A comparative study of MIM model with a novel hyperbolic cosine and conventional distance-dependent dispersion models

The present study proposes a novel hyperbolic cosine distance-dependent dispersion model and is implemented in a mobile-immobile (MIM) model. Dual-porosity media is also termed MIM (mobile-immobile) regions. The pollutants are intended to drift through two adjacent homogeneous zones. An advective–dispersive equation governs mobile regions of the porous media. However, immobile regions are controlled by diffusive flux. The dispersivity as a measure of location determines the dispersion coefficient’s scale dependence. Though linear and exponential dispersivity functions were devised and implemented a few decades ago, in which the exponential distance-dependent dispersion model could provide comparatively satisfactory results, that, too, could not make a stronger correlation with the laboratory results. The linear and exponential dispersion models showed over-predicted data with insignificant skewness and tailing effects. Therefore, the present study further explores the distance-reliant dispersion model by introducing a novel hyperbolic cosine distance-reliant dispersion formulation. The transport model is discretized using a substantially implicit finite-difference-based Crank–Nicolson technique, and Thomas’ approach is applied to solve the output set of simultaneous algebraic problems. The present model is verified with the experimental data, and sensitivity analyses have been performed to look into how model parameters affect the model’s output. The present study reveals that contaminants move faster when using a scale-dependent dispersion model. Sensitivity analyses have revealed that an increase in the mobile regions and distribution of contaminants with the soil matrices reduces the breakthrough profiles. The reduced breakthrough profiles culminate retarded transport of contaminants in the soil media.