A fractal model for threshold pressure gradient of tight oil reservoirs

In tight oil reservoir, the flow channel of oil and water is tiny and the boundary layer effect is obvious, resulting in large flow resistance and high threshold pressure gradient. Taking into account of the fractal dimension of the pore throat and the tortuosity, a fractal model for calculating the threshold pressure gradient of tight oil reservoir is established. In this model, the rock is considered as a capillary bundle with different diameter distribution as obtained from high-pressure mercury injection measurements for tight rocks. The mathematical model expresses the fractal threshold pressure gradient as a function of ultimate shear stress (eta(0)), pore throat fractal dimension (D-f ), tortuosity fractal dimension (D-T), the maximum pore radius (r(max)), the characteristic length of the core (L-0), and the connate water saturation (S-wi). For 27 tight cores obtained from Changqing oilfield, threshold pressure gradients were determined using the established model and compared with experimental results to check its accuracy. A good fit was found especially for the rock with lower permeability. The relative error is less than 14% for all the rock tested and is only 1.77% for the cores with permeability in the range of 0.001-0.01mD. This model has the advantage of being able to check the impact of the connate water saturation on the threshold pressure gradient of tight rock, which is usually neglected in previous work. The results show that higher S-wi results in largely increased threshold pressure gradient especially for the rock with permeability lower than 0.01mD. This fractal model is of great importance in predicting the threshold pressure gradient of tight oil reservoir and researching on the flow mechanism of tight oil in porous media.