Notes af Material Balance Calculations

of Gas-condensate Fields

Ga.s-Gond. M.B. Page 1 of 8

The usual material balance method used for analyzing past performance and predicting future behavior of dry ga.s fields is often refered to as the p/Z method. Figure 1 illustrates the principle of this method - cumulative

i z ,,

I ......... G ~_j;p.ndo_n _ _ ~ \

I!" - _/>!._~_ - - - - - _I_

0

produced gas, Op , is plotted against p/Z • Provided that the hydrocarbon pore volume remains constant ( no water influx, no pore compaction ) a straight line should result. The slope of the straight line defines the initial gas in place as indicated by F,q. 1, or the straight line can be

Pi (pi/zi - 15) p/Z • - - G

Zi G p (1)

<:ip--­Figure 1. extrapolated to p/Z=· 15 and the value of the

initial gas in place, G , obtained by reading the value o:f Gp at the intersection.

Equation 1 comes about from a molal material balance. That is, the moles of gas remaining in the re~ervoir at any pressure is equal to the initial moles in the reserv6ir minus the moles that have been produced. This molal balance is expressed by Eq. 2.

n "' ni - np Equation 1 develops from Eq. 2 by use of the gas law equation

n .. pV/ZRT

(2)

Material balances of gas-condensate fields can be made on the same basis as dry gas field material balances. A plot such as Fig 1 may be used provided (1) the two-phase compressibility factor, Z2, is tEed in the p/Z term, and (2) the cumulative production, Gp , accounts far all produced gases plus the produced stock tank oil (condensate) • Fluid analysis reports on gas-condensate systems developed by Core Laboratories, Inc. and most other cormnercial laboratories contain the necessary data to handle the material balance in this manner. Where laboratory data are not available it is possible to make the stock tank oil correction from correlations. However, there seems to be no correlation avail­able with which to detennine two-phase Z factors. In this case it becomes necessary to accept an unknown degree af inaccuracy in the material balance by using single-phase Z factors. ·

Tm following calculations illustrate a procedure for making a material balance af a gas-condensate field. The reservoir pressure and surface production data used in the example are fabricated data. The fluid property data discussed in the example come from Core Laboratories' fluid analysis report n Reservoir Fluid Study for Good OiJ. Company, Condensate No.7 Well, Samson County, Texas 11

The object of the example material balance is to evaluate

1. Initial hydrocarbons in place, a. SCF of total gases b. Barrels of stock tank oil •

•

Gas -Cond.. M. B. Page 2 of 8

2. Reserves based on an abandonment pressure of 750 psig a. SCF of total gases b. Barrels of stock tank oil.

Basic assumptions involved in the material balance calculations are

1. No water influx into the hydrocarbon reservoir 2. No water productidn 3. No reservoir retrograde liquid production 4. No compaction of reservoir rock.

Table 1 lists the reservoir pressure and production data used in the example. As stated before these are fabricated data.

Date

A B c D E F

Abandon

Table 1 Reservoir Pressure I Production Data

Vol. Avg. Res. Press.

psig

5713 5050 3380 2920 26oO 2350

750

Cumulative Production

1 o9 S CF Gas 1 06 Barrel STO

0 0 36.52 5.61

167.22 24.42 246.38 31.39 310.50 35.42 385.LB 38.74

As pointed out before, the p/Z vs Gp plot to be developed must account for both gas and stock tank oil production. Probably the easiest way- of doing this is to convert the stock tank oil production to an equivalent quantity of vapor and add it to the measured gas production. ~ then expresses all product­ion from the reservoir in terms of standard cubic reet of gas. The equivalent vapor volume of stock tank oil is developed from depletion data given in the fluid analysis report as a function of pressure. This is shown by Fig 2. How to develop Fig 2 is the subject of the next s ection.

1 .1

1.0

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0.9

o.B 0

++1 +1 ~-i-=++ -7-TT . : i ; ~ 1 ' : Pressure - psig +· : ' ' : : ;-i-H-- --;-;-. : +:~-. : · I i I ' i 1 , l , I I : I I I I 1 I I I I I I I ! I ' , 1 I :-+-1-f,-i-j -+- ~: --'-;-

1000 2000 3000 6000

Vapar Equivalent of STO vs Pressure

Gas-Cond. M.B. Page 3 of 8

Figure 3 is a reproduction of page 5 of Core Laboratories' fluid analysis report. The dew point pressure of this system is 4CX)() psig at 186° F. At all reservoir pressures greater than 4000 psig the vapor equivalent of stock tank oil will have the same value. Refering to the first column of nwnbers in Fig 3 it is seen that 1000 MSCF of reservoir material produces 878.78 MSCF ( 757.87 + 96.68 + 24.23 ) of surface gases plus 135.7 bbl of stock tank oil. The vapor equivalent of stock tank oil is, therefor 1 ( 1CX)() - 878.78 )/ 135.7 -= 0.893 MSCF/bbl • This value is plotted as the horizontal line at pressures above 4000 psig in Fig 2 •

AE pressure declines below the 4000 psig dew point the stock tank oil components held in gaseous solution in the reservoir become progressively lighter in nature. The stock tank oil consequently shows an increasing trend of degrees API, and the vapor equivalent of the stock tank oil also increases. Refering now to the pressure interval 3500 + 2900 psig of Fig 3 , we see that the reservoir material produced during this pressure interval amounts to ( 154.38 - 53.74 ) MSCF. This material splits into ( 140.03 - 47.90 ) MSCF of surface

CORE LAB"RATORIES, INC p,1ro/n"11 J f"llOl1 Eniintt~inl

Page__5__of _ . _J ) _ _

DALLA.5 . TCJCAS File _______ ___ __ _

WeJI Cnndrnsale No. _1 ___ ___ _

Calculated Cumulative Rtto\'er)· During Dr:plelion

Cumulative Ret oHry pn lnitil.I

)DfSCF o: Ori.l!inal Fluid In Place 4000• 3500

Well Stream-~ISCF 1000 0 53.74

1'orm;:i.I Ttmperatur' Separation•• Stor k tank hquid-harrels 1 35. 7 0 6.4 rrimar:r Hparetor gas.-~ISCF 757.87 0 4 I . 95 S('('nnd !)l;i.~r ll'as.---MSCF 96. 68 0 4. 74 Stock un;, gas-~lSCF 24. 23 0 I. 2 I

Tot.al "'Pinnt Pro<iucts" in

Pr i marv Sq?:arator Gas-Gallon s ••• Propant' 1198 0 67 BuLanrs. (t ntal) 410 0 i3 Pent.anr ~ plu !- 180 0 I 0

Total "Plant Products" rn

Second Sta.re S"earator Gas-Gallons• • • Propane 669 0 33 But ant>~ (total) 308 0 1 5 Pent.a.nes plus 138 0 7

Tot.al "'Plant PrC'ducts"' in \.\"ell Stream-Gallons•••

rropanP 2296 0 121 nutan'" ~ llot.a.IJ 1403 0 73 Prntane!- J.i l u~ 5519 0 2b2

• Dr ' ' p c. int pr~ssur e.

•• Rl!'•n·.· · :'" \ Ba fi s . Primary separ•t1on at 500 psia and 70• F.,

Se c ond t.ta~e at 50 psia and ?o• f" . Srot~ ta:'"IY at 14.7 p!11a and 10• F .

Reservoir PressurE>-PSlG

~ 2100 1300

I 54. 38 350 . 96 576 . 95

IS. 4 24. 0 29. 7 I 24. 78 30 I. 5 7 5 I 2. 32

12. 09 20. i 5 27.95 3. I 6 5 . 61 7. 71

204 5 I 3 910 72 190 346 3 I 81 144

as 149 205 41 76 1 08 I 9 35 49 -

342 750 1229 202 422 6b5 634 1022 I 3 I 5

••• Ht· <. u\' (': ·. a ~ sumes 100 pr.r tent plant efficiency.

r.:::; ·::::::~·~ .: :~.· ::' ::· :~:·~::·~f:.?.:Ti~ f.~:::::;.~::f ~~·~:":ii'~:::?::..,::: :~ .-':_~?.'· -~ --= ·.'..·:· . · · -. !.· :·' ~- · .'.~ ~.:::, :-::: .~!.

Figure 3

605 0

767.87 9 35. I 5

35. 1 b8S.02

37. 79 10.40

1276 4 91 I 92

286 159 69

1706 927

I 589

/ Gas-Cond. M.B • Page 4 of 8

gases plus ( 1.5.4 - 6.4 ) barrels of stock tank oil. Therefor, in this pressure interval the average vapor equivalent of the stock tank oil is (( 1.54.38 - .53.74 ) - ( 140.03 - 47.99 }) / ( 1.5.4 - 6.4 ) • 0.946 MSCF /bbl. This value is plotted in Fig 2 as a horizontal line between pressure values of 3.500 and 2900 psig to indicate that it is an average value in that pressure interval.

Similar calculations for the other pressure intervals result in the average vapor equivalent values shown in Fig 2 • Finally, a smooth curve is constructed through the average values so as to preserve the areas under the interval values. Values from the smooth curve are then used in material balance calculations in converting stock tank oil quantities to equivalent gas quantities.

Where specific laboratory data, such as above, are not available with which to develop vapor equivalent values the following eiuation can be used to calculate values from the API gravity of the stock tank oil. -

2.

V1 (SCF/STB) c 250.8 + 9.7.5°API - O.oo6 ('API) (4)

Two-phase Z Factors

TOO concept of a two-phase Z factor is foreign to many petroleum engineers. However, it iB easy to see that Eq 3 , connnonly called the gas law equation, is a gereneral equation of state of the hydrocarbon system §!ld that it can apply to any number of phases as long as V refers to the total phase volumes and n represents the total moles af material in the system. It is to be expected that the pressure - temperature behavior of a two-phase Z factor will not be exactly like that of the familiar single-phase Z factor. It is somewhat sur­prising, though, how closely the two behaviors match over a wide range of press­ure. The reason for u::iing two-phase Z factors in material balance calculations of gas-condensate systems is that it is the total hydrocarbon volume in the reservoir that remains constant during depletion, not just the gas phase volume.

Figure 4 reproduces a page of data by Core Laboratories, Inc. summarizing · the step-wise gas depletion test of the Condensate No 7 Well system. The equil­ibrium gas deviation factors shown correspond to the gas compositions shown above. The two-phase deviation factors correspond to the gas phase whose composition is given in the table plus a quantity of retrograde liquid phase. The amount of retrograde liquid is .given in a different table,, but at 2900 psig it amounts to 19.3 % of the total system volume. Af3 can be seen, down to 2900 µ:;ig there is no appreciable difference in the single-phase and the two-phase deviation factors. At the lower pressures there is considerable difference as well as a different trend with pressure. As indicated above, it is the two­phase Z factor that should be used in plotting p/Z vs °t:> •

1.fuen two-phase deviation factors are not available, it is probably best to use single-phase values calculated from the composition of the richest gas. Tre richest gas normally is the initial gas in the reservoir. Thus refering to Fig 4, in the absence of two-phase :_z factors the composition of the 5713 psig fluid wruld be used to generate values at the lower pressures.

* Curve-fit of data presented by C.K.Eilerts in USBM Monograph 10 (1957)

COlllE LABOI! C>IU Ell , I NC .

,~,,.., R",.,...ir &t"-''""l DAU-A• . TVt.A8

Depletion Study a l 18 6 .,.. Hyd roc&rhnn An a lYA"I of Produce-d W e ll Str ea m- Mol Pu Cent

a-rvoir Prouu,.. - PSIG

Component 5 71 3• 4 000• • _2iQQ_ ~ 2100

0. 18 0. 18 0 . 18 0. 18 0 . I 8 Carbon dloxldr

0 . I 3 o . 14 0 . 15 NitTo~ 0 . 13 0. 13

61 . 7Z 61. 7Z 63 . I 0 65 . Z I 69 . 79 Mt lhanr

14 . 10 14 . 1 Z Ethan• 14. I 0 14 . 10 14 . Z7

Propan• 8. 37 8 . 37 8.25 8 . I 0 7 . 57

i~o-Bulane 0 . 98 0 . 98 0. 91 0 . 95 0 . 81

n· Bulan' 3 . 45 3 . 45 3. 40 3. 16 2. 71

iso- Pent.Me 0 . 91 o . 91 0 . 86 0 . 84 0 . 67

n-P, nt.&nt I. 52 I. 52 I. 40 I. 39 0 . 97

Hc1ant11 I . 79 I. 79 I. 60 1 . 52 I. 0 3

Hrpt.anu p)u1 6.85 6. 85 ~ ~ ~ I 00. 00 100.00 100.00 I 00. 00 I 00. 00

Mol0< ular w•iirh t oi h•Plan" plu• 143 143 138 128 116

Sp«ific fT&Vity or h•plan•• plu> 0. 795 0 .7 95 0. 790 0 . 780 0 . 767

~vi&L.ion Factor - Z 0. 7£.Z Equilibrium ru I. I 07 0.867 0 . 7 99 0.7 48

Tv.•o-phue I. I 07 0 .867 0.8 02 0 . 744 0. 704

Well S trca..m produced-Cumul a tive per cent of lnitia.l 0 . 000 5 . 374 I 5. 4 38 35. 09&

~PM from Sm ooth Composition' 8. 476 5 . I 71 Propane plus 9 . z 18 9. Zl 8 7 , I 74

Butanes plu s 6.922 6. 922 6. 224 4.980 3.095

Penta..neti plus 5. 51 9 5. 519 4 . 876 3.b92 I. 978

• 011£_inal r rs crvoir pre~surc .

Paro- - 4 -

Gas- Cond . M.B. Page 5 of 8

1. }_ - - · o( .

Fil.__ - - - - - · - ---- · w.n . __ C:,on~D..1&.1LN<l~ 1- _ ·- -

_!l.QQ_ ~ _ _ o_

0. 19 0 . ZI

O. I 5 0 . 14 70.77 66 . 59

14. 63 16 . 06 7.73 9 . 11

0 . 79 I. 01

Z. 59 3. 31

0 . 55 0.68

0 . 81 I. oz o . 7 3 0.80 I. 0 6 ___!_.:_Q2

I 00. 00 100.00

Ill 11 0

0 . 762 0. 761

0 . 819 0 . 902 0 . 671 0 .576

57 . 695 76 . 787 a 3, 51 5

4. 4 90 5. 30;

z. 370 2 . 8 08 I. 294 l.4 E

•• !Jt"w point µr c~!lurc. ~:,,tr;---"l'!" I~ ~~~~~--~ =.t= .:.=-,.:~...:..:~:~·~~ :r ~·It:-!.!:~ .~ /:J, =~..._.:,.:=.:..-:~~~~. ':it C..: .... Lat->tw.....,••- · 111 r &" d 11 ... a11o_... . ... -pie..,-• ..-.- n o ,...P'""'" l l>L!tt , and r-.•• an ~•u OT ""l',,_tl ... U.-..., ..,. \loot ~'-"II.I . f'"'P9' ..,."' . 11 0.,, • r ''" '"·"'"1 • ..- of ... , ell . ...., • ~ . 1...-.r -11 .. •"' I• _.....,..,. , •• •10. ·~I~ .udl ~ I.I -' ., nl,,_. .,.,.

Figure 4

Material Balance Calculation

Table 2 shows the calculations involved in the material balance of data from Table 1 and Figs 3 and 4. Note that at the last date ( F ) the equivalent vapor volume of the produced stock tank oil amounts to almost 10 % of the total gases removed from the reservoir. Had the stock tank oil not been included in the analysis t he material balance would yield an error of about this magnitude in the initial hydrocarbons in place. A plot of the cwnulative gas produced listed in the last column of Table 4 vs p/Z values in the fourth column is shown in Fig 5 • From this plot it is deduced that the initial hydrocarbons in place (surface gases+ Stock tank oil equivalent vapor) amounts to 1. 14(1012) SCF • Also , at the specified 750 psig abandonment pressure the cumulative · production amounts to 880 (109) SCF, leaving ( 1140 - 880 ) 109 = 260(109) SCF reserve as of date F.

(

Gas-Cond. M. B. Page 6 of 8

Table 2 . Example Calculation for a Gas-

c ondens ate Reservoir Material Balance .

CD ® Q) ® ® ® (j) ® ® Avg • . Sep . Gas Inter- Avg. Cum.

Press Prod. val STO Vap. :Eq. Eq . Vap. 10~SCF Date psi a z -1?1.!:_ 109scF 106 bbl SCF/STB 109 SCF

A 5728 1 . 101 5174 0 'f' -I< 0 0

B 5065 1 . 016 4990 36. 52 5. 61 893 s.010 41 . 53

c 3395 o. 792" 4287 167 . 22 18 . 81 900 21. 94 189 . 15

D 2935 o. 750 I' 3913 246 • .38 6 . 97 955 28 ~ 60 274. 97

E 2615 o. 727 .. 3597 310. 50 4 . 03 987 .32. 57 343 . 07

F 2365 o. 71 s .. 3308 385. 48 3. 32 1004 35. 91 421 . 39

Ab an. 765 0 . 620 .. 1234

* (Fig 4) v s Pressure. **From plot of two-phase Z Fig 2. From

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11 I I I : : i:T

~-,--'--+ -~-- I I I ~--'-- j I '. I I I ! I I I I I ' I I : I 1 I I I , ; ; I I I

T '

~ 4000

"" co p. $-"J=t~ Jri~ -, -. ,- ~-- ~~ 1L +~ _J,:--=~ · R~~e~e ~·~, ~·_;__is'~tlTICti:j

--t---'- --1-~ j_ ---~-- }:::,..... ~l.+-t-- I _J__ ; i_j__!_ I I I

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t--:1

' p..

2000

~ ·~ _ _2_..!___1_L ~ . I ! i ' I I ' ! ~ ~ ! I ' l I j -~__'._C--L.!."'°_; __ __ I ! I 1 I ~~--"---'-+--, -t--"--t,-.'--1-+-T1-t1-+--+-+ 1 -J--lf--i-I -1--1--l\-l-L_,__J I ~-___;__u-'-- _J 1 ! I _, L , ' : I : - ' ' 1- ,:-'i I I i , I , I

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·-t-:-i-j ! : I I '. ,,· I I' : ' M l- ._;_;_J_j __ 1234 ...l : _l_ I t!I---.__ i I ' I ' ~- -i---,--'----- -'-l- ' -- ;_____...J___ - .......,., ITl ...... -~11 -t-l--+-4-4--+-..; 1-'-· _,

_,__J~ I J I ; ~ , T • I 1 ' i I ' I °' l ] ' I'> , j i I ' ' I ' ' ' : ' I • I I I I I : • I I I I

' I I I I i I I i ' ' : I I I I : i I I I ' I I t-.. ' : I I : i I I I ! I I I I I I I I I J I .. I . I 1 ! T .I I. I , I

T : : : i : i '. : f : : J J { : ; : : : J i G a 1140 ( 1 o9) SCF 0 I ' I I : I ' I I I I I I ! I I I I I : l I I ! I I I I I

0 200 400 600 Cum. Prod. Hydrocarbons 1 o9 SCF.

800 1000

Figure 5 . Material Balance Plot

Initial Surface Gases and Stock Tanlc Oil in Place. In order to separate the initial hydrocarbons in place into surface gases and stock tank oil it is necessary to fix the initial producing gas- oil r atio . As this reservoir system was init­ially above it's dew point pressure in the r eservoir the surface gas oil-ratio should remain constant until the dew point p ressure of 4000 psig is r eached. As pressure declines below the dew point pressure the surf ace gas - oil ratio will increase. This increase in surface gas-oil rati<I> is caused by the heavy hydro-

I j

Gas-Cond. M.B. Page 7 of 8

carbons remaining in the reservoir as components of the retrograde liquid phase.

There are two sources af initial gas-oil ratio data ; production data and data from the fluid analysis report. Referlng to the production data in Table 1, it is seen that the producing gas-oil ratio during the first time interval ( lot;ile the reservoir pressure was still above 4000 psig ) is 36.S2(109) SCF I 5.61(1ob) STB • 6510 SCF I STB. The fluid analysis report value can be determined from the figures in the first column of Fig 3. We see that the gs.s­oil ratio computes to be (757.87 + 96.68 + 24.23)SCF / 13S.7 STB • 6476 SCF / STB. Either of the two values could be used, but selecting the latter one allows one to calculate the initial gas and stock tank oil quantities as follows :

Then Let x "' barrels of stock tank oil initially in place.

x • 0.893(103) + 6476 • x • 1140(109) SCF. The ref or

Stock tank oil E 1140(109) / (6476 + 893) • 1.SS(10B) barrels. Surface gases • 1.55(108) • 6476 • 1002(109) SCF.

SUrface Gases and Stock Tank Oil Reserve. By extrapolation of the p/Z material balance line from date point F to abandonment conditions it was determined that the hydrocarbon material reserve amounts to 260(109) SCF. To split this quantity into surface gases and stock tank oil quantities requires the same calculation as above. However, in this instance both the stock tank oil equivalent volume factor and the producing gas-oil ratio number must be average values in the pressure range 2350 ~ 750 psig. A vapor equivalent vs pressure plot has already been developed (Fig 2 ) and refering to it it can be seen that the average value in the pressure range is approximately 1 .040 MSCF / bbl.

To obtain the average gas-oil ratio af the future production requires construction of a surface ga.s-oil ratio vs pressure chart. The manner of doing this is similar to that used in producing Fig 2 • Data for the chart comes from Fig 3. For example, in the pressure interval 3500 -.2900 psig the average gas oil ratio is (140.03 - 47.90)SCF I (15.4 - 6.4)bbl c 10,237 SCF I STB • Similar calculations for the other pressure intervals listed in Fig 3 yield the values plotted in Fig 6. A smooth curve is placed through the average values to yield the required producing gas-oil ratio vs pressure curve.

From Fig 6 , the average producing gas-oil ratio between 23SO and 750 psig calculates to be about 36,000 SCF I STB. This was obtained by determining the area under the smooth curve in the above pressure interval by Simpson's Rule integration and then dividing the area by the pressure interval width. Using the above two average values and the total hydrocarbon reserve yields

Let y = barrels of reserve stock tank oil

Then

y • 1.040(103) + 361 000 • y a 260(109) SCF.

From which

stock tank oil reserve ., 26o(1o9~ / (1040 + 36ooo) E l.02(10 ) barrels

Surface gases • 7.02(10 ) • 36,000 • 253(109) SCF.

. (

Ga.s-Cond. M. B. Page 8 of 8

40 ·agi----J I ' ' I _J_' : I I ., ., I J . I I I i I I UL+-J-;--~1· _,_1_,l_e---rl_I_' 1 _ _J_j _J -.~ ~...J -~~...l.~· 11-~- -- ,1 t 1 I

- - r- I .,... 386oo I I I I : I I I I I I I I ....,-~ I - T' -+- 11__.J_~+-f-J--!-f-+-'-+-i-t--f-+-r-f-+,-f-+-i--+-<-

I , ~ · f\ ~' -r-~t-i'r--~' -+-+-' _i_,__1 J -+- I I '·-+- -l--,-'-~.· - -':' I L . ' r --,~-~ - - ,,· . ' ' ' --. I '

~- · 1 I \ 1 i ; ; ! lj I , ,·, , I I I I ; 34300 17 -- --,-,-=, -.-+o,· -,,+ 1+-11-1,r-, -~,:-:-+-!1-+-1 :-i+ -11r+-, :-1 -+-;rl,-:-, -l1-t-ri-H1-t-t--t-n11H -H1 --t-n1 ; : . ~-: I 1 \ ; I i ' j ~ ' _! ! I I :

t:·=1=~~=t::1(~= .... --l--~-+--,-;-J.~-,--+' -t-+--t--~'\--·-L-f-+-~' -11-+-t-+-+<1 -r' -t-+-t-<1 '--i--t---r-+-~+-1 t-i-r-t-+-~'rt'-r-41-t ; I I : ~ I I : ;. I I I I I I I I I . \ I . I I : I I

30 I I I I I I I I I I _l ~ i l 1 _l I I I . I I I I I

I i I I ! I I I ' I I I ' i I I I I I I I ' I I

I i i I I I I I ! I \ I i i I I ; I I I '

I ! I I I ~ J 1 1 \ Iii j J _l 1 11 I ! I I' i I I : l 1 I I I I\ I I I : I I I ! I I I

I I I ! I I I . I ' ' I ! I I I ' I ! I I i l-+-1-, -+,-+--+-"--l-+-+-+-i!-+-+-.-1-tl-1--;,-+-11-t-1 -+-+-f-'t, -+-,. ;1-1-1 21-8 so I I I I l I I I I

: I I j J _l J I I \ 1 I : . i : I j ' +-J--+_J_ 1-+-+~!l-+-l--t--'"-l-t1 -l--r-.-r--,-+-.,;-i--+-+--t-i=l.=r-~1=<1 ~,~. -.-=-~!-+-'-,-+-+-1:f'-+-+~.-+11 =~j=t1: ~:, 1=r·, j=:~:1=tj:!=~··· ~=r! ~~-.,-l-'--i--1'-+-+ ·-+-.-1-t-+-.-+-t-i1-+-+--+-+-1-t-+-+--t-H-~;. , ·:--; i I I

20 I I 1, , 1 i i I' 1_,l l J ' J.1 I I II 'LJ_ : ! · H;-+-1!-+-i--+-+-t-i-+-r-:;--:·-t-H1 J-t--H1 -t--t--t-HIH. !\ • I 1

I I J I ;;I l -!H--rl '""f-1

' I I I I I : I ~ I j I I I ! ). I I I I I I ' ! : I ~-! ~J_; 1 ' 1 I I I I I I I I \: I I i i • i . I ~

! : - -i:-+-+---'-~-+-+--+-+-lr-1 -1--il-+ I, -t-i 1 1-+-r-t1-1 ·-+--t-+-11--;-; 1 1\ I I I I I • I I i . i I I I

· J ! • _l I I ' I I ! ] I ; I ,, I II I J_J_; · I i--,-.,.-- -+-i-+-r-+-+-+-+-1-t-+-+--t-+-:-11 I I • • ' I I ;-:1 ~ • I 1 1 ! I I ; I : : ; I i 1 : 1 : ~ ~-= 10240 I ' I i I : !_.__ -t+:t-J-=-

: I-+-+,-+--+,-<-,. ~--+~, 1 ' -1 l I I I I I I I : ! l.". lJ_!·--+-~' -.,_,l',_.-1,___~-r-.,-r-!-J_j_j_ . I

1 1 1 1 1 1 1 1 1 : i 1 1 •• ,~ t 1 r I : 1 1 1 1 J i _ _'. . 10 i I ! I : _; I I i : . .2'*· ' _ _J_ L : I I I _)_;_' .;_,._

• : l : ! I l : I I I ~;-1,-t-1, -+,~~~ . ' 7500 _--.--·_,·_1,,_,_,1 ' .. ~-+---Ti~.--,c-+.-+, '· 1-+~-+-t-, ~-i-r-0,-0-l-;--il-c-l -l:-t-,-, -;-;--,-,-,--,,-,--, --;--! ;- -----= . _j-----1---.'.--! I I !_,---;-; '.__j_ ~-

.-..T-'~::;:_::-.~+-i;-~-:·=.+-'--'~-, ==: ==:==~:=~=r,~-i~--~!l ~====. ~=~:==,~.=~,~~,_l-,====~·-t=~r::~, :~::t.--:::-, ~1~: ~::==;-=:==:=-r:;s,~~.S::::=~~:::;::~:=:i ,_._,'~-'-' _,_..,..-1-t-i_ i.---1 . _[ I I I I i I I I i -+-.J-i---: I I I I i ' ! I 1-'-1 ~? ~ : :::: ~ ~i-~..,.;-1-_j;-+: =:· :,=r==~:=r; :,::::+=t1

1 J1=~=~·· :+=+=.~~ 1=r:+=~ :. =~, =·::::::-+-: -1_,~. ~-'-lH' -++·~' --r-.,-+-: -;1-r;-r--t.-,-, -t-•,-t-trtt 1-'--L-,-, .-+-11--i-,+---t-++-i-;J.rl-:-, -i-T-rll-t-' -;rl-H 1 rl-:--:,-r, -t-'"'."1-,-1 -:j-r-r-i,-,-, -,-; ' : I I i I i I i .

0 0 1000 2000 3000 4000 . - sooo · 6ooo

Pressure - psig

Figure 6 Producing Ga.s-oil Ratio vs Pressure

M.B.~.