Mathematical models for the simulation of combined depth and cake filtration processes

In this work, mathematical models for combined depth and cake filtration are developed. Their formulation is either based on a moving or free boundary description. For the free boundary model existence and uniqueness of the solution is shown. To study the influence of the model parameters, two different tools are introduced, namely model reduction and parameter identification. Model reduction is used to study the sensitivity of the parameters and to accelerate the solution procedure. Multiple ways to construct a projection basis are discussed and reviewed. For parameter identification, an optimization framework for the free boundary problem is derived. Therefore a gradient algorithm in combination with an adjoint formulation is used. The models are compared to several experimental data and different mathematical aspects of the problem are tested, too. The results show that it is possible to reproduce the experimental data. It is further shown that a nonlinear pressure drop, often arising in cake filtration, can be explained by the model without considering compression of the cake.