Pressure Transient Testing presents the fundamentals of pressure-transient test analysis and design in clear, simple language and explains the theoretical bases of commercial well-test-analysis software. Test-analysis techniques are illustrated with complete and clearly written examples. Additional exercises for classroom or individual practice are provided. With its focus on physical processes and mathematical interpretation, this book appeals to all levels of engineers who want to understand how modern approaches work.

Summary. Values of oil compressibility are required in all solutions of transient fluid-flow problems. Oil compressibility can be calculated directly if reservoir-fluid studies are available. In this paper, empirical equations are presented to provide accurate estimates of the compressibility of black oil at pressures below the bubblepoint when laboratory measurements are not available. The equations were developed with data from reservoir-fluid studies of 260 oil fields worldwide. The data encompassed a wide range of oil compressibilities, surface-gas specific gravities, stock-tank oil gravities, solution GOR'S, reservoir pressures. reservoir temperatures, and bubblepoint pressures. Introduction Values of total system isothermal compressibility are required in the analysis of pressure-buildup and drawdown tests of saturated oils. Calculation of total system isothermal compressibility for a saturated system containing oil and free gas involves, among other things, evaluation of the isothermal compressibility coefficient of the oil phase. In this discussion, the term compressibility refers to the coefficient of isothermal compressibility. Oil compressibility is the fractional change of the volume of oil as pressure changes. For a system with pressure below the bubblepoint, the volume occupied by the gas evolved from the oil during the differential change in pressure must be taken into account in the calculation of oil compressibility. This is done by including the change in solubility of gas in the oil-compressibility equation. When reservoir-fluid studies are available, oil compressibility can be calculated directly with an equation developed by Perrine and extended by Martin. Often, fluid-property data are unavailable and oil compressibility must be estimated. The only previously published correlations of this physical property were by Ramey. The correlations presented in this paper are based on a much larger and more geographically diverse sample than that on which previous correlations were based. These equations provide accurate estimates of oil compressibility at pressures below the bubblepoint when laboratory measurements are unavailable. Background Several methods to calculate oil compressibility have been published, but only two consider oils at pressures below the bubblepoint. Martins presented an extension of Perrine's equation for saturated oil compressibility, expressing volume in terms of FVF and considering the change in solubility of gas in the oil phase: ...................(1) Martin's equation can be used to obtain values of oil compressibility when FVF values of oil and gas, Bo and Bg, respectively, and the solution GOR, Rs (all as functions of pressure), are available from reservoir-fluid studies. Previous research resulted in correlations for estimating oil compressibility at pressures below the bubblepoint. These correlation were based on existing correlations of Bo and the dissolved gas/oil ratio. They are based on limited data and thus yield only approximate results, as illustrated in Figs. 1 through 3. Development of Equations Previous research suggested that oil compressibility is a function of the solution gas/oil ratio, stock-tank oil gravity, surface gas gravity, bubblepoint pressure, reservoir temperature, and pressure. These variables were used to develop equations empirically for estimating black-oil compressibility at pressures below the bubblepoint. The data base used in developing the equations was compiled from differential liberation and separator test data of black-oil samples from 260 well locations worldwide. Because the data were proprietary, individual wells were not identified by geographic location; hence, the dependence of oil compressibility on geographic location could not be evaluated. The data base consisted of values of isothermal compressibility, stock-tank oil gravity, surface-gas specific gravity, total solution GOR, reservoir pressure, reservoir temperature, and bubblepoint pressure. A summary of the data is given in Table 1. Values of oil compressibility were calculated with Eq. 1. Differential vaporization data were used in conjunction with the results of separator tests to calculate values of Bo, and Rs, as functions of pressure. These values were calculated from the assumptions that the reservoir operates in differential liberation and that the flow stream from the sandface to the stock tank operates as in the separator tests. The derivatives of Bo, and Rs, with respect to pressure were obtained by first fitting these values with smooth curves using the cubic-spline interpolation method and then differentiating the approximation function to obtain the derivatives at any point. The boundary conditions were established by calculating the second derivatives at the endpoints of the spline by means of finite-difference calculus. Stock-tank oil gravity was obtained from the separator test of each reservoir-fluid sample. Separator and stock-tank gas gravity were combined to calculate the total gas gravity for a given solution GOR. The solution GOR at bubblepoint conditions, Rsb, was calculated as the sum of the separator and the stock-tank GOR. Rs, was also tested as an explanatory variable. The t-statistic for the regression coefficient of Rs indicated that, in conjunction with the other explanatory variables, Rs does not contribute significantly to explaining oil compressibility. An evaluation of the data was the first step in specifying the form of the regression equation. The data were evaluated by means of vertical histograms, scatter diagrams, and Pearson's correlation coefficient. SPEFE P. 659^

Summary. An empirical equation was developed to estimate stock-tank GOR from field data for black oils. Solution GOR at or above bubblepoint pressure can be obtained as the sum of the estimated stock-tank GOR and the measured separator GOR. The equation was derived with data from two-stage separations of 301 black-oil samples. Introduction Volumetric and material-balance calculations of oil in place require estimates of oil FVF and bubblepoint pressure. Several correlations, the most applicable of which was proposed by Standing, I are available for determining bubblepoint pressure and oil FVF when an estimate of solution GOR is available. Frequently solution GOR, Rsb, is estimated for pressures at or above the bubblepoint by setting its value equal to the initial producing GOR. However, the initial producing GOR often does not include gas vented from the stock tank. This omission can cause the estimate of Rsb to be low by 20 % or more. 2 The inaccurate estimate of Rsb then introduces error into estimates of bubblepoint pressure and FVF, and hence into oil-in-place calculations. This paper presents a method of using readily available field data to obtain an accurate estimate of Rsb. Total producing GOR, R, is equal to the sum of stocktank GOR, Rst, and separator GOR, Rsp.

The sliding phenomenon which is reported to impose a restriction upon the slope of slurry pipelines is investigated experimentallv. Two different types of behavior which could be called "sliding" were observed.At pipe inclianations greater than 22" to the horizontal, fully settled layers of solid particles would slide with shear occurring a t or near the pipe wall. The critical angle of inclination increased as the particle size decreased.When the slurry was not fully settled, a natural convective flow process was observed to move the slurry down a pipe incline. This flow occurred at much lower pipe inclinations. Concentration profiles measured near the bottom of a pipe incline showed little effect of slurry type or concentration, provided the slurry contained a significant amount of slowly settling solids. In this case, pipe slope was the most important variable.he experimental work reported in this communi-T cation was stimulated by the statement"' that in the design of the Savage River Iron Concentrate slurry pipeline, pipe slopes were restricted to values less than 14% (9") to prevent sliding of the slurry on the pipe wall a t shutdown. The practical effect of such a restriction could be to increase construction costs of slurry pipelines in hilly terrain. In view of the importance of capital costs upon the economics of slurry pipelines, it was considered desirable to investigate this phenomenon as fully as possible using laboratory scale equipment. It was hoped that laboratory experiments using short lengths of small (2-in I.D.) pipe could establish the effects of slurry type, slurry concentration and pipe slope and could contribute a qualitative understanding of the process. The extremely important variables of pipe diameter and pipe length were not amenable to systematic investigation and no definitive conclusions about these variables can be drawn from the studies reported here. However, it is fortunate that such inferences as may be drawn from the present work suggest that it may well be relevant to the problem of larger, longer pipelines. Experimental studies of the effect of these two variables are currently being planned. Static friction at the pipe wallWhen one considered the angle of internal friction of a fluid-particle mixture of the concentration of a typical settled bed, the original statement was difficult to understand. Since the angle of repose approaches the angle of internal friction fairly nearly and since angles of repose of the order of 30" are not uncommon, even for submerged solid particles, it was very difficult to accept the sliding phenomenon as one which resulted from shear within the particle On a ktudik expkrimentalement le phknomhne de glissement qui, rapporte-t-on, nkessite des restrictions sur la pente des pipe-lines dans lesquels on transporte des matikres solides m suspension. On a observk deux types diffkrents de "glissements".Lorsque les inclinaisons des canalisations exddaient un angle de 22" par rapport B I'horizontale, les couches bien ktablies des matitres solides ont g...

Permeab~i!y in.a f?~tio~ fr~~ently follows a unim~ p~obability distribution. In many formations, particularly sedimentary ones, the permeabIhty dIstrIbutIOn IS sImIlar to the log-normal dIstnbution. Theoretical considerations field cases and a reservoir simulation example s~~w t~at ~e ~ed~an, rather ~an the arithmetic mean, is tlte appropriate measure of ~entral tend~ncy or average ~alue of tlt~ pe~eablh~ dIstrIbutIon In a formatIOn. Use of tlte correct estimate of average permeability is of particular importance In the claSSIficatIOn of tIght gas formations under statutes in tlte 1978 Natural Gas Policy Act (NGPA).