Oil and Gas Relative Permeabilities Determined From Rate-Time Performance Data

Abstract

SUMMARY This paper presents a method of determining kg/ko, oil relative permeability, kro, and gas relative permeability krg, using oil and gas rate-time performance data from individual wells and from a total field. Advanced decline curve analysis is used to obtain original oil in place, N, and thus saturation; the Δp2 form of an oil inflow performance equation is used to determine kro below the bubble point pressure. The procedure was used on production data from several wells in a North Sea naturally fractured limestone volatile oil field. Results indicate the calculated oil and gas relative permeabi1ity curves differ from laboratory and correlation calculated curves. By analyzing the oil and gas relative permeability curves of each of the seven wells in the field, it was found that the degree of natural fracturing of a specific well influences the position of the oil and gas relative permeability curves. The results expressed as kg/ko curves appear to be consistent with the field case history findings of Arps for limestone reservoirs – i.e., as the degree of fracturing increases, the kg/ko curves become more unfavorable with respect to oil recovery. Initial pressure surveys on-each well determine its degree of fracturing while a later field-wide pressure survey confirms the oil-in-place calculated for each well using rate-time decline curve analysis. Pressure-time data to make these calculations is seldom available for all wells in a field or, when available, is much less frequent than rate-time data. In contrast, the principal calculation methods shown in this paper use rate-time data, thus taking advantage of the most frequently collected and the most widely available information.

Well-Test Analysis for Solution-Gas-Drive Reservoirs: Part 1—Determination of Relative and Absolute Permeabilities

“…Note that work similar to that presented here was done independently and concurrently by AI-Khalifah et al 23 Moreover, Fetkovich et al 15 presented a procedure to determine points on the oil relative permeability curve from boundary-dominated flow data if the reservoir PV and the PI can be determined by type-curve matching long-time data with decline curves. of the effective oil and gas permeabilities as functions of time or pressure and as functions of oil saturation by direct computation with the logarithmic time derivative of the flowing wellbore pressure and by performing semilog analysis of the flowing wellbore pressure squared.…”

Well-Test Analysis for Solution-Gas-Drive Reservoirs: Part 3—A Unified Treatment of the Pressure-Squared Method

“…6). Fetkovich et al 16 presented a procedure for determining a point on the oil relative permeability curve by assuming that kro/(f.l.oBo) is a linear function of pressure. This method uses data from the boundary-dorninated flow period and assumes that the reservoir PV and the PI can be determined by type-curve matching of late-time data.…”

Constant-Pressure Production in Solution-Gas-Drive Reservoirs: Transient Flow

“…Then it is shown that pressure distributions in the reservoir can also be correlated in terms of the Boltzmann variable provided that differences in the square of pressures are used. These results may be used to provide a theoretical foundation for the work of Fetkovich et al 7,8 and are also related to the results of Al-Khalifah et al 9 Variations in the sandface saturation with time are examined, and observations pertinent to well-test analysis are discussed.…”

“…7 with respect to t D , we obtain dppwD/d In tD = 112 =tD (dppwD/dt)(dtldi D ) ........... (8) Using the definition of tD given by Eq. 3, we have respectively.…”