SPE 69724 Thermodynamic Characterization of a PVT of Foamy Oil Douglas J. Romero and Belkis Fernandez, SPE, Schlumberger, and Gonzalo Rojas,SPE, UDO
Copyright 2001, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2001 SPE International Thermal Operations and Heavy Oil Symposium held in Porlamar, Margarita Island, Venezuela, 12-14 March 2001. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. 01-972-952-9435.
Abstract This work is based on theoretical studies and/or experimental observations carried out diverse authors whom have investigated on the " foamy oil phenomenon " developing a methodology to characterize these crude oils thermodynamically, taking as bases nonconventional PVT analysis and using as research tool the application of equations of state and methods known for the determination of the equilibrium constants liquid-gas. It is presented two new correlations developed in this work for the calculation of the viscosity of heavy crude oils, which are based on values of molar fractions of liquid and gas in equilibrium. The proposed methodology was validated using conventional and nonconventional PVT data of wells located in the Orinoco Belt, Jobo Field, Morichal Area obtaining excellent results and showing that the proposed methodology is applicable to conventional and nonconventional heavy crude oils in all the possible scenes, that that is to say, whether necessary necessary information information is available. Introduction When we analyse foamy crude oils under the optics of primary production mechanisms known traditionally, traditionally, have not been able to explain with exactitude the production behavior in these reservoirs1; this has given basis to many people to do research with the objective of explainning the origin of this atypical behavior. To such extreme to establishment establishment the theory of "foamy oil phenomenon ", which considers a transient state or supersaturation condition, in which take place the characteristics named " atypical " that identify to this type of heavy crude oils. It’s of extreme importance for the petroleum industry to model the thermodynamic behavior of foamy oils reservoirs, since a good characterization fluid increases the
probabilities to obtain better numerical numerical reservoir simulations simulations of and thus to be able to consider with most exactitude the total recovery. Characterization Characterization of Foamy Oils The foamy oil phenomenon has appeared only in heavy and extra-heavy crude oils, since in these crudes the viscous forces surpass to the gravitational forces on the productive life of reservoirs, reason why this phenomenon goberns the production behavior of these reservoirs. This phenomenon to appear after that reservoir pressure reaches the bubble point pressure, from this pressure the petroleum production increases, the gas bubbles expand to displace petroleum towards wells quickly. Depending of pressure and extraction rate of wells placed in the reservoir is possible that gas bubbles be produced with the oil. With the purpose to characterize characterize the ability that have some heavy crudes to show the foamy oil behavior and entrap gas that is released by each decrease of pressure. Nonconventional PVT analysis were developed which defer from the method used traditionally. The conceptual difference between this analysis and the method used conventionally, is that the flash and differential liberation tests are carried out without agitation of the cell 2. Generally, the results obtained by means of conventional and nonconventional PVT analysis differ remarkably mainly in the values of bubble point pressure obtained by both methods for foamy oils. Frequently values of bubble point pressure smaller are obtained in nonconventional PVT analysis because occurs entrapping of gas within the oleic phase of the crude reason why it’s deduced that supersaturation phenomenon occurs, the gas bubbles released to pressure far below the bubble point pressure are dissolved and/or dispersed within the phase of petroleum in a perfect hydrodynamic equilibrium. equilibrium. It later on that such hydrodynamic equilibrium should be broken to obtain free gas. It had been determinate determinate by laboratory laboratory experiences experiences that viscosity of foamy crude oils obtained using capillary viscometers are more suitable to make reservoir numerical simulations than those obtained with rotational viscometers, in this case, strench caused by shaking the crude sample breaks the dispersion gas/oil and release bubble gas to build a free gas cap separated of the crude oil.
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D. ROMERO, B. FERNANDEZ AND G. ROJAS
Methodology A set of correlations were selected to be used in the determination of thermodynamic properties of heavy and extra heavy crude oils, throw an analysis of correlations presented in texts of reservoirs engineering4, also were considered diverse methods to determine the equilibrium constants of hydrocarbons systems and several correlations published to calculate the viscosity of those crudes. The criteria used for the selection was the range or conditions for which these correlation’s can be used, the cut parameter was the value of gravity API of the crude. Worksheets were created to study the correlations, with the purpose of choosing those that displayed minor percent error with respect to PVT conventional and nonconventional data. Afterwards of selecting the correlations to be used, a methodology to calculate fluid thermodynamics properties was development which may be applicable in all the possible scenes, that is to say, whether necessary data is available from a conventional or no-conventional PVT test. The methodology proposed (Fig. 2), shows two options to use depending of the case is analysed. Option 1 From data PVT (conventional or nonconventional) the equilibrium constants condition by the method proposed by Zhou3 are determined, which are modified to supersaturation condition (foamy oil) by Sheng and Maini method 5 to determine gas and liquid molar fractions at different pressure and temperature conditions, for both, differential and viscosity test. Then the crude thermodynamic properties are determined according to the following expressions:
X=1/K
a=
R * T * ρo * 5.6146 MWo * P
Rs =
X * a 1 − X
(1) (2)
(3)
Option 2 With data obtained from separator test, GOR’s are calculated to pressure and temperature required using Millán 6 equation developed specifically for heavy oils, afterwards to determine gas and liquid molar fractions in equilibrium condition applying method proposed by Zhou3, this to be modifycated to foamy oil condition according to Sheng and Maini 5 method , finaly the thermodynamic properties and viscosity of the crude oils are caculated. In the determination of other thermodynamic properties of fluids as Bo, Bg, ρo, Co,etc, both options use the same correlations, basically the difference between both options is in the calculation of solution GOR, depending on the available information (Fig.2). To determine formation volumetric factor of oil (FVFo) at pressures below bubble point pressure, a modification of
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Standing4 correlation is recommended: Bo=0.972+0.000147*(Rs*(γ g/γ o)0.5+1.25*T)1.175
(4)
the oil density at different pressures was determined using Millán6 correlation by heavy oils. The compressibility and viscosity, two very important properties to study the behavior of foamy oil under pressure and temperature variations. The compressibility was caculated according to Sheng and Maini 5, whereas for viscosity no one of the correlations found in the bibliography yields good results since the error with respect to experimental values were superior to 98%. The complet set correlations used in this work are showed in Appendix A. Viscosity Given the situation that not exist reliable mathematical correlation for calculation viscosity of foamy crudes oil, two new correlations were developed for the calculation of the viscosity of heavy crude oils and foamy oils, which are based on values of molar fractions of liquid and gas in equilibrium. One to be used at pressures below or equal to bubble point pressure and the another one at pressures above bubble point pressure. These correlations are the following:
At pressures below or equal bubble point pressure: µ =
0.5*( µ liqY +µ g X )+0.25((Y*µ liq + X*µ g )+( µ liqY *µ g X ))
(5)
At pressures above bubble point pressure: µ =
0.55* X*(P – Pb ) + µ ob
(6)
liq values used are reported in experimental tests as average values for each field in study. The criteria raised by Smith1 was considered widely for development of these new correlations. Mathematical and statistical algorithms and sensitivities analyses were applied to obtain a mathematical expression based on molar fractions of gas and liquid in equilibrium and viscosities of liquid and gas values respectively. These new equations reproduce with greater exactitude the viscosity behavior with respect to pressure variation, above and below of bubble point pressure.
µ
Validation of Mathematic Model The validation of the selected mathematical model was made from a group of 8 conventional and nonconventional analyses PVT pertaining to reservoirs of the Orinoco Oil Belt and to the Jobo Field of the Morichal area. The PVT analyses used in the validation of the model correspond to following wells:
• • •
Well 1 (conv. and nonconv.). Bare Field – Hamaca Area Well 2 (conv.). Bare Field – Hamaca Area Well 3 (conv.and nonconv.) Cerro Negro Field – Morichal
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• •
THERMODINAMIC CHARACTERIZATION A PVT OF FOAMY OIL
Well 4 (conv. and nonconv.) Arecuna Field – Hamaca Well 5 (conv.) Jobo Field – Morichal Area
Figure 3 shows results obtained in GOR calculation for the conventional tests, is observed a good match with respect to the experimental values, average error percent was 4,5 %. Whereas for nonconventional tests, the average error percent was 6.4 %, graphically can be observed in Figure 4. Figure 5 shows compare results obtained for GOR calculation in all the possible scenes for well 1. Values obtained through Option 2 of proposed methodology are named synthetic PVT, these results obtained are very reliable because are very close to experimental values. FVFo results obtained, both, for no-conventional PVT test of Well 1 (Fig 6), like for all possible scenes in which the methodology proposed can be applied (Fig 7), in these cases the error percentage not surpass 1%. In validation of correlations developed and presented in this paper (4 & 5), a comparison between this and other recommended correlations by others authors to calculate viscosity of foamy oil and heavy oil crudes was made. As it’s displayed in Figures 8 and 9, a much better match with experimental values of all PVT analyses used was obtained applying correlation’s developed in this job (4 & 5), in comparison with those results obtained using others correlations. The average relative error for the developed correlations (4 & 5) was 10,8%, in comparison with obtained by other correlations, which were superior to 98%. Viscosity tests in PVT analysis used for validation are different between themselves, only three were made using capillary viscometer and the other were made with rotational viscometer, all results show that these correlations have a good confiability grade, considering that viscosity is a property very difficult to determinate in heavy oils and foamy oils. The compressibility of foamy oil crudes presumes that it’s between 5 to 10 times greater than conventional heavy oil crude, nevertheless this hypothesis has not been verified experimentally. The calculations of isothermal compressibility was made by Sheng and Maini5 method proposed for foamy crude oils, introducing values of liquid and gas molar fractions in equilibrium determined according to proposed methodology, was obtained compressibility of foamy oil much greater than conventional heavy oils, in three analyzed cases, as it’s showed in Figure 10. Conclusions 1. The correlations developed in this work for calculation viscosity of heavy oils provide good results for any heavy crude type, conventional or foamy oil. The average error percentage is located between 10 and 20 %, considering that viscosity is one of the most difficult property to predict. 2. The developed methodology reproduces in very acceptable degree the behavior of the fluids with respect to the variations of pressure and temperature and is applicable for conventional or foamy heavy crude oils in spite of the little existing information. 3. A reliable synthetic PVT can be made, applying the
3
developed methodology, avoiding the accomplishment of PVT tests, which reduces the total costs of a developing project. Nomenclature µ =
Viscosity, cps Y = Molar fraction of liquid phase in equilibrium, adim. X = Molar fraction of gas phase in equilibrium,adim. K = Equilibrium constant, adim. GOR, Rs = Solution gas-oil ratio, scf/STB. γ = Specific gravity, adim. FVF = Formation volume factor, bbl/STB. P = Pressure, psia. T= temperature, F. Kv1 , Kv2 , Kv3, Kv4 and Kv5: Constant values for each hydrocarbons system K’(p): Equilibrium constants modified for foamy oils, adim. K(p): Equilibrium Constant for convencional crude oils, adim. psc: Normal pressure, 14.7 psia. Subscripts o = oil g = gas ob= bubble point oil b = bubble point liq = liquid Acknowledgments The authors wish to thank Schlumberger and Universidad de Oriente for permission to publish this work. We also with to thank engineers Juan Cova, Cesar Diez and Marcelo Laprea, for his assistance as well as numerous practicing engineers who provided us data for the study. References 1. Smith, G.E. :“Fluid Flow and Sand Production in Heavy Oil Reservoirs Under Solution Gas-Drive”, SPE 15094, (1986) 2. Huerta, M.; Otero, C.; Rico, A.; Jimenez, I.; Mirabal, M. y Rojas, G. : “Understanding Foamy Oil Mechanisms for Heavy Oil Reservoirs During Primary Production”, SPE 36749, Annual Technical Conference and Exhibitio,. Denver,Colorado,USA.6-9 October 1996. 3. Zhou, X.: “Computin and Selecting Parameters in numeriacal Modelling of Oil Field Thermal Recovery”, Special Oil & Gas Reservoirs , 2 (3) 15-22, (1995) 4. McCain, W: “The Properties of Petroleum Fluids”, PennWell Books, Tulsa, Oklahoma, USA (1973) 5. Sheng, J.; Maini, B. y Hayes, R.E.: “ A Dynamic Model to Simulate Foamy Oil Flow in Porous Media”, SPE 36750, (1996). 6. Millán, E: “Correlaciones para Crudos Pesados Venezolanos”, Thesis, Universidad de Oriente.
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D. ROMERO, B. FERNANDEZ AND G. ROJAS
•
Appendix A – Correlation Set.
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Modification of equilibrium constants at foamy oil state:Sheng and M ain i method
Solu tion GOR ( Rs ). • Extra heavy oils: Millán correlation
K’(p) = K(p), Rs =
Rsb ∗ ( P / Pb)^0.83
(p > pb)
(A-1)
1.031
K’(p) = K(pb), When PVT analyses report don’t displayed results of separators test, Standing correlation is recomended to determinate GOR at temperature differents. This calculation is made to determinate equilibrium constants coeficients (Kvalues) for obtain equilibrium constants (K), Standing correlation are following:
Rs = γ g ∗ ((
P 18.2
+ 1.4) ∗10^ (0.0125 ∗ API − 0.00091∗ Ty ))^1.2048
(A-2)
•
OFVF (Bo): Standing & Beggs correlation at pressures below bubblepoint pressure
Bo = 0.972 + 0.000147 ∗ F ^1.175 γ g F = Rs ∗ ( )^ 0 .5 + 1 .25 ∗ T γ o
(A-3)
•
Density extra h eavy oil s: At bu bbepoint pressur e: M il lán cor relati on
=
ρ ob
(1 .2353 * Pb ^ − 0 . 02483 ) e ^ ( 0 .00075 * T )
(A-4)
Below bubblepoint pr essur e:M il lán corr elation ρo
=
ρ ob
* 1 . 6499
e ^ ( 0 . 50074 * ( Bo / Bob )
(A-5)
Above bubblepoin t pr essur e ρo
= ρ ob * e ^ (Co * ( P − Pb ))
(A-6)
•
I sothermal compressibil ity Vasquez & Beggs correlation Co =
•
(A-9)
− 1433 + 5 ∗ Rsb + 17 . 2 ∗ Ty − 1180 ∗ γ g ∗ 12 .61 ∗ API . (A-7) P * 10 ^5
Equi li bri um constants: Sheng & Zhou method
K = Kv1 +
− Kv4 Kv 2 e * T + Kv5 P
(A-8)
Ê' (p) = K(p)+
(psb> p> pb)
K(pb)- K(psb) * (p - psc) psb − psc
(A-10)
,(psc> p> psb) (A-11)
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THERMODINAMIC CHARACTERIZATION A PVT OF FOAMY OIL
5
Sucre Anzoátegui Monagas Guárico
Define Input
Delta Amacuro
L T O B E I N O C O R
N
Option 2: Input Data To Use Correlations
Option 1: Input Data from Laboratory and define analysis type
GOR Calculation by Correlations
Calculate Equilibrium Constants Coefficients( K - value )
Define Pressure Stage of LD, CCE, and Viscosity Tests
Determination of Equilibrium Constants ( K ) at Pressure of LD test andTyac.
Thermodynamics Properties Crude Determination of LD ρo,etc) Test (GOR, Bo,
CERRO NEGRO MACHETE
ZUATA
HAMACA
Thermodynamics Properties Crude Determination of CCE Test (Co, V. rel)
Determination of Equilibrium Constants ( K ) in Foamy Oil State to Viscosity Test
Yes
To Consider This Crude in Foamy Oil State
No
Determination of Equilibrium Constants ( K ) at Pressures of Viscosity Test
Calculate Viscosity.
Show Results
Figure 2. Methodology proposed diagram
Figure 1. Orinoco Belt localization
120
120
100
100
80
80
b t s / f c s 60 , R O G
40
We l 1 C al c.
W ell 1 E xp .
b t s / f c 60 s , R O G
We l 4 C al c.
W ell 4 E xp .
40
We l 3 C al c.
W ell 3 E xp .
We l 5 C al c.
W ell 5 E xp .
We l 2 C al c.
W ell 2 E xp .
Well 4 Calc Well 1 Calc Well 3 Calc
Well 4 Exp. Well 1 Exp Well 3 Exp
600
800
20
20
0 0
0 0
200
400
600
800
1000
1200
1400
1600
Pressure, psia
Figure 3. Validation of methodology,GOR results obtained from conventional PVT tests.
100
200
300
400
500
700
Pressure , psia
Figure 4. GOR results obtained for nonconventional tests
900
1000
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D. ROMERO, B. FERNANDEZ AND G. ROJAS
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1.2
120
100 1.15
80
Well 1 Calc.
Well 1 Exp.
Well 3 Calc.
Well 3 Exp.
Well 4 Calc.
Well 4 Exp.
B T S 1.1 / l b b , ) o B ( F1.05 V F O
b t s / f c s , 60 R O G Calc.PVT Conv 40 Exp.PVT Conv Calc.PVT Sintetic Conv Calc.PVT No-Conv
1
20 Exp.PVT No-Conv Calc.PVT Sintetic No-Conv 0 0
200
400
600
800
1000
0.95
1200
0
100
200
300
400
Pressure , psia
500
600
700
800
900
1000
Pressure, psia
Figure 5. GOR results for well 1 (all possible scenes)
Figure 6. Oil formation volume factor results obtained for nonconventional tests
1.15
4000 Smith.(1) 3500
Visc. Exp. Smith.(2)
3000
1.1
Maini Correl. Developed
B T S / l b b , ) 1.05 o B ( F V F O
2500 ) s p c ( y t i s o c s i V
Calc.PVT Conv
2000 1500 1000
Exp.PVT Conv Calc.PVT Sintetic Conv
1
500
Calc.PVT No-Conv Exp.PVT No-Conv
0
Calc.PVT Sintetic No-Conv
0
500
1000
0.95 0
200
400
600
800
1000
1500
2000
2500
Pressure ( psia )
1200
Pressure , psia
Figure 8. Comparison between correlations developed in this job and others correlations recomended by others authors to calculate heavy oils viscosity
Figure 7. FVFo results for well 1 (all possible scenes)
0.0016
5000
4500
4000
3500
Well 1 Exp.
Well 1 Calc.
Well 2 Exp.
Well 2 Calc.
Well 3 Exp.
Well 3 Calc.
Well 4 Exp.
Well 4 Calc.
Well 5 Exp.
Well 5 Calc.
0.0014
a i s p / 0.0012 1 , ) o C ( 0.001 y t i l i b i s 0.0008 s e r p m o C0.0006 l a m r e h 0.0004 t o s I
s3000 p c , y t i 2500 s o c s i V2000 1500
1000
Well 1 Conv Well 1 Foamy Well 4 Conv Well 4 Foamy Well 3 Conv Well 3 Foamy
0.0002 500
0 0 0
500
1000
1500
2000
2500
3000
3500
4000
Pressure , psia
Figure 9. Results obtained for all PVT analises used in validation of new viscosity correlations
4500
0
200
400
600
800
1000
Pressure , psia
Figure 10. Isothermal compressibility results obtained for nonconventional tests
1200
