Semi-analytical modeling of pressure-transient response of multilateral horizontal well with pressure drop along wellbore

Abstract

The primary purpose of this work is to develop a generalized model to rigorously account for the pressure drop within multilateral horizontal well (MLHW) with any number of laterals in arbitrary configurations. The finite-conductivity wellbore model ranging from laminar to turbulent-flow regimes is implemented to incorporate a three-dimensional flow in the reservoir. Reservoir inflow for entire time period is handled by integrating the instantaneous Green's function over space in the Laplace-transformed domain. A semi-analytical approach using the dimension-transform technique is proposed to solve the coupled reservoir-wellbore model, which is then verified against alternative results. On the basis of solutions, the transient responses are investigated in terms of wellbore pressure, pressure derivative, and pressure/flux profiles along laterals. Two common patterns (i.e., radial-clustered and pinnate-branched MLHWs) are proposed to investigate transient pressure responses. The results demonstrate that the pressure-transient behaviors depend on the interaction between wellbore hydraulics, Reynolds number, and MLHW configuration. This work provided some insights into better understanding the differences and similarities between a finite-conductivity single-lateral and multi-lateral systems.