This work addresses the problems of design and interpretation of layered reservoir tests (LRT) in commingled wells when the layer potentials are different; the difference may be in the conditions either at the initial time or at the outer layer boundaries. The multilayer models for commingled wells are constructed from existing single-layer analytic solutions to account for different layer properties and boundary conditions. A general situation is considered in which some layers have a constant pressure condition and others have a no-flow condition at the outer boundary. The algorithms developed here will allow the reservoir engineers, for the first time, to rigorously design and interpret the multi-transient LRTs using the extensive catalog of existing single-layer analytic models, rather than relying on numerical simulation. This development will not only save a great deal of computer time, but will also enable interpretation of tests in reservoirs whose geometries and parameters place them beyond the capability of existing simulators.
An LRT design consists of calculating the transient wellbore potential and the individual layer rates for a given variation of the total flow rate. Two alternative scenarios are considered for the initial state of the reservoir: Either the reservoir is in equilibrium and the well is put on production at t = 0, or the well is initially producing in a steady state. Algorithmic procedures are derived from the first principles and validated by comparison with the results of finite difference numerical simulation for three different reservoir systems. A fourth example, which is beyond the capability of simple reservoir simulators, is presented to demonstrate the power of the new procedure.
The LRT interpretation requires the calculation of the total and individual layer flow rates during a multitransient test, given the measured wellbore potential over the test period and the production history of the well. The scheme presented for this problem relies on a synthesis of the new test design calculation procedures with the existing algorithms for flow rate calculation.
The work of Lefkovits et al. appears to be the first among many in the petroleum technical literature that address the problem of calculating the transient response of a well producing a multilayered reservoir in which communication among the layers occurs only through the wellbore (commingled systems). However, apparently only three papers deal with reservoirs in which the layers are initially at different potential. The assumption of equal initial potential in all layers is impractical due to stratigraphic barriers and/or differential depletion.
The importance of properly treating unequal potential distributions in commingled systems is twofold. First, if the presence of unequal layer potentials is neglected, the individual layer properties (and thus the relative layer producibility/injectivity) obtained from well test analysis can be in gross error. This has been shown both in practice as well as in theory. Secondly, the ability to model commingled systems with unequal potential distributions allows the engineer to apply material balance concepts on a zone-by-zone basis for more reliable analysis and prediction. Papadopulos appears to have been the first to consider layers having unequal initial potential distributions.