A Fractal Permeability Model of Tight Oil Reservoirs Considering the Effects of Multiple Factors

Abstract

The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip length. Furthermore, the porous size distribution (PSD), stress sensitivity, irreducible water, and pore wall effect must also be taken into consideration when conducting the prediction and evaluation of tight oil permeability. Currently, few studies on the permeability model of tight oil reservoirs have simultaneously taken the above factors into consideration, resulting in low reliability of the published models. To fill this gap, a fractal permeability model of tight oil reservoirs based on fractal geometry theory, the Hagen–Poiseuille equation (H–P equation), and Darcy’s formula is proposed. Many factors, including the slip length, PSD, stress sensitivity, irreducible water, and pore wall effect, were coupled into the proposed model, which was verified through comparison with published experiments and models, and a sensitivity analysis is presented. From the work, it can be concluded that a decrease in the porous fractal dimension indicates an increase in the number of small pores, thus decreasing the permeability. Similarly, a large tortuous fractal dimension represents a complex flow channel, which results in a decrease in permeability. A decrease in irreducible water or an increase in slip length results in an increase in flow space, which increases permeability. The permeability decreases with an increase in effective stress; moreover, when the mechanical properties of rock (elastic modulus and Poisson’s ratio) increase, the decreasing rate of permeability with effective stress is reduced.