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. The simplest 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) is developed to predict the permeability reduction by external particle invasion in non-consolidated porous medium. A comparison was also made with the results of a Fuzzy Model (FM) developed for the same purpose. For the training process the results of 42 laboratory experiments were employed. The input data covered an extensive range of porosity, permeability, injection rates and fines concentrations. The developed ANN and FM were tested with 8 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 moderated precision.

Introduction

The transport of fine particles in formations followed by plugging has been recognized as the major cause of formation damage1. According to Liu et al.1, the fine particles that can 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, bacteria and insoluble material.

A number of mathematical models have been developed to predict formation damage, Civan2 presents an evaluation and comparison of six of them. In general, analytical and numerical models involve phenomenological constants that need to be determined for the 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.

Artificial Neural Networks (ANN), Fuzzy Models (FM) and fuzzy neural networks have been increasingly used for prediction of complexes non-linear systems with good results. Previous applications of ANN in formation damage included the prediction of changes in relative permeability curves and wettability associated to formation damage processes4. Nikravesh et al.5, used ANN to predict wellhead pressure as a function of injection rate, and viceversa, for a waterflood project in the South Belridge Diatomite (California). They also used an ANN to correlate pressures, flow rates and temperature responses in steam injection wells in the same field.

Fuzzy models (FM) have been applied to predict waterflood infill drilling oil recovery in carbonate reservoirs6 and to the design of well stimulation treatments7. A fuzzy regression analysis was applied for the determination of the Archie equation parameters from core resistivity measurements8. Fuzzy neural networks have been used for the determination of reservoir properties from well logs based on fuzzy sets and selforganizing mapping neural networks9.

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