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COMPUTER CALCULATIONS OF COMPRESSIBILITY OF

NATURAL GAS

J.H. ABOU-KASSEM L.MATTAR P.M. DRANCHUK

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w h er e bo th P r an d 0. 2 70 ( ap r a p , D R a n d D P in b ot h th e Dr an c hu k et a l. a nd D ra n ch uk a nd A b ou - Ka ss e m Z - fa ct o r s u br ou t in es . T h i s m e th od i s i n co rp o - e xp r es s io ns f 'o r Z a n d r a te d i n to t he s e r o ut i ne s by a dd in g a si ng le F OR TR A N s ta t e- T m en t CR = 0 . 2 70 1( D R * D P) b e f or e t h e R E T UR N s t a te me n t. T hi s me th o d i s su it ab l ef o r c om p ut er a nd h an d- h el d c a lc u la to r a p pl ic a ti on s . I tp ro du ce s t he s a me r e du ce d c om pr es si bi li ty a s v al ue s o f T , a nd P , w he re 0 .7 J CP T9 0- 05 -1 0 T EC HN IC AL N OT E C om pu te r c al cu la ti on s o f c om pr es si bi li ty - o f n at ur al g as J .H . A BO U- KA SS EM T he P en ns yl va ni a S ta te U ni ve rs it y L . M AT TA R F ek et e A ss oc ia te s, I nc . a nd P .M . D R AN CH UK T he U ni ve rs it y o f A lb er ta A BS TR AC T - az / A + A 2 + A + 2 ( A , + A 5 P , a p,

, I An a lte rnat ive method for the calcula tion of pseudo reduced T T,T, compressib ili ty of natural gas i s presented. The method applies ap,@ 4+ 2

A exp(- A, (5) + 5 A6Pr3 P, l (I + A p2 2p4 P,2) TT r 8 1) the defin ition of reduced compressib ility, @ = - ( - ) ,

r P, ap, @ are variables available as Recently Chen and ZhOU(5) have presented a method of calcu- lating c, based on equation (2). They provided analytical ith applicability restricted to Z - 1. 1. These expressions were other available methods but is computationally superior. based on a truncated form of the Dranchuk etal.(4) Z-factor equation (i.e., A, A8 = 0) as follows, Methodology A2 A A A A The methods of calculating compressibility of natural gas are Z = I + + + )P, + (A + 1 )p2 + 7 p 2 .... (6) derived from the following relationship between c and Z: T, T3 4 T T3 T

r r I I az c = - - (- ).... ..... .... ..... .... ..... .... ..... .... ..... .... ..... .. p Z aP T and This equation may be expressed in ar e d uc e d f o r m a s : ( ') I Z " - - - . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. ( 2 ) Z . . .. . . .. . .. . . .. . . . ( 7 ) C r = P r Z ( ' a P r ) T .. . . .. . .. . . .. . . .. . . Z , + O P. .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . T w h e re w h er e C r = C P.. . . .. . .. . . .. . . .. . .. . . .. . . .. . .. . . .. . . .. . .. . . .. . . .. . .. . . .. . . .. . .. . . .. . . .. . .. . . ( 3 ) T r u b e( l ) pr e s en t e d a g r ap h i ca l c or r e la t i on o f c , a s a f u n c- 0 . 27 A 2

A3 A5 '7 )p2 tion of P, and T, based on equation (2) using the Brown e t- (A I + ++ 2 A + + ....... T T

4 T3 r] ai. (2) Z-factor chart. While this correlation is useful for handr calculation, it is not suited to computer usag e. Mattar et a l.(3) used the follo wing expression for c, that was based on the Although the last two methods are suited to computer usage; manipulation of equation (2) they require th e Dranchuk eta l.(4) Z-factor subroutine that cal- l 0.27 (aZIap,),, culates Z which in turn would be used to calculate p,. Both Z C2 = - - -

.. .... .... ..... ..... .... ..... .(4) and p , are use d in equ ation s (2), ( 4), (5) , (7) an d (8). Cl ose exa- P , Z2T, P , ( az ,mination of the Dranchuk et al .(1) Z-fac tor rout ine reveals that + - - th is routine solves for p, for a given T, and P, using thez 'ap') T, Newton-Rap@Lson iteration. The form of the e quation u sed i s An analy tical expression for (aZ/aP')T was ob tained f rom t he Dranchuk e t ai. (') Z-fac tor equation, P, = f(T ,,p ,).. ... .... ... .... ... ... .... ... .... ..(9)

P ap er re vi ew ed an d a cc ep te d f or pu bl ic at io n b y t he Ed it or ia l B oa rd of Th e J ou rn al of Ca na di an Pe tr ol eu m T ec hn ol og y. .. Se pt em be r- Oc to be r 1 99 0, Vo lu me 29 , N o. 5 1 05

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