Transient Wellbore Pressure and Flow Rates in a Commingled System With Different Layer Pressures

Abstract

ABSTRACT 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.