COMPRESSIBILITY OF NATURAL GASES L. MATTAR G.S. BRAR K. AZIZ. this article begins on the next page

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Reynold York
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1 GAS TECHNOLOGY Compressibility of Natural Gases L. Mattar and G. S. Brar, Energy Resources Conservation Board, Calgary, Alberta, and K. Aziz, Professor, Department of Chemical Engineering, The University of Calgary, Calgary, Alberta Abstract A new correlation for the comprssibility of sweet and sour natural gases is presented. This correlation is derived from an equation of state which adequately represents the Standing-Katz Z-Factor chart. The algebraic expression for compressibility presented here is suitable for computer calculations. A FORTRAN subroutine to perform this computation is also presented along with a graphical form of correlation. Introduction IN THE PRESSURE ANALYSIS of transient or pseudo steady-state flow data acquired during gas well testing, a knowledge of the variation of fluid compressibility with pressure and temperature is essential. For liquid flow, the compressibility is small and is usually assumed to be constant. For gas flow, the compre-ssibility is neither small nor constant. In such a case, th(@ ideal gas law assumption that compressibility equals 1/pressure is often made. However, this assumption. is neither valid nor necessary for natural gases, I)because the compressibility of a real gas can be computed readily. Tritbe (.1957) has presented graphs from which the compressibility of natural gases may be obtained. This correlation is, however, difficult to use in a computer program. Ilecent developments have made possible a more consistent and convenient approach. The purpose of this paper, therefore, is to present an aiialvtical technique for calculating the compres- sibility of natural gases. The procedure may be read- ily c(@mputerized and was used to generate curves of pseudo-reduced compressibility, which are useful for manlit] calculations. Theory The isothermal compressibility, c, of a substance i.-, define(i as c E)V I... I... v I -ap The (-ompressibility factor, Z, of a substance is defined as: z (2) R T... The compressibility factor, Z, is a correction factor _ which defines the deviation of a real gas from ideal gas behaviour. It should not be confused with the com- pressibility, c, which is the isothermal coefficient of compression of any given substance. Equations (1) and (2) may be combined to give a relationship be- tween C alld Z: (3) 1 ap - I ZZ IT A pseudo-reduced compressibility, C., may be defined by mtiltirilying each term in Equation (3) by p.: 1- cp.... I.. (4) p@ For reasons that will become clear in subsequent discus- sions, it is necessary to express c, as a funtion of (az/ap,), rather than (az/@p')t The pseudo-reduced density, P,, may be exl3ressed in the form (1.27 (5) ( z I-,) in which 0.27 is the critical value of Z, considered to be an appropriate value for mixtures composed chiefly 77 L. Mattar worked as a project en- gineer at the Energy Resources Con- servation Board, Calgary, during , at which time he was re- sponsible for a complete revision of the 1965 edition of the "Theory and Practice of the Testing of Gas Wells". He graduated with a B.Sc. (Hons.) in chemical engineering in 1965 from the University of Wales, Swansea, and obtained an M.Se. in chemical engineering in 1973 from The Uni- vei@sitv of Calgary. He is curredtly involved in engineer- ilig construction operations in Sierra l,eone, West Africa. fie is a member of CIM and a member of the Association i,f Professional Engineers of Alberta. G. S. Brar is a project engineer at the Energy Resources Conservation Board, Calgary. He graduated with a B.E. (Hons.) in chemical engineering in 1971 fi-oni Birla Institute of Tech- nology an(i Science, India, and ob- tained an M.Se. in chemical engineer- ing, with specialization in environ- mental engineering, in 1973 from the University of Calgary. His latest woi@k includes completion of a tech- nical manual entitled, "Theory and Practice of the Testing of Gas Wells", a publication of the Energy Resources Conservation Board. He is a mem- bei- of CIM and a member of the Association of Profes- sional Engineers of Alberta. Khalid Aziz is a Professor of Chem- ical Engineering at The University of Calgary and a consultant to several Canadian and international organiza- _ tions. He holds engineering degrees from The University of Michigan, The University of Alberta and Rice University. His research interests in- clude i-nultiphase flow in pipes, re- servoir simulation and well testing. He is author or eo-author of over 70 technical papers and one book. In 1975, be received the Distinguished Service Award of the Petroleum Society. He is a registered professional en- gineer in Alberta an(i member of several technical so- cieties, including The Petroleum Society of CIM. Technology, October--December, 1975, Montreal,J C -PT7,5 - e) q- C) R, COMPRESSIBILITY OF NATURAL GASES L. MATTAR G.S. BRAR K. AZIZ this article begins on the next page

Chapter Two Reservoir Properties Porosity

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