The Need for Accurate Osmotic Pressure and Mass Transfer Resistances in Modeling Osmotically Driven Membrane Processes

Abstract

The widely used van ’t Hoff linear relation for predicting the osmotic pressure of NaCl solutions may result in errors in the evaluation of key system parameters, which depend on osmotic pressure, in pressure-retarded osmosis and forward osmosis. In this paper, the linear van ’t Hoff approach is compared to the solutions using OLI Stream Analyzer, which gives the real osmotic pressure values. Various dilutions of NaCl solutions, including the lower solute concentrations typical of river water, are considered. Our results indicate that the disparity in the predicted osmotic pressure of the two considered methods can reach 30%, depending on the solute concentration, while that in the predicted power density can exceed over 50%. New experimental results are obtained for NanoH2O and Porifera membranes, and theoretical equations are also developed. Results show that discrepancies arise when using the van ’t Hoff equation, compared to the OLI method. At higher NaCl concentrations (C > 1.5 M), the deviation between the linear approach and the real values increases gradually, likely indicative of a larger error in van ’t Hoff predictions. The difference in structural parameter values predicted by the two evaluation methods is also significant; it can exceed the typical 50–70% range, depending on the operating conditions. We find that the external mass transfer coefficients should be considered in the evaluation of the structural parameter in order to avoid overestimating its value. Consequently, measured water flux and predicted structural parameter values from our own and literature measurements are recalculated with the OLI software to account for external mass transfer coefficients.

Modeling and Evaluation of the Permeate Flux in Forward Osmosis Process with Machine Learning

“…However, the nonlinear relationship occurs between DS molarity and water flux, particularly at high DS molarity in Figure S5b. It can be observed that the SHAP value of DS molarity rises with the increase of DS molarity and then remains constant, which is due to the effect of ICP in the support layer of the FO membrane. , The feature importance reveals that the DS molecular weight, flow orientation, and DS type could be ignored in the XGBoost model since they have little influence on the concentrative internal concentration polarization (CICP) process …”

“…It can be observed that the SHAP value of DS molarity rises with the increase of DS molarity and then remains constant, which is due to the effect of ICP in the support layer of the FO membrane. 37,38 The feature importance reveals that the DS molecular weight, flow orientation, and DS type could be ignored in the XGBoost model since they have little influence on the concentrative internal concentration polarization (CICP) process. 15 The unimportant input features could decrease the accuracy of XGBoost model due to the introduced noisy data.…”

Impact of the Recovery on Concentrating Acetic Acid with Low-Pressure Reverse-Osmosis Membranes

“…For acetate, the coefficient equals 0.8, since it is partially dissociated, as discussed in Section 2.2. The assumption of linearity in the range of concentration of the present work is validated by Nagy et al [26]. In the case of NaCl, as soon as the concentration reaches 4 M, this assumption does not hold anymore.…”

Nuclear pores as conduits for fluid flow during osmotic stress

“…The osmotic pressure Π across a semi-permeable membrane is proportional to the difference in osmolyte concentration Δ C , where i, R , and T denote the van ‘t Hoff index, ideal gas constant and temperature, respectively. The osmotic pressure drives a water flux through the membrane 145 , where is the number of translocated water molecules (in unit of mole) per unit time and unit area from the cytosol to the outside; k mem is the membrane water permeability; and Δ P hydro = P O – P C is the difference in the hydrostatic pressure between the nucleus and cytosol. Without hydrostatic pressure change across the plasma membrane, P O ≈ P C , the flux from the cytosol to the outside (in unit of mole per unit time) is, We treat the NE as a single entity, ignoring its small luminal volume.…”