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C.2. Governing equations The species and energy conservation equations are solved using the DASOLV mathematical solver in gPROMS ModelBuilder (Process Systems Enterprise, 1997-2015). The solver uses an implicit variable time backward differentiation formulation for discretizing the equations. Sample formulation of species and energy conservation is shown, with calculations for the process instance of 0.392 s and for calculation node at 0.5 m from each end of the microchannel after initialization. In the equations, i is the iterator for species, whereas j is the iterator for axial locations for node points. This is the exact instant shown schematically in Figure C.2. For all the equations in the governing equations sections, the switches implemented for altering equations assume the following values. 1. Sads = 0, feed supply is cut off. 2. SLDG = 1, gas displacement by liquid in progress, product collection can continue. 3. Sdeso = 0, desorption stage not activated yet. 4. Scool = 0, desorption stage not activated yet. 5. SGDL = 0, desorption stage not activated yet. 6. SPurge = 0, desorption stage not activated yet. For the considered sample data point, as gases are being displaced by liquid at an axial location of 0.5 m from both the ends of the microchannel, the switches maintain their value indicated above. However, the gas and liquid phase identifiers are switched as follows. 1. XG =1,XL =1,attimet=t.Nodeoccupiedbygas. 2. XG = 0, XL = 0, at time t= t+Δt. Node occupied by liquid. This technique allows the model to select the appropriate set of equations for each of the stages in the process, without the need for a complex computational approach. 184PDF Image | TEMPERATURE SWING ADSORPTION PROCESSES FOR GAS SEPARATION
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