Limits of power production due to finite membrane area in pressure retarded osmosis

Abstract

Dimensionless analytical expressions for the power attainable from an ideal counterflow pressure retarded osmosis (PRO) system model are developed using a one-dimensional model that accounts for streamwise variations in concentration. This ideal PRO system has no salt permeation or concentration polarization. The expressions show that the optimal hydraulic pressure difference, for which the maximum power is produced, deviates significantly from the classical solution of one-half of the trans-membrane osmotic pressure difference, Δπ/2, as the dimensionless membrane area (MTU π ) increases and the ratio of draw to feed mass flow rates (MR) varies. The overall maximum power attainable from a PRO membrane is found to occur in the limit of infinitely large MTU π (an effectiveness of unity) and infinite MR. For an ideal PRO system which mixes seawater (35 g/kg) and river water (1.5 g/kg), the overall maximum power of 1.57 kJ per kilogram of feed can be attained at roughly MTU π of 15, an MR of 10, and a pressure of 0.83Δ . Due to economic considerations, a PRO system in practice will have limited membrane area and will operate at an effectiveness of less than unity.The present work can be used to estimate the operating conditions and area required for a PRO system of given performance. The effect of concentration polarization on optimal hydraulic pressure difference and maximum power performance is also investigated using a numerical model.

Thermodynamic analysis of brine management methods: Zero-discharge desalination and salinity-gradient power production

“…Few researchers studied the variation of the osmotic driving force of a module-scale system. For example, Banchik et al developed the concept of mass transfer unit (MTU) to properly represent the difference between coupon and module-scale systems [29,54]. This is why the limitation of single stage operation resulting from its poor distribution of driving force has not been stressed.…”

“…Prante et al [28] considered a wide range of salinities, but their PRO model was set up in parallel flow configuration, which is always less efficient than the counterflow configuration [29], and the analysis used an average flux, which results in an inaccurate representation of the variations actually found in a module-scale system.…”

System scale analytical modeling of forward and assisted forward osmosis mass exchangers with a case study on fertigation

“…A similar extension of this heat exchanger analogy has been applied to two other osmotically driven membrane processes: RO systems [26] and pressure-retarded osmosis (PRO) systems [25,27]. Using the presented equations, designers can either 'size' an exchanger given operating conditions (inlet feed and draw mass flow rates, osmotic pressures, and hydraulic pressures) and a desired performance or 'rate' an exchanger given the size and operating conditions of an existing exchanger.…”

“…We have included β, a streamwise average dimensionless correction factor, to account for concentration polarization and non-linearity in the osmotic pressure as a function of salinity. In our previous work [27], we considered a correction factor for the feed and draw stream separately, but here, for simplicity, we consider an average β used to de-rate the net driving pressure in an exchanger of finite length. In the ideal case where no internal and external concentration polarization is present and osmotic pressure is linearly proportional to salinity β = 1.…”

“…Table 1 displays the parameters used to non-dimensionalize the governing equations in this work. Because concentration polarization increases the area required to achieve the same recovery ratio [26,27], the correction factor β is included in the number of mass transfer units parameter MTU π to modify the amount of membrane area required when β = 1. For FO operation the pressure ratio parameter P * = 0 while for AFO operation, P f > P d so that the pressure ratio parameter P * < 0.…”