Modeling liquid transport in the Earth’s mantle as two-phase flow: Effect of an enforced positive porosity on liquid flow and mass conservation

Abstract. Fluid and melt transport in the solid mantle can be modeled as a two-phase flow in which the liquid flow is resisted by the compaction of the viscously deforming solid mantle. Given the wide impact of the liquid transport on the geodynamical and geochemical evolution of the Earth, the so-called “compaction equations” are more and more incorporated in geodynamical modeling studies. The implementation of these equations requires a regularization technique to handle the porosity singularity in dry mantle. Moreover, it is also common to enforce a positive porosity (liquid fraction) to avoid unphysical negative values of porosity. However, the effects of this “capped” porosity on the liquid transport and mass conservation have not been quantitatively evaluated. Here, we investigate these effects using a series of 1- and 2-dimensional numerical models using the commercial finite element package COMSOL Multiphysics®. The results of benchmarking experiments against a semi-analytical solution for 1- and 2-D solitary waves illustrate the successful implementation of the compaction equations. We show that the solutions are accurate when the element size is smaller than half of the compaction length. Furthermore, in time-evolving experiments where the solid is stationary (immobile), we show that the mass balance errors are similarly low for both capped and uncapped experiments (i.e., allowing negative porosity). When Couette flow, convective flow, or subduction corner flow of the solid mantle is assumed, the capped porosity leads to overestimations of the mass of liquid in the model domain and mass flux of liquid across the model boundaries, resulting in intrinsic errors in mass conservation even if high mesh resolution is used. Despite the errors in mass balance, however, the general trends of porosity evolution in the capped experiments are similar to those in the uncapped experiments. Hence, the use of the regularization of the compaction equations with the enforced positive porosity is reasonable for modeling fluid and melt transport in a deforming mantle.