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^