Modeling of shear stress distribution on mud surface in the subsea sand-mud alternate layer

This study aims at showing that the shear stress distribution on a flat surface in the porous media can be expressed by just one probability density function. It is known that methane hydrate exists in the sand layers off Kii Peninsula in Japan within the turbidite sand-mud alternate strata. One of the concerns about gas production from methane hydrate is mud erosion and consequent reservoir clog caused by skin formation. The erosion rate of mud particles depends on the shear stress distribution on the surface of the mud layer in the alternates. The distribution of shear stress should depend on the flow and reservoir properties. Being able to predict the total mass of the eroded mud in advance would definitely be convenient. The objective of this paper is to propose a mathematical model of shear stress distribution on a flat interface between sand and mud layers, because it is believed that the maximum mud-erosion rate is given at the very beginning of the gas production when the mud surface is almost flat. To obtain the shear stress distribution on a flat surface, we conducted pore-scale numerical simulations using computational domains including numerically generated sand-mud beds. Interestingly, we found that the histograms of the shear stresses fit just one curve by means of proper non-dimensionalization. These consistent histograms of the non-dimensional shear stress were then matched with a Gamma distribution function, to develop a mathematical model. This new finding may make possible to predict the maximum rate of mud erosion if we know water flow velocity and reservoir properties, such as porosity and permeability.