New Log-Log Derivative for Transient Oil Flow Rate Drop Diagnostics Caused by Depletion-Formation Damage in Fractured Wells

Managing the damage from the effective permeability loss in stress-sensitive reservoirs becomes essential to productivity maintenance. This paper proposes a new transient poroelastic solution for the nonlinear hydraulic diffusivity equation (NHDE) in Biot's effective stress-sensitive fractured oil wells. The NHDE in terms of pressure is transformed for Biot's effective stress dependence using Biot's equation. A new dimensionless function, mD, models the reservoir damage caused by depletion-dependent compaction and has a dimensionless time, tD, a first-order nonlinear term, mD(1), as well as a dimensionless constant permeability solution, pD dependence. A new dimensionless time-dependent derivative, ∂mD/∂tD = keffD(pD)∂pD/∂tD is presented to compute the transient behavior of the reservoir permeability, keffD(pD), Productivity Index (PI) and reservoir-fracture compaction damage, Δh. The solution developed in this paper couples field data with an asymptotic expansion. The influence of the geomechanical and hydraulic parameters such as vertical overburden stress (σob), oil flow rate (qo), pore pressure (p), Young's modulus (E), and Poisson's ratio (ν) 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. This modeling may be an attractive graphical tool to identify flow regimes, control permeability loss, and support well-reservoir management for oil flow rate choice and history matching.