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By J. C. Wilhoit, E. M. Galle

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelastic-ity was used to determine the stresses within the model. Two separate problems were solved: (1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore, induced by an uneyual system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For uneyual principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. INTRODUCTION Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eeninkl have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. whitworth2 and woods3 have obtained numerical solutions. word415 obtained a three-dimensional photoelastic solution, Durelli and Deily 6 obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit7 determined the stresses around the bottom of a short cylindrical cavity. While Miles and McGuire, Harrison and Kieschnick and Hubbert and Willis 10 obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomo-geneous, permeable and anisotropic. Previous

By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By R. H. Jacoby, V. J. Berry

When dry gas is injected into a reservoir containing a volatile crude oil, a significant amount of the reservoir liquid phase may become vaporized. The resultant rich gas phase, when subsequently produced, con-tributes to tank oil production. This contribution assumes greater importance, the more volatile the oil in-olved. Oil recovery may be sub-stantially greater than that predicted by conventional frontal-drive methods, which do not consider the vaporization equilibrium between the reservoir oil phase and the injected gas. A calculation method has been (developed to account for vaporiza-. tion of the reservoir liquid phase during gas-injectiorz operations, and for the tank oil production which results from this factor. Recovery performance calculations are presented for a reservoir containing a highly volatile oil. Tank oil recovery is calculated to be about twice that predicted by the use of the conven-rional frontal-drive equations. In contrastto usual pressure maintenance performance results, in which the gas-oil ratio rises at an increasing rate after gas breakthrough, the pre-dicated gas-oil ratio rises rapidly to about 12,000 scf/bhl and then rises much less rapidly. During gas inje-tion, most of the reservoir liquid phase contacted is evaporated by the dry injection gar. The gas-oil ratio during this period is dependent upon reservoir pressure. The higher the operating pressure, the lower the gas-oil ratio. The predicted behavior i., in accordance with laboratory PVT tests made to .simulate the vaporization behavior. In addition to recovery performance predictions, results of the calculation procedure include complete wellstrearn composition data of value in the design of gasoline plant facilities often used in con-rrction with gas-injection operations. INTRODUCTION In the cycling of gas-condensate reservoirs, dry gas is injected to maintain reservoir pressure during wet gas production and to thereby eliminate or reduce ultimate loss of liquids due to retrograde condensation within the reservoir. Gas injected into crude oil reservoirs has a dual function. It displaces oil to the producing wells and at the same time serves to partially or fully maintain reservoir pressure. Oil shrinkage which would occur upon pressure reduction is thereby minimized or eliminated. Accepted calculation methods are available'= for predicting recovery performance of either gas-condensate reservoirs or crude oil reservoirs which are being subjected to gas injection. In gas-condensate reservoirs, any retrograde liquid formed does not flow, and it is necessary to account only for the vaporization equilibrium between this liquid and the injected gas. Conversely, in normal crude oil reservoirs, both the oil and gas phases flow, but it has not been considered necessary to account for any vaporization of the reservoir liquid which might occur upon contact with the dry injection gas. Recently, high shrinkage reservoir fluids known as "volatile oils" have been found in increasing amounts. These oils are characterized by tank oil gravities above 4.5" API, solution gas-oil ratios above 1,000 scf/bbl, and reservoir volume factors above two. Special techniques have been devised for predicting depletion performance of reservoirs containing such oils.74.5.1; One of the characteristics of reservoirs producing volatile oils is that the reservoir gas phase carries a significant amount of oil which is recoverable as stock-tank liquid. This unusual vaporization be-havior implies that an appreciable amount of reservoir liquid would be vaporized upon contact of the oil with dry injection gas. In a gas-injection operation, tank oil recovery would he obtained not only through frontal displacement of the reservoir liquid by the injected gas, but also through production of the rich gas phase. This means that not only are improved methods needed to predict recovery of such oils from reservoirs undergoing gas injection, but it would also be expected that high oil recoveries might be obtained by such operations. When relatively dry gas is injected in to a volatile oil reservoir, phase equilibrium between the injected gas and the reservoir oil will tend to bc established. Initially the most volatile components, such as propane, the butanes and the pentanes, will account for most of the material transferred from the oil phase to the gas phase. As the partially stripped oil phase is contacted with additional dry injection gas, the heavier intermediate components, such as the hexanes, the heptanes and the octanes, will gradually transfer to the gas phase in increasing amounts. This is because the supply of lighter components in the oil phase dwindles due to the stripping action of the injected gas. This stripping action will usually continue to be effective down

By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By D. M. James, J. C. Martin

The results are presented of a study of the application of analytical methods to the solution of two-phase flow into single wells. Approximate analytical expressions for the pressure distribution in two-phase flow are found ;;; a number of conditions. The results obtained from the analytical solutions me found to be in good agreement with results obtained by finite difference techniques using a high speed digital computer. Mathematical solutions for four sets of boundary conditions are presented. All of these solutions are composed of a short-term transient plus a steady or quasi-steady state. The rates of decay of the short-lived transients are analyzed. It is found that the durations of the short-term transients may be characterized by a parameter defined as the time constant which can be determined from simple relations. It is shown also that if the outer radius is much greater than the radius of the well. the short term transients decay at rates which are proportional to the square of the exterior radius, and the rates of decay are only slightly dependent upon the radius ratio. Numerical solutions based on finite difference techniques are presented for a number of conditions. The numerical solutions are in good agreement with the predictions based on the theoretical analysis for small and moderate drawdowns. Examples involving large drawdowns indicate that the nonlinearities in the equations of flow do not appreciably alter the longevity of the short-term transients. In all cases the time required for the short-tern transients to disappear is predicted satisfactorily. INTRODUCTION The mechanism by which oil and gas flow into a single well is of vital interest to the petroleum industry. The fundamental equations of two-phase flow which describe this mechanism are nonlinear partial differential equations. Numerical solutions of these equations describing pressure transients have been obtained with the aid of electronic computers. Although solutions obtained in this manner take into account a large number of effects, the reduction of this information to useful generalities is difficult. One method of obtaining generalities is the use of linearized approximations of the nonlinear equations. Since it is possible to obtain explicit solutions of the linearized equation, general properties of the role of pressure in the flow mechanism may be ascertained. Results obtained from this approach are limited to some extent by the linearizing assumptions. The severity of these limitations may be evaluated by comparing solutions of the linear equation with numerical solutions of the more exact nonlinear equations of two-phase flow. In the past considerable amount of work has been devoted to studying pressure build-up using the single-phase flow theory. Unfortunate1y, most prep sure build-up tests involve multiphase flow. A small amount of work has been done studying pressure build-up where the flow is two-phase. The encouraging results of these studies suggest that useful results may be found from additional studies of not only pressure build-up, but also the rapid transients associated with placing a well on production. This paper presents the basic theory of the pressure transients associated with placing a well on production and with closing it in. The paper is concerned chiefly with two-phase compressible flow; however, the results also apply to single-phase flow. The results are based on analytical solutions of the flow equations, and they are verified by numerical solutions using finite difference techniques. Much of the previous work on compressible flow into wells has been confined to single-phase flow. Some work has been done on compressible two-phase steady state flow, and solutions of the equations of flow have been found by finite difference techniques using high-speed computers. Muskat1 presents some rather general solutions to the equations of single-phase compressible flow into wells. Much work has been done on pressure build-up in wells (see, for example, Refs. 2-6). Almost all of the work on pressure build-up concerns single-phase flow with the exception of Ref. 5 and part of Ref. 2. Some work has been done on pressure fall-off in injection wells.718 Muskat9 presents the solution of the equations for radial steady state two-phase compressible flow. Handyl0 extends Muskat's solution to obtain

By W. H. Bassett, C. Davis

Although brasses and bronzes have been made for ages, a systematic study of their physical properties has been carried out only during the years of the present century. Among these properties may be included those which are to be detected by means of microscopic examination; in other words by the science of metallography. The earlier workers in this field, both in this country and abroad, gave their attention to steel. When the senior author explored the situation in 1902, there was little encouragement to be found in undertaking the study of the non-ferrous alloys. A start was made, and the metallography of the brasses and bronzes, as well as of the copper-nickel-zinc alloys developed materially under his direction. Annealing experiments were begun in 1902, and in the succeeding years the effect of temperature, and the influence of previous working, on the grain size of brass were studied. The conclusions so well known and widely published today were largely reached during those earlier years. In 1905 the first complete annealing series were made. By this it is meant that brass and copper sheet, 5 B & S Nos. hard, was machined into tensile test specimens, then annealed under accurate control for 30 min. at temperatures up to the melting point of the material. Various determinations were made, including tensile strength and elongation in 2 in. There rapidly followed similar series on all of the copper-zinc alloys from 100 to 60 per cent, copper, on the bronzes, cupronickels, and on copper-zinc-nickel alloys. At this point there was published by Grard, in October, 1909,' the very comprehensive and complete work on the tensile properties of cartridge brass, 90-10 copper-zinc, and electrolytic copper. The excellent photomicrographs in that paper illustrated the changes in structure produced by cold rolling as well as by annealing at different temperatures, but where Grard's work was confined to copper and to two alloys, the investigations in this laboratory have been over the entire fields of the commercial copper-zinc alloys, copper-tin alloys, representative copper-nickel and copper-nickel-zinc alloys as well as aluminum bronzes and others of a more special nature.

By J. Lohrenz, R. J. Francis, G. C. Clark

Compositional material balance methods have been extended to solution gas-gas cap-water drive reservoirs. Partial or complete pressure maintenance as well as reservoir repressuring by gas and/or water injection may be considered. Increrments of reservoir withdrawals and injections equivalent to a given time increment are used as the basic iterative step to allow the extension. An example field study shows how the reservoir volumes. extent of the water drive, and relative permeability ratio function may be estimated. Knowing these, the methods can be used to predict reservoir behavior. INTRODUCTION The compositional material balance is similar to conventional material balances in many aspects. The assumption of a pressure-homogenous reservoir with no transients is common to all conventional material balances1-1 although numerical methods are different. The compositional material balance also contains this assumption. Inclusion of phase equilibria directly in reservoir calculations is the key difference and improvement in the compositional material balance. A continuous account of the compositions of the reservoir fluids and effluents is determined. Calculations of fluid phases and properties can be based on these compositions. Excepting fluid phases and properties determined in this manner, the compositional material balance uses procedures exactly analogous to conventional methods. Brinkman and Weinaug5 and Jacoby and Berry6 have given compositional material balances for simple solution gas drive reservoirs; subsequently Jacoby and Berry' extended their procedure to include pressure maintenance by gas injection at constant reservoir pressure. This paper extends compositional material balance techniques to a more general combination drive reservoir with various types of pressure maintenance operations. The procedure for this extended compositional material balance and an example of its field application are presented. PROCEDURE The numerical calculations of this compositional mate- rial balance are performed on a high-speed digital computer. The most comprehensive case the present compositional material balance program can handle is a solution gas-gas cap-water drive reservoir with (1) water production, (2) water influx, (3) separate or commingled production from the oil and gas zones, (4) any surface processing arrangement including LPG and gasoline production, and (5) gas injection into the gas and/or oil zones." This description of the procedure applies to this most comprehensive case. Appropriate deletions in the procedure can be made for more simple mechanisms. ASSUMPTIONS In common with conventional material balances, the compositional material balance makes the following assumptions: (1) the total reservoir is at a uniform pressure at a given time; (2) the volumetric ratio of gas to liquid withdrawal at reservoir conditions is directly proportional to their mobilities; and (3) instead of assuming a pressure-dependent total gas-oil equilibrium, the cornpbsitional material balance makes a sianificantly different and more rigorous assumption as follows. Thermodynamic equilibrium exists for each component in the liquid-gas mixtures in the reservoir and in surface processing. These three assumptions are fundamental in the compositional material balance procedure. Other assumptions involve arbitrary simplifications of the reservoir mechanisms. This compositional material balance uses the following simplifying assumptions: (1) no bulk mixing occurs between the gas and oil zone; (2) total mixing occurs between any injected gas and the contents of the injection zone; (3) no in situ hydrocarbon liquid is produced from the gas zone; (4) no reservoir gas is retained behind any net bottom-water influx; (5) the residual saturation of hydrocarbon liquid at reservoir conditions behind any net bottom-water influx is constant; and (6) fluids retained behind any net bottom-water influx exert no further influence on the reservoir. These six assumptions are not fundamental. Modifications of the present procedure can be made for different assumptions of the reservoir mechanisms. THE TIME INCREMENT Previous compositional material balances have used a pressure increment for simple solution gas drive reservoirs"" and an increment of injected gas for pressure maintenance.' These increments are suitable for these simple cases. They are, however, inadequate for reservoirs with time dependent drive mechanisms including water drive. A time increment removes this inadequacy and is

By G. M. Webster, G. E. Dawsongrove

The use of percussion-type side-wall cores as an aid in detection and evaluation of hydrocarbon shows and in examination of rock properties has become increasingly popular in recent years. Sidewall coring has an advantage over normal bottom-hole coring methods in that the zones may be surveyed with the electric log prior to selection of sample depths. This allows an efficient sampling of all zones of interest, a procedure not possible with bottom-hole coring techniques unless the costly procedure of continuous coring is utilized. Percussion sidewall coring presently provides the most rapid and lowest cost method of obtaining sidewall cores. It has been recognized for some time that certain discrepancies exist between core analysis data obtained from percussion cores and data obtained from other types of core Samples. This paper presents existing field and laboratory data that were available to the authors. Several examples of comparative core analysis data obtained from various fields are presented along with photomicrographs of thin sections of conventional and percussion cores. The results of this investigation are presented to throw more light on the possible disturbed condition of percussion sidewall cores. SAMPLE DISTURBANCE AND FRACTURING The principal cause of discrepancy between conventional core analysis data and percussion sidewall core analysis data is believed to be the shattering and re-adjustment of the grains due to the large impact shearing forces produced by mechanics of percussion coring. Figs. 1 through 5 are photomicrographs of thin section slides of formation samples obtained by means of diamond cores, conventional cores, and percussion sidewall cores. Figs. 1 and 2 show samples of the

By Frederic E. Carter

The gold, silver, copper alloys have been the subject of several fairly complete investigations by Janecke, Sterner-Rainer&apos; and others, and indeed it would seem as if almost too much labor had been expended on them when one thinks of the numerous other ternary alloys calling for more light; however, the combinations of the three metals are actually so widely used in jewelry that they merit perhaps the work done on them. There are a few properties of importance and interest not treated by the authors mentioned which the writer investigated some little time ago, and therefore he has ventured to put on record the results of some of his tests made at that time. He has chosen, as being the two series of most importance to the jeweler, only the 14 and 18-kt. golds, so the subjcct is by no means so inclusive as that previously treated. As statecl, this paper is merely a record of tests made in a practical manner on two itucbful series of alloys, and is not at all a critical study of their properties. 14-Karat Alloys These alloys are important because they arc the most generally II,<(S(I in 14-kt, jewelry; by changing thc proportions of silvcbr and copper Iliero are obtained all shades of color from the green of the alloy contiainng gold and silver but no copper, to the red of the alloy containing gold ;,, copper but no silver. Many 14-kt. gold alloys are made with the sdditjon of zinc to the three metals mentioned here; the added lnetnl does not appreciably alter the color of the alloy nor has it, in general, much effect on the working properties; it may, however, prove useful as ynrt of thc zinc added may act as a deoxidizer and render the alloy free of ga,s. 11, iy not a necessary addition because with proper precautiolls :111 I lie 14-At. gold alloys containing only silver and copper in :tcltlitiotl to the gold ran be made free of gas and capable of being cold rolled without craci The alloys in which approximately equal quuntiticrs of silver ami

By D. J. McAdam

Results of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station, Annapolis, Md., have been discussed by the writer in several recent paper~.1,2,3,4 In those papers references were also given to the work of Haigh in 1917.= Efforts by the writer to obtain a better understanding of some of the factors involved in corrosion-fatigue finally developed into a general investigation of the effect of time and cyclic stress on corrosion of metals. Corrosion-fatigue of Metals As described in the papers mentioned, rotating-cantilever specimens, conically tapered so that the stress is nearly uniform over a length of about 1.5 in., were subjected to simultaneous fatigue and corrosion. For this purpose a stream of water was diagonally applied so as to sweep the specimen from the outer to the inner fillet and surround the stressed surface with water. The fresh water is a calcium carbonate water, the composition of which has been given in a previous paper.2 The salt water is Severn River water having a saline content about one-third that of sea water. The previous papers described results obtained with ferrous and non-ferrous metals. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at nominal stresses far

By F. S. Young, K. E. Gray

Drilling tests with a 11/4-in. diameter roller bit were performed on Berea and Bandera sandstones and Leuders limestone using water and two conventional drilling muds as circulating fluids to evaluate the influence of dynamic filtration on penetration rate. The muds possessed widely differing API fluid-loss properties. Mud filtrate was constrained to flow beneath the bit; no filtrate flowed radially through the borehole wall. Rock pore pressure at three different locations ahead of the bit, cumulative filtrate volume, borehole pressure and bit location were monitored during drilling. The rock samples, cored in three orientations with respect to bedding planes, possessed a wide range of liquid permeabilities. and were drilled at borehole-to-formation pressure differentials of 0, 250, 500 and 1,000 psig. The effect on penetration rate of API fluid loss, borehole pressure and rock permeability was studied. Rock permeability damage and pore pressure gradients beneath the bit were evaluated. The importance of borehole-to-formation pressure differential was illustrated for each drilling fluid and rock permeability combination. Penetration rates decreased with increased borehole pressure and reduced fluid loss. The observed penetration rate reduction due to changing fluid Ioss was attributed to decreased filtrate flow and improved mud cake plastering hy the low fluid-loss mud. The reduction in filtrate flow could not be related to spurt-loss phenomena. Rock permeability influences penetration rate through particle invasion ahead of the hit, which damage leads to high pressure gradients. Penetration rate variance with sample orientation was evident for water-drZled samples but less obvious for mud-drilled rocks. Permeability damage beneath the bit ranged from 1 to 3 cm. Maximum damage occurred in the first 0.1 cm. Pressure gradients varied with API fluid 10.s.s and could be correlated with penetration rate. The pressure gradient was found to influence penetration rare in rocks of all permeabilities tested. INTRODUCTION Early microbit and small-scale drilling experiments proved to be invaluable contributions to understanding the mechanics of drilling at depth. For example, the effect of borehole-to-pore pressure differential on drilling rate was demonstrated conclusively by Murray and Cunningham&apos;, Eckel&apos; and others .&apos; However, the effects of various drilling fluid properties on drilling rate, particularly filtration, have not been studied extensively on a laboratory basis. Microbit correlations of penetration rate with different viscosity and API fluid-loss muds led EckelV o conclude that viscosity and density. more than API fluid loss, were the most important fluid properties in controlling drill bit penetration rates. Ferguson and Klotz6 studied filtration beneath the bit and stated that the maximum amount of filtrate which could conceivably flow beneath a drilling bit could be described by a potential function associated with flow from a moving disc source. and be characterized by a depth-of-filtrate invasion. Invasion depth is a function of penetration rate, formation porosity and permeability, flooding efficiency, pressure difference between borehole and formation and borehole radius, assuming that no filtrate flows through the borehole walls. Electric analog and experimental measurements were obtained, assuming no plugging of the formation pores. Theoretically, filtrate invasion was predicted to extend from 1- to 15-hole radii beneath the cutting surface; experimental results indicated that the extent of invasion was only Y2 in. Comparing these data with results of core-plugging experiments by Norwak and Krueger&apos; led Ferguson and Klotz to state that the drilling operation apparently contributes to higher filtration rates than are observed in nondrilling core filtration tests in which the core face is jetted and scraped. Glenn and Slusser: in describing a linear filtering system in which a rotating bit continuously scraped mud cake from the surface but did not penetrate Alundum cores, stated that mud-solids invasion and permeability damage of the cores were most severe in the first 2 to 3 cm. The filtrate flow rate through the core was found to stabilize after sufficient time had elapsed for the formation of an internal mud cake whose effective permeability was estimated to be 50 to 300 times as high as that of bulk filter cake. Krueger and Vogel reported core permeability damage depths up to 12 in. during a 5-day exposure period in which filter cake buildup was prevented. Havenaar pointed out that the discrepancy between reported and calculated values of filtrate volume obtained in the experiments of Ferguson and Klotz was due, among other things, to failure of the reported API fluid loss to truly represent filtration beneath the bit. Williams," Pro-koplz and others"" have shown that dynamic filtration tests (where a flow of fluid parallel to the filter surface continually erodes the deposited filter cake until a dynamic equilibrium between wall-shearing forces and normally directed compaction forces is attained) yield higher filtration rates than do static tests. Cunningham and Goinss reported results of drilling tests in impermeable shales. They found that by reducing

By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett&apos; theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy&apos;s law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By J. S. Aronofsky, A. S. Lee

Results and experimental procedures are presented covering a preliminary laboratory investigation of the compaction of reservoir rocks and its effect on porosity and permeability. "Egective" compressibility was measured by subjecting core material to an overburden load and reducing pore pressure. Preliminary results showed relatively high effective compressibilities which varied from 1.8 X 10-&apos; pore volume/pore volume /lb / in.~ for limestones to 7.7 X 10-6 pore volume/pore volume/lb/in.&apos; and even higher for sandstone reservoirs conmining large amounts of fine clay material. It appeared from the initiol results that the effective compressibility of the material could not be correlated directly with porosity and that other factors, such as the amount of clay material present might have to be taken into account. The work to date has indicated that effective compressibility factors will have to be measured for the particular reservoirs heing studied. Oil permeability of core materid was measured under various effective overburden loads from 0 to 8,000 psi. It has been found than reduction of permeability in clean sands was relatively small and the results agreed with published data. For sandstones containing large amounts of clay, preliminary tests indicated very large reductions in permeability with increasing effective overburden pressures. It is planned to continue laboratory work on this phase because of its importance in low-permeability reservoirs. INTRODUCTION During the past few years increasing interest has been shown in the differences obtained between conventional laboratory measurements on cores at atmospheric pressure and those when reservoir conditions are simulated. Since these data are used as the basis for calculations and the prediction of reservoir behavior, their evaluation under reservoir conditions is most important. The effect of the compressibility of the rock upon the reservoir behavior, as fluid pressure declines, is an important subject which has been insufficiently studied. The total pressure on any plane through a reservoir is the result of the grain-to-grain rock pressure due to the overburden and the pressure of the interstitial fluid on the plane. As reservoir fluid pressure declines, the net load on the rock phase must increase, and the result is the compaction of the rock structure which produces a decrease in pore volume. Simultaneously, the rock grains expand into the pore space as the fluid pressure declines. The result of these two effects is defined as the effective compressibility of the rock and is expressed in units of pore volume/original pore volume/psi. Work was started by Imperial in 1954 on the effects of pressure on the porosity of reservoir rock. These studies established effective compressibility factors for some limestones and dolomites. Since that time effective compressibilities have been obtained for other Canadian and some U. S. reservoir rocks. In conjunction with the study of porosity, an investigation has also been initiated to determine the effects of pressure on permeability. One outcrop and several reservoir sandstone cores have been tested to date. ROCK COMPRESSIBILITY Apparatus anD Procedure A diagram of the apparatus used in these studies is shown in Fig. 1. The equipment was constructed so that a uniform pressure, equivalent to the reservoir overburden, could be applied by the oil pump and transmitted on all sides of the core through the Lucite sheath. The sample was completely saturated by circulating brine through the mounted core. Pressure in

By John N. Dew, William L. Martin, `

This paper describes the results of a laboratory investigation conducted to obtain data for an evaluation of the in situ combustion process as a method of producing crude oil from reservoirs. Air and fuel requirements, rates of advance, com-bustion temperatures, and coke and fluid distributions are presented. The mechanism of oil recovery by in stiu combustion is discussed. Five crude oils ranging in gravity from 10.9 to 34.2"&apos; API were prodrrced from a semiadiabatic, uncon-.solidnted sand pack by in situ combustion. Experimental conditions were varied over a wide range in order to determine the inter-relation-.ships of process variables. The mini-mum air flux requirement for self-sustained combustion was found to he less than 10 scf/hr-ft&apos;l. The rate of advance of a self-sustained combustion zone was found to be nearly proportional to the air flux at the combustion front. The effects of presrure and injected air flux were studied in a series of experiments using a 21.2" API crude. A minimum air require-ment was observed at an air .flux of 20 scf/hr-ft&apos;. The oil saturation con-sumed as fuel averaged 5.5 per cent of pore volume. The effect of air pressure was, found to be .small for experiments having high combustion eficiencies. This study should promote a better understanding of the problems and mechanisms involved in labora-tory investigations and field applications of the in situ combustion pro-cess. The data presented will be use- ful in the interpretation of results of field tests. When tempered with volu-metric sweep efficiencies, the data can be used in making preliminary economic appraisals of the process as applied to reservoirs containing high porosity unconsolidated media. INTRODUCTION The purpose of this work was to obtain laboratory data for an evaluation of the in situ combustion process as a method of producing crude oil from reservoirs. In situ combustion basically consists of (1) injecting air into a reservoir through selected input wells to create an air sweep through the reservoir, (2) igniting the crude at the injection well, and (3) propagating the combustion front through the reservoir by continued air injection. By this means, oil is swept toward producing wells in the area. The fuel for combustion is supplied by heavy residual material (coke) which has been deposited on the sand grains during distillation and cracking of the crude oil ahead of the combustion front. Recovery of petroleum by a combustion or heat wave process is not a new idea. F. A. Howard was granted a patent in 1923 on a process in which air and a combustible gas were pumped into an injection well and ignited.&apos; Russian engineers reported on field experiments with a crude oil gasification process in 1935&apos;. Other known early field tests include those conducted near Bar-tlesville and Ardmore, Okla., in 1942." More recently completed field tests include an inverted seven-spot by Sinclair Oil Co. in the Delaware-Childers field, Nowata County, Okla.&apos;; a three-well and an inverted five-spot test by Magnolia Petroleum Co. in Jefferson County, Okla."."; and a test by California Research Corp. in the Irvine-Furnace field in Kentucky. The Worthington Corp. has completed a test in cooperation with the Forest Oil Corp. in Clark County, 111.l Several field tests are now in progress. Sinclair has acquired a 600-acre lease in the Humboldt-Chanute field, Allen County, Kans., and is under way with a large-scale operation. Three field tests are under way in California. The General Petroleum Corp. is conducting an inverted five-spot pattern test in the South Bel-ridge field in Kern County under a cooperative agreement with 11 other companies, including Continental Oil Co. California Research Corp. is conducting a four-well pattern test in Midway-Sunset field near Maricopa, and Richfield Oil Corp. is under way with a test in the Ojai field in Ventura County. Although the published information is valuable concerning results of field tests, little laboratory data other than that reported by Kuhn and Koch5 are available to aid in appraising the tests from a technical or economic standpoint. Engineering data needed to evaluate the process include the amount of air required per barrel of oil recovered, minimum injection rates which will support combustion, rates of advance, air required per unit volume of reservoir cleaned, amount of oil recovered, and amount of oil consumed as fuel. The present laboratory investigation was undertaken to provide these data for that portion of the reservoir swept by the combustion zone. The first phase of this investigation was exploratory in nature and was conducted at injection pressures less than 100 psig. Data were ob-

By B. H. Caudle, A. B. Dyes

In a recent publication&apos; it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n &apos;. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/q, = 1/(1 + y) y and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The resrilts obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce all infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of diflerent permeabilitv and thicktress or two lnyers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when wing only data over early years 01 decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index INTRODUCTION As a result of both experimental work with models and theoretical deductions, it was recently concluded&apos; that wells having a free surface in a homogeneous reservoir producing by pure gravity drainage should have a hyperbolic decline with n = 2. The present report details efforts to extend this work on ideal homogeneous reservoirs to actual field cases. It should be remembered that both the previous work and the present extension are based on the assumption that the reservoir is at very low pressure, and hence, nearly all the potential available for driving fluid to the well is the gravity head. Attempts to apply conclusions of this study to reservoirs which have considerable pressures supplementing the gravity drive may lead to difficulty. WELLS WITH NO FREE SURFACE In a dipping gravity-drainage reservoir such as that shown in Fig. 1, some of the down-dip wells have no free surface. The previous study&apos; showed that the up-dip wells, which have a free surface, should follow Eq. 1. The following approximate analysis, of a type which was justified experimentally for up-dip wells in the work just mentioned, leads to results for the down-dip wells.

By E. F. Johnson, F. H. Brinkman, H. J. Welge, S. P. Ewing

This paper presents a method for predicting the manrler in which oil will be displaced from a porous body by enriched gas. The calculations apply to a gas rich enough to give a partially, but not a completely, misci-ble displacement. The method — a three-component, two-phase analysis — takes into account condensation of some of the intermediate hydrocarbons from the injected gas into the oil, as well as enhanced volatility of heavier hydrocarbons at elevated pressures and temperatures. The condensation swells the oil and decreases its viscosity, thus aiding in its recovery. The calculations have been extended to apply to actual crude oil-natural gas systems by arranging the components into three groups according to their volatility. As an approximation, each group is then treated as a single component in the analysis. The influence of an angle of dip for an inclined displacement is also taken into account. The recovery predictions are corroborated by experiments which used both consolidated sand cores and un-consolidated glass beads. In some of these tests, actual live crude oil was displaced by a multicomponent gas typical of enriched gases used in oil fields. INTRODUCTION This paper presents a method for predicting the amount of oil that can be displaced from a homogeneous, linear, porous body at various stages during the injection of enriched, or "wet", gas. The porous body can be in either a horizontal or an inclined position. &apos;This type of displacement is sometimes known as condensing gas drive The method is developed especially for the case in which the injected gas is enriched enough to be partially, but not completely, miscible with the reservoir oil. The need for a calcula-tive procedure for this type of operation is emphasized by the number of field projects where completely miscible drives are not practical, but where near-miscible conditions are feasible. The factors taken into account in the predictive calculations include: (1) the condensation of gas components into the oil, with a resulting increase in oil volume; (2) the lowering of oil viscosity by the addition of lighter ends from the gas; (3) the increase in oil volatility at high temperatures and pressures; and (4) the physical displacement of the oil by the gas. The techniques developed in the paper can be extended to other nonequilibrium displacement processes. Other such processes that we have analyzed include a displacement by lean gas which stripped intermediates from the oil, and a water flood in which the water con. tained in solution a substance somewhat soluble in the oil. ANALYSIS OF ENRICHED-GAS DRIVE GENERAL PRINCIPLES Our method for predicting the amount of oil that can be displaced by an enriched gas uses an analogy between a three-component and a multicomponent system.&apos; The predictive method is based on these assumptions: (1) constant, or nearly constant, pressure; (2) complete equilibrium by diffusion perpendicular to the main direction of flow, but no significant mixing along the direction of flow; (3) constant injection velocity; and (4) flow in a linear porous body. The composition of a liquid or a vapor with respect to three components can be plotted on a three-component, or ternary, diagram like that in Fig. 1. Let Point A represent the composition of the oil originally in place. In this case, Oil A is undersaturated with gas. If Point A lay on the equilibrium Curve BF, the oil would be saturated. In the extreme case where the original oil contained no intermediates or dissolved gas, Point A would lie at the lower left-hand corner of the ternary diagram. In a displacement of Oil A by Gas D, there will be a progressive change in the composition of the oil phase as more and more gas is brought into equilibrium with the oil. The end result of this progressive change is an oil having the composition represented by Point F. This oil is richer in intermediate hydrocarbon and methane than the original oil and, therefore, has a greater forma-

By R. O. Leach, O. W. Wagner

Because of unfavorable wetting conditions much residual oil is left when a porous material is Pushed by water. Methods suggested to change reservoir wetting to improve oil displncernrnt efficiency are generally expensitlr. The present 1aborator.y study was undertaken to gain an under.standinx of the factors which determine reservoir wettability, arid to find out if oil displacement efficiency might be improved by a wettahility change accomplished at low cost in on oil reservoir. Contact angle measurements were made on mineral surfaces using sevc.r~zl sets of reservoir oil and water samp1es. Results of the contact angle studies suggest that reservoir wetta-hility may he primarily determined by natural surface-active substances present in the reservoir fluids. The effect of changing sa1inity and pH of the water phase was studied. The re.suits suggest that gross changes in preferential wettability might be acc~o~npli.shed by injection of water containing simple chernicnls to alter pH or salinity in the reservoir. Such treatment could he much less expensive than injection of commercial surface-active agents. Waterflood tests have also been made using synthetic cores and oil and water having wening characteristics similar to those of reservoir fluids. Cores initially oil-wet were flooded in such a way that they were made prefermtial1y water-wct by the advancing flood water. This reversal in preferential wettability achieved greater oil displacement efficiency than when either oil-wet or water-wet conditions were maintained throughout the flood. For the systems studied, the higher the oil viscosity the greater the percentage improvement obtained over conventional waterflood recovery. This suggests that a flooding process making use of wettability-reversal may extend the oil viscosity range over which water flooding is attractive. Because a precise adjustment of reservoir wettability does not seem to be required, and because altering the pH or salinity in some reservoirs may be inexpensive, it appears that a waterflooding process employing wet-[ability-reversal could find .succesful field application. I NTRODUCTION The efficiency with which water will displace oil from a porous material is related to the nature of the capillary forces present. These in turn are controlled by the preferential wetting of the solid by the two fluids. Because of unfavorable wetting conditions, 30 per cent or more of the original oil in place may remain unrecovered in that portion of a reservoir flushed by water. This paper is concerned with the possibility of improving waterflood oil displacement efficiency by alterations in the wettability of the porous material. A laboratory study was made to gain a better understanding of the factors which control reservoir wettability, and to determine if the oil displacement efficiency could be improved by some inexpensive means of manipulating wettability of the porous medium. Contact angle measurements were made with several natural and synthetic oil, water and solid systems (1) to obtain a better understanding of how to duplicate reservoir wettability in the laboratory, and (2) to discover possible means for changing preferential wettability of natural reservoir systems. Flooding tests were also made in synthetic systems to determine if oil displacement efficiency could be improved by those wettability manipulations suggested by the contact angle measurements. Based on these studies a possible method for improving waterflood oil displacement efficiency is presented. This method involves causing an originally oil-wet porous material to become preferentially water-wet during the course of a water flood. The purpose of this paper is to present results of the laboratory studies. THEORY Rock surfaces in some oil reservoirs are believed to be covered with a firmly attached bituminous or other organic coating. Such surfaces would be preferentially oil-wet in the presence of both oil and water, regardless of composition of reservoir fluids. Other reservoirs are believed to contain rock surfaces not permanently coated with such materials, and which would be preferentially wet by water in the presence of water and oil free from surface-active substances. However, when the reservoir fluids do contain certain natural surface-active materials in sufficient quantity, rock surfaces acquire a degree of preferential oil wettability caused by adsorption of these natural surface-active materials on the solid. The equilibrium amount of these materials adsorbed per unit surface area is believed to depend upon their concentration in the bulk liquid phases.

By W. M. Rutherford

A knowledge of the limits of miscibility between reservoir oil and possible injection fluids is required for selection of the optimum miscible-injection fluid. Limits of miscibility can be estimated from the results of equilibrium phase-behavior experiments. They can also be determined by means of displacement experiments conducted in a high-pressure sandpack. This paper describes the equipment and procedure which have been developed for determining miscibility conditions by stable displacement. A systematic series of displacements of a West Texas reservoir oil was carried out. The results indicate that, at constant pressure, miscibility is a function only of the pseudocritical temperature of the injection gas. This fact, together with improved experimental methods, makes the displacement technique a rapid, reliable means for determining miscibility conditions. In conjunction with the displacement experiments, phase diagrams were constructed for the oil with dry gas and propane and with dry gas and ethane. Phase behavior of the methane-ethane-propane system was determined at 110°F. The experimental work demonstrates the feasibility of using ethane-rich gases to reduce cost and pressure requirements for miscible displacement. INTRODUCTION In recent years, interest in the miscible displacement of oil by light hydrocarbon mixtures has been high. Many pilot and a few field scale projects have been started.1 These projects have made use of various methods for achieving miscibility: (1) the LPG-slug process, (2) the enriched-gas-drive process and (3) the high-pressure gas-drive process. Some field projects have been successful; the results of others are debatable. In general, projects which have performed best have involved the injection of an appreciable fraction of a pore volume of miscible material. Economical application of miscible displacement depends strongly on the cost of the miscible-injection fluid. If an appreciable fraction of a pore volume of material is required for successful application of these methods, a precise knowledge of the minimum requirements for miscibility in terms of composition of injection fluid is essential. Therefore, reliable experimental methods for determining miscibility conditions are important, and a procedure for estimating these conditions from the composition of the reservoir fluid is highly desirable. The subject of this paper is the problem of determining conditions which result in miscible displacement of oil by light hydrocarbon mixtures. Miscibility conditions can be estimated by means of equilibrium experiments conducted in a PVT cell, or they can be determined by means of high-pressure displacement experiments. This paper describes the equipment and procedure which have been developed for the determination of miscibility by high-pressure displacement experiments. These methods have been applied to the displacement of a West Texas reservoir oil with mixtures of dry gas, ethane and propane. In conjunction with the displacement experiments, triangular phase diagrams have been constructed for mixtures of the oil with dry gas and propane and with dry gas and ethane. The effect of injection-gas composition on conditions for miscible displacement in high-pressure sandpacks and cores has been the subject of several published papers.2-5 The experimental methods used in these investigations were such that displacements were unstable, and the effects of fingering and/or gravity layover are clearly evident in the results. Miscibility conditions were probably correct in spite of the instability phenomena, but the experiments evidently were time-consuming, and limited data were reported. Systematic high-pressure flow studies which would support a correlation of miscibility conditions have not been reported; however, Wilson5 has proposed the use of pseudocritical temperature of the injection gas as a parameter and Benham, et al,6 have based a miscibility correlation on observed and calculated equilibrium data.