Nonlinear consolidation model for the prediction of constant pressure expression of semi-solid materials

Abstract

Nonlinear model of constant pressure expression is proposed for semi-solid materials and filter cakes. In this model the compressive pressure PS is replaced by the special power-law pressure function θ=1+PSPa1-nconsidering constitutive equation for the specific cake resistance α=α01+PSPan, where α0, Pa and n are the constants. The linearized form of obtained equation has analytical solution, which is similar to the solution of classical Terzaghi equation, but in terms of the proposed power-law pressure functionθ. Consequently, pressure profiles and local characteristics of compressed semi-solid materials can be better described. Constitutive relations for the compressibility modulus G and consolidation coefficient C are presented as power-law functions of the compressive pressure PS and used for the approximative analytical and numerous solutions of the obtained nonlinear consolidation equation. Consolidation coefficient (filtration diffusivity) of highly compressible filter cakes can vary little with compressive pressure increase or even remain constant due to the concurrency between G and α, which are both rise with higher compressive pressure PS.Several examples of the application of proposed model are presented for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO3, silica, activated sludge, water treatment (WT) plant residue). The profiles of local compressive pressure PS and local cake characteristics (specific cake resistanceα and solidosity εS) are simulated and compared for different filter cakes based on the analytical and numerical solutions of this model. The values of apparent consolidation coefficient Ca are simulated based on the adjustment of numerical and analytical solutions of the proposed model. These values can be used for better prediction of solid–liquid expression behavior.