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A new semi-analytical solution to the advection-dispersion-reaction equationfor modelling solute transport in layered porous media is derived using theLaplace transform. Our solution approach involves introducing unknown functionsrepresenting the dispersive flux at the interfaces between adjacent layers,allowing the multilayer problem to be solved separately on each layer in theLaplace domain before being numerically inverted back to the time domain. Thederived solution is applicable to the most general form of linearadvection-dispersion-reaction equation, a finite medium comprising an arbitrarynumber of layers, continuity of concentration and dispersive flux at theinterfaces between adjacent layers and transient boundary conditions ofarbitrary type at the inlet and outlet. The derived semi-analytical solutionextends and addresses deficiencies of existing analytical solutions in alayered medium, which consider analogous processes such as diffusion orreaction-diffusion only and/or require the solution of complicated nonlineartranscendental equations to evaluate the solution expressions. Codeimplementing our semi-analytical solution is supplied and applied to aselection of test cases, with the reported results in excellent agreement witha standard numerical solution and other analytical results available in theliterature.

New semi-analytical solutions for advection-dispersion equations in multilayer porous media