Use of semi-analytical and dual-porosity models for simulating matrix diffusion in systems with parallel fractures

Abstract

A semi-analytical method and the dual-porosity model are used to simulate matrix diffusion between parallel fractures. The semi-analytical modeling parameters can be computed directly using the fracture spacing, aperture, and matrix properties. Those parameters do not require calibration to match an analytical solution for matrix diffusion. The dual-porosity model is applied under the same conditions, and its first-order mass transfer coefficient is estimated using a shape factor formula. An expression of the characteristic diffusion time of the dual-porosity method is defined based on fracture spacing and matrix characteristics. The dual-porosity method can adequately simulate matrix diffusion with a single mass transfer coefficient when the simulation time of the parallel fractures system exceeds the characteristic diffusion time. For large fracture spacing, the characteristic diffusion time becomes large, and the dual-porosity method produces less satisfactory results. The highest average marginal normalized root mean square error (NRMSE) of the dual-porosity model was 18% (with calibrations) under no decay and no retardation conditions. Considerations of decay and retardation increased the dual-porosity's highest calibrated NRMSE to 20%. Meanwhile, the errors between the semi-analytical method and the analytical solution were low at NRMSEs of 5% or less, with or without decay and retardation over a range of fracture spacing.