<p>Cake filtration is a unit operation to separate solids from fluids in industrial processes. The build up of a filter cake is usually accompanied with a decrease in overall permeability over the filter leading to an increased pressure drop over the filter. For an incompressible filter cake that builds up on a homogeneous filter cloth, a linear pressure drop profile over time is expected for a constant fluid volume flow. However, experiments show curved pressure drop profiles, which are also attributed to inhomogeneities of the filter (filter medium and/or residual filter cake).</p><p>In this work, a mathematical filter model is developed to describe the relationship between time and overall permeability. The model considers a filter with an inhomogeneous permeability and accounts for fluid mechanics by a one-dimensional formulation of Darcy's law and for the cake build up by solid continuity. The model can be solved analytically in the time domain. The analytic solution allows for the unambiguous inversion of the model to determine the inhomogeneous permeability from the time resolved overall permeability, e.g. pressure drop measurements. An error estimation of the method is provided by rewriting the model as convolution transformation.</p><p>This method is applied to simulated and experimental pressure drop data of gas filters with textile filter cloths and various situations with non-uniform flow situations in practical problems are explored. A routine is developed to generate characteristic filter cycles from semi-continuous filter plant operation. The model is modified to investigate the impact of non-uniform dust concentrations.</p>

Cake filtration is a unit operation to separate solids from fluids in industrial processes. The build up of a filter cake is usually accompanied with a decrease in overall permeability over the filter leading to an increased pressure drop over the filter. For an incompressible filter cake that builds up on a homogeneous filter cloth, a linear pressure drop profile over time is expected for a constant fluid volume flow. However, experiments show curved pressure drop profiles, which are also attributed to inhomogeneities of the filter (filter medium and/or residual filter cake). In this work, a mathematical filter model is developed to describe the relationship between time and overall permeability. The model considers a filter with an inhomogeneous permeability and accounts for fluid mechanics by a one-dimensional formulation of Darcy's law and for the cake build up by solid continuity. The model can be solved analytically in the time domain. The analytic solution allows for the unambiguous inversion of the model to determine the inhomogeneous permeability from the time resolved overall permeability, e.g. pressure drop measurements. An error estimation of the method is provided by rewriting the model as convolution transformation. This method is applied to simulated and experimental pressure drop data of gas filters with textile filter cloths and various situations with non-uniform flow situations in practical problems are explored. A routine is developed to generate characteristic filter cycles from semi-continuous filter plant operation. The model is modified to investigate the impact of non-uniform dust concentrations.

<div>In this study, three ducts have been built in Herrick Labs, Purdue University, West Lafayette, representing the real HVAC systems. Different types of filters have been tested in each duct, including MERV8, MERV14 mechanical filters, and MERV13 electret filter. One of this study's main objectives is to compare in-situ filter performance with the MERV rating, which comes from laboratory testing. Eventually, we can explain the variations and have a better understanding of the in-situ filter performance. Another primary objective is to evaluate the aging process of tested filters. Typically, HVAC filters will not be replaced or maintained frequently, so they tend to stay in HVAC systems for an extended period. In this study, the evolution of filter aging performance is tested continuously for the experiment's entire duration, including temporal evolution of pressure drops, filtration efficiencies, and loaded particulate mass on the filter media.</div><div><br></div><div>This study will continue for 52 full weeks. This thesis is a part of the on-going study, including the data up to the first 18 weeks so far. As a result, the pressure drops are steadily increasing over time for most filters due to the natural filter loading process, except for the MERV13 electret filter, which shows no significant change at all. In terms of the filtration efficiencies, two efficiency categories are included: mass-based efficiencies (ePM x ) for sizeintegrated particulate mass (PM) and size-resolved efficiencies. It can be seen that there is no significant change in ePM x for MERV8 and MERV14 filters, MERV13 electret filter whereas shows a degradation in ePM x efficiencies. Size-resolve efficiencies provide additional filtration efficiencies as a function of particle sizes, therefore more comprehensive. It can be found that for MERV8 and MERV14 filters, the efficiencies are slowly increasing for particles above 300 nm, with some variations. MERV13 electret filter has an explicitly decreasing trend for efficiencies across all particle size ranges.</div><div><br></div><div>Besides the filter loading process, another component affecting the filter performance is the environmental factor, such as temperature, relative humidity (RH), and precipitation events, including rainfall and snowfall. As a result, it can be observed that when precipitation events, the pressure drops trend to decrease for that period. It is also evident that decreasing temperature tends to promote pressure drops.</div>