Summary
Experience with material-balance data sets from the field and from simulation has revealed some procedures that can be used to improve analysis of both oil and gas reservoirs:Failure to account for a weak waterdrive can result in significant material-balance errors.The assertion of previous authors that weak waterdrive exhibits a negative slope on the Cole (gas) and Campbell (oil) plots has been confirmed. A weak waterdrive is much more unambiguous on these plots than on commonly used plots, such as the p/z plot for gas.A modified version of the Cole plot is proposed to account for formation compressibility.The reservoir drive indices are a useful tool for determining the correctness of the material-balance solution because they must sum to unity. The drive indices should never be normalized to sum to unity because this obscures their usefulness and leads to a false sense of security.A modified version of the Roach plot (for gas) is proposed that improves interpretation in some waterdrive situations.Material balance has not been replaced by reservoir simulation; rather, it is complementary to simulation and can provide valuable insights to reservoir performance that cannot be obtained by simulation.
Introduction
Classical material balance is one of the fundamental tools of reservoir engineering. Many authors have addressed the difficult problem of solving the material balance in the presence of a waterdrive (Refs. 1 through 5 are just a few of the more significant ones). The emphasis in the literature has been on strong and moderate waterdrives. In this paper, examples of weak waterdrives are shown in which the effects on the material balance are significant. All aquifers studied here are of the "pot aquifer" type, which is time-independent.
In gas reservoirs, the plot of p/z vs. cumulative gas production, Gp, is a widely accepted method for solving the gas material balance1 under depletion-drive conditions. Extrapolation of the plot to atmospheric pressure provides a reliable estimate of original gas in place (OGIP). If a waterdrive is present, the plot often appears to be linear, but the extrapolation will give an erroneously high value for OGIP. Many authors have addressed this problem (including those in Refs. 2 and 5 through 8), especially in cases of strong or moderate waterdrives. The p/z plot is actually more ambiguous in weak waterdrives than in strong or moderate ones.
The Cole plot7,9 has proven to be a valuable diagnostic tool for distinguishing between depletion-drive gas reservoirs and those that are producing under a waterdrive. The analogous plot for oil reservoirs is the Campbell plot.10 The literature has emphasized strong and moderate waterdrives, the signature shapes of which are a positive slope and a hump-shaped curve, respectively, on these plots. Previous authors have recognized that weak waterdrives can produce negative slopes on these two diagnostic plots, but this author is not aware of any example plots in the literature. This paper shows examples, using simulation and actual field data, wherein a negative slope clearly reveals a weak waterdrive. These plots are much more diagnostic than the p/z plot. Once a weak waterdrive has been diagnosed, the appropriate steps can be taken in the material-balance equations to yield more accurate results.
The Cole plot assumes that formation compressibility can be neglected, which is frequently the case with gas. However, in those reservoirs in which formation compressibility is significant, a modification to the Cole plot is presented that incorporates formation compressibility and gives more accurate results.
The reservoir drive indices have been used to quantify the relative magnitude of the various energy sources active in a reservoir. It is shown here that the drive indices are also a useful diagnostic tool for determining the correctness of a material balance solution because they must sum to unity. If they do not sum to unity, a correct solution has not been obtained. In some commercial material-balance software, the drive indices are automatically normalized to sum to unity, which not only obscures their usefulness but also leads to the false impression of having achieved a correct solution.
The Roach plot has been presented11 as a tool for solving the gas material balance when formation compressibility is unknown, with or without the presence of waterdrive. This paper shows that for waterdrives that fit the small pot aquifer model, incorporating cumulative water production into the x-axis plotting term improves the linearity of the Roach plot and gives more accurate values for OGIP.
Finally, it is argued that even in those reservoirs for which a simulation study is performed, classical material-balance evaluation should be performed on a stand-alone basis. Simulation should not be viewed as a replacement for material balance because the latter can yield valuable insights that can be obscured during simulation. Performing a separate material balance study usually will improve overall reservoir understanding and enhance any subsequent simulation study. Material balance should be viewed as a complement to simulation, not as a competing approach.
In this paper, formation compressibility, cf, is assumed to be constant and unchanging over the reservoir life under investigation. References are given for recommended methods to be used in those cases in which cf is variable.
New Waterflooding Characteristic Curves Based on Cumulative Water Injection