An Analytical Extension of the Dykstra-Parsons Vertical Stratification Discrete Solution to a Continuous, Real-Time Basis

Publisher Website
Google Scholar
Abstract
Analytically exact and continuous solutions are developed for the space-time relationships of a linear waterflood in a vertically stratified reservoir model. The solutions represent simple extensions of the analytical, but discrete, spatial relationships of Dykstra and Parsons to analytically continuous expressions. Explicit solutions for time are presented that permit the coupling of all instantaneous and cumulative performance parameters to a completely rational time basis. The continuous nature of the solutions permits unusual fluid behavior to be observed between successive bed breakthrough points. Although the model assumes pistonlike displacement, these novel phenomena do not appear to be artifacts of this limiting assumption. This work develops the concept of a bed property time that forms the basis for a generalized bed-ordering parameter. For the case of constant injection pressure, property time is shown to be identical to the real or process time. For the common case of constant overall injection rate, the customary use of property time concepts to determine real or process time is shown to be completely erroneous, yielding values that are incorrect both in magnitude and in trend. A bed flood-front passing phenomenon is presented that allows the flood fronts of "slower" beds initially to lead those of "faster" beds if specified constraints are satisfied. It is shown that these constraints can be satisfied for moderate bed-fluid property variations. The analytical nature of the solutions provides greater insight into the controlling factors of such processes. The use of real time as a process parameter provides a more realistic basis for comparative performance between floods under the same or different injection conditions. The relationship between injected PV and time can be used to extend the linear model to approximate predictions for stratified, nonlinear, pattern floods.