Use of Statistical Dispersion Model to Study Polymer Clogging in Sandstone Samples
Authors: Ates H. , Kasap E. , Tomutsa L. , Gao H.W. 
Published: December 2007

Abstract
Improved recovery techniques are hampered by highly permeable thin layers when they preferentially receive most of injected fluid and leave the rest of the productive zones unswept. Injected fluid distribution can be improved by selectively injecting polymer solutions into high permeability zones. Large polymer molecules can clog smaller and lessen larger pore spaces thus reduce permeability. Too large polymer molecules may not be appropriate for low permeability formations and small polymer molecules may not satisfactorily clog large pores. A design study involving polymer molecule size, permeability and pore size distribution for the zones in consideration may be required to optimize the performance of a polymer treatment.
Tracers by dispersing into flow paths of porous medium provide very useful information on formation pore size distribution. Models are utilized to extract pore size distribution and to upscale laboratory tracer test results to field applications. Conventional models are flawed by utilizing Fickian diffusion for dispersion.
A statistical model to generate a pore size distribution from the dispersion of injected tracer concentrations is developed. Its predictions are compared with the laboratory data from various studies, and in all cases, an excellent match is observed. The model is applied to polymer injection studies and used for analyzing the tracer test data before and after polymer treatment. The model predicts the alteration to the pore size distribution because of the polymer clogging.
Based on the laboratory studies, we developed a polymer performance prediction model. The model quantifies the polymer clogging performance as a function of polymer molecule size, permeability and variation in the initial pore size distribution.

Introduction
The prediction and interpretation of the spreading pattern in porous media is of growing interest for engineers because of the importance of environmental and improved recovery operations. Modeling such a spread in naturally porous formations is a difficult and challenging problem. Heterogeneity, anisotropy and variations in pore size and geometry complicate the problem by causing uneven spread of species.
Uneven spread is called dispersion and observed in many engineering problems involving flow through porous media. Dispersion, a measure of flowing solute spread, is caused by the variation in conductivities of the flow paths. Because of the variation, a mixing zone develops between leading and tracing fluids.
The theoretical foundations for the analysis of dispersion in permeable media stem from the pioneering work of Taylor. His approach yields a convection-diffusion equation with a Fickian dispersion model, which is originated from the molecular diffusion concept. The validity of Fickian assumption has been questioned by many researchers. Fried showed the results of the laboratory experiments in which the experimental results did not fit the solutions of convection-dispersion equation. Anderson found that dispersivities measured in the field are much larger than those measured in the laboratory for the same type of porous material. Dagan stated that there is no priori reason to believe that the diffusion type of equation is valid for solute transport through permeable media.
Some theoretical studies show that the dispersion coefficient is increased with distance for constant velocity. These studies, however, did not attempt to change the Fickian dispersion model.
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