TUTORIAL 1 1. A petroleum petroleum reserv reservoir oir has has an areal areal extent extent of 20000 20000 sq. sq. ft and a pay one thi!"ness of 100 ft. The reservoir ro!" has a uniform porosity of #$%. &hat is the pore volume of the t he reservoir'
(olution) *ul" volume of the reservoir + 20,000 - 100 ft # + 2 - 10 ft # /ore volume of the reservoir + 2 - 10 x 0.#$ ft# + - 10$ ft #
2. Assumin unit formation thi!"ness, determine the averae porosity for folloin system hen φa + 0.20, φ3 + 0.11, φ! + 0.24, L1 + 0.#$L and ha + h3 + 0.$h!. (ol. 8rom the iven fiure, 5φiAi + φa 9ha - L: ; φa 9h3 - .#$L: ; φ3 9h3 - .$L: ; φ! 9h! - L + φa 9.$h! - L: ; φa 9.$h! - .#$L: ; φ3 9.$h! - .$L: ; φ! 9h + h! - L 9.$ φa ; .#2$ φ3 ; φ! : + h! - L 9.$ x .20 ; .#2$ - .11 ; .24: + .70$ - h! - L 5Ai + 1.#$L - ha ; .$L - h3 ; L - h! + h! - L 91.#$ x.$ ; .$ - . + h! - L 9.$ ; .#2$ ; 1:
φa, ha φ3, h3
L1
φ!, h! L
5φiAi Area6eihted Area6eihted averae porosity + 6666666666 6666666666 5Ai .70$h!L + 6666666666666666 6666666666666666 +.2# or 2# %
#. A #.$7<$ !leaned and dried !ore plu as flooded ith a 0.$ =!m# !rude oil for several days to ensure !omplete saturation. On termination of the flood, the plu eihed 77.71< . &hat &hat is is the oil storae !apa!ity of the plu'
&et eiht of the !ore plu 9&&: + 77.71< >ry eiht of the !ore plu 9>&: + #.$7<$ >ensity of the !rude oil + 0.$ =!m # &eiht of the !rude oil saturated the !ore plu + && ? >& (o, *@ - 9/ore volume: - B + && ? >& /ore volume + 9&& ? >&:=B + 977.71< ? #.$7<$:=0.$ !m # + 4.1$40 !m# Oil storae !apa!ity of the !ore plu + 4.1$40 !m #
7. Assumin a sandstone rain density of 2.$ =!m #, !al!ulate the porosity of a # in!h lon sandstone !ore sample of 1.$ in!h idth and 3readth, respe!tively, if the !ore eih 2$0.0 '
8rom the dimension of the !ore sample. *ul" volume 9*@: of the !ore sample + # - 1.$ - 1.$ - 92.$7:# !m# + 110.12 !m# Crain volume 9C@: + 2$0=2.$ !m # + 47.##4 !m#
/ore volume 9/@: + *ul" volume ? Crain volume + 110.12 ? 47.##4 !m # + 1.2# !m# /orosity + 9/@=*@: -100 + 91.2#=110.12: - 100 + 17.1 %
$. Dal!ulate the eiht of 1 m# sandstone of 17% porosity, assumin a sand rain density of 2.$ =!m#.
*ul" volume of the sandstone !u3e + 1 m # + 10 !m# /ore volume of the sandstone !u3e + .17 - 10 !m# Crain volume of the sandstone !u3e + 91 ? 0.17: - 10 !m# + 0.< - 10 !m# &eiht of the sandstone !u3e + 0.< - 10 - 2.$ + 2.24 - 10 + 224 "
. Dal!ulate the arithmeti! averae and thi!"ness6eihted averae porosity for the folloin !ore data) (ample Eo. >epth 9ft: /orosity 9%: 1. #0$.$ 70.1 2. #0.$ #$.1 #. #0.$ #4.# 7. #0<.$ #.$ $. #04.$ 24.1
Arithmeti! averae porosity + ∑ n= ∑ n + 970.1 ; #$.1 ; #4.# ; #.$ ; 24.1:=$ 24.1:=$ + #.02 % Thi!"ness eihted averae porosity + ∑ hii= ∑ hi + 970.1 ; #$.1 ; #4.# ; #.$ ; 24.1:=$ + #.02 %
/ro3lems 1. Dal!ulate the arithmeti! averae and thi!"ness6eihted averae from the folloin measurements) Sample Thickness, ft Porosity, % 1 1.0 10 2 1.$ 12 # 1.0 11 7 2.0 1# $ 2.1 17 1.1 10 Solution F Arithmeti! averae 10 ;12 ;11;1# ;17 ;10 φ + 666666666666666666666666666666 666666666666666666666666666666666 666 + 11. % F Thi!"ness6eih T hi!"ness6eihted ted averae 91: 910: ; 91.$: 912: ; 91: 911: ; 92: 91#: ; 92.1: 917: ; 91.1: 910: 666666666666666666666666666666666666666666666 66666666666666666666666666666 666666666666666666666666666 666666666666666666666666666 66666666666666 φ + 666666666666666666666666666666 1;1.$ ;1; 2 ; 2.1;1.1 + 12.11%
/ro3lems 2. A. Dal!ulate the oil !ontent of one a!re6foot of reservoir ro!" hi!h hi!h has a !onnate ater saturation of 2$ per!ent and an effe!tive porosity of 10 per!ent *. Dal!ulate the oil !ontent if the effe!tive porosity is in!reased to #0 per!ent.
Donversion fa!tor )
!u3i! feet to 3arrels per a!re6foot
7#$0ft2=a!re 6666666666666666666 6666666666666666666 - 1ft + $< 33ls=a!re6feet $.2 ft#=33l Solution: A. Oil !ontent 933ls=a!re6feet: + $
A + areal extent of reservoir, a!res h + averae thi!"ness of reservoir, feet φ+ effe!tive porosity, fra!tion (i + !onnate ater saturation, fra!tion
/ro3lems #. An oil reservoir exists at its 3u33le6point pressure of #000 psia and temperature of 10G8. 10G8. The oil oil has an A/I ravity ravity of 72G 72G and as6oil ratio of 00 s!f=(T*. The spe!ifi! ravity of the solution as as is 0.$. The folloin additional data are also availa3le) Reservoir area + 70 a!res, Averae thi!"ness + 10 ft Donnate ater saturation + 0.2$, Hffe!tive porosity + 1$% Dal!ulate the initial oil in pla!e in (T*. Temperature
e r u s s e r /
> e e2 p o (inle phase reion (inle o i i n n t t ! u u r rv e v 9Cas: e To6phase reion * u ithin the phase 3 3 l e 6 envelope p o i #a n t ! u 1 a r v e 2a
(inle phase reion (inle 9Liquid: Driti!al point Dri!onden3ar Dri!ondentherm
3
3 1i
Oil reservoirs
2i
#i
Gas reservoirs
Solution st o!"6tan" oil from Hquation Step 1. >etermine the spe!ifi! ravity of the sto!"6tan" 171.$ 9 0 A/I + 66666666666666 6 1#1.$: γ o
171.$ 6666666666666666666 + 0.<1$ γ o + 6666666666666666666 72 ; 1#1.$
Step 2. Dal!ulate the initial oil formation volume fa!tor 3y applyin (tandinKs equation
0.$ βo + 0.4$4 ; 0.000120 0096666666666: 0096666666666: 0.$ 0.<1$ +1.#0 33l =(T*
; 1.2$910: J
1=2
Standing’s Standing’s orrelation (tandin 9147: presented a raphi!al !orrelation for estimatin the oil formation volume fa!tor ith the as solu3ility, as ravity, oil ravity, and reservoir temperature as the !orrelatin parameters. This raphi!al !orrelation oriinated from examinin a total of 10$ experimental data points on 22 different Dalifornia hydro!ar3on hydro!ar3on systems. An averae error of 1.2% as reported for the !orrelation. (tandin 914<1: shoed that the oil formation volume fa!tor !an 3e expressed more !onveniently in a mathemati!al form 3y the folloin equation) γ βo + 0.4$4 ; 0.000120 Rs966666:0.$ ; 1.2$9T670: J 1=2 γ o here T + temperature, GR γ o + spe!ifi! ravity of the sto!"6tan" oil + spe!ifi! ravity of the solution as
Step 3. Dal!ulate the pore volume from Hquation
Hxpressin the reservoir pore volume in 3arrels ives) /@ + ,$< Ahf, 33l /ore volume + $< 970: 910: 90.1$: + ,77,<0 33l
Step 4. Dal!ulate the initial oil in pla!e. Initial oil in pla!e + ,77,<0 91 6 0.2$:=1.#0 + 7,2,44< (T*
TUTORIAL # 1. In an experim experiment ent similar similar to that that of >ar!yKs, >ar!yKs, the flo flo rate of of ater ater as o3serve o3served d to 3e $.0 !m#=min. If the experiment ere repeated ith oil, hat ould 3e the flo rate for oil ' The differen!e 3eteen the upstream and donstream hydrauli! radient ∆h are the same for 3oth the experiments. Additional data) Oil vis!osity + 2.$ !/, oil density + 0.<$ m=!m# &ater vis!osity + 0.< !/, ater density + 1.0 m=!m# "A ∆/ "A ∆hB + 6 66666666666 + 6 66666666666666 µL µL
666666 o
Bµo + 66666666666 Boµ
"A ∆/ "A ∆hBo o + 6 6666666666 + 6 66666666666666666 66666666666666666 µoL µoL
Boµ o + 66666666666666666 66666666666666666 + Bµo
1.#$47 !m#=min
TUTORIAL # DontdM 2. *rine flood in a 1.4 in6lon and 1.$ in6diameter !ore plu from the Eorth (ea resulted in a sta3ilied pressure drop of 7.0$ psi. The flood as !arried out at 0.0$ mL=min ith 3rine vis!osity of 0.77# !/. >etermine the a3solute permea3ility of this plu in millidar!ies. L + 1.4 in!h + 7.<2 !m A + 22= - 1$=2 - 1$=2 - 92.$7:2 !m2 + 11.#4$ !m2 ∆/ + 7.0$ psi + 7.0$=17. atm + #.1#2 atm + 0.0$ !m#=min + 0.0$=0 !m#=se! µ+ 0.77# !p "A ∆/ + 6 66666666666
µL µL 0.0$ - 0.77# - 7.<2 N + 66666666 + 66666666666666666666666666 66666666666666666666666666666666 666666 + 7.44 - 106$ >ar!y + 0.0744 md A∆/ 0 - 11.#4$ - #.1#2
TUTORIAL # DontdM
#. Three 3eds of equal !ross se!tion have permea3ilities of 100, 200 and #00 m> and lenths of $0, $0, 1$ 1$ and <$ ft, respe!tively. respe!tively. &hat &hat is is the a3solute permea3ility of the 3eds pla!ed in series'
ΣLi K avg = --------Li Σ -------ki
i= 1 to n
$0 ; 1$ ; <$ 1$0 Nav + 6666666666666666666666666 6666666666666666666666666666666666666 666666666666 + 666666666666 + 1$.7#<$ md 9 $0=100 ; 1$=200 ; <$=#00: 0.<$$
TUTORIAL # DontdM
7. The 3eds of $0, 110 and 4$ m>, and , and 1$ ft thi!" respe!tively, are !ondu!tin fluid in parallel flo. If all are of equal lenth and idth, hat is the averae permea3ility'
Σkihi Kavg = --------Σ hi
i= 1 to n
9 $0- ; 110- ; 4$-1$: Nav + 66666666666666666666666666 66666666666666666666666666666666666666 666666666666 + 7#1.20 md 9 ; ; 1$:
TUTORIAL # DontdM $. 8olloin data ere o3tained durin a nitroen flood in a 1.$ !m diameter and #.0 !m lon !ore plu sample. >etermine the Nlin"en3er !orre!ted a3solute permea3ility of the !ore. Eitroen vis!osity µ + 0.02 !/, donstream pressure 9/2: is maintained atmospheri!.
Run Eum3er
9! 9!m#=s:
Upstream pressure, / 1 9atm:
1
$.11
1.4$
2
1<.1$
2.7$
#
#$.1
#.11
7
2.#1
#.$$
(olution is not iven
TUTORIAL 7 1. A petroleu petroleum m reservoi reservoirr has has an areal areal extent extent of $$,000 $$,000 ft2 and oil pay one thi!"ness of 100 ft. The reservoir ro!" has a uniform porosity of 2$% and the !onnate ater saturation is #0%. Dal!ulate the initial oil in pla!e.
(ol. *ul" @olume + $$000 - 100 ft # + $$ - 10$ ft# Initial oil in pla!e + @ - φ x 9 1 ? (: + $$ x 10$ - 0.2$ - 0. ft# + 42$00 ft# + 42$00 - Donversion fa!tor for 33l
2. A !hal" !ore plu plu havin a pore pore volume of 1.0#0 1.0#0 !m# is fully saturated ith reservoir 3rine. A syntheti! oil 9Isopar6L: flood is !ondu!ted on this plu. It is found that 12.2$ !m# of reservoir 3rine as displa!ed from this plu 3y the Isopar6L. After rea!hin this value, no further reservoir 3rine !ould 3e displa!ed from the !ore plu. &hat is the !onnate ater or irredu!i3le ater saturation of this !ore plu'
(ol /ore @olume + 1.0#0 !m# @olume of 3rine displa!ed + 12.2$ !m# @olume of !onnate ater + 1.0#00 ? 12.2$ !m# + 7.<0 !m# Thus, Donnate ater saturation + 100 - 97.<0=1.0#0: + 2<.0 %
TUTORIAL 7 DontdM #. 8or the folloin !ore plus, as floods ere !arried out usin nitroen. The oil produ!ed from plu plu 1 and and 2 for the as flood flood as as 4.0 4.0 and .4 !m#, respe!tively. &hat is the residual oil saturation 9(or: in these to plus' /lu Eo
Initial (aturation 9%:
φ 9%:
*@ 9!m#:
ρrain 9=!m#:
ρo 9=!m#:
ρ 9=!m#:
ρ 9=!m#:
(o
(
(
1
7.7
#$.#
0
#<.2
#.0$
2.14
0.2#
1.021
0.001
2
1.4#
2<.0
0
#7.#
$1.0$
2.27
0.2#
1.021
0.001
/lu 1 @olume of the oil produ!ed + 4.0 !m# /@ + #.0$ - 0.#<2 + 27.124 !m# @olume of initial oil in the sample + /@ - (oi + 27.124 - .77 !m# + 1$.$4 !m# @olume of the residual oil + 91$.$4 ? 4.0: m# + .$4 !m# en!e, Residual oil saturation + 100 - 9.$4=27.124: + 2.#7 %
/lu 2 @olume of the oil produ!ed + .4 !m# /@ + $1.0$ - 0.#7# + 1.4 !m# @olume of initial oil in the sample + /@ - (oi + 1.4 - .14# !m# + 12.1 !m# @olume of the residual oil + 912.1 ? .4: !m# + $.<1 !m# en!e, Residual oil saturation + 100 - 9$.1<=1.4: + #2.4 %
TUTORIAL 7 DontdM
7. A dean6star" extra!tion is performed on the Eorth (ea !hal" !ore plu sample, hi!h extra!ted $. !m# of ater. The !ore plu has a porosity of #.1 % and 3ul" volume of 27.$ !m#. The et and dry eihts of the sample are $0.7 and 72.## , respe!tively. respe!tively. The as, oil and ater densities are 0.001, 0.<$ and 1.0#$ =!m#, respe!tively. Dal!ulate the as, oil, and ater saturations in the !ore plu sample.
(olution /ore @olume 9/@: + *ul" @olume 9*@: - /orosity 9φ: + 27.$ - #.1 !m# + <.<77$ !m# Eo , && ? >& + Po ; P ; P $0.7 ? 72.## + (oρo ; (ρ ; (ρ + 0.<$@o ; 0.001@ ; 1.0#$ - $. <.#1 + 0.<$@o ; 0.001@ ; $.44 Or, 0.<$@o ; 0.001@ + 2.##1 666666666666666666666666661 666666666666666666666666661 Eo, /@ + @o ; @ ; @ <.<77$ + @o ; @ ; $. Or @o ; @ + #.07$ 66666666666666666666666666 666666666666666666666666666666666662 6666666662 (olvin equation 1 and 2, @o + 2.72, @ + 0.##2$ en!e, (o + 100 - 92.72=<.<77$: + #1 % ( + 100 - 90.##2$=<.<77$: + #. % ( + 100 - 9$.=<.<77$: + $.27 %
$. The folloin data is availa3le for the end trim of a !hal" !ore plu sample) ( + $%, (o + 7<% and ( + 7%, ρrain + 2.1# =!m#, φ + #<.#1%. Additional data in!lude as, oil and ater densities densities 0.001, 0.<$#2 and and 1.0#$1 =!m#. The 3ul" volume of the !ore plu sample sample 9in a preserved state:, from from hi!h the end trim # as ta"en, is $.41 !m , and its measured eiht 9trimless: is 1##.0 . Eo additional data are are availa3le for the !ore plu sample. /erform an assessment !he!" to evaluate if the end trim data is also valid for the !ore !ore plu, so that the !ore plu sample !an !an either 3e used or dis!arded dis!arded for (DAL test.
(olution ( + $%, (o + 7<%, ( + 7 % ρrain + 2.#1, φ + #<.#1 %, *ul" volume + $.41 !m#, Peasured eiht + 1##.0 ρ + 0.001=!m#, ρo + 0.<$#2 =!m#, ρ + 1.0#$1 =!m# &e "no that &eiht of the Dore + eiht of the rain ; eiht of fluids f luids /ore volume + $.41 - .#<#1 !m# + 2$.2$ !m# Crain volume + $.41 ? 2$.2$ !m# + 70. !m# &eiht of the rains + 70. - 2.1# + 110.#1 &eiht of the fluids + 2$.2$ x 0.7< - 0.<$#2 + 22.2 Dal!ulated eiht + 9110.#1 ; 22.2: + 1#2.4# Dal!ulated eiht 91#2.4# : Q measured eiht 91##.0 : en!e the !ore plu sample !an 3e used for (DAL test t est
