An analytical solution for pseudosteady-state flow in a hydraulically fractured stratified reservoir with interlayer crossflows

This work presents an analytical solution for the pseudosteadystate (PSS) flow in a hydraulically fractured stratified reservoir with finite fracture conductivity in the presence of interlayer crossflows. Specifically, a three-layer configuration is considered, with the midlayer hydraulically fractured and sandwiched between two adjacent layers feeding the midlayer by crossflows. The circular drainage area is approximated as elliptical, allowing the problem to be solved in elliptical coordinates analytically. Explicit expressions in the physical-variable space for the dimensionless productivity index (PI) and the wellbore-pressure drawdown for the PSS flow of such a hydraulically fractured system with interlayer crossflows are derived for the first time. Compared with the case without interlayer crossflows, the dimensionless PI is reduced because of additional pressure drawdown occurring in the sandwiching layers; on the other hand, the time rate of increase of the pressure drawdown at the wellbore is also decreased because of the addition of the producible fluid stored in the sandwiching layers. This slower time rate of increase of the wellbore-pressure drawdown prolongs the PSS production period, which can lead to a larger accumulative production. It is also shown that when the layers have comparable thickness, fracturing the higher-permeability layer provides the best performance because the wellbore-pressure drawdown experiences the slowest time rate of increase during the PSS flow period. The analytical solution can also be used for fracture-design optimization as well as production-decline analysis for fractured stratified systems.