This paper presents a mathematical analysis of how incorrect estimates of initial reservoir pressure, pi, may affect rate-transient analysis (RTA) in ultra-low permeability reservoirs. Measured values of pi are rarely available, and the value estimated using alternative approaches, such as a DFIT test, can be time consuming, expensive, and may also be inaccurate. Rate transient analysis (RTA) includes flow regime identification with a log-log plot of rate-normalized pressure drawdown (which requires pi) vs. material balance time (MBT). Several published works have shown that these plots exhibit power-law behavior (straight line with slope 1/n) during the transient flow regime. This may introduce errors when the pi value is incorrect. For example, estimating reservoir properties (such as reservoir permeability or total hydraulic fracture area) from a Cartesian plot of rate normalized pressure (RNP) vs a time (t) function (e.g., tn) is frequently important. In this paper, we examine what we can and cannot do accurately when reliable estimates of pi are not available.
We used the power-law model to analytically derive how different pi estimates affect the log-log diagnostic plot between RNP and MBT and estimation of reservoir properties from the Cartesian plot between RNP and tn for a reservoir producing under constant bottomhole pressure. We extended the derived analytical results using simulated production data for a reservoir producing under smoothly changing bottomhole pressure. Finally, we validated our findings using field data.
Our results showed that the slope of a log-log plot of RNP vs MBT is relatively insensitive to the value of pi. Flow regimes can be identified with reasonable certainty with only an estimate of pi. However, different values of pi change the shape of the Cartesian plot between RNP and tn. This may lead to inaccurate estimates of permeability and total area of hydraulic fractures.
We conclude that a reasonable estimate of pi should be sufficient to identify flow regimes. However, analysis results from RNP vs. Cartesian plots may be unreliable and can introduce large errors in absence of correct values of pi.