The paper describes a new analytical solution for combined liquid and vapor flow with solute transport, in an attempt to ensure proper interpretation of experimental data. The solution shows that the relative magnitude of the separate transport coefficients produces many of the flow features seen in experimental data, and significant liquid transport can occur in regions without apparent solute transport. This development is new and represents a significant addition to understanding solute transport. As such, its methods and results can be applied to other problems in multiple-phase transport and to materials such as high volume mining wastes and some hazardous waste disposal sites. The paper shows that an earlier analysis by the authors, that a critical water content exists in retorted oil shale below which solute transport ceases, is unjustified.