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### NARROW

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P.B. Crawford

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Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*30 (12): 1715–1716.

Paper Number: SPE-6445-PA

Published: 01 December 1978

Abstract

JPT Forum articles are limited to 1,500 words including 250 words for each table and figure, or a maximum of two pages in JPT. A Forum articles may present preliminary results or conclusions continuing investigations that the author wishes to publish before completing a full study; it may impart general technical information that does not warrant publication as a full-length paper. All Forum articles are subject to approval by an editorial committee. Letters to the editor are published under Dialogue, and may cover technical or nontechnical topics. SPE-AIME reserves the right to edit letters for style and content. Introduction Hydrocarbon miscible displacement was suggested by Wharton and Kieschnick in 1950 and later received considerable attention. The low price and large supply of natural gas favored its use for injection. Other fluids now are being investigated because natural gas supplies are limited. CO2 and soluble-oil slugs have proved favorable as miscible agents, but their use depends largely on economics and availability. In 1958, Koch and Hutchinson reported on miscible displacement using flue gas. They presented oil-recovery data for displacing gases containing zero to 100% nitrogen. McNeese presented a study in 1963, but his work was not available to us when writing this paper. Some recent work on nitrogen injection shows the effect of GOR on oil recovery and indicates oil recoveries greater than 90% on a 43 degrees API gravity crude oil. Other recent work describes equipment and shows the flow diagram of a gas-fired, cryogenic nitrogen plant designed for offshore platforms or remote installations. Pure, dry, noncorrosive, cryogenic nitrogen may be obtained by liquefaction of air and separation at the surface. The cost of nitrogen is less than one-fourth that of intrastate natural gas. A cryogenic nitrogen plant may be located at the oil field. With the elevated temperatures and pressures encountered in deep oil reservoirs, injected gaseous nitrogen was believed to lead to a miscible displacement process for some crude oils. In the tests described here, commercially pure nitrogen was used as the displacing gas to explore the feasibility of miscible displacement of crude oils with nitrogen. Oil Recovery Fig. 1 shows the effect of pressure and temperature on oil recovery using high-pressure nitrogen injection. These data cover the pressure range from 2,500 to 5,000 psi and were obtained on a 54.4- degrees API gravity crude oil with a GOR of 700 scf/bbl. The linear pack was 40 ft long and temperatures were 72 to 250 degrees F. At 2,500 psi and 250 degrees F, oil recovery was about 61% of the stock-tank oil originally in place (Fig. 1). At 3,000 psi, oil recovery was near 70% for temperatures of 72 to 250 degrees F. At 4,000 psi, oil recovery ranged from about 78% at 72 degrees F to about 85% at 250 degrees F. At 5,000 psi, oil recovery ranged from 85 to 92% for a temperature range of 72 to 250 degrees F. It is entirely possible that miscibility occurs in the last few feet of the tube in Fig. 1, even though total oil recovery is only about 85%. McNeese pointed out that although recovery was only 85% in the first 123 ft of equipment, miscibility and substantially 94% oil recovery were obtained in the last 22 ft of the 145-ft pack. Some systems require a long path to achieve miscibility. Fig. 2 is a cross-plot showing the effect of temperature on oil recovery using high-pressure nitrogen injection for this particular fluid system. Fig. 2 indicates that oil recovery was substantially independent of temperature at 3,000 psi for this system. At 4,000 and 5,000 psi, oil recovery increased with temperature (Fig. 2). JPT P. 1715

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*18 (05): 624–636.

Paper Number: SPE-1243-A-PA

Published: 01 May 1966

Abstract

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 solutions 2 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 ., 2 MacRoberts 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 Wilts 8 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 Jenkins 9,10 and Bruce et al . 11 gave numerical solutions for linear andradial gas flow. Douglas et al . 12 gave a solution for asquare drainage area. Aronofsky 13 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 andJenkins 14 that solutions for the liquid flow case 15 couldbe used to generate approximate solutions for constant rate production of idealgases.

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*15 (03): 237–242.

Paper Number: SPE-571-PA

Published: 01 March 1963

Abstract

CRAWFORD, H.R., THE WESTERN CO. DALLAS, TEX. JUNIOR MEMBER AIME NEILL, G.H., THE WESTERN CO. FORT WORTH, TEX. BUCY, B.J., THE WESTERN CO. FORT WORTH, TEX. MEMBERS AIME CRAWFORD, P.B., TEXAS A and M COLLEGE COLLEGE STATION, TEX. MEMBER AIME Abstract This paper presents the physical and chemical properties of carbon dioxide whic h 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. Introduction Carbon dioxide is normally associated with carbonation of soft drinks and the extinguishing of fires. Now, however, its unique physical and chemical characteristics have been utilized as a multipurpose additive for well stimulation fluids. Some of the advantages which can be expected from the use of carbon dioxide are as follows: eliminates swabbing in most cases; provides rapid clean-up which helps remove muds, silts, etc.; removes or prevents water and emulsion blocks; retards acid reaction with formation; helps prevent clay swelling and precipitation of iron and aluminum hydroxides; reduces friction loss of oil-base fluids; and increases permeability of carbonate formations. 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 are given. Physical Properties Carbon dioxide (CO2) is familiar in all of its physical forms-gas, liquid and solid (dry ice). Its low boiling point is one of the highly desirable qualities utilized in fracturing and acidizing operations. Fig. 1 is a pressure-enthalpy-temperature chart for CO2. The right-hand side represents the gaseous region, the upper left-hand is the liquid region and the lower left represents solid CO2. The area under the curve represents the two-phase region. The upper portion is liquid-gas and the section below 75 psia represents solid-gas equilibria. This chart shows that, for a pressure of 300 psi (a normal pressure maintained when transporting liquid CO2), the temperature of the liquid will be about 0 F. At atmospheric conditions CO2 exists as a colorless, odorless gas which occupies about 8.57 cu ft/lb.It may also be seen from Fig. 1 that, at temperatures above 87.8 F, pure CO2 will exist as a gas regardless of the pressure applied. Fig. 1 also shows that at pressures below 75 psia liquid CO2 cannot exist and only solid or gaseous CO2, is possible. The solid (dry ice) sublimes directly to gaseous CO2.Fig. 2 shows the specific gravity of saturated liquid CO2. For example, at 0 F the specific gravity of liquid CO2 is about 1.0, or the same as water. Fig. 3 shows the specific heat of saturated liquid CO2 as a function of temperature. For example, at 0 F the specific heat is about 0.5 Btu/lb F, and at 75 F the specific heat is about 1.0 Btu/lb F. This chart is useful when calculating the temperature of a combined stream of water or oil with carbon dioxide. Fig, 4 gives the compressibility factor z for gaseous carbon dioxide. This is used to calculate gas densities from the equation(1) For carbon dioxide, PV = 0.243 zMT where P = pressure, psiaV = volume, cu ftM = weight, lb, andT = temperature, deg. R. Solubility of CO2 in water (from Dodds, et al ), as a function of pressure and temperature, is given in Fig. 5. The solubility of the gas in brines is less than in fresh water. This solubility may be obtained by multiplying the solubility in fresh water obtained from Fig. 5 by the correction factor obtained from Fig. 6.The solubility of CO2 in oils is not so well known, but Holm' and Beeson and Ortloff have published some recent data. These are given in Fig. 7. The volumetric behavior of CO2 dissolved in oil is presented in Fig. 8. JPT P. 237^