The effect of variations of pressure-dependent viscosity and gas lawdeviation factor on the flow of real gasses through porous media has beenconsidered. A rigorous gas flow equation was developed which is a second order, non-linear partial differential equation with variation coefficients. Thisequation was reduced by a change of variable to a form similar to thediffusivity equation, but with potential-dependent diffusivity. The change ofvariable can be used as a new pseudo-pressure for gas flow which replacespressure or pressure-squared as currently applied to gas flow. Substitution of the real gas pseudo-pressure has a number of importantconsequences. First, second degree pressure gradient terms which have commonlybeen neglected under the assumption that the pressure gradient is smalleverywhere in the flow system, are rigorously handled. Omission of seconddegree terms leads to serious errors in estimated pressure distributions fortight formations. Second, flow equations in terms of the real gaspseudo-pressure do not contain viscosity or gas law deviation factors, and thusavoid the need for selection of an average pressure to evaluate physicalproperties. Third, the real gas pseudo-pressure can be determined numericallyin terms of pseudo-reduced pressures and temperatures from existing physicalproperty correlations to provide generally useful information. The real gaspseudo-pressure was determined by numerical integration and is presented inboth tabular and graphical form in this paper. Finally, production of real gascan be correlated in terms of the real gas pseudo-pressure and shown to besimilar to liquid flow as described by diffusivity equation solutions. Application of the real gas pseudo-pressure to radial flow systems undertransient, steady-state or approximate pseudo-steady-state injection orproduction have been considered. Superposition of the linearized real gas flowsolutions to generate variable rate performance was investigated and foundsatisfactory. This provides justification for pressure build-up testing. It isbelieved that the concept of the real gas pseudo-pressure will lead to improvedinterpretation of results of current gas well testing procedures, both steadyand unsteady-state in nature, and improved forecasting of gas production. Introduction In recent years a considerable effort has been directed to the theory ofisothermal flow of gases through porous media. The present state of knowledgeis far from being fully developed. The difficulty lies in the non-linearity ofpartial differential equations which describe both real and ideal gas flow. Solutions which are available are approximate analytical solutions, graphicalsolutions, analogue solutions and numerical solutions. The earliest attempt to solve this problem involved the method ofsuccessions of steady states proposed by Muskat.1 Approximateanalytical solutions2 were obtained by linearizing the flow equationfor ideal gas to yield a diffusivity-type equation. Such solutions, thoughwidely used and easy to apply to engineering problems, are of limited valuebecause of idealized assumptions and restrictions imposed upon the flowequation. The validity of linearized equations and the conditions under whichtheir solutions apply have not been fully discussed in the literature. Approximate solutions are those of Heatherington et al.,2MacRoberts 4 and Janicek and Katz.5 A graphical solutionof the linearized equation was given by Cornell and Katz.6 Also, byusing the mean value of the time derivative in the flow equation, Rowan andClegg 7 gave several simple approximate solutions. All the solutionswere obtained assuming small pressure gradients and constant gas properties. Variation of gas properties with pressure has been neglected because ofanalytic difficulties, even in approximate analytic solutions. Green and Wilts8 used an electrical network for simulatingone-dimensional flow of an ideal gas. Numerical methods using finite differenceequations and digital computing techniques have been used extensively forsolving both ideal and real gas equations. Aronofsky and Jenkins9,10and Bruce et al.11 gave numerical solutions for linear andradial gas flow. Douglas et al.12 gave a solution for asquare drainage area. Aronofsky13 included the effect of slippage onideal gas flow. The most important contribution to the theory of flow of idealgases through porous media was the conclusion reached by Aronofsky andJenkins14 that solutions for the liquid flow case15 couldbe used to generate approximate solutions for constant rate production of idealgases.

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This paper presents the physical and chemical properties of carbon dioxide which form the theoretical basis for its use in well stimulation. The means of applying this unique chemical in fracturing and acidizing treatments are described, and some results of its use in the field are given.

A method has been developed :0 calculate wellbore temperatures during mud circulation and the actual cementing operation to aid in t?w design of cement slurries. The method agrees within 10F with previously measured values. The calculation technique pro vides temperatures, as fun:tions oj time, at varying depths in both the casing cord anntdus, The technique also provides this infortnadon if a relc:ively cool cement slurry is pumped info the well immediately following circsdatiots of hot mud. Circulating bottom-hole temperatures of brine and a benfonite mud were measured. JOURNAL OF PETROLEUM TECHNOLOGY

Theoretical and potentiometric model studies have been made of the effect of non-uniform lateral permeabilities on pattern sweep efficiency and production capacity in waterflood and gas-cycling programs. It is shown that a difference in directional permeability by a factor of three may result in a sweep efficiency of only 43 per cent for a five-spot pattern or a sweep of either 79 or 38 per cent for a direct line-drive square pattern, depending on the direction of the line-drive flood. Changes in the pattern conductivity varied from about 0.8 to 1.34 over this same permeability variation, depending on the pattern used. It is suggested that measurements be made to determine the possible magnitude and extent of the directional permeability phenomenon early in the field development and certainly prior to the initiation of any fluid-injection program. Introduction Irregularities in reservoir sand properties long have been a major difficulty to anyone attempting to explicitly describe the field characteristics of oil production. In particular, it is well known that vertical and lateral permeabilities often differ appreciably; however, the existence of large regions with lateral permeability variation is not widely recognized. A number of years ago, extensive studies were conducted by the Secondary Recovery Research Laboratory of the Pennsylvania Grade Crude Oil Association, primarily on the Bradford field. Johnson and Hughes reported a permeability trend in the northeast-southwest direction. They indicated that flow in the preferred direction may be 25 to 30 per cent greater in that direction than in the northwest-southeast direction. They also reported that similar effects may be found in other nearby fields. The origin of the permeability variation has been discussed by Griffith. Hutchinson described the results of laboratory tests on limestone cores, pointing out that preferential directional permeabilities were significant in one-half of 10 formations studied and that the average permeability ratio was 16:1.