Coupled Numerical Modelling of Reservoir Flow with Formation Plugging
Authors: Mojarad R. Salehi , Settari A. 
Published: March 2010

Abstract
Permeability decline occurs during injection of produced water and seawater, resulting in injectivity declines and significant cost increases in waterflooding projects. It is necessary to have a reliable model to predict injectivity decline for preventive water treatment and waterflood design purposes.
A classical deep bed filtration (DBF) model has been widely used to predict the injectivity decline. According to this model, the injectivity decline can be characterized by two empirical parameters: filtration coefficient, λ, and formation damage coefficient, β. Different methodologies developed to extract these parameters involve expensive and difficult concentration measurements, laboratory-scaled pressure drop measurements (not truly representative of the real reservoir) and simplifying assumptions of analytical solutions.
A simple empirical velocity-based damage model proposed by Bachman et al.(1) is adopted in this work, and extended to multidimensional flow. This model is then compared to the deep bed filtration-based model. The advantage of the empirical model is that it can be easily tuned to either field or laboratory data, and can be easily implemented in reservoir simulators.
The paper presents the formulation and numerical implementation of the two coupled reservoir flow and damage models. Different methods of implementing the velocity-based model in multidimensional flow are presented and evaluated. The comparison with the DBF model shows that the two models yield similar damage characteristics.
Finally, application of the model to analysis of the published data for offshore Gulf of Mexico is presented. The relationship between the parameters of the two different approaches is validated for these case studies.

Introduction
As oil fields mature, the volumes of produced water requiring disposal increase significantly. Re-injecting produced water is an attractive, environmentally sound solution to water disposal problems, but entails the risk of poor injectivity.
Produced water normally contains varying concentrations of particles, which have a direct effect on the injectivity decline (injectivity index is defined as the ratio of the injection rate to the given pressure head). It has been shown that declining well injectivity is the major cost-increasing item in the case of re-injection.
Standard formulation of damage mechanics is based on the classical deep bed filtration (concentration-based) model (DBF). Injectivity decline is characterized by two parameters: filtration coefficient, λ, and formation damage coefficient, β. Methodologies developed to determine these parameters involve expensive and difficult measurements, scaling problems and simplifying assumptions of analytical solutions. Moreover, the model is not easily implemented in reservoir simulators.
Bachman et al.(1) proposed an empirical velocity-based damage model that could be easily tuned to field or laboratory data, and easily implemented in reservoir simulators. However, the model was formulated in 1D and its extension (and validity) in multidimensional flow was not shown.
This paper presents the development of a 2D formulation and numerical implementation of permeability impairment based on the velocity-based model. The results will be compared with the classical DBF approach to validate the result against deep bed filtration theory. Application of the model to published data from offshore Gulf of Mexico is presented.