This paper presents a practical method to estimate the storativity ratio of a dual-permeability layered reservoir with crossflow from pressure-transient data. The method uses an analytical formula for the storativity ratio in terms of the separation between the two semilog straight lines on the pressure vs. log-time plot, similar to the method used for dual-porosity systems. Knowing the storativity ratio from a well test allows individual-layer properties to be estimated if the layer flow rates are available from production logs. Demonstrations of the method to estimate the storativity ratio and individual-layer properties are presented by examples. Comparison of the results with those obtained from the existing techniques is also provided to highlight the accuracy of the proposed technique.
Depletion characteristics of commingled multilayer reservoirs are determined by the characteristics of interlayer-fluid transfer, which is dictated by the properties of the individual layers. In such systems, to obtain the individual layer properties from pressure-transient tests, two parameters are required: the storativity ratio, ?, defined as the ratio of the storativity of the layer with higher flow capacity to the total system storativity, and the transmissivity ratio, ?, which is the ratio of the higher of the layer flow capacities to the total system flow capacity. If the layer skin factors are equal, the transmissivity ratio is equal to the ratio of the flow rate of the layer with higher flow capacity to the total flow rate and may be obtained from production logs. The storativity ratio, on the other hand, needs to be determined from the pressure-transient data or by independent means.
In the literature, dual-porosity and dual-permeability system definitions are usually associated with naturally- fractured and layered systems, respectively. In principle, dual-porosity systems constitute a subset (a limiting case) of the dual-permeability systems and, as such, possess many characteristics that resemble those of dual-permeability systems (Bourdet 1985).
For dual-porosity systems, such as naturally fractured reservoirs, ? may be determined from the vertical separation,dp, between the two parallel straight lines on the pressure vs. log-time plot (Pollard 1959; Warren and Root 1963). However, for dual-permeability systems, as in layered reservoirs with crossflow, the separation between the two parallel semilog straight lines is not only a function of ? but also a function of ?. Therefore, the objective of this study is to obtain a practical relation for the storativity ratio of layered systems with crossflow in terms of the separation between the two semilog straight lines on pressure vs. log-time plot and the transmissivity ratio. We demonstrate that having an initial estimate of ? is crucial for the estimation of the other layer properties from straight-line or regression-analysis techniques.