Hydro-mechanical aspects of the sand production problem

This paper examines the hydro-mechanical aspect of the sand production problem and sets the basic frame of the corresponding mathematical modelling. Accordingly, piping and surface erosion effects are studied on the basis of mass balance and particle transport considerations as well as Darcy's law. The results show that surface erosion is accompanied by high changes of porosity and permeability close to the free surface. Quantities which can be measured in experiment, like the amount of produced solids or fluid discharge, can be used in an inverse way to determine the constitutive parameters of the problem.Notation dV Volume element - dV _s Volume of solids pt - dV _v Volume of voids - dV _ff Volume of fluid phase - dV _fs Volume of fluidized-particles - Volume of mixture - dM _s Mass of solids - dM _ff Mass of fluid phase - d _{M fs} Mass of fluidized-particles - Mass of mixture - s Density of solids - f Density of fluid - ff Density of fluid phase - fs Density of fluidized-particles - Density of mixture - _i ^ff Velocity of fluid - _i ^fs Velocity of fluidized-particles - _i ^s Velocity of solids - Velocity of mixture - q ^ff Volume-discharge of fluid - q ^fs Volume-discharge of fluidized-particles - Volume-discharge of mixture - m ^ff Mass-discharge of fluid - m ^fs Mass-discharge of fluidized-particles - Mass-discharge of mixture - _er Rate of mass-eroded - _dep Rate of mass-deposited - Mass generation term - dS _i Surface element - Pore-surface element - D _IJ Tensor of mechanical dispersion - x _i Location - t Time - Porosity - c Transport concentration - c _cr Critical value ofc - p Fluid-pressure - k Permeability coefficient - _k Kinematic viscosity - Spatial frequency of erosion starter points