Dynamic modeling for membrane with fixed charge groups in membrane separation process

Membrane separation processes actively use mathematical models to describe and simulate a wide range of operating conditions. Various membrane processes (pressure driven, electrical driven, salinity driven, or temperature driven) exist in industry. They can be applied as sustainable and environmentally sound alternatives to several conventional processes, including desalination, purification, gas separation, water treatment, resource concentration, food technology, biotechnology, pharmaceutical industries, biomedical engineering. Pressure driven membrane processes are energy intensive but have been widely used as water treatment processes including filtration and desalination, while salinity driven processes are promising for energy extraction from salinity gradient. This thesis is aimed at evaluating the separation performance of pressure driven and salinity driven processes for polymer membranes with a charged surface. A general predictive model for polymer membranes with charged surface coupled with electrical migration for ionic transport was developed. An accurate representation of the surface charge density on the membrane and thermodynamic properties of species in saline waters are used to model the ionic transfer. Mathematical models are solved numerically to predict water and salt flux for further analysis on rejection rate for pressure driven process and energy extraction for osmosis driven process. Chapter 1 provides a general introduction and basic phenomena that can be expected in a charged membrane system. Also, in this chapter, a literature review reveals advantages and drawbacks of existing models for the processes. Chapter 2 focuses on developing a model to accurately represent the fixed charge density on ionic transport, especially for polyamide membranes, in membrane separation process by regressing total concentration of functional groups and equilibrium constant. The degree of dissociation of functional groups, bulk concentration, pH, and surface potential effect in types of membrane are investigated and the model results agree with experimental observations. Chapter 3 uses results from Chapter 2 to develop a mathematical model of a pressure driven membrane process using the extended Nernst-Planck equation. By accounting for electro migration, the negative rejection of monovalent ion in the environment of a divalent ion is represented well in this model. Also, the effect of multiple ions is studied, and the model results are in good agreement with available data, which indicates the validity of this model in predicting ionic rejection. In Chapter 4, we develop a thermodynamic framework based upon the electrolyte non-random two liquids model to accurately predict the thermodynamic properties for Na+-Ca2+-Cl–-HCO3–-CO32–-CO2 system. The model, when used in concert with previous work defining the model parameters for of other important electolytes, can describe thermodynamic properties, including activity coefficient, osmotic coefficient, heat capacity, molar enthalpy, and solubility constantsfor concentrated salt solutions.
In Chapter 5, a two-dimensional and fully coupled computational fluid dynamic model is developed to describe the transport in the salinity drive processes of forward osmosis and pressure retarded osmosis. The model represents bulk experimental data well. The sensitivity to flow concentration and membrane characteristics that mitigate concentration polarization is investigated. This model allows evaluation of the energy consumption by pressure retarded process. Chapter 6 addresses the energy consumption during pressure retarded osmosis and reverse electrodialysis accounting for the non-ideality of solutions. The model is used to evaluate performance of energy extraction, power density and energy conversion efficiency in pressure retarded osmosis. The model provides a tool to optimize the operating condition for each process.

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