Asymptotic-Convolution Model for Compaction Damage Evaluation in Depletion-Dependent Oil Reservoirs During Alternating Drawdown/Buildup Cycles

The mechanical formation damage induced by pore collapse within production curve depletion-dependent reservoirs significantly influences oilfield development. This paper proposes a new perturbative solution for transient pores collapse hysteresis modeling in depletion-dependent oil reservoirs with compaction effects during alternating loading/unloading cycles. The nonlinear hydraulic diffusivity equation is perturbed through a first-order expansion technique using the depletion-dependent permeability, k(p) as a perturbation parameter, \(\epsilon\). The practical uses of the model developed in this work are identifying flow regimes and hysteresis responses in pressure-sensitive reservoirs, estimating buildup pressure, specifying oil flow rate to prevent severe hysteretic behavior, and history matching during reservoir surveillance. The log–log analysis shows that the shut-in pressure has an influence on permeability loss. However, the comparisons between the permeability loss and its partial recovery curves show that this loss represents less than 5\(\%\) of the permeability value from the previous drawdown cycle. The derivative was also used to compute the instantaneous permeability loss using the relationship: \(\partial m_\textrm{D}/\partial t_\textrm{D}=k_\textrm{D}(p_\textrm{D})\partial p_\textrm{D}/\partial t_\textrm{D}\). The main advantages of the solution derived in this work are the simple implementation, practical graphical analysis of the pores collapse hysteresis effect, the possibility of simulating different boundary conditions and well-reservoir settings, and the requirements of only a few pressure and permeability field data to input in the deviation factor. The solution proposed can be applied to choose the production time to shut the well and monitor the adequate oil flow rate during the production curve.