Natural systems are heterogeneous, most subsurface systems markedly so.
These heterogeneities are manifest as variations in the parameter values that are used to characterize and model fluid flow, as well as species transport and reaction phenomena. Understanding how variations in model parameter values relate to changes in quantities such as fluid pressures, fluid velocities, or species concentrations is an issue of central concern. Methods commonly used to describe such variations are often based upon low-order perturbations, which become increasingly inaccurate as the variance of the parameter increases. The development and application of diagrammatic methods provide the means to characterize stochastic flow and transport phenomena accurately and efficiently.