We derive a set of analytical solutions for the transport of adsorbing solutes in an immiscible, incompressible two-phase system. Our analytical solutions are new in two ways: First, we fully account for the effects of both capillary and viscous forces on the transport for arbitrary capillary-hydraulic properties. Second, we fully take hydrodynamic dispersion for the variable two-phase flow field and adsorption effects of the solutes into account. All previously obtained results for component transport in immiscible two-phase systems account for changes in the flow field due to the components presence but they ignore dispersive effects. This is surprising given the enormous practical importance of diffusive effects both in hydrological settings and for situations that arise in the context of oil production for chemical flooding, polymer flooding and the transport of wettability altering agents. In both cases, one often faces the situation of fractured media or thin-layer structures where the diffussive transport processes of components dominate over viscous forces. We consider a situation where the components do not affect the flow field and focus on dispersive effects. For the purely advective transport we combine a known exact solution for the description of flow with the method of characteristics for the advective transport equations to obtain solutions that describe both co- and countercurrent flow and advective transport in one dimension. We show that for both cases the solute front can be located graphically by a modified Welge tangent and that the mathematically obtained solutions correspond to the physical notion that the solute concentrations are functions of saturation only. For the advection-dispersion case, we derive approximate analytical solutions by the method of singular perturbation expansion. We give some illustrative examples and compare the analytical solutions with numerical results.

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We have developed a new finite element - finite volume based simulation approach to study flow and transport processes at sub-grid scales, i.e. at scales below the typical size of a reservoir simulation grid block, using real 3D geometries in carbonate reservoirs. We complement the simulations by high-resolution X-Ray CT experiments which provide us with the 3D structures, allow us to visualise flow processes at the core-scale in real time, and help us to compare the observed processes to numerical simulations to validate and verify the latter. We use this combined numerical-experimental approach to analyse the fundamental processes controlling fluid flow in carbonates at sub-grid scales. Results can be incorporated in existing reservoir simulation workflows to increase the confidence in reservoir performance forecasting. We show applications related to fractured carbonate reservoirs and enhanced oil recovery processes due to injection of low-salinity fluids and hot water.@en