A nonequilibrium well productivity decline model is developed and solved analytically under the same simplifying conditions of the previous equilibrium models. The solution is compared with the analytical solutions of the equilibrium models. It is demonstrated that deposition for nonequilibrium flow conditions is less compared to equilibrium flow conditions. Charts are developed and presented for the productivity index and skin factor in terms of relevant dimensionless parameters. In addition, the formulae for estimation of the radius of the plugging region (skin radius), and the producing time required for partial plugging of the formation at various percentages of the initial porosity and the time for complete plugging of the formation are derived. Numerical examples are presented, illustrating the applications of the formulations, and the predictability of the productivity decline of wells. The new improved model alleviates the limitations of the previous equilibrium models and more accurately predicts the productivity decline. This model can be used for determination of the rate of productivity decline by scale formation, the skin radius, and hence the well inflow performance and for scheduling of the treatments necessary for effective well stimulation.

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