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.

采用半解析法和双孔隙度模型模拟平行裂缝间的基质扩散。可以使用裂缝间距、孔径和基质特性直接计算半解析建模参数。这些参数不需要校准来匹配矩阵扩散的分析解决方案。在相同条件下应用双孔隙度模型，利用形状因子公式估算其一阶传质系数。基于裂缝间距和基质特征定义了双孔隙度法特征扩散时间的表达式。当平行裂缝系统的模拟时间超过特征扩散时间时，双孔隙度法可以充分模拟单一传质系数的基质扩散。对于较大的裂缝间距，特征扩散时间变大，双孔隙度法产生的结果不太令人满意。在无衰减和无延迟条件下，双孔隙度模型的最高平均边际归一化均方根误差 (NRMSE) 为 18%（经过校准）。衰减和延迟的考虑将双孔隙度的最高校准 NRMSE 增加到 20%。同时，半解析方法和解析解之间的误差在 5% 或更低的 NRMSE 下很低，在一定的裂缝间距范围内有或没有衰减和延迟。在无衰减和无延迟条件下，双孔隙度模型的最高平均边际归一化均方根误差 (NRMSE) 为 18%（经过校准）。衰减和延迟的考虑将双孔隙度的最高校准 NRMSE 增加到 20%。同时，半解析方法和解析解之间的误差在 5% 或更低的 NRMSE 下很低，在一定的裂缝间距范围内有或没有衰减和延迟。在无衰减和无延迟条件下，双孔隙度模型的最高平均边际归一化均方根误差 (NRMSE) 为 18%（经过校准）。衰减和延迟的考虑将双孔隙度的最高校准 NRMSE 增加到 20%。同时，半解析方法和解析解之间的误差在 5% 或更低的 NRMSE 下很低，在一定的裂缝间距范围内有或没有衰减和延迟。