PARAMETER ESTIMATION AND MODELING OF SPIRAL-WOUND

The hydraulic transport parameter (A) and the solute (TDS) transport parameter (B) need to be determined for the membrane used in the pilot-scale element. An iterative algorithm (Appendix C) is used to determine A and B values from pilot-scale experimental data. Initially the assumed A and B values (close to the actual) along with the operating conditions (i.e. feed pressure (Pf), feed flow rate (Qf) and feed TDS concentration (Cf)) are used as inputs to the deterministic process model developed in the previous part, to predict the values of permeate flow rate (Qp) and permeate TDS concentration (Cp). The predicted values for above parameters are compared with the experimental results to determine converge1 and converge2 values as follows:
converge1 =Qp (predicted)/Qp (observed) (21)
converge2 =Cp (predicted)/Cp (observed) (22)
The converge1 and converge2 values approach unity as A and B reaches the accurate values. Therefore, the convergence criteria are based on the deviation of converge1 and converge2 values from unity:
E1 = 1 - converge1, and E1 ≤ 0.001 (24)
E2 = 1 - converge2, and E2 ≤ 0.001 (25)
If the assumed values of A and B satisfy the convergence criteria, they are considered acceptable. Otherwise the assumed values are changed as follows:
A = A/converge1 (26)
B =B/converge2 (27)
Same procedure is repeated using the new A and B values until the convergence criteria stated in equation (24) and (25) are satisfied.
Alternatively, the transport parameters can be estimated by using Simplex search method from a given set of experimental data. An initial guess for each of the model parameters to be estimated is used to initialize the estimation of parameters. The predicted exit permeate flow rates and concentrations obtained based on the initial guess are compared with experimental values. If the values chosen for the parameters are not correct, the values are refined so that the predicted and experimental permeate conditions are as close as possible. The Simplex search algorithm is given in Appendix D.