Prediction of Permeability Reduction by External Particle Invasion Using Artificial Neural Networks and Fuzzy Models
Authors: Zuluaga E. , Alvarez H.D. , Alvarez J.D. 
Published: March 2010

Abstract
The transport of fine particles is one of the major causes of permeability reduction in porous media. A number of mathematical models have been suggested in the literature to simulate and quantify this reduction. Simple models include analytical solutions of the equations that describe the phenomenon, while more complex models are solved by numerical methods. In this study, an Artificial Neural Network (ANN) and a Fuzzy Model (FM) were developed to predict the permeability reduction by external particle invasion in non-consolidated porous media. For the training process, the results of 42 laboratory experiments were employed. The input data covered a wide range of porosity, permeability, injection rates, and fines concentrations. The developed FM and ANN were tested with eight sets of experiments that were not used in the training. The results show that the ANN can match and predict, with high precision, the permeability reduction as a function of pore volumes of fine suspensions injected. The FM predicts the permeability reduction with moderate precision.

Introduction
The transport of fine particles in formations followed by plugging has been recognized as the major cause of formation damage. According to Liu et al(1), the fine particles that cause permeability reduction can be classified according to their origin as externally injected, chemically generated, and mobilized particles. External particles are the result of injection processes with fluids containing particulate material, including solids, emulsions, and bacteria.
A number of mathematical models have been developed to predict formation damage, Civan(2) presents an evaluation and comparison of six of them. In general, analytical and numerical models involve phenomenological constants that need to be determined for formation damage prediction; for example, the numerical model developed by Civan et al(2, 3) requires the determination of 11 phenomenological constants to predict formation damage caused by externally injected, chemically generated, and mobilized particles. These constants generate uncertainty, in addition to high computational efforts, in the numerical models developed to predict permeability reduction.
Artificial Neural Networks, Fuzzy Models and Fuzzy-Neural- Networks have been increasingly used for prediction of complex non-linear systems with good results(4–7). ANN and FM are artificial tools developed to provide machines with man-styled logical procedures. Although there are differences in their structure and operation, their range of application is similar: modelling, forecasting, estimating, etc. The main difference between ANN and FM comes from their basis. While ANN imitates the human brain in its structural configuration, FM imitates the human brain in its operational performance. As a first approach, it could be said that ANN (especially Feed-Forward Networks) have their optimum performance when pattern recognition tasks are required. FM (especially Takagi-Sugeno Fuzzy Models) are suitable for function approximation, given that prior knowledge of the problem is provided. There has been a growing interest in the development of Neuro-Fuzzy systems. Neuro-Fuzzy systems take advantage of both ANN and FM models to enlarge the range of application of the resulting model.