A new design of gas absorption that winds the permeable membrane onto an inner concentric tube to conduct a concentric circular gas–liquid membrane module has been studied theoretically in the fully developed region. An analytical formulation, referred to as conjugated Graetz problems, is developed to predict the concentration distribution and Sherwood numbers for the absorbent fluid flowing in the shell side and CO2/N2 gas mixture flowing in the tube side under various designs and operating parameters. The analytical solutions to the CO2 absorption efficiency were developed by using a two-dimensional mathematical modeling, and the resultant conjugated partial differential equations were solved analytically using the method of separation variables and eigen-function expansion in terms of power series. The predictions of CO2 absorption rate by using Monoethanolamide (MEA) solution in concentric circular membrane contactors under both concurrent- and countercurrent-flow operations are developed theoretically and confirmed with the experimental results. Consistency in both a good qualitative and quantitative sense is achieved between the theoretical predictions and experimental results. The advantage of the present mathematical treatment provides a concise expression for the chemical absorption of CO2 by MEA solution to calculate the absorption rate, absorption efficiency, and average Sherwood number. The concentration profiles with the mass-transfer Graetz number, inlet CO2 concentration, and both gas feed and absorbent flow rates are also emphasized. Both theoretical predictions and experimental results show that the device performance of the countercurrent-flow operation is better than that of the concurrent-flow device operation. The availability of such simplified expressions of the absorption rate and averaged Sherwood as developed directly from the analytical solutions is the value of the present study.
