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328 C.C.K. Beh and P.A. Webley/Adsorption Science & Technology Vol. 21 No. 4 2003 relationship for the two species (oxygen and nitrogen) was used to characterise the equilibrium loading,neiq: where neq m1biPyi m2diPyi i22 1 biPyi 1 diPyi i1 i1 (5a) bi boieQ1i /RT; di doieQ2i /RT (5b) While simpler isotherm forms could certainly be used, the above isotherm form and parameters were available for the sieve used in the present study and represented very little additional com- putational burden. Square-wave output (representing the on/off valves) boundary conditions have been used to simulate the various steps in the cycle (refer to Figure 3) as well as fixed valve coef- ficients (which represent the control valves on the plant). However, for this cycle, a constant vol- umetric flow rate boundary condition was assumed for stream 8 (due to the use of a constant volumetric flow rate rotary vane pump in the pilot plant). Calculation of the volumetric flow rates across valves is given by the valve equation as specified by the Fluids Control Institute. For pressure-driven flow, the volumetric flow rate, Q (NL/s), is described by: (6a) where PU and PD are the upstream and downstream pressures of the valve, respectively. For con- ditions experiencing choked flow, Q is represented by: (6b) However, if the upstream pressure is greater than the downstream pressure, a ‘No Flow’ condi- tion is employed. This models logic in the experimental plant whereby solenoid valves are not opened until the upstream pressure is greater than the downstream pressure to avoid backflow. Q 77.01Cv P2 P2 UD SgT PD 0.53PU Q 65.31CvPU 1 SgT PD 0.53PU Q 0 PU PD (6c) The dynamic model consists of eight coupled time-variant ODEs (representing molar flows, tank pressures and adsorbate species uptake) with an additional 15 ODEs to allow verification of numerical mass-balance closure and achievement of cyclic steady state. The set of ODEs are solved in the time domain using LSODA (Petzold 1983) or DVODE (Brown et al. 1989), stiff/non- stiff, first-order, backward difference integrator packages. OPEN LOOP RESULTS AND DISCUSSION In this section, we show and discuss the transient and cyclic steady-state profiles for each of the system responses (bed pressure, product tank pressure, product flow, feed flow, evacuation flow, oxygen purity and thermal responses). It is worthwhile noting that the relevant time variable used inPDF Image | Dynamic Response and Characteristics of an Oxygen Vacuum Swing Adsorption
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