Numerical Simulation of Dual-Porosity Multiphase Flow Using Poroelasticity Theory

Abstract

Changes in reservoir pore pressure and temperature during injection or production affect rock deformation, which, in turn, causes alteration of porosity and permeability. Specifically, an increase in pore pressure (or a decrease in rock temperature) can create significant rock deformation and increase of the shear stress that could lead to rock fracturing and microseismic activity in the reservoir. Furthermore, porosity and permeability of rocks decrease because of the pore pressure decrease during depletion. Thus, stress-dependent deformation in hydrocarbon bearing shale formations affects the production decline trends. This paper addresses these issues and presents a computationally efficient in-house numerical simulator for poroelastic dual-porosity reservoirs. The governing transport equations for the fluid flow and rock deformations use two interacting environments consisting of a continuous fracture medium and a discontinuous rock matrix medium. The transport and rock deformation equations are fully-coupled and solved numerically using a stationary coordinate frame. A proper assignment of rock frame modulus, affected by the interconnected fractures, versus the rock matrix modulus is a major focus of this work. The rock frame modulus is smaller than the matrix modulus. The numerical model is compared to a single-phase model and validated with a closed form of analytical solutions. We used field data from a fractured unconventional reservoir to assess our formulation. The field data includes flow rates and pressures during an extended production period in the Bakken formation, Williston basin in North Dakota. Finally, we conducted a sensitivity analysis to determine the effect of bulk rock deformation on reservoir performance as compared to conventional engineering approaches which utilize pore compressibility without accounting for the bulk rock deformation.

Hydraulic and Poroelastic Rock Properties From Oscillating Pore Pressure Experiments

“…Additionally, specific storage of rocks is defined as an undrained poroelastic modulus by some researchers (e.g., Green & Wang, ) and is effective pressure dependent. Neglecting the pressure dependence of permeability and specific storage can introduce significant errors in flow simulations (Eker et al, ; Franquet et al, ; McKernan et al, ).…”