Effect of Errors in Initial Pressure Measurement on Rate-Transient Analysis in Unconventional Reservoirs

This paper presents a mathematical analysis of how incorrect estimates of initial reservoir pressure, p_i, may affect rate-transient analysis (RTA) in ultra-low permeability reservoirs. Measured values of p_i 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 p_i) 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 p_i 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 p_i are not available.

We used the power-law model to analytically derive how different p_i 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 p_i. Flow regimes can be identified with reasonable certainty with only an estimate of p_i. However, different values of p_i 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 p_i 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 p_i.