Thermodynamic analysis of energy density in pressure retarded osmosis: The impact of solution volumes and costs

Abstract

A general method was developed for estimating the volumetric energy efficiency of pressure retarded osmosis via pressure-volume analysis of a membrane process. The resulting model requires only the osmotic pressure, , and mass fraction, , of water in the concentrated and dilute feed solutions to estimate the maximum achievable specific energy density, , as a function of operating pressure. The model is independent of any membrane or module properties. This method utilizes equilibrium analysis to specify the volumetric mixing fraction of concentrated and dilute solution as a function of operating pressure, and provides results for the total volumetric energy density of similar order to more complex models for the mixing of seawater and riverwater. Within the framework of this analysis, the total volumetric energy density is maximized, for an idealized case, when the operating pressure is , which is lower than the maximum power density operating pressure, , derived elsewhere, and is a function of the solute osmotic pressure at a given mass fraction. It was also found that a minimum 1.45 kmol of ideal solute is required to produce 1 kWh of energy while a system operating at "maximum power density operating pressure" requires at least 2.9 kmol. Utilizing this methodology, it is possible to examine the effects of volumetric solution cost, operation of a module at various pressure, and operation of a constant pressure module with various feed.

Gross vs. net energy: Towards a rational framework for assessing the practical viability of pressure retarded osmosis

“…Since there are economic and energy costs that scale with the volume of the draw solution [15], normalizing gross energy output by the feed volume seems to provide a poor rationale for optimizing the flow ratio and the applied pressure-the two important operation parameters in a practical PRO system [25]. Recent studies have attempted to provide a more reasonable evaluation metric by normalizing the gross energy output using the total volume of the feed and draw solutions combined, with the argument that both the feed and draw solutions require economic and energy costs for uptake, pretreatment, and flow circulation along the module [15,25,26,29,30]. Such a normalization method based on total solution volume leads to convenient optimization of the operation conditions in PRO, resulting in analytical expressions for the optimal applied hydraulic pressure and flow rate ratio between the feed and draw streams for different system configurations [25].…”

“…While most early studies on PRO investigated either the membrane materials or the local mass transfer kinetics [12,23], recent studies have identified the critical importance of analyzing the thermodynamics and energy efficiency of a full scale PRO system [24][25][26][27][28][29]. In fact, even though the technological feasibility of PRO has been demonstrated, the practical or economic viability of this seemingly promising technology remains challenging to determine [30].…”

“…Existing system-scale analyses on the energy efficiency of a PRO system typically use gross energy output as the evaluation metric [24][25][26][27][28][29]. However, gross energy output alone does not suffice to assess the practical viability of a PRO process due to the presence of non-negligible parasitic energy losses in a PRO system, such as those from pretreatment, flow circulation (i.e.…”

Optimization of Osmotic Desalination Plants for Water Supply Networks

“…An additional cost of 50 k$ was considered for the installation of additional control valves. RO-PRO was analyzed for the only the CS4 case representing the most advanced possible configuration (Reimund et al 2015).…”

Recent Advances in Osmotic Energy Generation via Pressure-Retarded Osmosis (PRO): A Review

“…More recently, analysis and optimization of PRO was attempted via a dimensionless parameter referred to as normalized specific energy production, and then the influence of the dilution of draw solution was intensively studied [60]. In the same year, a novel approach to estimate a volumetric energy density of PRO was reported [61]. Based on the method, the maximum achievable specific energy density can be determined by the osmotic pressure and the mass fraction of the feed and draw solutions regardless of the membrane properties.…”