Fluid Rate in Flowing Granular Medium with Moving Boundary

Sand production instability is considered as a result of weilbore fluid pressure reduction (drawdown) below some critical level. A continuum model for massive continued sand production is developed by considering coupling of fluid flow and flow of granular matrix. The model provides a physical mechanism of yielding front propagation away from the welibore as the process of sand production continues. Mass balance analysis leads to a relation between cumulative sand production and the current yielding front location. Short-term enhancement of fluid production because of simultaneous sand production turns out to be dependent not only on instantaneous sand flux, but also on the current radius of the yielded zone around wellbore, that is, the history of sand production for the well. Long-term enhancement is stipulated mainly by growth of a yielded, highly permeable zone around the wellbore.