Moisture movement in a horizontal soil column under the influence of an applied pressure

Abstract

When moisture moves into a dry horizontal soil column under the influence of an applied pressure, there will be two distinct regions in the soil‐water system: a saturated region and an unsaturated one. Both of these regions grow larger with time. A theoretical solution of the problem is obtained by combining Darcy's equation with a modified diffusion equation that accounts for the moving interface between the two regions. The nonlinear partial differential equation of diffusion is transformed to a nonlinear ordinary differential equation, and a numerical procedure for its solution is presented. A set of experiments was conducted at various applied pressures using silica flour as the soil sample. Moisture content as a function of time and position was determined by use of γ‐ray attenuation equipment. The experimental results compare favorably with the results given by numerical procedures based on theory. It is also shown that an analysis based on the assumption of a soil fully saturated to the wetting front with capillary forces acting at the air‐water interface gives very good results provided that the proper capillary suction is selected.

Multilayer Asymptotic Solution for Wetting Fronts in Porous Media with Exponential Moisture Diffusivity

“…We use a shooting algorithm wherein a value of is chosen, and then is updated iteratively until Θ is sufficiently close to the right‐hand boundary value . This approach is similar to that employed by others for the exponential diffusion problem , and more details on our shooting algorithm are given in Section . For illustration purposes, we choose physical parameters corresponding to a typical soil water uptake experiment .…”

Surfactants are Ineffective for Reducing Imbibition of Water-Based Fracturing Fluids in Deep Gas Reservoirs

“…Thus, the magnitude of P c,f relative to P o determines the relative importance of surfactant additions on reducing imbibition. It is worth noting that the equivalent effects that P c,f and P o have in driving imbibition are evident from their additive influences in eq and have been supported by experimental tests conducted over ranges of elevated injection pressures. , For the purpose of this study, we focus on the relative magnitudes of P c,f and P o under commonly employed laboratory spontaneous imbibition experiments and under field reservoir conditions.…”

Reply [to “Comments on the paper by R. Singh and J. B. Franzini, ‘Unsteady flow in unsaturated soil-water movement from a cylindrical source’”]

“…It has, however, been successfully applied to the one-dimensional case, for then ro = 0 and t is thus removed from the conditions. Philip [1959], Yeh [1967], Singh [1967], and others have used this transformation for the onedimensional case. Yeh [1967] used the numerical method outlined in Singh and Franzini [1967] to solve the case of horizontal absorption.…”

“…Philip [1959], Yeh [1967], Singh [1967], and others have used this transformation for the onedimensional case. Yeh [1967] used the numerical method outlined in Singh and Franzini [1967] to solve the case of horizontal absorption. This approach requires that the diffusivity of the soil be expressible in exponential form.…”