FRACTAL MATHEMATICAL MODEL FOR INVESTIGATING THE MICRO-DISPLACEMENT BEHAVIOR OF A TEMPERATURE-DEPENDENT NON-NEWTONIAN FRACTURING LIQUID FLOW IN TIGHT MATRIX

Abstract

Micro-displacement behavior during hydraulic fracturing greatly influences damage formation. Formation temperature and the non-Newtonian behavior of fracturing liquid are the major influencing factors in the micro-displacement process. In this work, to investigate the influencing factors on micro-displacement process, we built a mathematical model for the micro-displacement of a fracturing liquid on the basis of the fractal theory. Then, the analytical expression for penetration equation was obtained according to the model, and explicit solution for the relationship between the volume driven into formation and time was derived. Finally, the influences of non-Newtonian behavior, formation temperature, wettability, and pore size complexity on the micro-displacement process were discussed. Results show that the decrease in formation temperature or decrease in the non-Newtonian degree of fracturing liquid reduce fracturing liquid leakage.