Contents--------~~~~~~~~~--------------------------------------------t_-------.r".cfiaf T R, Imp Iying a dissolved gas drive resenoir.bon Production and Separation

in-.~itu

ReserVOir 2, occurring in the two-phase region, is an oil reservoir with an initiaJ gas cap. With declining pressure, COR increases, and the reservoir flUid Composition changes. Reservoir 3. OCCurring in the retrograde region, is a gas condensate reservoir. On pressure reduction. liquid begins to condense at and beyond the dew-point Curve, Since it clings to the pore spaces in the resenoir, a Critical saturation has to be bUilt up before it can flo\.\.- toward the weJlbore, Thus, the producing COR (at the surface) increases, The intermediates that condense out of the gas are verr valuable and their loss is a serious affair. How_ ever, as pressure is reduced further, the liquid begins to revaporize into the gaseous phase, This revaporization aids liquid recovery and, assuming that the '''''"voi, flUid oomposition oonstant, may lead to a decline in the producing GOR at the su,face, The """"'oi, fluid oomposition, howeve" changes as retrograde condensation OCCUrs: the p- T phase envelope shifts to the right, increasing retrograde liqUid condensation into gas, This retrograde 'ross" is greater for a greater shift of the p_ T phase envelope to the right, lower reservoir temperature, and higher abandonment pressure. ReserVOir 4, OCCurring in the single-phase gas region, is a true gas reservoir. It is generally known as a wet gas reservoir if 4 is inside the moo-phase J region, Or as a dry gas reservoir if 4. is in the single-phase gas region. In this reservoir type, the reservoir (point 4,) is aJwars in the single-phase gas region, of the pressure. So, the reservoir fluid maintains a constant composition since there is no change of phase in the reservoir. The prodUCing COR for a reservoir is an exOOlent indication of the reservoir tYPe. Cenerally, a reservoir is claSSified as a gas reservoir if the GOR> 100,000 scflSib, "an oil """"'oi, if the GOR < 5,000, and as a gas condensate reservoir if the GOR is between 5,000 to 100,000 scf/stb. The relationship between the critical temperature, T , and the reservoir t temperature, T R, determines whether retrograde condensation OCCUrs or not. For retrograde condensation to OCCur, the reservoir temperature must be in between the Critical temperature and the cricondentherm. ReserVoir systems in Single phase with a surface COR::> 10,000 scf/stb are likely to have a high C, fraction, and consequentJy, a low T Expect retrograde cont densation for such reservoirs, Reservoir systems in single phase that exhibit a

g",e~ften

~

to the gas, andhto optimization of h d arbons For tees 'I'b . parameters m );e::t ph"'; behavio, and gas-oil the of the p>;. ce the phase relationsh,ps ace a unc uipment that is op"mum fluid, we can nevee ,eall, it for the "avmge" all conditions. The onlf'h f.lI~:r to cha~e the installation at some POlOt ed the life 0 t e Ie , d so expect it over become econom icalJy attractive to 0 . where may

~:m

Hydrocar f 'I'res depends upon the nd surface .aCI hase gas and oi I Wit a I, 'h d' of the producing weII a , The ""gn 'rod ced' gas 0.1,0< tM-P h d a bons ature of the fluid bemg p uf 't Since the inte,mediate y coc , I n. COR and the presence 0 \\-a cr. ts it is highl) desirable not to ose the most valuable - uid as possible fcom the p,oduced

d~gn~e::~ ;;rat;~nald~~~",(

''Ompon~J'

d~:OO

(m :io~u07

oompositio~

~e:s~'~~,~:

u~d", oond,"~n

G

Processing and Transport

regardJ~

, nds from the gas so that the g:" It may. be n""""",)' to remo,'e heaVIer e pressure- temperature changesI10 " ted does not condense liquids upon ahnhCd'PI"ang s)'stems. 10 enable suc~ c~dslcu ad ng an an be k LlqUl aecune fo, ; ; ; in the lines, in the piping :,',:,,,,,, of the instability caused by and are genmll, undes"a e f p,""ure and tempeca'ure, 'cs changes occurring as a befunc"on t~ ne'" the phase envelope boun a~, eq uipment must never opera ature or composition can cause IS. ressure temper where small changes 10 p i~ vapor-liquid, ratio, proportionately large changes

as

cum~ate

:~ensrr:~~:::'t::="po;nt

s)~te~s,

~~~;~~~a~;:;"ure

ph~.:: P''''';''

I

. , . ReserVOir Engmccnng and Enhanced Oil Recovery . h as reservOir reserve estimates, . Reservoir engineering calculahons, su~ rs require reliable phase behavpredictions, and simulations uSin~,ooalmih~~ i~ miscible enhanced 7~"'y ior data. Nowhere is it more ,cn IC urate hase equilibrium re atJontechniques, where highly deta'~dede :::g::f conltions, The perfbe0rm~n~l~f ' be known over a WI , 'ected fluid to mLSCI . horls depends upon the ability of the InJ . fluid The injection ships must these met , 'bTty with the ..,.,vo" , , 'b ' m or be able to generate mLSC1, I I , ts dictated solely by phase eqUlh nu . fluid must be tailored to reqUiremen

I

3'

Gas Producti()n Enginnring

Phose Behavior FrmdafflCfllais

35

Prediction of the Phase Envelope

Tt: - molar a,erage boiling point o( mixture, O R ~ - mole (raction of 100"'-boiling component The calculation prooedure is quite tedious. The mixture composition. pure component critical temperatures, and normal boiling points are require(l. Values for T b can be calculated using a mixing rule, or obtained from laboratory measurements. One proceeds by taking two successive components. calculating their T, and T p values, then adding one component at a time and calculating the Tt and T p values for this new mixture until all the components ha,e been included. Grieves and Thodos (1963) report maximum errors of less than 5% in cricondentherm, but significantly larger errors up to 13 % for cricondenbar temperatures. Such a correlation is dificult to use, and the results are not very reliable.

To accurately predict the phase envelope for a muiticomponent hydrocarbon system such as oil or gas is almost impossible. Experimental means must be used, since imprecise results can be quite dangerous to use in the innumerable planning. desi~, and operational problems. However, it becomes \'ery necessary to use correlations and predictive methods in many instances where such studies cannot be readily performed. A'i a bare minimum. an accurate compositional analysis of the reservoir fluid is essential. Estimates of the critical point. the cricondentherm. and cricondenbar can then be used in conjunction with ,,'apor-liquid equilibrium

calculations for bubble-point and dew-point curves to generate reasonable phase equilibrium curves. Sometimes, only a portion of the phase curves rna)" be required. Cricondcntherm and CriCQndenbar Grieves and Thodos ( 1963) presented the following equations for the prediction of cricondentherm temperatures:(2-18)

Critical Point Many different studies have focused on the problem of characterizing hydrocarbons for predictions of their physical properties. Watson and Nelson (1933) and Watson et al. (1935) characterized the chemical makeup of petroleum mixtures using the boiling point and specific gravity. They defined the Watson characterization factor, K. as follows:(2-22)

and Tt/T; ""'(T~Tb

- l)(e6 31 gas OCCUpies 378.6 ft1 at 14.73 psia and 60F (5200R).R - pV'nT - (14.73 x 378.6)/(1 x 520) "" 10.732 (psia ft1)/(lbmole OR)

nZRT

(3-2)

Thus, if p is in psia T is in OR and V' . ft1 t h R is 10.732 psia-ft1:lbmole-0R' I 51 IS.IO "h en t.h~ appropriate value of V' . . n umts,w erepISm kPa T" K d IS 10 m-', the value of R to use is 8.314 kPa-mJ'"kgmole-K.' IS In ,an Behavior of Real Cases In general, gases do not exhib't 'd al beh . tion from ideal behavior can bel I e -, __~Vlor. The reasons for the deviasumma.1L.C'.! as follows; 1. Molecules for even a spa~ S\'Stem . such as gas, occupy a jnite volume. . 2. Intermolecular forces are exerted bern'een the these forces are: molecules. Some ofic !i'ec:rostTa'h forces. also called Coulomb forces, betv.een ions and po es. ese are long-range forees. [~d~ced fO.rees between a dipole and an induced dipole, for examp e In a mlXture of a polar and a non-polar gas Attraction/repulsion fo h' h . short distances ani T~ w IC a~ generally exerted over very I y. ese forees eXISt even for a perfectly non~ po ar gas such as argon.

The Z-factor can therefore be considered as being the ratio of the volume occupied by a real gas to the volume occupied by it under the same presure and temperature conditions if it were ideal. This is the most widely used real gas equation of state. The major limitation is that the gas deviation factor, Z, is not a constant. Numerous attempts have been made to define the functional dependence of Z on various other parameters that define the state of the system, and se\'eral correlations are available for the Z-factor as a result of these studie;. More complex equations of state that do not represent the deviation through the Zfactor, but through other correlation constants, are often used to derive quite precise Z~factor values that can be used in Equation 3-2.

\an der \\aals EquationThis equation is probably the most basic EOS and, though seldom used today, it serves as a conceptual basis for understanding and developing other equations. It corrects for the volume occupied by the molecule; in a gas, by using v - B as the true gas volume. instead of v; and loss in pressure exerted 2 by the gas due to attractive forces and inelastic collisions, by using p + Alv as the true pressure. (p + A/")(v - 8) - RT(3-3)

where A and B are empirical constants. This equation serve; as a good approximation only for low pressures. It can also be written as:.. _ (RT

3. Molecular collisions are never perfectly elastic.

+ Bp)v'/p + (A/p)v - AB/p - 0

(3-4)

'2

Go, Production Enginring

Propntie6 oj Natural Cases

43

or, in terms of the Zfactor as:Z3 _ Z2(1

Waals equation, which makes it applicable in developing gencral correlations in terms of reduced variables.(~5)

+ SpiRT) + Z Apl(RT)2 - ABp'l/(RT)3 - 0

p .. RTd + (B"RT - ~ - Co/r.)d Z + (bRT - a)d J + aad6 At the critical point, the three roots of the cubic equation in v (Equation 3-4) are identical. Thus. if \'~ represents the critical volume, then at the critical point:(3-6)

+ (00'11')[(1 + ,d') exp( - ,d')]

(3-10)

where a. b, c. a, -y, ~. Bo. and Co are constants for a gi\"cn ~as_ d is the molar density (lbmole/ft3), and p, T are the absolute pressure and temperature. respectively.Redlich-Kwong Equation

Comparing Equations 3-4 and 36. it can easily be shown that:(3-7) Redlich and K\\'ong (1949) proposed the following equation: An alternative procedure for obtaining the values for A, B. and R is to use the fact that the critical isotherm, that is, the curve relating pressure and volume al the critical temperature. must show an inflexion point:(3-8)

RT A P .. v - B - '}"Q.~(" + B)

(3-11)

These conditions are known as the Van der Waals conditions for the critical point. The first and second partial diHerentials of Equation 3-4 with ~pect to v would yield the results shown in Equation 3-7 upon substitution of parameter \'aJues relevant to the critical point and use of Equation 3-8. Van der Waals equation may be written in the reduced form by substituting the values for A. Band R from Equation 3-7 into Equation 3-3:

where A and B are constants. Other details \\ill be discussed later. The Redlich-Kwong (RK) equation, along with modifications by Zudke\'itch and Joffe (1970) and Joffe et al. (1970) (ZJRK). and by Soavc (1972) (SRK), is widely used.PeJlg-Robin!lOn Equation

Another \..idely used equation is the Peng and Robinson (1976) (PR) equation:

RT A p- - - \" - B v(v + B) + B(,

B)

(3-12)

thill, [po + 3/,,][3v, - lJ - ST,Benedict- "ebb-Rubin Equation

(3-9)

where A and B are functions of temperature. Note that the RK and PH equations cannot be written explicitly in the reduced form. A General Form for Cubic Equations of State

This equation was developed by Benedict et al. (1940) for describing the behavior of pure, light hydrocarbons. It has found a lot of application in computing thermodynamic properties and phase equilibria for gases due to two reasons: it gi\'es sufficient accuracy for natural gases, since natural gases are a mixture of light hydrocarbons for which this equation was originally developed; and it can be written explicitly in the reduced form, like Van der

Martin (1979) showed that all cubic equations of state can be represented in the following general form:

RT arT) ofT) p - -;- - (v + ~)(v + -y) + ... (v + ~)(v + -y)

(3-13)

.where

Go.! Production Engineering

Propertiet of Natural GaUl

45

where cr and {) are functions of temperature, and R and l' are constants. Coats (1985) presents the following equivalent form of Martin's equation,with {) .. 0:

Zl + [(rn, + ffi2 - 1)8 - IJ Z2 + [A + - (m, + m,)(B + I)B) Z - (AB + ffilffiZBZ(B + I)) .. 0A ..

ffi,ffi Z B2

(3- 14) (3- 15a) (3-15b) (3-15c) (3-1Sd) (3- 15e)

r:r. r:r _ x,xkAi~I I

where p.,. is the vapor pressure of the f1LLid at a temperature of o. 7Te and Pc is its critical pressure. As expected, w is equal to zero for noble gase;: like argon, and is close to zero for gases like methane. In the$e equations, putting m, .. 0 and ffi2 .. 1, yields the RK or SRK equations. For the PR equation, m, = 1 + ~!i, and m2 .. 1 - 2

Critical Pressure and Temperature Determination For pure components, physical property data are readily available. Table 3-1 shows critical temperatures (T...;), pressures (Pc.:). and other useful properties of typical components in hydrocarbon fluids. For mixtures, Kay's mixing rule can be used to find the effective critical properties:

the critical pressure and temperature from the gas gra\ity. Corrections may be made for the presence of non-hydrocarbon oomponents: Thomas et .al. (1970) took data from Figure 3-1 and other sources to obtam the followmg relationship: Ppc _ 709.604 - 58.718 "f, T pc" 170.491 + 307.344 "fit (3-20a)

(3- 19)where Pp..., T po: are the pseudocritical pressure and temperature, respectively, for the mixture, and r! is the mole fraction of component i in the mixture. These properties are termed "pseudo" because they are used as a correlation basis rather than as a very precise representation of mixture critical properties. Equation 2-23 in Chapter 2 can be used to predict the critical properties of a hydrocarbon fluid from its normal boiling point and gravity. IT the composition oflhe gas, {y;}. is not known , Figure 3-1 may be used to determine

(3-20b)

where "fl is the gas gravity with respect to air. Thomas et al. recommend the use of this equation in allowable limits of up to 3% H~, 5% Ni , or a total impurity (no n-hydrocarbon) content of 7%, beyond which errors in critical pressure exceed 6%. It should be noted that the gas gravity method of obtaining pseudocritical pressures and temperatures is not very acc:urate. 1 ~he analysis of the gas is available, it must be used in accordance With EquatIOn 3-19.

..

Ga., Producl/on Engineering

PropN'tie3 of Natural Gases

.9

Find the gas gravity. Also, find the critical pressure and critical temperature for this gas using (I) Kay's mixing rule, (2) Brown et al.'s method, and (3) Thomas et al.'s equations.

Solution~omp.

...iL0.9300 0.0329 0.0136 0.0037 0.0023 0.0010 0.0012 0.0008 0.0005 0.0140

M,16.043

k667.8 707.8 616.3 550.7 529.1 488.6 490.4 436.9 332.0 493.0

To 343.1 549.8 665.7 765.4

c, c,C,n-C 4 i-C 4

3O.0iO44.097 58.124 58.124 72.151 72.151 86.178 128.259 28.013

734.i845.4 828.8 913.4 1070.4 227.3

i-e.,CoC,.

n-e,N,

-

" 5~

M .. E y,M 1 ,. 17.54 The gas gravity 'Y& - 17.54/28.97,.. 0.6055 1. Ppc" I: YIPd - 664.47 psia

, u0~

,

Tpt - I: YiTe; _ 356.93 OR2. From Figure 3-1,

g "v"'~ GUVlfY

.." "

PI'" - 670 psia Tpt - 360 ORApplying the correction factor for 1.4 % N2,!'po 670 - 5 665

!"ia

"'I~' \

T,,' 360 - 5.355 OR3. Using Equation 3-20a:!'po - 709.604 - (58.718)(0.6055) 674.05 ps;a

Figure 3-1. PseudocriticaJ properties of miscellaneous natural gases and condensate flUids. (After Brown at aL, 1948; courtesy of GPSA.)

Example 3-1. The analysis of a sweet gas, in mole%, is known to be as follows: N2 .. lAO, CRt .. 93.0, CtHe" 3.29, 0

F ... ~'.. f

~""Pil '

c

o.ou