Expanded Material Balance Equation
Principles
The so-called Schilthuis (1936) material balance equation is one of the fundamental relations in reservoir engineering. In "expanded" form, which includes water influx, it may be stated:
Production of oil and gas = Expansion of oil and gas initially in place + Water influx
Assuming an initial gas cap and — at this time — ignoring compressibility of pore volume and interstitial water, the equation may be written:
Np[Bt + Bg(Rp - Rsi)] + WpBw = N[(Bt - Bti) + mBti(Bg - Bgi)/Bgi] + We (1)
where the left-side terms account for the reservoir volume of oil, gas, and water production, and the right side terms account for the expansion of the oil and free gas initially in place, plus the water influx. (All notation in this section is SPE standard.)
Equation 1 is consistent with the formulation of Schilthuis, who ignored compressibility. However, compressibility effects should be considered for material balance calculations involving oil reservoirs above the bubble-point. Depending on the magnitude of rock-fluid compressibility compared to overall system compressibility, it may be desirable to include rock-fluid compressibility for oil material balance calculations below the bubble-point.
In Equation 1, it is assumed that the reservoir can be treated as a "tank," with spatial variations in PVT properties and reservoir pressure being averaged.
There are three unknowns in Equation 1:
· STB oil initially in place (N);
· size of the initial gas cap as a fraction of initial oil zone volume (m) ; and
· cumulative water influx (We).
In application, Equation 1 is solved at the end of successive time periods, generally quarterly, using the cumulative production data at the end of each period and PVT properties evaluated at the average static reservoir pressure at the end of the period. Theoretically, given enough pressure-production history and repetitive solutions of Equation 1, it should be possible to solve for all three unknowns. In practice, this is rarely possible, mainly because of errors in measuring, and problems in interpreting and averaging, bottomhole pressures. If both a significant initial gas cap and water influx are a possibility, efforts should be made to determine initial gas cap size using volumetric methods.
Limitations
Limitations to reliable application of the material balance equation are both theoretical and practical.
Theoretical limitations are imposed by assumptions necessary for a tractable methodology, which are
· The assumption that oil and free gas in the reservoir are in thermodynamic equilibrium. Wieland and Kennedy (1957) report about 20 psi supersaturation in experiments conducted using East Texas and Slaughter field cores.
· The assumption that the PVT data, obtained from differential liberation, replicates the liberation process in the field. As discussed by Dodson (1953) and others, both flash and differential liberation of gas may occur at various times and places between the reservoir and the stock tank, with the differences in PVT properties between the two processes increasing with more volatile oils.
· The assumption that free gas in the reservoir has the same composition as free gas on the surface, differing only in volume, as expressed by the gas formation volume factor. With progressively more volatile oils, free gas in the reservoir contains progressively more liquids in the vapor phase that are recovered as stock tank liquids but are not accounted for by the differential liberation process.
Practical limitations are imposed by data requirements and reservoir conditions. Data required for reliable application of the material balance equation include PVT analyses of representative fluid samples, accurate static bottomhole pressure history of key wells in the reservoir and accurate monthly production data for oil, gas, and water. The accuracy requirements usually exceed the routine needs for many field operations.
Reservoir conditions that may limit the reliability of a material balance estimate include:
· Strong water drive and/or a large gas cap which maintain reservoir pressure at nearly initial pressure. Under these conditions the material balance equation generally does not yield stable solutions, because the small pressure drops in the reservoir are frequently of the same magnitude as the errors in the measurements.
· A really extensive reservoirs with different areas at different stages of development and production. Generally, this leads to wide variations in gas saturation and reservoir pressure that cannot readily be "averaged."
· A really extensive reservoirs with low values of kh/m. These conditions make it difficult to determine the static bottom-hole pressure reliably and often cause large areal variations in pressure that are difficult to average.
· Very heterogeneous reservoirs with zones of high permeability interbedded with zones of low permeability, or highly fractured reservoirs. Under these conditions the lowpermeability zones, or the matrix blocks, usually pressure deplete more slowly than the high-permeability zones, or the fractures, and it is practically impossible to determine volumetrically weighted average reservoir pressure.
Some of these limitations may be overcome by using a multidimensional reservoir simulator, rather than a zero-dimensional material balance, or tank, model.
Irrespective of the material balance method used — tank model or multidimensional simulator — it is good practice to plot all of the bottomhole pressure data versus time on the same graph for all the wells suspected of being in a common reservoir. Such a plot usually provides valuable insight of the degree of communication between wells. It may help in identifying wells that are in separate reservoirs, contrary to the current geologic interpretation.
Principles
The so-called Schilthuis (1936) material balance equation is one of the fundamental relations in reservoir engineering. In "expanded" form, which includes water influx, it may be stated:
Production of oil and gas = Expansion of oil and gas initially in place + Water influx
Assuming an initial gas cap and — at this time — ignoring compressibility of pore volume and interstitial water, the equation may be written:
Np[Bt + Bg(Rp - Rsi)] + WpBw = N[(Bt - Bti) + mBti(Bg - Bgi)/Bgi] + We (1)
where the left-side terms account for the reservoir volume of oil, gas, and water production, and the right side terms account for the expansion of the oil and free gas initially in place, plus the water influx. (All notation in this section is SPE standard.)
Equation 1 is consistent with the formulation of Schilthuis, who ignored compressibility. However, compressibility effects should be considered for material balance calculations involving oil reservoirs above the bubble-point. Depending on the magnitude of rock-fluid compressibility compared to overall system compressibility, it may be desirable to include rock-fluid compressibility for oil material balance calculations below the bubble-point.
In Equation 1, it is assumed that the reservoir can be treated as a "tank," with spatial variations in PVT properties and reservoir pressure being averaged.
There are three unknowns in Equation 1:
· STB oil initially in place (N);
· size of the initial gas cap as a fraction of initial oil zone volume (m) ; and
· cumulative water influx (We).
In application, Equation 1 is solved at the end of successive time periods, generally quarterly, using the cumulative production data at the end of each period and PVT properties evaluated at the average static reservoir pressure at the end of the period. Theoretically, given enough pressure-production history and repetitive solutions of Equation 1, it should be possible to solve for all three unknowns. In practice, this is rarely possible, mainly because of errors in measuring, and problems in interpreting and averaging, bottomhole pressures. If both a significant initial gas cap and water influx are a possibility, efforts should be made to determine initial gas cap size using volumetric methods.
Limitations
Limitations to reliable application of the material balance equation are both theoretical and practical.
Theoretical limitations are imposed by assumptions necessary for a tractable methodology, which are
· The assumption that oil and free gas in the reservoir are in thermodynamic equilibrium. Wieland and Kennedy (1957) report about 20 psi supersaturation in experiments conducted using East Texas and Slaughter field cores.
· The assumption that the PVT data, obtained from differential liberation, replicates the liberation process in the field. As discussed by Dodson (1953) and others, both flash and differential liberation of gas may occur at various times and places between the reservoir and the stock tank, with the differences in PVT properties between the two processes increasing with more volatile oils.
· The assumption that free gas in the reservoir has the same composition as free gas on the surface, differing only in volume, as expressed by the gas formation volume factor. With progressively more volatile oils, free gas in the reservoir contains progressively more liquids in the vapor phase that are recovered as stock tank liquids but are not accounted for by the differential liberation process.
Practical limitations are imposed by data requirements and reservoir conditions. Data required for reliable application of the material balance equation include PVT analyses of representative fluid samples, accurate static bottomhole pressure history of key wells in the reservoir and accurate monthly production data for oil, gas, and water. The accuracy requirements usually exceed the routine needs for many field operations.
Reservoir conditions that may limit the reliability of a material balance estimate include:
· Strong water drive and/or a large gas cap which maintain reservoir pressure at nearly initial pressure. Under these conditions the material balance equation generally does not yield stable solutions, because the small pressure drops in the reservoir are frequently of the same magnitude as the errors in the measurements.
· A really extensive reservoirs with different areas at different stages of development and production. Generally, this leads to wide variations in gas saturation and reservoir pressure that cannot readily be "averaged."
· A really extensive reservoirs with low values of kh/m. These conditions make it difficult to determine the static bottom-hole pressure reliably and often cause large areal variations in pressure that are difficult to average.
· Very heterogeneous reservoirs with zones of high permeability interbedded with zones of low permeability, or highly fractured reservoirs. Under these conditions the lowpermeability zones, or the matrix blocks, usually pressure deplete more slowly than the high-permeability zones, or the fractures, and it is practically impossible to determine volumetrically weighted average reservoir pressure.
Some of these limitations may be overcome by using a multidimensional reservoir simulator, rather than a zero-dimensional material balance, or tank, model.
Irrespective of the material balance method used — tank model or multidimensional simulator — it is good practice to plot all of the bottomhole pressure data versus time on the same graph for all the wells suspected of being in a common reservoir. Such a plot usually provides valuable insight of the degree of communication between wells. It may help in identifying wells that are in separate reservoirs, contrary to the current geologic interpretation.
No comments:
Post a Comment