Multidimensional Velocity-Based Model of Formation Permeability Damage
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 97169, "Multidimensional Velocity-Based Model of Formation Permeability Damage: Validation, Damage Characterization, and Field Application," by R.S. Mojarad, SPE, and A. Settari, SPE, U. of Calgary, prepared for the 2005 SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October.
The loss of injectivity in produced-water and seawater injectors results from formation plugging. Reliable modeling of the permeability loss is key to analysis of field data and to the design and economics of projects. Standard formulation of damage mechanics uses the concentration-based, classical deep-bed filtration (DBF) model, which is not easily implemented in reservoir simulators. This alternative damage-modeling approach is based on the formulation proposed by Bachman et al.: "Coupled Simulation of Reservoir Flow, Geomechanics, and Formation Plugging With Application to High-Rate Produced-Water Reinjection," paper SPE 79695. The numerical implementation of this empirical, velocity-based damage model (VBDM) is extended to 2D flow and is validated by a comparison with the DBF model. The velocity model provides a remarkably accurate approximation of the more complex concentration model.

Introduction
Injectivity decline caused by particles in the injection water occurs to some extent in most injection wells. To understand and predict this decline, it is necessary to know about the water quality, formation characteristics, and deposition rate. In the classical DBF model, injectivity decline is characterized by two parameters: filtration coefficient, λ, and formation-damage coefficient, β. Methods to determine these parameters involve difficult measurements, scaling problems, and simplifying the assumptions of analytical solutions. Moreover, the model is not easily implemented in reservoir simulators.
An empirical VBDM was developed previously that could be tuned to field or laboratory data and easily implemented in reservoir simulators. However, the model was formulated only in 1D, and its extension (and validity) in multidimensional flow was not shown.
The full-length paper presents a 2D formulation and numerical implementation of permeability impairment that uses the VBDM. The results were compared with the classical DBF approach to validate the result against the DBF theory. A unique relation between the parameters of the two models was found that was key to developing a new method to determine the λ and β damage-characterization parameters on the basis of matching laboratory or field data with the velocity-based model. In this way, the number of parameters that need to be determined experimentally can be reduced.

Mechanisms
The injectivity decline caused by contaminated-water injection can be attributed to several primary mechanisms including internal filtration and external filter-cake buildup and its associated permeability reduction. Depending on details of the case studied (e.g., particle-size/pore-throat-size ratio, surface charge, or injection rate), either of the mentioned mechanisms could dominate. Large particles will be intercepted at the porous formation face, resulting in an external filter cake. Small particles can travel through the formation and initially plug the pore throats by bridging, thus creating internal pore restrictions. Continued buildup of internal plugging over time can also lead to an external filter cake. Once valid models have been obtained for each of these mechanisms, they can be coupled to describe the complete system of formation damage.