Modeling Well Performance Under Nonequilibrium Deposition Conditions

Abstract

Abstract 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. Introduction Civan1 presents a comprehensive review of the various modeling efforts for predicting near-wellbore damage and its effect on well performance. Approximate simplified models, such as the leaky-tank reservoir model given by Civan2 and the precipitation-induced well performance model given here, are frequently resorted in reservoir analysis, because they can be solved analytically, and they can provide insight into the prevailing trends and convenience in the analysis and understanding of the key parameters of the governing mechanisms. There have been a number of reported efforts for simplified modeling of deposition in the near-wellbore region, including by Muskat3 for liquid-condensate dropout in condensate reservoirs, Roberts4 for sulfur deposition from sour gas, Leontaritis5 for asphaltene deposition from crude oil, and Satman et al.6 for calcite deposition in geothermal wells. The factors affecting the flow performance of wells by deposition include (Roberts4):Transport of the precipitate-forming substance by the flowing reservoir fluid to the region having favorable condition for separation and deposition of the substance.Dropout of deposits proportional with the pressure gradient due to the reduced solubility of the precipitating substance by the pressure drop.Reduction of the effective pore volume available for deposition, inversely affecting the impairment, andReduction of the effective permeability of the flowing fluid by deposition. Roberts4 and Satman et al.6 carried out formulations for predicting solid deposition and its effects in the near-wellbore region, assuming equilibrium deposition conditions. Here, their formulations are extended for nonequilibrium deposition conditions and compared with the equilibrium deposition model. This paper presents an improved simplified analytical model and its validation for prediction of the productivity decline due to deposition of organic and inorganic scales under the non-equilibrium conditions of rapidly converging flow and solid phase deposition in the near-wellbore formation. Rapid flow conditions do not allow for sufficient time to attain phase equilibrium. Consequently, there is less scaling and formation damage, and slower productivity decline than predicted by the equilibrium models. The equilibrium models may over predict the productivity decline, because the equilibrium assumption allows for more precipitation than it can actually occur under nonequilibrium.