Dense gas extraction using a hollow fiber membrane contactor: experimental results versus model predictions

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for mass transfer operations such as extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. A mathematical model of a membrane contactor was developed that predicts the steady state fluid velocities and solute concentrations by solving the applicable conservation equations. The gravitational force term was included because the low kinematic viscosity of dense gases can render buoyancy-induced flow significant. A method of calculating the individual and overall mass transfer coefficients from the model results is also presented. The model was validated by comparing predicted Sherwood versus Graetz numbers for tube flow to those obtained from the classical equations that have been repeatedly confirmed by experiment. The three boundary conditions examined were constant wall concentration, constant flux, and linear variation of wall concentration with length. For all three cases the model predictions were in close agreement with those of the classical equations over a wide range of Graetz numbers, except for the constant flux condition at Graetz numbers greater than about 1000. This exception reflects a limit on the mass transfer rate imposed by the constant flux boundary condition. Graetz numbers greater than 1000 (found with short tubes or very high velocities) are not usually encountered in practical applications. Model results are compared to experimental data for the extraction of isopropanol or acetone from water into dense CO2, obtained over a range of flow rates using modules of different packing densities. Overall the model predicted the data reasonably well, proving the model to be a useful tool for evaluating potential new applications of the technology. For the isopropanol extractions the average absolute errors in the predicted mass transfer coefficients and yields were 29% and 31%, respectively, while for the acetone work the average absolute errors were 39% and 11%. In both cases the predicted mass transfer coefficients were lower than the observed values at the highest aqueous flow rates studied; usually the error became less negative (then increasingly positive in some instances) with decreasing flow rate. This trend is partly attributable to flow maldistribution (leading to reduced efficiency) caused by unavoidable non-uniform fiber spacing and variation in fiber diameter. Other possible sources of modeling error are discussed as well. With acetone, most of the resistance to mass transfer was in the aqueous phase boundary layer, as expected for a solute with a relatively high partition coefficient (mA). On the other hand, for isopropanol (a lower mA compound) a greater portion of the resistance was attributable to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant. Mass transfer coefficients and yields were higher for acetone than for isopropanol, and aqueous boundary layer penetration was more rapid; both results were a consequence of the higher mA of acetone. For both solutes, usually the mass transfer coefficient increased with increasing aqueous phase Graetz number, as expected when the aqueous phase mass transfer resistance is important. Moreover, yield generally increased with increasing solvent/feed ratio as anticipated.