Predicting stagnant pore volume in porous media using temporal moments of tracer breakthrough curves

The heterogeneity in complex porous media like oil reservoirs and aquifers many times renders a fraction of fluid in the pores immobile. The tracer breakthrough curves that are used to characterize the porous media are impacted by the immobile volume fraction and show a tailing effect. It is important to first recognize the presence of the immobile volume and quantify it based on a single tracer breakthrough curve in complex geological environments. In this work, we use the method of moments on the tracer breakthrough curve to solve the inverse problem of porous media characterization with stagnant volume fractions. In particular, we use a three parameter model describing the tracer transport in a porous medium with an immobile fluid fraction and solve the forward problem analytically. We derive mean, variance, skewness, and kurtosis of the analytical solution for the exit age density of the injected tracer in the porous medium. We then describe the behavior of the moments in the parameter space of the transport model and relate it with the tracer transport behavior in the porous medium. We then develop the solution for the inverse problem of using these higher order temporal moments of the effluent tracer concentration to estimate the immobile fluid volume in the porous medium.