perc rcen entt brin brine e (a go good od esti estima mate te for irreducible water saturation in the unproduced and uninvaded reservoir); additional calculations were made for other mixtures. Table 1-4 gives the values for different mixtures of the Lobster fluids (used to create the modulus density crossplot in Figure 1-20), 1-20), computed using the mixtures feature in the spreadsheet of Table 1-3. 1-3 . These data demonstrate how the fluid properties in the reservoir will change through time as fluid saturation changes during production. Water begins to move through the reservoir due to water injection and oil production, and gas comes out of solution due to a decr de crea ease se in pres pressu sure re be belo low w the the bub ubb ble po poin int. t. The The rese reserv rvoi oirr was disc discov over ered ed at irre irre-ducible water saturation, eighty percent live oil and twenty percent water; this point is the second green square above the live oil box in Figure 1-20. 1-20. As more water is introduced into the system as the reservoir is produced, the reservoir prop propert ertie ies s will will mo mov ve up upwa ward rd alon along g the the gree green n line line (X-A (X-A), ), assu assumi ming ng as this this time time that that the pressure does not change. The moduli are calculated as functions of changing saturation, but the pressure and temperature conditions are not assumed to change in the construction of Figure 1-20. 1-20. This is a significant simplification, but calculations based on reas reason onab able le pres pressu sure re drop drops s with with prod produc ucti tion on (up (up to 25 2500 00 psia psia)) show show that that the the satu satura ra--

48

tion change itself is much more significant than the pressure change as it affects each ea ch ph phas ase e sepa separa rate tely ly.. The The pres pressu sure re chan change ge,, of cour course se,, is acco accomp mpan anie ied d by a satsaturation change. If the pressure and saturation changes are modeled simultaneously, the modulus decreases rapidly (as gas is liberated) and the density decreases slowly. slowly. Table 1-4: Modulus and density values for Lobster Field as fluid saturation changes during reservoir production.

This This de decr crea ease se in pres pressu sure re (mod (model eled ed he here re as chan changi ging ng satu satura rati tion on with with pres pres-sure constant) with production has little effect on the fluid properties until the bubble po poin intt is reac reache hed. d. Once Once the the bub ubb ble po poin intt is reac reache hed d the the rese reserv rvoi oirr chan change ges s from from a two two ph phas ase e (oil (oil-w -wat ater er)) syst system em to a mo more re comp comple lex x thre three e ph phas ase e (oil (oil-g -gas as-w -wat ater er)) syssystem, as gas begins to exsolve from the live oil. This transformation is significant 49

because even a small amount of gas has a very large effect on the fluid properties. The oil-gas-water saturations are posted along the orange line and the gaswater properties are posted along the red line in Figure 1-20. 1-20. The large effects due to gas are obvious. There are significant decreases in the modulus and density values with a small amount of gas in the system, as little as 5 percent.

A

X

Figur Figure e 1-20: 1-20: Cros Crossp splo lott of fluid fluid mo modu dulu lus s an and d de dens nsit ity y as satu satura rati tion on value alues s chan change ge.. The saturation change, in percent, are given for (oil, gas, water) in the labels.

50

A likely path for the fluid properties of the reservoir during production is shown as a solid black line in Figure 1-20. 1-20. This shows the effect of, first, water encr en croa oach chme ment nt (tra (traje ject ctory ory X-A) X-A),, an and d late laterr, the the evolut olutio ion n of a ga gas s ph phas ase e as the the pres pres-sure drops below bubble point. The effect of changing saturation can be incorporate rated d into into a mo mode dell for the the ho host st rock rock (Gas (Gassm sman annn-Bi Biot ot mo mode del) l),, in orde orderr to inv investi estiga gate te its its eff effect ect on bulk ulk seis seismi mic c prop propert ertie ies s of the the format ormatio ion, n, an and d late laterr, into into a lay layered ered ea earth rth mode mo dell to pred predic ictt the the seis seismi mic c resp respon onse se as the the rese reserv rvoi oirr is de depl plet eted ed.. This This will will aid aid in production and reservoir engineering decisions and forecasting. Figure 1-21 is a well log for Well A-2, Lobster Field, showing gamma ray, resistivity, P-wave velocity, velocity, and bulk density. The yellow blocks on the gamma gamm a ray curv curve, e, in gree green, n, are are sand sands s an and d the the oran orange ge bloc locks are are shal shales es.. The The resi resist stiv ivit ity y curv curve, e, in orange, shows high resistivity kicks (oil zones) which are shaded in green. The oil zone at approximately 12,000 feet is the reservoir unit in the Bul 1 formation. Notice that the P-wave velocity, in red, and the density, in black, both decrease in the oil zone. In contrast, a water-saturated sand is located at approximately 11,800 feet and does not show a decrease in P-wave velocity. The bulk density decreases slightly in the sands due to the change in lithology. The layer above the reservoir unit is shale and has a value of 2900 m/s (950 (9500 0 ft/s ft/s)) for P-w P-wave ave veloc elocit ity y, 12 1250 50 m/ m/s s (410 (4100 0 ft/s ft/s)) S-w S-wave ave veloc elocit ity y (not (not show shown n on the log) and 2.4 g/cm 3 for bulk density. The reservoir unit is a sand (Bul-1 formation) and has an average value of 2225 m/s (7300 ft/s) for P-wave velocity, 1280 m/s (4200 ft/s) for S-wave velocity (not shown on the log), and 2.1 g/cm 3 for bulk

51

density. These properties for the reservoir unit and overlying layer are needed to determine the AVO response of the boundary between the two layers.

ft/s

g/cm3

Figure 1-21: Well log showing sh owing gamma ray, ray, resistivity resisti vity,, compressional compres sional (P-wave) velocity, and bulk density curves for Well A-2, Lobster Field. Tab able le 1-5 de demo mons nstr trat ates es the the use use of the the Gass Gassma mann nn-B -Bio iott eq equa uati tion ons s with with fluid fluid and rock properties to determine the overall reservoir rock seismic properties such such as veloc elocit ity y an and d de dens nsit ity y. The The inpu inputt value alues s incl includ ude e po poro rosi sity ty,, soli solid d ma mate teri rial al bulk ulk modulus (K  (K s ) and density ( ρs ), brine density and bulk modulus ( ρw , K w ), and hydrocarbon density and bulk modulus ( ρhyd , K hyd ). The important output values 52

are the bulk density ( ρd), P-wave velocity (V p), S-wave velocity (V s), acoustic impe impeda danc nce e (AI) (AI),, an and d Poiss oisson on’’s rati ratio o ( σ) as the they vary ary du due e to chan change ges s in satu satura rati tion on.. The dry frame modulus is held constant. Table able 1-5: Gass Gassman mann-B n-Biot iot mod model el to calcu calculat late e veloc velocity ity an and d de dens nsity ity at various water saturation conditions (core samples measured at 0.26, 0.39. and 0.53 saturation).

Figur Figure e 1-22 1-22A sho shows P- an and d S- wave veloc locity ity and bulk densi nsity as a fun function tion of water saturation, the result of fluid substitution into the Gassmann-Biot equation tions. s. The The shea shearr wa wav ve veloc elocit ity y ( V s , green reen curv curve) e) is no nott sign signifi ifica cant ntly ly aff affecte ected d by the the change in saturation, because it is not affected by the change in fluid saturation but it is affected by the slight change in density. The compressional wave velocity (V p , red red curv curve e) tre trends fro from 2605 m/ m/s s (854 545 5 ft/ ft/s) at full water sat satura uratio tion to 2229 m/  s (7312 ft/s) at full oil saturation. At reservoir conditions, the saturation during

53

production varies from irreducible water saturation (0.2 saturation) to residual oil saturation (0.7 or 0.8 saturation). Within this saturation range the compressional veloc elocit ity y varie aries s from from 22 2264 64 m/ m/s s (742 (7428 8 ft/s ft/s)) to 24 2460 60 m/ m/s s (810 (8100 0 ft/s ft/s), ), a varia ariati tion on of nine nine percent. The density (shown as the blue line in Figure 1-22) 1-22) also increases from 2.1 to 2.15 g/cm 3, a difference of only two percent, as the water saturation increa increases ses.. Thes These e calcul calculat ated ed valu values es can can be used used to det determi ermine ne reserv reservoi oirr cond conditi itions ons from logging conditions (invaded conditions). These data are modeled with varying saturation and constant pressure conditions. Figure 1-22B 1-22B shows acoustic impedance and Poisson’s ratio as functions of saturation. Both acoustic impedance (shown in blue) and Poisson’s ratio (PR, shown in maroon) increase as water saturation increases.

A

B

Figure 1-22: A) Velocity and density versus saturation B) impedance and PR versu ersus s satu satura rati tion on show showin ing g ho how w water ater satu satura rati tion on aff affects ects a two two ph phas ase e mixt mixtur ure e of liv live oil and brine in a sandstone matrix from water to oil saturated conditions.

54

The properties of the pore fluids have significant effects on the impedance and Poisson’s ratio of the reservoir rock as shown in Figure 1-23A. 1-23A. This figure shows changes in the impedance and Poisson’s ratio values as the reservoir (sh (shown as point int X in Figure Figure 1-20 1-20)) be beco comes mes more more wa water ter-sa -satur turate ated. d. The The imped impedanc ance e and Poisson’s ratio can be directly correlated to the seismic amplitude and amplitude variation with offset at the interface between the overlying shale and the reservoir. At reservoir conditions, the impedance is 4755 m/s*g/cm 3 (15,600 ft/s*g/  cm3) and Poisson’s ratio is 0.27. The impedance and Poisson’s ratio of the reservoir formation increase as the water saturation increases and the reservoir becomes depleted. At full water saturation, the impedance is 5650 m/s*g/cm 3 (18,536 ft/s*g/cm 3) and Poisson’s ratio is 0.35. The smaller impedance value at reservoir conditions produces a larger impedance contrast with the overlying shale layer which in turn creates a larger amplitude seismic response. The smaller Poisson’s ratio at reservoir conditions prod produc uces es a larg large e cont contra rast st be betw twee een n the the rese reserv rvoi oirr forma ormati tion on an and d the the over overly lyin ing g shal shale e layer, in turn creating a class III amplitude variation with offset (AVO) effect. Figure 1-23B 1-23B shows the predicted percent changes in impedance and Poisson’s ratio of the reservoir rock due to changes in the pore fluid properties. The point labeled reservoir conditions in Figure 1-23A 1-23A and B is related to point labeled X in Figure 1-20. 1-20. If the water saturation increases, the fluid bulk modulus and density increase according to the trajectory labeled X-A in Figure 1-20, 1-20, this has ha s an incr increa easi sing ng aff affect ect on Poiss oisson on’’s rati ratio o an and d the the acou acoust stic ic impe impeda danc nce. e. Ther There e is a 12 pe perc rcen entt incr increa ease se in impe impeda danc nce e an and d a 21 pe perc rcen entt incr increa ease se in Poiss oisson on’’s rati ratio o as

55

saturation values change from reservoir conditions (0.2 water saturation) to residual oil conditions (0.7 water saturation), when the reservoir is depleted. Figur Figure e 1-24 1-24 is a plot plot of the the comp compre ress ssio iona nall veloc elocit ity y of a comp compre ress ssio iona nall wa wav ve passing through the fluid and rock matrix versus the bulk density. This figure shows the changes in velocity and density values as the reservoir becomes increasingly water saturated. At reservoir conditions, the velocity is 2264 m/s (74 (7428 ft/s ft/s)) and the the density sity is 2.10 .10 g/cm3. The The veloc elocit ity y an and d de dens nsit ity y of the the rese reserv rvoi oirr increase as the water saturation increases and the reservoir becomes depleted. At full full water ater satu satura rati tion on,, the the veloc elocit ity y is 26 2605 05 m/ m/s s (854 (8545 5 ft/s ft/s)) an and d the the de dens nsit ity y is 2.17 2.17 g/cm3.

AA

B

wet

wet depleted

wet

depleted reservoir conditions

depleted

reservoir conditions

reservoir conditions

Figure 1-23: A) Impedance versus PR B) Percent change in impedance versus percent change in PR showing how water saturation affects a two phase mixture of live oil and brine in a sandstone matrix from water saturated to oil saturated conditions.

56

wet

depleted

reservoir conditions

Figure 1-24: P-wave velocity versus density showing how water saturation affects a two phase mixture of live oil and brine in a sandstone matrix from water saturated to oil saturated conditions. Figur Figure e 1-25 1-25 is a grap graph h of shea shearr veloc elocit ity y versu ersus s comp compre ress ssio iona nall veloc elocit ity y. The The shea shearr veloc elocit ity y chan change ges s very litt little le as water ater satu satura rati tion on incr increa ease ses s wh whilile e the the comp compre resssional velocity changes significantly. The compressional velocity is much more susceptible to fluid changes and is used to help determine fluid properties. The shear velocity is useful in determining frame properties and is not affected by fluids in the reservoir.

57

reservoir conditions depleted wet

Figure Figure 1-25: 1-25: Co Comp mpre ress ssio iona nall vs. vs. shea shearr veloc elocit ity y for a two two ph phas ase e mixt mixtur ure e of liv live oil oil and brine in a sandstone matrix from water saturated to oil saturated conditions. 1.3.2.1 Predicted Reservoir Response to Production for Lobster Field In this section, the previously developed models will be used to evaluate the dependence of seismic properties on saturation and pressure changes expected during reservoir production. The following figures illustrate how the predic dictors tors may be used to mode dell the the reserv servo oir thro hrough tim time as it is produce uced and the the pressure decreases. Figures 1-26 and 1-27 are concerned with fluid properties above while Figures 1-28A and 1-29 show the effect of changing both saturation and pressure conditions within a rock assuming a constant dry frame modulus. Figures 1-28B and 1-30 show the effect of varying saturation and pressure conditions while also assuming the dry frame modulus is a function of pressure. 58

Figur Figure e 1-26 1-26 is a plot plot of the the pred predic icte ted d fluid fluid mo modu dulu lus s versu ersus s pres pressu sure re for Lo Lobbster Field beginning at an initial discovery pressure of 51 MPa (7400 psi). At a given pressure, the fluid can have a wide range of fluid moduli possible for different satur saturati ation on cond conditi ition ons. s. In Figure Figure 1-26 1-26, the the diff differ eren entt fluid fluid mo modu duli li po poss ssib ible le for the the initial reservoir pressure conditions are shown by the dark blue diamonds. The numb nu mber ers s ne next xt to the the diam diamon onds ds indi indica cate te the the corr corres espo pond ndin ing g satu satura rati tion on value alues s as (% oil,% gas,% water) in the reservoir. Logging conditions are posted as a teal circle above the blue diamonds, which is at 80 percent water and 20 percent oil due to water invasion. The initial reservoir saturation is 80 percent oil and 20 percent water (80,0,20). The bubble point pressure is 29.3 MPa (4250 psi).

Figure 1-26: Modulus of the fluid mixture versus pressure showing changes in the fluid modulus as the pressure and saturation in the reservoir changes. Saturation values are shown as (% oil,% gas,% water). The Bubble-point (P BP) for this fluid mixture is 29.3 MPa.

59

The black line connecting several data tracks is the expected modulus response to pressure changes. The line starts at the initial reservoir saturation poin po intt (80, (80,0, 0,20 20)) an and d slig slight htly ly incr increa ease ses s as wa wate terr be begi gins ns to inv invad ade e the the rese reserv rvoi oirr. The The effects of pressure then take over and the modulus begins to drop slightly as it approaches the bubble point. Once the bubble point is reached, the modulus of the reservoir drops significantly as free gas begins to exsolve in the system. The modulus continues to decrease significantly as the pressure drops further and more mo re ga gas s exsol xsolv ves from from solu soluti tion on.. The The satu satura rati tion on of the the fluid fluids s an and d ga gas s in the the rese reserrvoir is posted at several points along the black line. Figure 1-27 shows the fluid density of the reservoir versus pressure. The blac lack line line on the the plot plot is the the expec xpecte ted d de dens nsit ity y resp respon onse se to pres pressu sure re an and d satu satura rati tion on changes in the reservoir. The saturation of the fluids and gas in the reservoir is posted at several points along the black line in the same format as Figure 1-26. 1-26. The density is not affected as strongly as the modulus by pressure changes and variations of saturation. The expected conditions start at the initial reservoir saturati ration on po poin intt (80, (80,0, 0,20 20)) an and d slig slight htly ly incr increa ease se as water ater be begi gins ns to inv invad ade e the the rese reserv rvoi oirr. Once Once the the bub ubb ble po poin intt is reac reache hed d an and d ga gas s be begi gins ns to exsol xsolv ve into into the the rese reserv rvoi oirr the the density begins to decrease more drastically. This This chan change ge in mo modu dulu lus s an and d de dens nsit ity y will will aff affect ect the the rese reserv rvoi oirr prop propert ertie ies s over over time. As the pressure drops, the fluid modulus and density also drop significantly when free gas is introduced into the reservoir. The changes in density and modulus will also change the P-wave velocity and Poisson’s ratio in the reservoir unit.

60

Figure 1-27: Fluid density versus pressure showing how the density changes as the pressure and saturation in the reservoir changes.Saturation values are shown as (% oil,% gas,% water). Figure 1-28A 1-28A shows the decrease in both P-wave velocity and Poisson’s ratio as the pressure in the reservoir decreases below the bubble point and saturation changes. The dry frame modulus is held constant. The The eq equa uati tion ons s for the the dry dry fram frame e bulk ulk an and d shea shearr mo modu duli li with with chan changi ging ng eff effecectiv tive pres pressu sure re ( P eff in MPa) MPa) are are list listed ed be belo low w an and d are are cali calibr brat ated ed for the the Lo Lobs bste terr Fiel Field d using known values at reservoir conditions. Dry Frame Bulk Modulus, K dp , in GPa: K dp  =

–

– 0.0582

4.1873e  4.1873 e 

( P ef f )

+ 3.61

Dry Frame Shear Modulus, G dp , in GPa: G dp  =

–

– 0.0549

5.089e  5.089 e  61

( P ef f )

+ 4.714

Figure 1-28B 1-28B also shows the decrease in both P-wave velocity and Poisson’s ratio as the pressure in the reservoir decreases below the bubble point and saturation changes where the dry frame modulus changes with pressure. Notice that that a varia ariab ble dry fram frame e mo modu dulu lus s de decr crea ease ses s the the Poiss oisson on’’s rati ratio o an and d incr increa ease ses s the the P-w P-wave veloc elocit ity y. The The eff effects ects of the the dry dry fram frame e are are du due e to the the stif stifffen enin ing g of the the fram frame e as pres pressu sure re de decr crea ease ses s. The The dry dry fram frame e eff effects ects coun counte tera ract ct the the eff effects ects of free free ga gas s in the reservoir. The changes in these variables will affect the seismic signature of the the rese reserv rvoi oirr over over time time (as (as pres pressu sure re de decr crea ease ses) s).. The The de decr crea ease se in P-wa P-wav ve veloc elocit ity y and Poisson’s ratio will increase the impedance contrast with the overlying shale layer and amplify the AVO effect. A

B

bubble point

bubble point

reservoir conditions

reservoir conditions

Figure 1-28: Velocity and Poisson’s ratio versus pressure demonstrating that when the reservoir drops below the bubble point (at 29.3 MPa) it significantly effects the reservoir properties. A) Modeled with a constant dry frame modulus. B) Modeled with a variable dry frame modulus with pressure. Figure 1-29 shows the AVO response for the reservoir as pressure and fluid saturations change. The dry frame effects are held constant. The green 62

seri series es are are thos those e that that are are satu satura rate ted d with with oil oil an and d water ater (con (conta tain inin ing g no free free ga gas) s).. The The red series are saturated with oil, free gas, and water (saturation values are listed in the legend as %oil,%gas,%water). The series are labeled P1 through P6. P1 corresponds to initial reservoir conditions when the field was discovered; P2-P6 show the progression through time as the pressure drops and gas begins to exsolve from solution at the same pressure as previous plots. It is apparent that the AVO response becomes more pronounced as free gas exsolves from the live oil when the pressure drops below the bubble point (P4, P5, P6), assuming dry frame effects with pressure are held constant. Although not shown, the response calculated from logging conditions is nearly identical to the AVO response at 60 percent oil and 40 percent water saturation (4250 psi), shown as P3.

Time

Figure Figure 1-29: 1-29: Re Refle flecti ction on amp amplit litud ude e versu versus s offse offsett showi showing ng the amp amplit litud ude e varia variatio tion n with offset as the pressure changes over time. Saturation values are shown in legend as (% oil,% gas,% water). 63

Figur Figure e 1-30 1-30 sho shows the the AVO resp respon onse se for the the rese reserv rvoi oirr as the the dry dry fram frame e an and d fluid saturation changes with pressure. The green series are those that are saturate rated d with with oil oil an and d water ater (con (conta tain inin ing g no free free ga gas) s).. The The red red seri series es are are satu saturrated ated with with oil, free gas, and water (saturation values are listed in the legend). The dry frame changes with pressure are included. The series are labeled P1 through P6. P1 corresponds to initial reservoir conditions when the field was discovered; P2-P6 show the progression through time as the pressure drops and gas begins to exsolve from solution. The AVO response decreases as water saturation incr increa ease ses s (P1 (P1 to P3 P3)) then then as free free ga gas s exsol xsolv ves from from the the liv live oil, oil, whe hen n the the pres pressu sure re drops below the bubble point (P4 to P6), the AVO response increases.

Time

Figure Figure 1-30: 1-30: Re Refle flecti ction on amp amplit litud ude e versu versus s offse offsett showi showing ng the amp amplit litud ude e varia variatio tion n with offset as the pressure changes over time including the effects on the dry frame. Saturation values are shown in legend as (% oil,% gas,% water).

64

This This resu result lt is very ery impo importa rtant nt be beca caus use e the the AVO resp respon onse se at P5 P5,, a pres pressu sure re sign signifi ifi-cant cantly ly be belo low w the the bub ubb ble po poin int, t, is the the same same as the the AVO resp respon onse se at init initia iall rese reserv rvoi oirr conditions, P1.

1.4 Conclusions The Batzle and Wang (1992) model predicts the Batzle and Han (1997) data da ta reas reason onab ably ly we wellll.. The The mo mode dell slig slight htly ly un unde derpr rpred edic icts ts the the veloc elocit ity y of liv live oils oils an and d overpredicts the velocity of dead oils. The model error increases as temperature increases and does not match live oil laboratory data below the bubble point due to experimental conditions. As a result, this model can be used for specific reservoir cases. Gas-oil ratio affects fluid properties by decreasing density, modulus, and veloc elocit ity y with with incr increa easi sing ng GOR. GOR. The The comp compre ress ssib ibililit ity y of the the fluid fluid incr increa ease ses s as the the ga gas s in solution increases. As temperature increases the velocity and density of the fluid decreases. The decrease in velocity as API gravity increases may be due to the composition of the sample and an increase in compressibility. The density and modulus can be calculated at different saturation and pressure conditions using the Batzle and Wang model and then plotted on a crossplot. This allows prediction of fluid properties as the reservoir is produced and shows the effect on the reservoir as it drops below bubble point. Using the Batzle and Wang and Gassmann-Biot model, the change in Pand S- wave velocity, velocity, bulk density den sity,, acoustic acousti c impedance, Poisson’s Poisson’s ratio, and bulk modu mo dulu lus s ma may y be pred predic icte ted d as the the rese reserv rvoi oirr chan change ges s from from irre irredu duci cib ble wa wate terr satu satura ra-tion conditions to residual oil conditions. This provides an avenue to calculate val-

65

ues at reservoir conditions (irreducible water saturation conditions) from logging conditions (saturated or residual oil conditions). Using the Batzle and Wang, Gassmann-Biot, and Zoeppritz models the acou acoust stic ic impe impeda danc nce e an and d Poiss oisson on’’s rati ratio o can can be de dete termi rmine ned d an and d the the am ampl plit itud ude e an and d AVO response can be predicted. Together, the models can be used to determine expected seismic responses throughout the production path of the reservoir. In an applica licattion ion to a Gulf of Me Mex xico ico field eld, it is shown tha that an AVO res response is present as a result of the fluid and rock properties. The modeling of Lobster Field illustrates how the predictors described in this thesis can be used to model the reservoir through time as the reservoir is produced and the pressure decreases. The evaluation of fluid properties enables seismic data to be used more eff effecti ectiv vely ely. Eval Evalua uati ting ng the the fluid fluid prop propert ertie ies s will will aid aid in de dete termi rmini ning ng the the usef useful ulne ness ss of time lapse seismic, predicting AVO and amplitude response, and making production and reservoir engineering decisions and forecasting.

66

1.5 References Batz Ba tzle le,, M. an and d Wan ang, g, Z., Z., 19 1992 92,, Se Seis ismi mic c prop propert ertie ies s of po pore re fluid fluids: s: Geop Geoph hysic ysics s, Vol. ol. 57, No. 11, p. 1396-1408. Batzle, M.L., Han, D., Wang, W., Wu, X., Ge, H., and Zhao, H., 1997, Fluid Property erty Eff Effects ects an and d Se Seis ismi mic c Gas Gas De Dete tect ctio ion n (Flu (Fluid id Proj Projec ect) t):: HA HAR RC & CS CSM, M, 16 163 3 pp. Biot, M.A., 1956, Theory of propagation of elastic waves in a fluid-saturated poro po rous us soli solid: d: Jour Journa nall of Acou Acoust stic ical al So Soci ciet ety y of Amer Americ ica, a, Vol. ol. 28 28,, p. 16 1688-19 191. 1. Brad Bradle ley y H.B. H.B.,, 198 1987, 7, Petrol etroleu eum m En Engin ginee eerin ring g Ha Hand ndbo book: ok: So Socie ciety ty of Petrole etroleum um EngiEngineers., Richardson, Richardson , Texas, Texas, USA, p. 48-4. Castagna, J.P., and Backus, M.M., 1993, Offset-Dependent Reflectivity - Theory and Practice of AVO Analysis: SEG Investigations in Geophysics Series, Volume 8, Tulsa, USA, 348 pp. Chen, C.T., Chen, L.S., and Millero, F.J., 1978, Speed of sound in NaCl, MgCl 2, Na2SO4, and MgSO4 aqueous solutions as functions of concentration, temperature, and pressure: Journal of Acoustical Society of America, Vol. 63, p. 1795-1800. Clark, V.A., 1992, The effect of oil under in-situ conditions on the seismic properties of rocks: Geophysics, Vol. 57, No. 7, p. 894-901. Craft, B.C. and Hawkins, M.F., 1991, Applied Petroleum Reservoir Engineering: Prentice-Hall, Inc., Englewood, New Jersey, USA, 431 pp. Dodson, C.R., and Standing, M.B., 1945, Pressure-volume-temperature and solubility relations for for natural-gas-water natural-gas-water mixtures: mixtures: in Drilling and Production Practices, 1944, American Petroleum Institute. Gassmann, F., 1951, Elastic waves through a packing of spheres: Geophysics, Vol. 16, p. 673-685. Hales, A.L., and Roberts, J.L., 1974, The Zoeppritz amplitude equations: more errors: Bulletin of Seismological Society of America, Vol. 64, p. 285. Han, D-H., Nur, A., and Morgan, D., 1986, Effects of porosity and clay content on wave velocities in sandstones: Geophysics, Vol. 51, No. 11, p. 2093-2107.

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Mavko, G., Mukerji, T T., ., Dvorkin, J., 1998, The Rock Physics Handbook: Tools Tools for Seismic Analysis in Porous Media: Cambridge University Press, Cambridge, New York, York, USA, 329 pp. McCain, W.D W.D., ., 1973, Properties Properti es of petroleum fluids: Petroleum Petroleum Publishing Company. Miller Millero o, F.J., .J., Ward, ard, G.K., G.K., an and d Ch Cheti etirki rkin, n, P.V., .V., 19 1977, 77, Re Relat lativ ive e sound sound veloc velociti ities es of sea sea o salts at 25 C: Journal of Acoustical Society of America, Vol. 61, p. 14921498. Murphy, W.F., Schwartz, L.M., and Hornby, B., 1991, Interpretation physics of V p and Vs in sedimentary rocks: Transactions SPWLA 32nd Annual Logging Symp., p. 1-24. Nur, A.M., Wang, Z., 1989, Seismic and Acoustic Velocities in Reservoir Rocks, Volume olume 1, Experi Experimen mental tal Studie Studies: s: SEG SEG Geop Geoph hysics ysics reprin reprintt serie series, s, No No.. 10, p. 405. Petro, D.R., Chu, W-C., Burk, M.K., and Rogers, B.A., 1997, Benefits of pressure transient testing in evaluating compaction effects: Gulf of Mexico deepwater turbidite sands: SPE paper #38938, Proceedings 1997 SPE Annual Technical Conference. Potter, R.W. II, and Brown, D.L., 1977, The volumetric properties of sodium chloride solutions from 0 to 500 oC at pressures up to 2000 bars based on regression of available data in the literature: U.S. Geological Survey Bulletin 1421-C. Sheriff, R.E., 1991, Encyclopedic Encyclopedic Dictionary of Exploration Exploration Geophysics, Geophysics, 3rd Edition: SEG Geophysical References Series 1, Tulsa, USA, p. 384. Sheriff, R.E., and Geldart, L.P., L.P., 1995, Exploration Seismology, Seismology, 2nd Edition: Cambridge University Press, New York, USA, p. 592. Standing, M.B., 1962, Oil systems correlations, in Frick, Frick, T.C. T.C. (editor), Petroleum production handbook, Volume II: McGraw-Hill Book Co., part 19. Thomas, L.K., Hankinson, R.W., and Phillips, K.A., 1970, Determination of acoustic veloc velociti ities es for na natur tural al gas: gas: Journa Journall of Petrol etroleu eum m Techno echnolog logy y, 22 22,, 88 889-8 9-892 92.. Wang, Z-W, 1988, Wave velocities in hydrocarbons and hydrocarbon saturated rocks--with applications to EOR monitoring: Ph.D. thesis, Stanford Unv.

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Wang, Z., Nur, A., and Batzle, M.L., 1988, Acoustic velocities in petroleum oils: SPE paper #15646, Proceedings 61st SPE Technical Conference. Wang, Z., and Nur, A.M., 1989, Seismic and Acoustic Velocities in Reservoir Roc Ro cks, ks, Volum olume e 2, Theo Theore reti tica call an and d Mo Mode dell Stud Studie ies: s: SEG SEG Geop Geoph hysic ysics s repr reprin intt series, No. 10, p. 457. Wan ang, g, Z., Z., Nu Nurr, A.M. A.M.,, an and d Ba Batz tzle le,, M. M.L. L.,, 19 1990 90 Acou Acoust stic ic Veloc elocit itie ies s in Petro etrole leum um Oils Oils:: Journal of Petroleum Technology, echnology, Vol. 42, p. 192-200. Western Atlas Log Interpretation Charts, 1996, Western Atlas Logging Services, Houston, TX. Wils Wilson on,, W.D., .D., 19 1959 59,, Sp Spee eed d of soun sound d in dist distilille led d wa wate terr as a func functi tion on of temp temper erat atur ure e and pressure: Journal of Acoustical Society of America, Vol. 31, p. 10671072. Wood, A.W., A.W., 1955, A Textbook Textbook of Sound, The MacMillan MacM illan Co., New York, York, 360 pp. Wyllie, M.R.J., Gregory, A.R., and Gardner, L.W., 1956, Elastic wave velocities in heterogeneous and porous media: Geophysics, Vol. 21, p. 41-70. Zarembo, V.I., and Federov, M.K., 1975, Density of sodium chloride solutions in the tem temper peratu ature re rang range e 25-35 25-350 0 oC at pres ressures res up to 1000 kg/cm3: Journ Journal al of Applied Chemistry USSR, Vol. 48, 1949-1953, (English trans). Zoeppritz, K., 1919, Erdbebenwellen VIIIB, On the reflection and propagation of seismic waves, Gottinger Nachrichten, I, p. 66-84.

69

2.0 A Search for for Seismic Attributes for Reservoir Characterization, Crystal Field, Michigan 2.1 Introduction The The Du Dund ndee ee forma ormati tion on (De (Devon onia ian) n) ha has s yiel yielde ded d mo more re oil oil than than an any y othe otherr proproducing interva rval in the Michigan Basin. Crys rystal Field is one of the more prolific oil fiel fields prod roducing ing from rom the Dundee forma rmatio tion. Recent dril rillin ling activ tivity ity has sho shown that a large amount of by-passed oil has been left between many wells in the Dund Du ndee ee field fields, s, incl includ udin ing g Cryst Crystal al Fiel Field. d. Whil While e the the ge geol olog ogy y of some some Du Dund ndee ee field fields s in the the Mich Michig igan an Ba Basi sin n is reas reason onab ably ly well ell kno known wn,, ma man ny old old field fields s ge gene nerrally ally lac lack mo moddern well logs and seismic studies. A parti rticular goal of this project is to enhance seismic imaging of faults or kars karsti tic c fea eatu ture res s in Cryst Crystal al Fiel Field d ba base sed d on seis seismi mic c attri attribu bute tes. s. The The refle reflect ctio ion n char charac ac-ter of the Dundee is also studied to determi rmine if the effects of a limestone cap or dolo do lomi miti tiza zati tion on are are dist distin ingu guis isha habl ble. e. This This proj projec ectt is de desi sign gned ed to prov provid ide e oil oil prod produc uc-ers ers with ith a ne new w int interpr rpretati tatio on tool to evalu aluate ate res reservo rvoirs irs and mo mon nito itor the overall all performance of a field. 2.1.1 Objectives The objectives of this project are to: 1.) Inte nterpr rpret seismi ismic c attri tributes, es, such as ins instan tantan taneous phase and amp mpli li-tud tude, in term terms s of litho ithollog ogy y and rese eservo rvoir propert erties ies, and use tha that inf informat rmatio ion n for reserv reservoir oir chara characte cteriz rizati ation. on. Sp Spec ecific ificall ally y, the seism seismic ic trav travel el time time an and d simple simple seism seismic ic attr attrib ibut utes es are are evalua aluate ted d an and d comp compar ared ed with with kno known stru struct ctur ure e an and d ge geol olog ogy y with within in the Crystal Field. 2.) Determi rmine the causes of changes in reflection character in Line C-3, over Crys Crysta tall Fiel Field. d. Asce Ascert rtai ain n if thes these e chan change ges s are are du due e to the the eff effects ects of a lime limest ston one e

70

cap or dolomitization. 3.) 3.) Eval Evalua uate te an and d inte interpr rpret et prepre- an and d po post st-- stac stack k seis seismi mic c attr attrib ibut utes es for Line Line C3, Crystal Field, for shallow shallow horizons such as the Dundee Dundee formation. 4.) 4.) En Enha hance nce imagin imaging g of fault faults s or karst karstic ic feat feature ures s using using proces processin sing, g, geo geolog logic ic maps, and seismic attributes.

2.2 Background 2.2.1 History Crystal Field was discovered in early 1935 by J.W. Leonard Jr. on the Dubin farm (NW1/4, NW1/4, NE1/4, Section 11, Crystal Township) (Eddy, 1936). The The Da Dailily y Crud Crude, e, J. Tow #1 #1,, Permit ermit # 21 2111 1170 7024 2406 06 (SE1 (SE1/4 /4,, NE NE1/ 1/4, 4, SE1/ SE1/4, 4, Se Sect ctio ion n 3, T10N R5W, Crystal Township), was the first long-term producing well and was spudded May 29, 1935 and completed October 1935. The field is 2000 acres in size size,, wa was s dril drille led d mo most stly ly in the the 19 1930 30s s an and d 19 1940 40s s, an and d ha has s prod produc uced ed ap appr pro oxima ximate tely ly 8 million barrels of oil. By 1939, 80 percent of wells were abandoned, and 95 percent of the cumulative production was reached by the end of 1940. In 1995, only seven producing wells remained, each producing less than 10 barrels of oil per day da y. It is volum olumet etri ricl cly y esti estima mate ted d that that Cryst Crystal al Fiel Field d ha has s 20 mill millio ion n ba barr rrel els s of orig origin inal al oil in place (Wines, 1997). At the height of its production, Crystal Field produced from 193 wells. These wells were drilled at a 10 acre spacing with high initial production rates. That, tied with the size of the oil column and the strong water drive present, may have caused early water coning affects in the reservoir leaving significant unrecovered reserves of oil.

71

The Department of Energy sponsored a Class II Project titled "The Recovery of bypassed oil in the Dundee formation of the Michigan Basin using Horizontal Drains" (PI: J.R. Wood, Contract # DE-FC22-94BC14983). This project reviewed 30 fields in the Michigan Basin that produced from the Dundee formation tion,, incl includ udin ing g Cryst Crystal al Fiel Field. d. A ho horiz rizon onta tall we wellll,, TOW 1-3, 1-3, wa was s spud spudde ded d on Se Sept ptem em-berr 20 be 20,, 19 1995 95 an and d dril drille led d in Crys Crysta tall Fiel Field. d. The The TOW 1-3 1-3 well ell was core cored d over 60 fee eett at the top of the Dundee formation and the vertical hole was logged for gamma ray ray, resi resist stiv ivit ity y, de dens nsit ity y, an and d po poro rosi sity ty.. The The TOW 1-3 1-3 wa was s a very succ succes essf sful ul we wellll with with initial production rates of 50-100 barrels of oil per day and estimated recoverable reserves of 200,000 barrels (Wood et. al., 1997). Rece Re cent ntly ly,, two two othe otherr ho horiz rizon onta tall we welllls s (the (the Ha Happ ppy y Ho Holilida day y Tree ree Farm 6-3 6-3 an and d the the Frost rost 5-3) 5-3) ha hav ve be been en dril drille led d by Cron Cronus us De Dev velop elopme ment nt in Cryst Crystal al Fiel Field, d, with with po poor or results (Montgomery et. al., 1998). These two horizontal tests were drilled in down do wndi dip p loca locati tion ons, s, off off stru struct ctur ure e in the the lime limest ston one e cap cap rock rock,, an and d orie orient nted ed pe perpe rpend ndic ic-ular to the TOW 1-3 well. Three more wells (the Danforth 2-3, the Robbins 3-3, and the Walker 1-35) were also permitted and scheduled for drilling by Cronus Development in 1998, (Wines, 1997). 2.2.2 Location Crys Crysta tall Fiel Field d is loca locate ted d in the the cent center er of the the Mich Michig igan an Ba Basi sin, n, Figur Figure e 2-1 2-1. The field is located in both Crystal (T10N R5W) and Ferris (T11N R5W) Townships, Montcalm County, about 12 miles west of Ithaca, Michigan (Eddy, 1936). The physical geography of the field area is gently rolling till and sandy or grav gravel ely y ou outw twas ash h plai plains ns.. The The field field lies lies be betw twee een n the the N-S N-S orie orient nted ed Fow owle lerr an and d Lyons yons moraines of the Saginaw ice lobe. The surface elevation ranges from 780 to 850 72

feet (Eddy, 1936). The field area lies on two watershed systems. The northeast side of the field lies on the Carpenter Creek drainage system that flows east into the Pine River. The central and southern side of the field lies on the Fish Creek drai draina nage ge syst system em that that flows flows sout southe heas astt into into the the Ma Mapl ple e Riv River. er. The The water ater tab table in this this area is only a few feet from the surface. Duck Lake is along the south edge of the field where the water table comes to the surface (Eddy, 1936).

Study Area

Scale 1:2500000.

10.

20.

0.

0.

10.

20.

20.

40.

30.

60.

40.

50.

80.

miles

100.

kilometers

Figure 2-1: Location of the project study area and surrounding Dundee fields (courtesy of C. Asiala and S.D. Chittick). The data used to create the forma rmation contour and isopach maps in Figures ures 2-6 2-6 thro throug ugh h 2-11 2-11 are are from from well ell reco record rds s an and d dril drilli ling ng repo report rts s. Thes These e da data ta were ere compiled by the Western Michigan University Core Research Laboratory and Michigan Technological University and obtained from open file records at the Michigan Department of Natural Resources.

73

2.3 Background Geology 2.3.1 Michigan Basin The The Mich Michig igan an Ba Basi sin n is a larg large e inte interc rcra rato toni nic c ba basi sin n ap appr pro oxima ximate tely ly 80 80,0 ,000 00 mi 2 (207,000 km2) in total area and filled with up to 16,000 ft (4850 m) of Paleozoic sedime sediments nts (Cata (Catacos cosino inos s et. et. al, al, 19 1990 90). ). Figure Figure 2-2 show shows s a thre three e dime dimens nsio iona nall stru struccture contour map of top subsea of the Dundee formation for the entire Michigan Basin. The intrabasinal structural grain of the Michigan Basin is characterized by Paleozoic anticlines trending northwest-southeast. The Michigan Basin attained its present structural configuration during Ordovician time (Wines, 1997). The stratigraphic succession of the Michigan Basin is shown in Figure 2-3. 2-3.

Perspective Azim: 252 Elev: 46 Twst: 22 VE: 30

- 500 0- -500 -1000 - -1500 -2000 - -2500

(WDE)

-3000 -

Figure 2-2: Three-dimensional contour of top subsea of the Dundee formation, Michigan Basin (courtesy of W.D. Everham).

74

Figure 2-3: Stratigraphic column showing the age of the Dundee formation, the stratigraphic succession of the Michigan Basin, and the oil and gas producing formations (from Wood et. al., 1998). 2.3.2 Crystal Field 2.3.2.1 Dundee Formation In Crystal Field, the reservoir unit is the Dundee formation. The Dundee formation is of middle Devonian age, deposited in marginal-marine and shallowmarine environments and consists of the Rogers City and Reed City members (Gardner, 1974). The Reed City member developed during local marine regression, depositing evaporites and shallow water carbonates in a sabkha environ-

75

ment. The Reed City member is present on the western side of the Michigan Basi Ba sin n an and d is ref referre erred d to as the the Du Dund ndee ee lime limest ston one e on the the ea east ster ern n side side.. The The Ro Roge gers rs City limestone deposits range in depositional environment from shallow marine shel shelff, in the the west, est, to de deep eper er op open en ma mari rine ne in the the cent centra rall pa part rt of the the ba basi sin n (Cat (Catac acos osiinos et. al., 1991; Wines, 1997). The Rogers City limestone is present over the entire Michigan Basin, shown in Figure 2-4. 2-4. Together, the Dundee limestone and the Rogers City member are known as the Dundee formation. The Dundee formation is over 150 feet thick at the center of the Michigan Basin. It is composed of 2 to 20 foot coarsening upward para sequences (Wood et. al., 1998). The Dundee formation consists of a brownish-gray limestone or dolomite. The thickness of the Dundee ranges from 0 to 38 feet within Crystal Fiel Field d (Edd (Eddy y, 19 1936 36), ), wh wher ere e it cons consis ists ts of thre three e ma majo jorr facie acies: s: 1) supr supraa-ti tida dall frac fractu ture red d micrit micrites es with with fene fenestr stral al po poros rosity ity,, 2) inter inter-ti -tida dall grain grainsto stone ne facie facies, s, an and d 3) op open en marine marine fractured biomicrites (Wines, 1997). The The Du Dund ndee ee lime limest ston one e inte interv rval al in Crys Crysta tall Fiel Field d (the (the cent centra rall pa part rt of the the Mich Mich-igan Basin), produces almost entirely from coarse crystalline dolomitized limestone in fractured, vuggy intervals where solution enhanced matrix porosity is present. This productive zone is informally known as the Dundee porosity zone and is below an impermeable limestone cap (Rogers City member) (Lilienthal, 1978; Montgomery et. al, 1998). The Dundee formation is overlain by the Bell shale and underlain by the Lucas formation, Figure 2-5. 2-5. The Bell shale formation is a dark gray, or blue to black shale, ranging in thic thickn knes ess s from from 12 fee eett to over 10 100 0 fee eet. t. In some some wells ells the the forma ormati tion on is spli splitt into into two two or thre three e me memb mber ers s by thin thin lime limest ston one e or shal shaly y lime limest ston one e stri string nger ers s (Edd (Eddy y, 19 1936 36). ). The The 76

Bellll shal Be shale e is pa part rt of the the Trav raverse erse grou group p an and d is a fossi ossililifferou erous s tran transg sgre ress ssiv ive e ma marin rine e shale. The deposition of the Dundee formation was followed by a time of erosion when the Dundee surface was deeply cut and karstified. The Bell shale was then deposited on the top or deposited simultaneously with Dundee karstification. The underlying Lucas formation (Detroit River Group) consists of interbedded anhydrites, dolomites, and salt which represent sabkha, tidal-flat, shoal, and restricted lagoonal environments (Fisher et. al., 1988; Catacosinos et. al., 1990).

Figur Figure e 2-4: 2-4: Cros Crosss-se sect ctio ion n acro across ss the the Mich Michig igan an Ba Basi sin n show showin ing g the the rela relati tion onsh ship ip of the two members and the Dundee formation and the depositional environment in Crystal Field (modified from Montgomery et. al., 1998). The res reservo rvoir at Cryst rysta al Fiel ield is at a dep eptth of 32 320 00 feet with ith a ne nett pa pay y inte interrval that that varie aries s from from 10 to 43 fee eet. t. The The oiloil-w water ater cont contac actt is loca locate ted d at ap appr pro oxima ximate tely ly 2410 24 10 fee eett subs subsea ea an and d the the rese reserv rvoi oirr ha has s a stro strong ng water ater driv drive e. The The pe perm rmea eabi bili lity ty vararies ies fro from 200 milli illid darcy rcys to 4 darcy rcys and the porosi osity ranges from from 8 to 16 perc ercent. nt. The The oil oil gravi ravity ty is 44 de deg gree ree API. API. The The wells ells in this this field field ha hav ve an expon xponen enti tial al de decl clin ine e rate.

77

Figure 2-5: Stratigraphic column of the Devonian section showing the Dundee, Bell Shale and Lucas formations (from Montgomery et. al., 1998). 2.3.2.2 Structure Crystal Field is on one of the northwest-southeast structural trends common in the Michigan Basin. The trap is a flat-topped structural anticline with a steeper dip on the northeast basinward side of the field. The southwest flank has a gentle slope (Eddy, 1936). The structural contour map of subsea depth of the top of the Dundee formation over Crystal Field is shown in Figure 2-6. 2-6. Notice the northwest-southeast trending anticlinal features with a narrow syncline in the center. Closure ranges from 20 ft (6 m) on the north rtheast dome to over 40 ft (12 m) on the elongated southwest culmination (Montgomery et. al., 1998). Some of the

78

irregularity seen on the top Dundee surface may be due to karsting and solution coll collap apse se.. The The pres presen ence ce of an eros erosio iona nall un unco conf nform ormit ity y or disc discon onfformit ormity y at the the top top of the Dundee surface is shown conclusively in most of the wells drilled (Eddy, 1936). Trapping mechanisms in Crystal field are also related to stratigraphic feature tures. s. OffOff-st stru ruct ctur ure e we welllls s are are comm common only ly we wet, t, bu butt ha hav ve go good od po poro rosi sity ty.. The The cap cap lime lime-ston stone e in thes these e area areas s is also also mu much ch thic thick ker than than in the the area areas s of high high stru struct ctur ural al reli relief ef so most of the good reservoir rock is below the oil/water contact. Figure 2-7 is an isopach map of the limestone cap at the top of the Dundee porosity. The limestone cap is thinner along the anticlinal features.

TOW 1-3

Figure 2-6: Structure contour map of top subsea of the Dundee formation over Cryst Crystal al Fiel Field, d, Mich Michig igan an (Con (Conto tour ur Inte Interv rval al = 7.5 7.5 ft). ft). Lo Loca cati tion on of the the seis seismi mic c line lines s are are shown in red. 79

Figure 2-8 is a contour map of top subsea of the Dundee porosity zone which is at the base of the limestone cap. The top of the Dundee porosity zone also also exhib xhibit its s the the same same no north rthwe west st-s -sou outh thea east st tren trendi ding ng an anti ticl clin inal al fea eatu ture res s as the the top top of the Dundee formation. The highest point on the anticlinal structure in the Dundee porosity zone should be the best place to explore for potential bypassed reserves ("attic oil"). This, in conjunction with the limestone cap thickness should help determine potential areas of interest.

TOW 1-3

Figur Figure e 2-7: 2-7: Isop Isopac ach h ma map p of the the lime limest ston one e cap cap at the the top top of the the Du Dund ndee ee forma ormati tion on over Crystal Field, Michigan (Contour Interval = 5 ft).

80

The The Be Bellll Sh Shal ale e format ormatio ion n can can prov provid ide e a stro strong ng indi indica cati tion on for the the po pote tent ntia iall for oil in the Dundee formation. Figure 2-9 is a contour map of subsea depth of the top of the Bell Shale formation. The northwest-southeast trending features present in the Dundee are also visible here. This formation was deposited either during or following the karstification of the Dundee formation, and is expected to be thicker in areas where karstification exists.

TOW 1-3

Figure 2-8: Structure contour map of top subsea of the top of the Dundee porosity over Crystal Field, Michigan (Contour Interval = 10 ft). Due Du e to the the inte interl rla ayerin ering g of lime limest ston one e an and d shal shale e in the the Be Bell ll Sh Shal ale e forma ormati tion on,, the picks on the drillers’ logs may be questionable. They are sometimes inconsis-

81

tent tent an and d all all of the the dril drille ler’ r’s s logs logs do no nott expla xplain in in de deta tail il the the lay layers ers that that were ere en enco coun un-tered. This probably degrades the contour and isopach maps. Figure 2-10 is a isopach map of the Bell Shale formation. The thickness of the shale increases to the northeast and southwest of the production area. The most productive areas in Crystal Field correlate to a Bell Shale thickness of approximately 50 feet or less, and the less productive area correlates to a thickness of 60 feet or greater. The area of best production lies to the east of MOC Line C-3 and between MOC Lines C-2 and C-5.

TOW 1-3

Figur Figure e 2-9: 2-9: Stru Struct ctur ure e cont contou ourr ma map p of top top subs subsea ea of the the Be Bell ll Sh Shal ale e forma ormati tion on over Crystal Field, Michigan (Contour Interval = 10 ft).

82

Figure 2-11 is a contour map of the initial production for the wells in the field. The initial production rates in this field are as high as 5000 barrels of oil per day da y. The The high higher er init initia iall prod produc ucti tion on rate rates s can can be corr correl elat ated ed to the the an anti ticl clin inal al stru struct ctur ure e for the Dundee and Dundee porosity, a small limestone cap thickness, and a smaller thickness for the Bell Shale formation. The initial production rates are somewhat useful but must be used with caution. During production of this field, the wells were produced as quickly as possible and water coning occurred. This may have an effect on the reliability of the results and the ability to use this data for correlation purposes.

TOW 1-3

Figure 2-10: Isopach map of Bell Shale formation over Crystal Field, Michigan (Contour Interval = 10 ft).

83

TOW 1-3

Figure 2-11: Contour map of initial production in bbls/day of Crystal Field, Michigan (Contour Interval = 1000 bbls/day). Figure 2-12 shows a possible geologic model for the subsurface beneath the TOW 1-3 well and the controls on by-passed oil production in Crystal Field. The thickness of the limestone cap is small and the thickness of the Dundee porosity zone is large compared to other non-productive areas in the field. The Dundee porosity zone is also shallower where the TOW 1-3 well (horizontal leg) was drilled compared to other areas around the well. This allows for a zone of "att "attic ic"" oil. oil. This This zon one e wou ould ld stil stilll rema remain in ab abo ove the the oiloil-w water ater cont contac actt afte afterr water ater conconing or encroachment of water in the original reservoir. The thickness of the Bell Shale was thick at the vertical well location of the TOW 1-3 well, apparently

84

caused by a small karst featured observed in the core. Because of this, the vertical well did not log the Dundee in the interval where the horizontal well (which encountered porosity much higher) found production.

Bell Shale in Collapse

Figure 2-12: Cross-section through Crystal Field showing the location and geologic controls on production for the TOW 1-3 well (modified from Wood et. al, 1998, Montgomery et. al., 1998, and Pennington, personal communication).

2.4 Procedures The The da data ta used used for the the cont contou ourr an and d isop isopac ach h ma maps ps are are from from well ell reco record rds s an and d drilling reports. These data were compiled by the Western Michigan University Core Research Laboratory and Michigan Technological University. The contour and isopach maps were created on a workstation using GeoQuest software. The well log data was evaluated and cross-sections were created on a works wo rksta tatio tion n using using GeoQ GeoQue uest st softw softwar are e from from Schlu Schlumbe mberg rger er GeoQ GeoQue uest. st. The The seismi seismic c data was interpreted poststack on a workstation using GeoQuest software. The prestack data was processed by J. Haataja using iXL from Mercury International

85

Technologies. A pseudo 3-D volume was created using offset for crosslines and interpreted for amplitude variation with offset effects and is shown in Appendix B.

2.5 Results and Interpretation 2.5.1 Geophysical Well Log Interpretations No cores or logs existed from Crystal Field prior to the drilling of the TOW 1-3 in 1995. The nearest wells with logs were located 2 to 5 miles away, and include: 1) Shuttleworth #1 (Gratiot County), 2) Leonard Lee #1 (Montcalm County), 3) Jennings-Smith #1-17 (Gratiot County), and 4) Chartreuse Rocha Buck # 1-15 (Montcalm County). These wells are used to create general regional cross-sections over the field area. The top of the Bell Shale is identified by a significant increase in gamma ray response, a slight decrease in resistivity, and a decrease in neutron porosity. The Dundee - Bell Shale contact is marked by a distinct decrease in gamma-ray values, an increase in resistivity, and an increase in neutron porosity in the upper Dundee. The lower boundary with the Lucas formation is difficult to pick due to lithologic similarity with the Dundee in the central Michigan basin. The DundeeLucas contact has most often been chosen at the top of the shallowest anhydrite bed (Montgomery, 1998). Figure 2-13 is a basemap showing the location of the wells with logs and seis seismi mic c line lines s (MO (MOC seis seismi mic c line lines s an and d COCO COCOR RP seis seismi mic c line lines) s) in the the area area arou around nd the field. County names and Section, Township, and Range numbers are also specified. Figure 2-14 and Figure 2-15 are cross-sections A-A’ and B-B’ which show the Bell Shale and Dundee markers and the log response for the correspon spondi ding ng format ormatio ions ns.. Thes These e figur figures es are are sho shown as me meas asur ured ed de dept pth h so some some of the the 86

apparent structure is surface topography but they give the general structure over the area.

Figure 2-13: Basemap showing the location of the seismic lines and crosssections over Crystal Field, Michigan. Figur Figure e 2-16 2-16 is a Pick Picket ettt plot plot,, cros cross s plot plotti ting ng the the ne neut utro ron n po poro rosi sity ty an and d resi resist stiv iv-ity well log responses, over the Dundee in order to determine the productivity of the zone of interest. The TOW 1-3 is plotted along with four other wells (from the Winterfield Field in Clare County) where well log data and production information are available. The TOW 1-3 log data indicate water saturation values of approximately 50 percent. This leads to the interpretation that the TOW 1-3 well (vertical leg) was drilled into a residual oil zone and that the horizontal kick-off tapped an attic oil zone in the uppermost Dundee porosity above the section logged in the vertical leg. The Thayer 3-29 well was drilled into a tight limestone in the upper Dundee interval and has a water saturation between 50 and 75 percent.

87

A (NW)

A’(SE) TOW 1-3

LL 1

JS 1-17

Bell Shale Bell Shale

Dundee Fm

Dundee Fm

Bell Shale

Dundee Fm

Figure 2-14: Cross-section A-A’ showing the Dundee formation and Bell Shale markers.

B (W)

B’ (E)

CRB 1-15

SEW 1-8

TOW 1-3

Bell Shale

Bell Shale Dundee Fm Bell Shale Dundee Fm

Dundee Fm

Figure 2-15: Cross-Section B-B’ showing the Dundee formation and Bell Shale markers. 88

The Marion 33-21-1 and Austin 3-31 wells have an approximate water saturation of 20 and 30 percent, respectively. This represents by-passed and some attic oil pres presen entt in the the wells ells.. The The John Johnso son n 4-31 4-31 well ell was dril drille led d into into a resi residu dual al oil oil zon one e an and d has a water saturation of 50 percent (with some attic oil present).

Figure 2-16: Pickett plot to show how the neutron porosity and resistivity responses can be used to evaluate wells for wet or residual oil zones. Figure 2-17 and Figure 2-18 show the log responses of the Thayer 3-29, Johnson 4-31, Austin 3-31, and Marion 33-21-1 wells (from Winterfield Field) comp compar ared ed to the the TOW 1-3 1-3 well ell in Cryst rystal al Fiel Field. d. The The Tha Thayer 3-29 3-29 well ell ha has s a simi simila larr resistivity response but consists of tight limestone in the upper Dundee. The Johnson 4-31 also shows a similar resistivity response to the TOW 1-3, and is

89

TOW 1-3

Johnson 4-31

Thayer 3-29

Bell Shale

Bell Shale

Bell Shale

Wet - Tight Limestone

Dundee Fm

Oil

Dundee Fm

Dundee Fm

Figure 2-17: Well log cross-section showing the log response for the residual oil and wet wells displayed on the Pickett plot, compared with the TOW 1-3 vertical well.

TOW 1-3

Austin 3-31

Marion 33-21-1

Bell Shale Bell Shale Bell Shale

Oil

Oil Dundee Fm

Dundee Fm Dundee Fm

Figure 2-18: Well log cross-section showing the log response for the by-passed oil wells displayed on the Pickett plot compared with the TOW 1-3 vertical well. 90

water ater satu saturrated ated excep xceptt for a coup couple le thin thin oil oil zon ones es.. The The Austi ustin n 3-31 3-31 an and d Ma Mari rion on 33 33-21-1 both have a much higher resistivity indicative of an increase in oil saturation and decrease in water saturation. This comparison of well logs strongly suggest that the vertical leg of the TOW 1-3 well was drilled (and logged) in a swept zone of resi residu dual al oil oil in the the Du Dund ndee ee.. The The ho hori riz zon onta tall leg leg of the the TOW 1-3 1-3 well ell en enco coun unte tere red d porous Dundee at approximately 18 feet higher, offset from the vertical well by 500 50 0 fee eet. t. Clea Clearl rly y the the ho hori riz zon onta tall well ell was dril drille led d into into a zon one e of un unpr prod oduc uced ed atti attic c oil oil at a high position in the reservoir. 2.5.2 Seismic Data Interpretations Four poststack 2-D seismic lines, made available by Marathon Oil Company, are used to evaluate the application of seismic attributes for reservoir characterization in Crystal Field. This study focuses on MOC Line C-3 because it is loca locate ted d over the the mo most st prod produc ucti tiv ve pa part rt of the the field field an and d pres presta tac ck da data ta is availa ailab ble for detailed studies and reprocessing. This MOC seismic data used in this study was originally acquired to evaluate potential for deeper horizons in and near Crystal Field. Due to the acquisition parameters, the shallow seismic data (the Dundee is located at approximately 0.54 seconds) has low fold and short offsets, causing limited usefulness for seismic attributes. The physical geography and water systems also have an effect on seismic data. Many traces are missing from this data because of the presence of lake lakes, s, swa wamp mps, s, an and d othe otherr ob obst stac acle les s that that the the acqu acquis isit itio ion n team team ha had d to shoo shoott arou around nd.. A significant glacial drift present in this area also causes statics problems in seismic data acquisition and processing.

91

Figure 2-19 is a map of the field area showing the wells, in blue, and the four 2-D seismic lines, in varying colors, where the two-way travel time for the Dundee formation has been interpreted. Purple or green represents a larger two way tra travel time time,, impl implyi ying ng that that the the forma ormati tion on is de deep eper er,, an and d yello ellow w an and d red red indi indica cate te higher time structures. Figure 2-20 is a map of the field area showing the wells and the four 2-D seismic lines where the amplitude of the seismic reflection at the Dundee formation is displayed. Green or purple represents where the amplitude is lower along the seismic lines, and yellow and red indicate larger amplitudes. The location of the TOW 1-3 well is specified. Figure 2-21 is a three dimensional display of the MOC seismic lines in Cryst Crystal al Fiel Field. d. This This disp displa lay y show shows s the the orie orient ntat atio ion n of the the seis seismi mic c line lines s an and d the the en enti tire re vertical time. MOC Line C-3 is the seismic line this study will focus on. Figure 2-22 is MOC Line C-3 showing interpreted horizons of the Traverse Limestone, Dundee formation, Salina formation, and C-Shale. The Dundee is the horizon of interest and is located at approximately 0.54 seconds. The other intersecting seismic lines are shown as a red vertical line. The study area of Crystal Field is located along MOC Line C-3 and between MOC Lines C-2 and C-5; it is indicated on each figure. Figure 2-23 shows the instantaneous phase along MOC Line C-3. The Dund Du ndee ee format ormatio ion n is loca locate ted d at ap appr pro oxima ximate tely ly 0.54 0.54 seco second nds s an and d ha has s a cont contin inuo uous us phase across the entire study area. The phase was important when correlating the horizons due to the discontinuous nature of the reflection character.

92

TOW 1-3

Figure 2-19: Two-way travel time for the Dundee formation. format ion.

TOW 1-3

Figure 2-20: Amplitude variation of Dundee formation.

93

Figure 2-24 shows the reflection character along MOC Line C-3 in the study area. Note the discontinuous nature of the reflection character along the Dundee (0.54 seconds). This may be due to the low fold of the seismic data and/  or the karstification at the Bell Shale - Dundee boundary. Karstification causes discontinuous reflections because of energy scattering and adsorption into the high highly ly po poro rous us surf surfac ace e, resu result ltin ing g in a low low sign signal al to no nois ise e rati ratio o, an and d coul could d be an indi indi-cati cation on of frac fractu turi ring ng an and d po poro rosi sity ty.. High High fold old can can he help lp this this prob proble lem m be beca caus use e stac stacki king ng sign signifi ifica cant ntly ly redu reduce ces s the the no nois ise e an and d incr increa ease ses s the the sign signal al to no nois ise e rati ratio o. The The glac glacia iall till present in the area also causes problems with residual statics and increases nois no ise e in the the seis seismi mic c da data ta.. A rela relate ted d stud study y, repo reporte rted d in Ap Appe pend ndix ix B, inv investi estiga gate tes s the the pre-stack data of MOC Line C-3, and shows that, after mute, the CMP fold at the Dundee was only six to eight traces. Figure 2-25 shows the reflection character along MOC Line C_3 in the study area after automatic gain control (AGC) has been applied. This improves the appearance of the reflectors and enhances the Dundee formation but cannot be used to determine the importance of seismic attributes, because AGC alters the attributes such as amplitude. Figur Figure e 2-26 2-26 is a thre three e dime dimens nsio iona nall disp displa lay y of the the seis seismi mic c line lines s over Crys Crysta tall Field with the top subsea Dundee structure contour map imposed. The highest area area on the the an anti ticl clin inal al stru struct ctur ure e is in red red an and d repr repres esen ents ts the the mo most st prod produc ucti tiv ve pa part rt of the the field field.. This This ma map p wa was s crea create ted d usin using g a ba basi sic c time time-d -dep epth th rela relati tion onsh ship ip,, know knowin ing g the the depth and time of the Dundee surface at certain points.

94

  -   4     C    e     i   n     L     C     O     M M O  C L i n  ne     C  e - 5  5   3  - 3  n e C  L i n  M O C

M O  C L  i n  ne    C  - 2  2 

Figure 2-21: Three-dimensional display of MOC seismic lines in Crystal Field.

Study Area

Figur Figure e 2-22: 2-22: Line Line C-3 C-3 show showin ing g inte interpr rpret eted ed ho hori rizo zons ns on an am ampl plit itud ude e disp displa lay y over over the study area.

95

Study Area

Figure 2-23: Line C-3 showing the instantaneous phase over Crystal Field.

Study Area

Figure 2-24: Line C-3 showing the reflection character over Crystal Field. 96

Study Area

Figure 2-25: Line C-3 showing the reflection character over Crystal Field after automatic gain control has been applied.

M     O    C     L  i     n    e    C     -  5   

M     O     C     L   i     n   e    C     -  2    

 4   C   e   n   L  i   C   O   M

 3  n e C - 3  L i n  M O C

Dundee Structure Contour Map over Crystal Field

Figure 2-26: Three dimensional display of MOC seismic lines and top subsea structure contour of the Dundee formation. 97

2.6 Conclusions The seismic data used in this study (MOC seismic lines) was initially acquired to look for potential in deeper formations; because it was acquired for deep de eper er da data ta,, it ha had d low low value alues s of fold old an and d offs offset et for the the shal shallo low w da data ta.. This This resu result lted ed in difficulties relating seismic attributes to lithology and reservoir properties for finding residual oil in shallow areas. Data acquired for shallow horizons may be very useful for evaluating the seis seismi mic c attr attrib ibut utes es in othe otherr field fields s in the the Mich Michig igan an Ba Basi sin n if the the fold old an and d offs offset et ran ange ges s are appropriate. Good quality seismic data for the horizons of interest is necessary to evaluate seismic attributes. Posts oststa tack ck seis seismi mic c attr attrib ibut utes es in MOC MOC Line Line C-3, C-3, such such as am ampl plit itud ude, e, are are influ influ-enced by the low fold and offset ranges in the seismic data (Appendix B) but phas ph ase e was cons consis iste tent nt.. Pres Presta tack ck seis seismi mic c attri attribu bute tes s are are stro strong ngly ly de depe pend nden entt on fold old and offset ranges available in the dataset (Appendix B). Resi Re sidu dual al stat static ics s are are ne nece cess ssary ary an and d very impo importa rtant nt in proc proces essi sing ng to pro provide vide a quality stack and good statics, especially in areas where glacial till is present. Some So me of the the no nois ise e an and d disc discon onti tin nuo uous us refle reflect ctio ions ns in the the MOC MOC seis seismi mic c line lines s ma may y be due to statics problems. The Bell Shale contour and isopach maps indicate that karstification is present but the seismic data could not be used to support or disprove this due to its poor quality in the shallow domain. The Bell Shale formation should be thicker in areas where karstification has taken place. In Crystal Field, areas where the Bell Shale is thinner tends to correlate with good initial production rates and a smaller limestone cap. 98

2.7 Future Work In orde orderr to ma mak ke seis seismi mic c da data ta usef useful ul chec checks ksho hott an and d soni sonic c logg loggin ing g da data ta are are need ne eded ed.. It is cruc crucia iall for seis seismi mic c da data ta an anal alys ysis is to acqu acquir ire e soni sonic c logs logs an and d chec checks ksho hott data in newly drilled wells. Perform 3-D visualization of the formation tops from the old wells and integrate the well trajectories of the 3 new horizontal wells. Perform advanced log interpretation techniques for fractured carbonates where a, m, and n, vary in Archie’s equations. Apply advanced refraction statics which may improve imaging of deeper horizons in the existing seismic data. If imaging is improved with refraction statics, successful attribute analysis may be applied.

99

2.8 References Annual statistical summary of oil and gas fields in Michigan 1935-1986: Michigan Department of Natural Resources, Geological Survey Division, Lansing, MI. Bassett, C.F., 1935, Stratigraphy and Paleontology of the Dundee Limestone of Southeaster Michigan: Bulletin of the Geological Society of America, Vol. 46, p. 425-462. Birchard, M.C., 1993, Stratigraphy and Facies of the Middle Devonian Dundee Formation: Ontario Geological Survey, Report # 5848. Brow Brown, n, L., L., Jens Jensen en,, L., L., Oliv Oliver er,, S., Ka Kauf ufma man, n, S., an and d Stei Steine nerr, D., 19 1982 82,, Rift Rift stru struct ctur ure e beneath the Michigan Basin from COCORP profiling: Geology, Vol. 10, p. 645-649. Catacosinos, P.A., P.A., Daniels, Daniel s, Jr., P.A., P.A., and Harrison III, W.B., 1990, Structure, Str ucture, Stratigraph Stratigraphy y and Petroleum Petroleum Geology of the Michigan Basin: in Interior Cratoni tonic c Ba Basi sins ns,, AAPG AAPG Me Memo moir ir 51 51:: ed edit ited ed by Le Leig ight hton on,, M. M.W W. et. et. al., al., p 56 5611-60 601. 1. Catacosinos, P.A., 1973, Cambrian Lithostratigraphy of Michigan Basin: AAPG Bulletin, Vol, 57, No. 12, p. 2404-2418. Chittick, S., 1995, Characterization of the Dundee Formation, Winterfield field, Clare County, Michigan: M.S. M .S. thesis, Michigan Technological Technological University, University, Houghton, Michigan, 150p. Curr Cu rran, an, B.C B.C., and Hu Hurle rley y, N.F N.F., 199 1992, 2, Geolo Geology gy of the De Devo vonia nian n Du Dunde ndee e Re Rese servo rvoir ir,, West Branch Field, Michigan: AAPG Bulletin, Vol. 76, No. 9, p. 1363-1383. Dorr Do rr,, J.A., .A., an and d Esch Eschma man, n, D.F., .F., 19 1970 70,, Geol Geolog ogy y of Mich Michig igan an:: The The Un Univ iver ersi sity ty of Mich Mich-igan Press, Ann Arbor, MI, 476 pp. Eddy, G.E., 1936, Geology of the Crystal Oil Field, Montcalm County, Michigan: Michigan Geological Survey, Progress Report #1, 8 pp. Gardn Gardner er,, W.C., .C., Middle Middle De Devo voni nian an strati stratigr grap aph hy an and d dep depos ositi ition onal al en envir vironm onment ents s in the Michig Michigan an ba basin sin:: Michig Michigan an Ba Basin sin Geolo Geologic gical al So Socie ciety ty,, Specia Speciall Pape aperr #1 #1,, 13 138 8 pp. Lilienthal, R.T., 1978, Stratigraphic Cross-Sections of the Michigan Basin: Michigan Geological Survey Report of Investigations, No. 19, 38 pp.

100

Michigan Department of Natural Resources, Geological Survey Division, Open File Records Correspondence, Operators Monthly Reports. Montgomery, S.L., Wood, J.R., and Harrison III, W.B., 1998, Devonian Dundee Formation, Crystal Field, Michigan Basin: Recovery of Bypassed Oil Through Horizontal Horizontal Drilling, AAPG Bulletin, Bulletin, Vol. 82, No. 8, 1445-1462. Vogler ogler,, E.A., E.A., Me Meye yers rs,, P.A. .A.,, an and d Mo Moore ore,, W.A. .A.,, 19 1981 81,, Co Comp mpari ariso son n of Michig Michigan an Ba Basin sin Crude Oils: Geochimica et Colmochimica Acta, Vol. 45, No. 11, p. 22872293. Wilson, S.E., S.E., 1983, Small gas fields in Michigan: in The Future of small energy resources: an International Internati onal conference, McGraw-Hill, M cGraw-Hill, New York, York, NY, NY, p. 6266. Wines, H., 1997, Crystal Oil Field: M.S. thesis, Western Michigan University, Kalamazoo, Michigan, 112 p. Wood, J.R., Pennington, W.D., and Harrison III, W.B., 1998, Recovery of bypassed oil in the Dundee Formation (Devonian) of the Michigan Basin using Horizontal Drains: Final Report Project DE-FC22-94BC14983, National Petroleum Technology Office, U.S. Department of Energy, 95 p. Wood, J.R., Allen, J.R., Huntoon, J.E., Pennington, W.D., and Harrison III, W.B., Taylor, E., Tester, Tester, C.J., 1996, Horizontal Hori zontal well taps bypassed Dundee oil in Crystal Field, Michigan: Oil and Gas Journal, Vol. 94, No. 43, p. 60-63. Wood, J.R., Allen, J.R., Huntoon, J.E., Pennington, W.D., and Harrison III, W.B., Taylor aylor,, E., Tester ester,, C.J., .J., 19 1996, 96, Ho Horiz rizon ontal tal we wellll succ success ess spurs spurs more more De Devo vonia nian n work in Michigan: Oil and Gas Journal, Vol. 94, No. 44, p. 86-89.

101

APPENDIX A: Effects of Fluid Properties on Seismic Response A.1 Figures from Chapter 1 in English (Oil Field) Units

Figure 1-7: Histogram showing the distribution of GOR for the samples in the study.

Perfect Perfect Correlation

Figure 1-8: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) versus the laboratory live oil velocity (Batzle and Han 1997 Fluid Study). A-1

Figur Figure e 1-9: 1-9: Plot lot of live ive and dea ead d oil densiti sities es for the samp mplles in the the stud tudy and the the relationship to GOR (the lines are a least squares regression through the data points).

Figure 1-10: Plot of the calculated velocity versus GOR for the samples in the study. A-2

Figure 1-11: Plot of the calculated velocity versus API gravity for the samples in the study.

Figure 1-12: Plot of calculated live oil modulus versus density for the samples in the study.

A-3

Figure 1-13: Plot of calculated live oil velocity versus density for the samples in the study.

Figure 1-14: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and the laboratory live oil velocity (Batzle and Han 1997 Fluid Study) versus pressure for a sample in the study.

A-4

.

Figure 1-16: Plot showing the calculated live oil velocity (Batzle and Wang 1992 Model) and the laboratory live oil velocity (Batzle and Han 1997 Fluid Study) versus pressure for a sample in the study modeled with a variable GOR.

A-5

A

X

Figur Figure e 1-20: 1-20: Cros Crossp splo lott of fluid fluid mo modu dulu lus s an and d de dens nsit ity y as satu satura rati tion on value alues s chan change ge..

A-6

B

A

Figure 1-22: A) Velocity versus saturation B) impedance and PR versus satu satura rati tion on show showin ing g ho how w water ater satu satura rati tion on aff affects ects a two two ph phas ase e mixt mixtur ure e of liv live oil oil an and d brine in a sandstone matrix from water saturated to oil saturated conditions.

B

AA

wet

wet depleted depleted

wet

reservoir conditions

depleted

reservoir conditions reservoir

conditions

Figure 1-23: A) Impedance versus PR B) Percent change in impedance versus percent change in PR showing how water saturation affects a two phase mixture of live oil and brine in a sandstone matrix from water saturated to oil saturated conditions.

A-7

wet depleted

reservoir conditions

Figure 1-24: Velocity versus density showing how water saturation affects a two phase mixture of live oil and brine in a sandstone matrix from water saturated to oil saturated conditions.

reservoir conditions depleted

wet

Figure 1-25: Compressional vs. shear velocity for a two phase mixture of live oil and brine in a sandstone matrix from water saturated to oil saturated conditions.

A-8

.

Figure 1-26: Fluid modulus versus pressure showing how the fluid modulus changes as the pressure and saturation in the reservoir changes. Saturation values are shown as (% oil,% gas,% water).

A-9

Figur Figure e 1-27: 1-27: Flui Fluid d de dens nsit ity y versu ersus s pres pressu sure re show showin ing g ho how w the the de dens nsit ity y chan change ges s as the press pressure ure an and d satur saturat ation ion in the reserv reservoir oir chan changes ges.S .Satu atura ratio tion n value values s are show shown n as (% oil,% gas,% water). .

A-10

A

B

bubble point

bubble point

reservoir conditions

reservoir conditions

Figure 1-28: Velocity and Poisson’s ratio versus pressure demonstrating that when the reservoir drops below the bubble point (at 29.3 MPa) it significantly effects the reservoir properties. A) Modeled with a constant dry frame modulus. B) Modeled with a variable dry frame modulus with pressure.

A-11

A.2 Definition of Variables for the Batzle and Wang (1992) model Input

Constants/Conversions

T

Temperature

ρair

Density of Air

P

Pressure

R

Gas Constant

G

Specific Gravity

Ta

Absolute Temperature

Rg

Gas Oil Ratio

ρo

Oil Density

AP I

API Gravity

Dead Oil

S

Weight Fraction NaCl

Kd

Dead Oil Modulus

ρd

Dead Oil Denisty

Live Oil Kl

Live Oil Modulus

Vod

Dead Oil Velocity

ρl

Live Oil Density

ρp

Density at Pressure, P

Vol

Live Oil Velocity (using Pseudoden-

Gas

ρpl

Density at Pressure, P

Vg

Gasl Velocity

ρgl

Density at Gas Saturation

Ks

Adiabatic Gas Modulus

Bol

Live Oil Gas Volume Factor

ρg

Gas Density

ρdl

Pseudodensity based on gas expand

γ o

Specific Gravity

Live Oil at Max GOR

(δz/ δPpr)T

Gas deviation factor function pres-

Rgmax

Maximum Live Oil Gas Oil Ratio

P pr

Pseudoreduced Pressure

Klm

Maximum Live Oil Modulus

Tpr

Pseudoreduced Temperature

ρlm

Maximum Live Oil Density

z

Gas Deviation Factor

Volm

Maximum Live Oil Velocity

E

Par t of of G Ga as D De eviation Fa Factor Eq E quation

ρpm

“Density at Pressure, P”

Input (for mixtures)

ρgm

Density at Gas Saturation

Sg

Gas Saturation

Bom

Maximum Gas Volume Factor

So

Oil Saturation

ρpdm

Pseu Pseudo dode dens nsit ity yb bas ased ed on gas gas e exp xpan andi di

Sb

Brine Saturation

Rgmax

Maximum Live Oil Gas Oil Ratio, l/l

Mixtures

Brine

ρmd

Dead Oil Mixture Density

Kgb

Live Brine Modulus

Kdo

Dead Oil Mixture Modulus

Kb

Dead Brine Modulus

ρml

Live Oil Mixture Density

Vb

Brine Velocity

Klo

Live Oil Mixture Modulus

Vw

Fresh Water Velocity

ρmml

Max Live Oil Mixture Density

ρw

Fresh water Density

Kmlo

Max Live Oil Mixture Modulus

ρb

Brine Density

Vdo

Dead Oil Mixture Velocity Velocity

log10 Rgb

Log of Gas Water Ratio

V lo

Live Oil Mixture Velocity

Rgb

Gas Water Ratio

Vmlo

Max Live Oil Mixture Velocity Velocity

A-12

APPEND APPE NDIX IX B: A Sear Searc ch for Seis Seismi mic c Attr Attrib ibut utes es for Re Rese serv rvoi oirr Char Char-acterization, Crystal Field, Michigan B.1 Work that Josh Haataja did processing a 2-D seismic line (MOC Line C3) in iXL. Figure B-1 shows the flow chart used in iXL to reprocess MOC Line C-3

Figure B-1: Flow chart showing the processing sequence for MOC Line C-3.

B-1

and export the line as a pseudo 3-D seismic data set. Line C-3 was processed through normal moveout. Figure B-2 shows two bad common midpoint gathers for the 2-D seismic line line (MOC (MOC Line Line C-3) C-3).. The The low low fold old (12) (12) an and d offs offset et is ob obvi viou ous s for thes these e two two comm common on midpoint gathers.

Figure B-2: Bad common midpoint gathers for MOC Line C-3.

B-2

Figur Figure e B-3 show shows s a be bett tter er comm common on midp midpoi oint nt ga gath ther er wh wher ere e the the fold old (60) (60) an and d offset are much larger, but the fold and offset are still very low in the shallow domain.

Figure B-3: Good common midpoint gather for MOC Line C-3. Figure B-4 and Figure B-5 are both common midpoint gathers that have been imported into GeoQuest to evaluate amplitude variation with offset (AVO). The hea ead ders of the the seismi ismic c segy file were alte ltered red in iXL to allo llow CDP and offs ffset to be load loaded ed as inli inline ne an and d cros crossl slin ine e in GeoQ GeoQue uest st.. This This resu result lted ed in a pseu pseudo do 3D seis seis-mic display where amplitude is more readily interpreted. Due to the low fold and offset a horizon could not be interpreted but this technique would be useful in areas where better seismic data is available.

B-3

Figure B-4: A common midpoint gather in GeoQuest showing AVO response.

Figure B-5: A common midpoint gather in GeoQuest showing AVO response.

B-4

Figure B-6: A time slice through the pseudo 3D volume at approximately 0.56 seconds.

B-5

Figure B-6 is a time slice at approximately 0.56 seconds showing the amplitude variation with offset (AVO) response. Figure B-7 is a crossline where Line C-3 is shown at a specified offset. As you can see a horizon along this line would be very difficult to interpret.

Figure B-7: Crossline showing MOC Line C-3 at a specified offset.

B-6

B.2 Formation Data Used to Create the Contour and Isopach Maps

B-7

B-8

B-9

B-10

B-11