In the present study, an analytical solution is obtained for two-dimensional advection–dispersion equation with variable coefficients in a semi-infinite heterogeneous porous medium. Dispersion coefficient and groundwater velocity are assumed to vary temporally as well as spatially while the retardation factor varies spatially only. The first-order decay and zero-order production terms are also considered into account. The variations in parameters along both longitudinal and transverse directions are of exponentially decreasing nature. Initially the geological formation is considered not solute free. The nature of pollutant is considered of conservative and is assumed to be originating from time-dependent varying point source. New time and space variables are introduced to convert the variable coefficients of the advection–dispersion equation into constant coefficients. Analytical solution of the proposed model is obtained by employing Laplace integral transformation technique (LITT). The proposed analytical solution is illustrated graphically to study the effects of various parameters on the solute transport for temporally exponentially decreasing and sinusoidal nature velocities.

在本研究中，获得了在半无限多相非均质多孔介质中具有可变系数的二维对流扩散方程的解析解。假定弥散系数和地下水速度随时间和空间而变化，而延迟因数仅随空间而变化。一阶衰减和零阶生产项也被考虑在内。沿纵向和横向的参数变化具有指数递减的性质。最初，地质构造被认为不是无溶质的。污染物的性质被认为是保守的，并被认为源自时间相关的变化点源。引入了新的时间和空间变量，以将对流扩散方程的可变系数转换为恒定系数。提出的模型的解析解是通过使用拉普拉斯积分变换技术（LITT）获得的。以图形方式说明了所提出的分析解决方案，以研究各种参数对溶质输运的影响，以实现时间上呈指数递减的正弦波速度和正弦波速度。