(387b) Application of Gams in the Validation of an Experiment-Based Full-Factorial Dual-Objective Adsorption System for the Analysis of Process Variable Effects

In the design of experiments intended for bigger and complex systems, the larger number of involved variables and experimental runs makes certain analyses impractical or prohibitive. Such analyses which include building predictive meta-models and finding the optimum variable settings are usually modelled and/or generated through mathematical programming and optimization platforms to produce suitable data for applied systems. The design of experiment (DoE) platforms such as the Design Expert^® and MINITAB^® are known for their capacity to predict interactive effects of variables and/or optimize processes. Amongst other methods, these platforms utilize response surface and factorial methods for experimental design, execution and analysis. However, the performance of factorial among other methods is still limited due to some uncertainties that usually intensify process complexities. Equally, General Algebraic Modeling System (GAMS) is a modeling and optimization platform that has unified concepts and designs drawn from both interactive database theory and mathematical programming. Hence, the purpose of this study is to characterize the capability of these two platforms in terms of the autocorrelation of the variable effects towards making a steadier trade-off decision on the appropriate choice of variable(s) having the most significant effect on the objective function(s). In this research, a full-factorial dual-objective adsorption process model is compared and validated with GAMS with respect to the regions of process variables that are germane for process analyses under uncertainty. The objective functions or responses analysed are the silica and total dissolved solids (TDS). The factorial technique is used to quantify the effect of uncertain variables and their interrelationships so that the decision makers will be provided with a comprehensive grasp of the variables and responses. Results of the factorial design unveil the interactive nature of the process variables and the effects of their curvatures on the responses, which are facilitative in divulging the expedient information concealed underneath the variable interactions that affect the system performance. In order to provide the accurate conclusions, the individual and combined models were solved with the IPOPT solver and implemented in GAMS. The analysis is conducted and the conclusions are drawn based on the marginal values, intensity of variable significance, and percentage errors of the results obtained from both platforms. It is revealed that the adsorbent dosage as a variable had the highest effect on the whole process based on its significant p-value of at least 0.0005 as suggested by the analysis of variance (ANOVA) from the factorial design and highly significant marginal value (the true magnitude effect on the objective function subject to a slight change in the process variable) from GAMS platform. This variable contributed the most effect that push towards obtaining the minimum silica and TDS contents of 13 mg/L and 814 mg/L (from DoE platform) and 13.6 mg/L and 815 mg/L (from GAMS platform), respectively. This indicates a concurrence between the results of the two platforms with percentage errors of 4.4 % and 0.2 % for silica and TDS, respectively. The effects of the mixing speed and contact time are observed to be negligible and are not as critical as that of the adsorbent dosage. The regression models for silica and TDS generated coefficients of determination (R²) of 0.9994 and 0.9999, respectively. This study further supports the use of the statistical design approach for the model development and implementation in GAMS with respect to the variable interactive effects contributing to the suitability of the desired changes in the process being considered. The comprehensive results of the study, which will be discussed at the meeting, will surely assist the decision makers in generating firm decision alternatives in any related sorption processes.