An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Image-based flow visualisation (IBFV) to enhance interpretation of complex flow patterns within a shallow tidal barrier estuary

We applied a texture-based flow visualisation technique to a numerical hydrodynamic model of the Pumicestone Passage in southeast Queensland, Australia. The quality of the visualisations using our flow visualisation tool, are compared with animations generated using more traditional drogue release plot and velocity contour and vector techniques. The texture-based method is found to be far more effective in visualising advective flow within the model domain. In some instances, it also makes it easier for the researcher to identify specific hydrodynamic features within the complex flow regimes of this shallow tidal barrier estuary as compared with the direct and geometric based methods.

Predicting flow and transport in highly heterogeneous alluvial aquifers

Successful prediction of groundwater flow and solute transport through highly heterogeneous aquifers has remained elusive due to the limitations of methods to characterize hydraulic conductivity (K) and generate realistic stochastic fields from such data. As a result, many studies have suggested that the classical advective-dispersive equation (ADE) cannot reproduce such transport behavior. Here we demonstrate that when high-resolution K data are used with a fractal stochastic method that produces K fields with adequate connectivity, the classical ADE can accurately predict solute transport at the macrodispersion experiment site in Mississippi. This development provides great promise to accurately predict contaminant plume migration, design more effective remediation schemes, and reduce environmental risks. Key Points Non-Gaussian transport behavior at the MADE site is unraveledADE can reproduce tracer transport in heterogeneous aquifers with no calibrationNew fractal method generates heterogeneous K fields with adequate connectivity

Mathematical modelling of gas production and compositional shift of a CSG (coal seam gas) field: Local model development

In this work we discuss the development of a mathematical model to predict the shift in gas composition observed over time from a producing CSG (coal seam gas) well, and investigate the effect that physical properties of the coal seam have on gas production. A detailed (local) one-dimensional, two-scale mathematical model of a coal seam has been developed. The model describes the competitive adsorption and desorption of three gas species (CH4, CO2 and N2) within a microscopic, porous coal matrix structure. The (diffusive) flux of these gases between the coal matrices (microscale) and a cleat network (macroscale) is accounted for in the model. The cleat network is modelled as a one-dimensional, volume averaged, porous domain that extends radially from a central well. Diffusive and advective transport of the gases occurs within the cleat network, which also contains liquid water that can be advectively transported. The water and gas phases are assumed to be immiscible. The driving force for the advection in the gas and liquid phases is taken to be a pressure gradient with capillarity also accounted for. In addition, the relative permeabilities of the water and gas phases are considered as functions of the degree of water saturation.