Reservoir Matrix-Fracture Compaction Damage Evaluation in Biot's Effective Stress-Dependent Permeability Oil Wells

ABSTRACT: This paper proposes a new transient poroelastic solution for the nonlinear hydraulic diffusivity equation (NHDE) in Biot's effective stress-sensitive reservoirs fully penetrated by fractured oil wells. The NHDE in terms of pressure is transformed for Biot's effective stress dependence using Biot's equation. In addition, another transformation of the new NHDE is derived using a dimensionless transient pseudo-function, mD(tD), and the NHDE is expanded in a first-order asymptotic series using the perturbation method. The mD(tD) function models the reservoir damage caused by depletion-dependent compaction and has a dimensionless time, tD, a first-order nonlinear term, mD(1) (tD, ∂pD/∂tD), as well as a dimensionless constant permeability solution, pD dependence. A new log-log derivative, ∂mD/∂tD = keffD(pD) ∂pD/∂tD is presented to compute the transient behavior of the effective reservoir-fracture permeability, keffD(pD), and compaction damage, Δh. To build the results, the solution developed couples field data with an asymptotic expansion. The influence of the Young's modulus, Biot's coefficient, Poisson ratio, formation volume factor, and reservoir thickness (E, α, ν, Bo, h), among other parameters, in a sensitivity tornado chart for the Productivity Index (PI) is simulated. The results show that these parameters are essential to minimize formation damage. The accuracy, ease of implementation, and low computational costs constitute the main advantages of the model addressed in this paper. Thereby, this modeling may be an attractive graphical tool to identify flow regimes, provide permeability loss control, and support well-reservoir management for oil flow rate selection and history matching.