A mathematical model of the sealing of earth-banked tanks for animal slurry

A mathematical model to quantify the extent of sealing of earth-banked tanks by animal slurry was developed and experimentally verified. The model was developed from first principles to describe the flow of a suspension through a semi-permeable membrane. The key parameter in the model was the specific resistance to filtration (SRF) of the suspension, a parameter widely used in water engineering to characterise the dewaterability of water and wastewater sludges. Experimental validation of the model was undertaken by constructing a laboratory-scale test column, 2 m high and 0.074 m diameter. The soil liner was simulated in the laboratory by a filter paper. Two suspensions were tested: inorganic waterworks aluminium hydroxide sludge and organic cattle slurry. The experimental results show that the mathematical model predicts a reduction in seepage due to the formation of a suspended solids ‘cake’ at the suspension/filter-membrane interface. The model is conservative i.e. it under predicts the extent of membrane sealing by cake formation. Only membrane sealing, resulting from advection of suspended solids, is accounted for. Sealing due to sedimentation of solids is not incorporated into the proposed simple model.