Production data generally consists of variable rate and variable flowing pressure. It is convenient to be able to use reservoir models that assume a constant flow rate, since these solutions have been previously derived in the well testing literature. Thus, it is necessary to have a time function capable of converting general production conditions into the equivalent constant rate solution. Blasingame1, and later Agarwal et al2 have shown that Material-Balance-Time provides an exact transformation of constant pressure data to constant rate type curves, during the boundary dominated flow regime. It also yields a reasonable approximation during radial flow, and when rate and/or pressure vary smoothly. Poe3 has investigated the effectiveness of using material-balancetime for other transient flow regimes using the constant pressure solution, rather than the constant rate solution as a base model.
The objectives of this paper are twofold. Firstly, it serves to investigate the applicability of materialbalance- time during the linear flow regime (fracture flow), where the difference between the constant rate and constant pressure solutions is more pronounced. Further to this, material-balance-time correction factors are quantified for both radial and linear transient flow regimes (this has not previously been done using the constant rate solution as the base model). Secondly, it serves to illustrate by synthetic and field examples, a comparison of material-balance-time against the logarithmic superposition time function, to determine under what circumstances material-balance-time errors significantly influence rate transient interpretation, in practice.
In pressure transient tests, the diagnostic plot (log-log plot of pressure and derivative) is an invaluable tool for reservoir characterization. For variable rate drawdown tests and flow and buildup tests, a time superposition function should be used to convert variable rates into an equivalent constant rate solution. Since pressure transient tests are usually dominated by infinite acting flow, the widely accepted time superposition function is one that assumes radial flow (logarithmic superposition time). One of the problems inherent in pressure transient analysis is that radial flow is not always the dominant flow regime. Thus, there is the potential for misinterpretation of the diagnostic plot in certain situations. In recent years, diagnostic plots of various different forms have been used to analyze production data. The nature of production data analysis is different than that of pressure transient analysis, primarily because of the greatly increased time scale, and because production data tends to be much noisier than pressure transient data. Most of the literature agrees that a time superposition function that assumes boundary dominated flow is more appropriate to use on a diagnostic plot of production data, than any transient superposition function, because most production data is under the influence of some sort of reservoir depletion. However, with very low permeability reservoirs, this is not necessarily the case.
Material-balance-time is the time superposition function for volumetric depletion. It is rigorous in converting variable rate production into equivalent constant rate production, provided that the flow regime is boundary dominated (volumetric depletion).
