Simulation of Pressure- and Temperature-Dependent Fracturing Fluid Loss in Multi-Porosity Multi-Permeability Formations

In this paper, the multi-porosity multi-permeability porothermoelastic theory is used to derive the analytical solution to calculate the pressure- and temperature-dependent fracturing fluid loss. A triple-porosity triple-permeability source rock formation is selected as an example to illustrate the model. The effects of fracturing fluid temperature and natural fractures on the fluid loss rate are systematically illustrated. The model successfully accounts for the varying leak-off rates in the multi-permeability channels through the hydraulic fracture faces. Furthermore, thermal diffusion near the hydraulic fracture faces contributes to a variation of pore pressure whose gradient at hydraulic fracture faces directly controls the fracturing fluid leak-off rate. The model shows that thermal effects bring almost 27% variation in the leak-off rate. Comparison study indicates that the single porosity model without considering multi-permeability systems or thermal effects significantly underestimates the rate of fracturing fluid loss and predicts nearly 84% and 87% lower leak-off rate, compared to the dual-porosity dual-permeability and triple-porosity triple-permeability models, respectively. Two case studies using published laboratory measurements on naturally fractured Blue Ohio sandstone samples are conducted to show the performances of the model. It is shown that the model presented in this paper well captures the total leak-off volume during the pressure-dependent fluid loss measured from laboratory tests. Matching the analytical solution to the laboratory data also allows rocks’ double permeabilities to be estimated.