Flash Calculations--Gas-to-Oil Ratio

9.2 VAPOR-LIQUID EQUILIBRIUM CALCULATIONS

9.2.1 Flash Calculations--Gas-to-Oil Ratio

I n typical flash calculations a feed fluid mixture of c o m p o - sition zi enters a separator at T and P. Products of a flash separator for F m o l of feed are V mol of vapor with composition Yi a n d L m o l of liquid with c o m p o s i t i o n x4. Calculations can be p e r f o r m e d for each mole of the feed (F = 1). By calcu- lating vapor-to-feed mole ratio (VF ---- V/F), one can calculate the gas-to-oil ratio (GOR) or gas-to-liquid ratio (GLR). This p a r a m e t e r is particularly i m p o r t a n t in operation of surface separators at the oil p r o d u c t i o n fields in which p r o d u c t i o n of m a x i m u m liquid (oil) is desired by having low value of GOR.

Schematic of a c o n t i n u o u s flash separator unit is s h o w n in Fig. 9.2.

F e e d 1 m o l e

zi T F , PF

: ' i ' i ' : ' : ' : ' i ' : ' i ' : ' i ' . "

:i:i:i:iT:ZZ:i:i:i

::::::::::::::::::::::::

9 ...:.... 9 ,..,...

...

:::::::::::::::::::::::::::::::::::::::::::::::::

.:::,.,.,,,.:::,...,.,...

i!ili!iiiii~ililili~ii!i!~i:i~i:i:i2i~i~i:i:i:i:i :::::::::::::::::::::::::::::::::::::::::::::::::

V a p o r

9 V m o l e s

Liquid 9 L moles

FIG. 9.2--A continuous flash separator.

Since v a p o r and liquid leaving a flash unit are in equilib- r i u m f r o m Eq. (6.201) we have

(9.1) Yi = gix4

in w h i c h Ki is the equilibrium ratio of c o m p o n e n t i at T and P a n d compositions xi a n d Yi. Calculations of Ki values have been discussed in Section 6.8.2.3. Mole balance equation a r o u n d a separator unit (Fig. 9.2) for c o m p o n e n t i is given by the following equation:

(9.2) 1 x zi = LF x xi + VF x yi

Substituting for LF = 1 -- VF, replacing for Yi f r o m Eq. (9.1), and solving for xi gives the following:

(9.3) x~ - - zi

1 + VF(Ki -- 1)

Substituting Eq. (9.3) into Eq. (9.1) gives a relation for calculation of Yi. Since for b o t h vapor and liquid p r o d u c t s we m u s t have ~ x4 = ~ Yi = 1 or ~ (Yi - x4) = 0. Substituting x4 a n d Yi f r o m the above equations gives the following objective function for calculation of VF:

~_, z ~ ( K ~ - 1)

(9.4) F(VF) ---- 1 ~ - - 1 ) -- 0

i = 1

Reservoir engineers usually refer to this equation as R a c h f o r d - R i c e m e t h o d [ 1 ]. W h e n VF = 0, the fluid is a liquid at its bubble point (saturated liquid) a n d if VF = 1, the system is a vapor at its dew point (saturated vapor). Correct solution of Eq. (9.4) should give positive values for all x~ a n d Yi, which m a t c h the conditions ~ xi = ~_, yi = 1. The following step-by-step p r o c e d u r e can be used to calculate VF:

1. Consider the case that values of zi (feed composition), T, and P (flash condition) are known.

2. Calculate all Ki values a s s u m i n g ideal solution (i.e., using Eqs. 6.198, 6.202, or 6.204). In this w a y knowledge of x4 and Yi are not required.

3. Guess an estimate of VF value. A g o o d initial guess m a y be calculated f r o m the following relationship [2]: VF = A/

(A - B), where A = ~ [ z i (Ki - 1)] and B = ~ [ z i ( K i - 1)/

Ki].

4. Calculate F ( V ) f r o m Eq. (9.4) using a s s u m e d value of VF in Step 3.

5. If calculated F(VF) is smaller t h a n a preset tolerance, e (e.g., 10-15), then a s s u m e d value of VF is the desired an- swer. If F(VF) > e, then a n e w value of VF m u s t be calculated f r o m the following relation:

F(VF)

( 9 . 5 ) V / ~ e w = V F dF(VF)

dVr

In w h i c h dF(VF)/dVF is the first-order derivative of F(VF) with respect to VF.

d F ( V F ) - L { z i ( K i - 1 ) 2 ] (9.6) d ~ - - i = 1 [VF~i---ii-+ 1] 2

The p r o c e d u r e is repeated until the correct value of VF is obtained. Generally, if F (VF) > O, VF m u s t be reduced a n d if F(VF) < O, V~ m u s t be increased to a p p r o a c h the solution.

6. Calculate liquid composition, xi, f r o m Eq. (9.3) a n d the vapor phase composition, Yi, f r o m Eq. (9.1).

9. A P P L I C A T I O N S : P H A S E E Q U I L I B R I U M C A L C U L A T I O N S 3 6 9

FIG. 9.3~Schematic of a three-stage separator test in a Middle East production field,

7. C a l c u l a t e Ki values f r o m a m o r e a c c u r a t e m e t h o d u s i n g xi and yi c a l c u l a t e d in S t e p 6. F o r e x a m p l e , Ki c a n b e calcu- l a t e d f r o m Eq. (6.197) b y a c u b i c e q u a t i o n of state (i.e., S R K EOS) t h r o u g h c a l c u l a t i n g ~/L a n d ~v u s i n g Eq. (6.126). Sub- s e q u e n t l y fL a n d f/v c a n be c a l c u l a t e d f r o m Eq. (6.113). F o r i s o t h e r m a l flash w e m u s t have

(9.7) ~.~ - 1 < e

i=1 ~ f/

w h e r e e is a c o n v e r g e n c e tolerance, (e.g., 1 • 10-13).

8. R e p e a t a n e w r o u n d of c a l c u l a t i o n s f r o m S t e p 4 w i t h calcu- l a t e d V~ f r o m t h e p r e v i o u s r o u n d u n t i l t h e r e is no c h a n g e in values of VF, Xi, a n d Yi a n d i n e q u a l i t y (9.7) is satisfied.

Various o t h e r m e t h o d s o f flash c a l c u l a t i o n s for fast convergence are given in different r e f e r e n c e s [ 1 4 ] . F o r e x a m p l e , W h i t s o n [1] suggests t h a t the initial guess for VF m u s t b e b e t w e e n two values of VF,mi n a n d VF,m~x to o b t a i n fast convergence. M i c h e l s e n also gives a stability test for flash calculations [5, 6]. A c c u r a c y of r e s u l t s of VLE c a l c u l a t i o n s l a r g e l y d e p e n d s o n the m e t h o d u s e d for e s t i m a t i o n of Ki values a n d for this r e a s o n r e c o m m e n d e d m e t h o d s in Table 6.15 c a n be u s e d as a guide for selection o f a n a p p r o p r i a t e m e t h o d for VLE calculation. A n o t h e r i m p o r t a n t f a c t o r for the a c c u r a c y of VLE c a l c u l a t i o n s is the m e t h o d of c h a r a c t e r i z a t i o n of C7+

f r a c t i o n of the p e t r o l e u m fluid. A p p l i c a t i o n of c o n t i n u o u s functions, as it w a s s h o w n in S e c t i o n 4.5, c a n i m p r o v e results of calculations. The i m p a c t o f c h a r a c t e r i z a t i o n on p h a s e be- h a v i o r o f r e s e r v o i r fluids is also d e m o n s t r a t e d in S e c t i o n 9.2.3.

The a b o v e p r o c e d u r e c a n be easily e x t e n d e d to LLE o r v a p o r - l i q u i d - l i q u i d e q u i l i b r i u m (VLLE) in w h i c h two i m m i s c i b l e liquids a r e in e q u i l i b r i u m w i t h t h e m s e l v e s a n d t h e i r v a p o r p h a s e (see P r o b l e m 9.1).

Once value of lie is c a l c u l a t e d in a VLE flash c a l c u l a t i o n , the g a s - t o - l i q u i d r a t i o (GLR) o r gas-to-oil r a t i o (GOR) c a n b e c a l c u l a t e d f r o m t h e following r e l a t i o n [7]:

(9.8) G O R [ s c f / s t b ] = 1.33 x 105pLVF

(1 - VF)ML

w h e r e PL (in g/cm 3) a n d ME (in g/mol) a r e t h e d e n s i t y a n d m o l e c u l a r w e i g h t of a l i q u i d p r o d u c t , respectively (see Prob- l e m 9.2). The b e s t m e t h o d o f c a l c u l a t i o n of PL for a l i q u i d m i x t u r e is to c a l c u l a t e it t h r o u g h Eq. (7.4), u s i n g p u r e c o m p o - n e n t l i q u i d densities. If t h e l i q u i d is at a t m o s p h e r i c p r e s s u r e a n d t e m p e r a t u r e , t h e n PL c a n b e r e p l a c e d b y l i q u i d specific gravity, SG~, w h i c h m a y also be c a l c u l a t e d f r o m Eq. (7.4) a n d c o m p o n e n t s SG values. The m e t h o d of c a l c u l a t i o n s is d e m o n - s t r a t e d in E x a m p l e 9.1.

E x a m p l e 9.1 (Three-stage surface s e p a r a t o r ) - - S c h e m a t i c o f a t h r e e - s t a g e s e p a r a t o r for analysis of a r e s e r v o i r fluid to p r o - d u c e c r u d e oil is s h o w n in Fig. 9.3. The c o m p o s i t i o n of reservoir fluid a n d p r o d u c t s as well as GOR in e a c h stage a n d t h e overall G O R are given in Table 9.1. Calculate final c r u d e c o m - p o s i t i o n a n d the overall G O R f r o m a n a p p r o p r i a t e model.

Solution--The first step in c a l c u l a t i o n is to express t h e C7+

f r a c t i o n i n t o a n u m b e r o f p s e u d o c o m p o n e n t s w i t h k n o w n TABLE 9.1--Experimental data for a Middle East reservoirfluid in a three-stage separator

test. Taken with permission from Ref. [7].

1st-Stage 2nd-Stage 3rd-Stage 3rd-Stage

No. Component Feed gas gas gas liquid

1 N2 0.09 0.77 0.16 0.15 0.00

2 CO2 2.09 4.02 3.92 1.41 0.00

3 H2S 1.89 1.35 4.42 5.29 0.00

4 H20 0.00 0.00 0.00 0.00 0.00

5 C1 29.18 63.27 31.78 5.10 0.00

6 C2 13.60 20.15 33.17 26.33 0.19

7 C3 9.20 7.56 18.84 36.02 1.88

8 n-C4 4.30 1.5 4.14 13.6 3.92

9 i-C4 0.95 0.43 1.24 3.62 0.62

10 n-C5 2.60 0.36 0.92 3.50 4.46

11 i-C6 ! .38 0.24 0.63 2.46 2.11

12 C6 4.32 0.24 0.57 2.09 8.59

13 C7+ 30.40 0.11 0.21 0.43 78.23

SG at 60~ 0.8150

Temp, ~ F 245 105 100 90 90

Pressure, psia 2387 315 75 15 15

GOR, scf/stb 850 601 142 107

3 7 0 C H A R A C T E R I Z A T I O N A N D P R O P E R T I E S O F P E T R O L E U M F R A C T I O N S

TABLE 9.2--Characterization parameters of the C7+ fraction of sample of Table 9.1 [7].

Pseudocomponent mol% wt% M SG Tb, K n20 Nc P% N% A%

C7+ (1) 10.0 12.5 110 0.750 391.8 1.419 8 58 22 20

C7+ (2) 9.0 17.1 168 0.810 487.9 1.450 12.3 32 35 33

C7+ (3) 7.7 23.1 263 0.862 602.1 1.478 19.3 17 37 46

C7+ (4) 2.5 11.6 402 0.903 709.0 1.501 28.9 6 34 60

C7+ (5) 1.2 8.2 608 0.949 777.6 1.538 44 0 45 55

Total C7+ 30.4 72.5 209.8 0.843 576.7 1.469 15.3 25 34 41

E x p e r i m e n t a l v a l u e s o n M7+ a n d SG7+. D i s t r i b u t i o n p a r a m e t e r s (for Eq. 4.56) a n d c a l c u l a t e d values: M7+ = 209.8; Mo = 86.8; So = 0.65; $7+ = 0.844; BM = 1; As = 0.119; n7+ = 1.4698; AM = 1.417; Bs = 3; May = 209.8; Say = 0.847.

characterization parameters (i.e., M, Tb, SG, n2o, Nc, and PNA composition). This is done using the distribution model described in Section 4.5.4 with M7+ a n d SG7+ as the input parameters. The basic p a r a m e t e r s (Tb, n20) are calculated f r o m the m e t h o d s described in Chapter 2, while the PNA composition for each p s e u d o c o m p o n e n t is calculated f r o m m e t h o d s given in Section 3.5.1.2 (Eqs. 3.74-3.81). The calculation results with distribution p a r a m e t e r s for Eq. (4.56) are given in Table 9.2. Molar and specific gravity distributions of the C7+

fraction are s h o w n in Fig. 9.4. The PNA c o m p o s i t i o n is needed for calculation of properties t h r o u g h p s e u d o c o m p o n e n t ap- p r o a c h (Section 3.3.4). S u c h i n f o r m a t i o n is also needed w h e n a simulator (i.e., E O R software) is used for phase behavior calculations [9].

To generate the composition of gases a n d liquids in separators, see Fig. 9.3, the feed to the first stage is considered as a mixture of 17 c o m p o n e n t s (12 c o m p o n e n t s listed in Table 9.1 a n d 5 c o m p o n e n t s listed in Table 9.2). For pure com- p o n e n t s (first 11 c o m p o n e n t s of Table 9.1), Tc, Pc, Vc, a n d to are taken f r o m Table 2.1. For C 6 fraction (SCN) a n d C7+ fractions (Table 9.3) critical properties can be obtained f r o m m e t h o d s of Chapter 2 (Section 2.5) or f r o m Table 4.6. For this example, Lee-Kesler correlations for calculation of To, Pc, a n d to and R i a z i - D a u b e r t correlations (the API methods) for calculation of Vc and M (or Tb) have been used. The b i n a r y interaction parameters (BIPs) for n o n h y d r o c a r b o n - h y d r o c a r b o n are taken f r o m Table 5.3 a n d for h y d r o c a r b o n - h y d r o c a r b o n pairs are calculated f r o m Eq. (5.63). P a r a m e t e r A in this equation has been used as an adjustable p a r a m e t e r so that at least one predicted property matches the experimental data. This property can be saturation pressure or a liquid density data. For this calculation, p a r a m e t e r A was d e t e r m i n e d so that predicted liquid specific gravity f r o m last stage m a t c h e s experimental value of 0.815. Liquid SG is calculated f r o m Eq. (7.4) using SG of all c o m p o n e n t s in the mixture. It was f o u n d that w h e n A -- 0.18, a g o o d m a t c h is obtained. Another adjustable pa- r a m e t e r can be the BIP of m e t h a n e a n d the first p s e u d o c o m -

0.01 0.008 0.006

~" 0 . 0 0 4 0.002 0

FIG.

0 200 400 600 800

9.4~Probability density 4 3

~ 2

0.6 0.8 1 1.2 1.4 SG functions for molecular weight and specific gravity of the C7+ fraction given in Table 9.2 [8].

p o n e n t of heptane-plus, C7(1). The value of BIP of this pair exhibits a m a j o r i m p a c t in the calculation results. Ki values are calculated f r o m S R K EOS and flash calculations are per- f o r m e d for three stages s h o w n in Fig. 9.3. The liquid p r o d u c t f r o m the first stage is used as the feed for the second stage separator and flash calculation for this stage is p e r f o r m e d to calculate composition of feed for the last stage. Similarly, the final crude oil is p r o d u c e d f r o m the third stage at atmo- spheric pressure. Composition of C7+ in each stream can be calculated f r o m s u m of mole fractions of the five p s e u d o c o m - ponents of C7i. GOR for each stage is calculated f r o m Eq. (9.8).

S u m m a r y of results are given in Table 9.3. Overall GOR is calculated as 853 c o m p a r e d with actual value of 850 scf/stb. This is a very g o o d prediction mainly due to adjusting BIPs with liquid density of p r o d u c e d crude oil. The calculated compositions in Table 9.3 are also in g o o d a g r e e m e n t with actual data of Table 9.1.

The m e t h o d of characterization selected for t r e a t m e n t of C7+ has a m a j o r i m p a c t on the results of calculations as s h o w n by Riazi et al. [7]. Table 9.4 shows results of GOR calculations for the three stages f r o m different characterization methods. In the Standing method, Eqs. (6.204) a n d (6.205) have been used to estimate K/values, assuming ideal solution mixture. As s h o w n in this table, as the n u m b e r of p s e u d o c o m - p o n e n t s for the C7+ fraction increases better results c a n be

obtained. #

9.2.2 B u b b l e a n d D e w P o i n t s C a l c u l a t i o n s

Bubble point pressure calculation is p e r f o r m e d t h r o u g h the following steps:

1. Assume a liquid mixture of k n o w n xi a n d T is available.

2. Calculate plat (vapor pressure) of all c o m p o n e n t s at T f r o m m e t h o d s described in Section 7.3.

3. Calculate initial values of Yi and Pbub f r o m Raoult's law as P = ~-~ x/Pi sat a n d Yi = xipsat/p.

4. Calculate Ki f r o m Eq. (6.197) using T, P, xi, a n d Yi.

5. Check if 1~ xiK,- - 1 [ < e, where e is a convergence tolerance, (e.g., 1 x 10 -12) and then go to Step 6. If not, repeat calculations f r o m Step 4 by guessing a n e w value for pressure P and yi = Kixi. If ~ x i K i - 1 < 0, reduce P a n d if

xiKi - 1 > 0, increase value of P.

6. Write P as the bubble point pressure and yi as the composition of vapor phase. Bubble P can also be calculated t h r o u g h flash calculations by finding a pressure at w h i c h Vr ~ 0. In bubble T calculation x4 and P are known. The calculation p r o c e d u r e is similar to bubble P calculation m e t h o d except that T m u s t be guessed instead of guessing P.

9. A P P L I C A T I O N S : P H A S E E Q U I L I B R I U M C A L C U L A T I O N S 3 7 1 TABLE 9.3---Calculated values for the data given in Table 9.1 using proposed characterization

method. Taken with permission from Ref [7].

No. Component Feed 1 st-Stage gas 2nd-Stage gas 3rd-Stage gas 3rd-Stage liquid

1 N2 0.09 0.54 0.12 0.05 0.00

2 CO2 2.09 3.91 4.09 1.44 0.02

3 H2S 1.89 1,47 4.38 5.06 0.14

4 H20 0.00 0.00 0.00 0.00 0.00

5 C1 29.18 64.10 32.12 5.68 0.03

6 C2 13.60 19.62 32.65 25.41 0.38

7 Ca 9.20 7.41 18.24 35.47 3.05

8 n-C4 4.30 1.48 4.56 13.92 4.38

9 i-C4 0.95 0.41 1.23 3.47 0.78

10 n-C5 2.60 0.36 1.01 3.98 4.81

11 i-C6 1.38 0.24 0.68 2.61 2.37

12 C6 4.32 0.27 0.61 2.22 9.01

13 C7+ 30.40 0.19 0.31 0.69 75.03

SG at 60~ 0.8105

Temp,~ 245 105 100 90 90

Pressure, psia 2197 315 75 15 15

GOR, scf/stb 853 580 156 117

F o r v a p o r s of k n o w n c o m p o s i t i o n d e w P o r d e w T c a n b e c a l c u l a t e d as o u t l i n e d below:

1. A s s u m e a v a p o r m i x t u r e of k n o w n Yi a n d T is available.

2. Calculate P y ( v a p o r p r e s s u r e ) of all c o m p o n e n t s a t T f r o m m e t h o d s of S e c t i o n 7.3.

3. Calculate initial values of xi a n d Pdew f r o m Raoult's l a w as 1/P = ~_, yi / P~ sat a n d x / = yi P / P~ sat.

4. Calculate Ki f r o m Eq. (6.197), u s i n g T, P, xi, a n d Yi.

5. Check if ]~]yi/Ki - 11 < e, w h e r e e is a c o n v e r g e n c e tolerance, (e.g., 1 x 10 -lz) go to S t e p 6. If not, r e p e a t cal- c u l a t i o n s f r o m S t e p 4 b y guessing a n e w value for pres- s u r e P a n d x~ = yi/Ki. If ~ , y i / K i - 1 < O, i n c r e a s e P a n d if

~ y i / K i - 1 > O, d e c r e a s e value of P.

6. W r i t e P as t h e d e w p o i n t p r e s s u r e a n d xi as the c o m p o s i t i o n o f f o r m e d l i q u i d p h a s e .

Dew P c a n also be c a l c u l a t e d t h r o u g h flash c a l c u l a t i o n s b y finding a p r e s s u r e at w h i c h VF = 1. I n d e w T c a l c u l a t i o n Yi a n d P are k n o w n . The c a l c u l a t i o n p r o c e d u r e is s i m i l a r to d e w P c a l c u l a t i o n m e t h o d e x c e p t t h a t T m u s t b e g u e s s e d in- s t e a d of guessing P. I n this case if ~ 3#/Ki - 1 < O, d e c r e a s e T a n d if ~ y i / K i - 1 > O, i n c r e a s e T. B u b b l e a n d d e w p o i n t c a l c u l a t i o n s a r e u s e d to c a l c u l a t e PT d i a g r a m s as s h o w n in t h e next section.

R e s e r v o i r e n g i n e e r s u s u a l l y use e m p i r i c a l l y d e v e l o p e d cor- r e l a t i o n s to e s t i m a t e b u b b l e a n d d e w p o i n t s for r e s e r v o i r fluid m i x t u r e s . F o r example, S t a n d i n g , Glaso, a n d Vazquez a n d Beggs c o r r e l a t i o n s for p r e d i c t i o n of b u b b l e p o i n t p r e s s u r e o f r e s e r v o i r fluids are given in t e r m s o f t e m p e r a t u r e , GOR, gas specific gravity, a n d s t o c k t a n k oil specific gravity (or API

gravity). These c o r r e l a t i o n s are w i d e l y u s e d b y r e s e r v o i r engineers for q u i c k a n d c o n v e n i e n t c a l c u l a t i o n o f b u b b l e p o i n t p r e s s u r e s [1, 3, 10]. The S t a n d i n g c o r r e l a t i o n for p r e d i c t i o n o f b u b b l e p o i n t p r e s s u r e is [1, 3]

Pb(psia) = 18.2(a x l 0 b - 1.4) a = ( G O R / S G g a s ) 0"83 (9.9)

b = 0 . 0 0 0 9 1 T - 0.0125 (APIofl)

T = T e m p e r a t u r e , ~

w h e r e / ~ is the b u b b l e p o i n t p r e s s u r e , SGgas is the gas specific gravity ( = Mg/29), APIoil is the API gravity of p r o d u c e d l i q u i d c r u d e oil at s t o c k t a n k c o n d i t i o n , a n d G O R is t h e s o l u t i o n gas- to-oil r a t i o in scf/stb. Use of this c o r r e l a t i o n is s h o w n in the following example. A d e v i a t i o n o f a b o u t 15% is expected f r o m the a b o v e c o r r e l a t i o n [3]. M a r h o u n d e v e l o p e d the following r e l a t i o n for c a l c u l a t i o n of Pb b a s e d o n PVT d a t a of 69 oil s a m p l e s f r o m the M i d d l e E a s t [10]:

Pb(psia) = a (GOR) b (SGgas) c (SGoiI) d ( T ) e

(9.10) a = 5.38088 • 10 -3 b = 0.715082 c = - 1 . 8 7 7 8 4 d = 3.1437 e = 1.32657 T = t e m p e r a t u r e , ~ w h e r e SGoi I is t h e specific gravity o f stock t a n k oil a n d G O R is in scf/stb. The average e r r o r for this e q u a t i o n is a b o u t 4-4%.

E x a m p l e 9 . 2 - - C a l c u l a t e b u b b l e p o i n t p r e s s u r e o f r e s e r v o i r fluid o f Table 9.1 at 245~ f r o m the following m e t h o d s a n d c o m p a r e t h e results w i t h a n e x p e r i m e n t a l value of 2387 psia.

TABLE 9.4--Calculated GOR from different C7+ characterization methods. Taken with permission

Method Input for C7+

Lab data

Proposed M7+ a n d SG7+

Standing (Eqs. 6.202 MT+ and SG7+

and 6.203)

Simulation 1 a Nc & Tb

Simulation 2 Nc & Tb

Simulation 3 M & PNA

Simulation 4 M & PNA

from Ref [7].

No. of C7+ Overall GOR,

~a~ions scffs~ Stage 1 Stage 2 Stage 3

850 601 142 107

5 853 580 156 117

1 799 534 134 131

1 699 472 141 86

5 750 516 142 92

1 779 542 142 95

5 797 559 143 95

aCalculations have been performed through PR EOS using a PVT simulator [9].

372 C H A R A C T E R I Z A T I O N A N D P R O P E R T I E S OF P E T R O L E U M FRACTIONS a. Thermodynamic model with use of SRK EOS similar to the

one used in Example 9.1.

b. Standing correlation, Eq. (9.9).

c. Mahroun's correlation, Eq. (9.10).

Solutions(a) The saturation pressure of the reservoir fluid (Feed in Table 9.1) at 245~ can be calculated along flash calculations, using the method outlined above. Through flash calculations (see Example 9.1) one can find a pressure at 245~ and that the amount of vapor produced is nearly zero (V~ -~ 0). The pressure is equivalent to bubble (or saturation) pressure. This is a single-stage flash calculation that gives psat = 2197 psia, which differs by - 8% from the experimental value of 2387 psia. (b) A simpler method is given by Eq. (9.9).

This equation requires GOR, APIoi], and SGga~. GOR is given in Table 9.1 as 850 scf/sth. APIofl is calculated from the specific gravity of liquid from the third stage (SG = 0.815), which gives APIo~ = 42.12. SGg~s is calculated from gas molecular weight, Mg~s, and definition of gas specific gravity by Eq. (2.6). Since gases are produced in three stages, Mgas for these stages are calculated from the gas composition and molecular weights of components as 23.92, 31.74, and 44.00, respectively. Mga~ for the whole gas produced from the feed may be calculated from GOR of each stage as Mg~, = (601 x 23.92 + 142 x 31.74 + 107 • 44.00)/(601 + 142 + 107) = 27.76. SGg~ = 27.76/29 = 0.957. From Eq. (9.9), A = 139.18 and Pb = 2507.6 psia, which differs by +5.1% from the experimental value. (c) Using Marhoun's correlation (Eq. 9.10) with T = 705~ SGoij = 0.815, SGgas = 0.957, and GOR = 850 we get Pb = 2292 psia (error of -4%). In this example, Marhoun's correlation gives the best result since it was mainly developed from PVT data

of oils from the Middle East, r

THERMODYNAMIC RELATIONS FOR PROPERTY ESTIMATIONS 247