Poroelastic Depletion-Dependent Dupui's Formula for Oil Production Forecast with compaction Formation Damage

This work develops a new theory to compute the steady-state oil flow rate and Productivity Index (PI), incorporating some poroelastic parameters in the well-reservoir pressure drawdown. A new compaction coefficient (Cm) that is a function of the inverse Young's modulus (E) is derived, and its effect on oil flow rate and Productivity Index (PI) is evaluated. The analytical model presented integrates the Dupuis formula with depletion-dependent rock and fluid properties, e.g., reservoir compaction (Δh), formation volume factor (Bo), dynamic viscosity (µo), reservoir porosity (ϕ), and permeability (k). After carrying out the integration, the analytical model developed in this paper allows the computation of the depletion-dependent oil flow rate and PI, analyzing the effects of the reservoir extension, wellbore radius, Young's modulus, Poisson ratio, undamaged net pay on initial condition, and Biot's coefficient. The validation of the proposed model is carried out by comparing the results with several depletion field data values, which are accurate (R2 = 0.9866). The main advantages of this model are accuracy and ease of implementation, which make it an attractive mathematical tool for calibrating new analytical and numerical models.