Nonlinear flow characteristics in low-permeability reservoirs with stress sensitive effect

Based on the continuity of the derivative of the nonlinear seepage velocity function in low-permeability reservoirs, the nonlinear kinematic equation in the real number field for the low-permeability reservoirs was deduced. The mathematical formula of the apparent permeability and the apparent pseudo threshold pressure gradient were defined. It was demonstrated that the continuous derivative of the seepage velocity function was consistent with the continuous permeability change. The mathematical model of the nonlinear flow in low-permeability reservoirs with stress sensitive effect under the condition of constant well production rate was constructed. Owing to its strong nonlinearity, efficient Douglas-Jones predictor-corrector finite difference method was adopted to obtain its numerical solution. Moreover, its accuracy was verified by comparison with the numerical solution obtained by the fully implicit finite difference method. Result analysis shows: log-log curves of dimensionless transient wellbore pressure corresponding to the nonlinear kinematic equation and pseudo-linear kinematic equation both have inflexions at the initial period. And the inflexion corresponding to the pseudo-linear one is more obvious; the permeability modulus has a major effect on the second half of these curves; the bigger its value, the sharper the pressure drop; there exists a moving boundary in the nonlinear flow in low-permeability reservoirs; the moving boundary of the pseudo-linear flow moves more slowly than that of the nonlinear flow.