In a previous paper, the authors have given correlations for seawater thermophysical properties as functions of temperature and salinity, but only for near atmospheric pressures. Seawater reverse osmosis (SWRO) systems operate routinely at pressures of 6 MPa or more; however, experimental data for seawater properties at elevated pressures (P = 0.1-12 MPa) are limited to a salinity of 56 g/kg. To accurately model and design SWRO and thermal desalination systems, a reliable method of estimating the effect of pressure on seawater properties is required. In this work, we present this method and new correlations for seawater thermophysical properties that are valid within the range: t = 0-120 °C, S = 0-120 g/kg, and P = 0-12 MPa. Seawater isothermal compressibility data, available until a salinity of 56 g/kg, were used to develop a correlation for compressibility that is extrapolated to 160 g/kg. Thermodynamic identities were then used to develop accurate pressure dependent correlations for seawater: density, isobaric expansivity, specific heat capacity, enthalpy, entropy and Gibbs energy. New correlations were proposed for 2 surface tension and osmotic coefficient were reviewed. Uncertainty bounds were calculated for each correlation.

On-site treatment and reuse is an increasingly preferred option for produced water management in unconventional oil and gas extraction. This paper analyzes and compares the energetics of several desalination technologies at the high salinities and diverse compositions commonly encountered in produced water from shale formations to guide technology selection and to inform further system development. Produced water properties are modeled using Pitzer's equations, and emphasis is placed on how these properties drive differences in system thermodynamics at salinities significantly above the oceanic range. Models of mechanical vapor compression, multi-effect distillation, forward osmosis, humidification-dehumidification, membrane distillation, and a hypothetical high pressure reverse osmosis system show that for a fixed brine salinity, evaporative system energetics tend to be less sensitive to changes in feed salinity. Consequently, second law efficiencies of evaporative systems tend to be higher when treating typical produced waters to near-saturation than when treating seawater. In addition, if realized for high-salinity produced waters, reverse osmosis has the potential to achieve very high efficiencies. The results suggest a different energetic paradigm in comparing membrane and evaporative systems for high salinity wastewater treatment than has been commonly accepted for lower salinity water.

Many membrane-based systems, such as reverse osmosis (RO), forward osmosis (FO) and pressure retarded osmosis (PRO), are being used in desalination, water treatment, and energy production. These systems work on the basis of mass transfer through a semipermeable membrane which allows for the permeation of water while rejecting salts and other substances. The membrane-based devices are essentially mass exchangers which are analogous to heat exchangers. The driving potentials in these mass exchangers are the concentration and pressure differences, whereas in heat exchangers the driving potential is the temperature difference. Closed form solutions of the permeation rate through an ideal PRO mass exchanger are obtained for parallel and counter flow configurations. The recovery ratio (RR) is obtained as a function of dimensionless parameters such as the number of mass transfer units (MTU), mass flow rate ratio (MR), and osmotic pressure ratio (SR). The resulting mathematical expressions form an effectiveness-NTU model for osmotic mass exchangers. These expressions are analogous to those for heat exchangers and can be used as an initial design for PRO membrane based mass exchange devices.

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.

A strong analogy exists between heat exchangers and osmotic mass exchangers. The effectiveness -number of transfer units (-NTU) method is well-known for the sizing and rating of heat exchangers. A similar method, called the effectiveness -mass transfer units (ε-MTU) method, is developed for reverse osmosis (RO) mass exchangers. Governing equations for an RO mass exchanger are nondimensionalized assuming ideal membrane characteristics and a linearized form of the osmotic pressure function for seawater. A closed form solution is found which relates three dimensionless groups: the number of mass transfer units, which is an effective size of the exchanger; a pressure ratio, which relates osmotic and hydraulic pressures; and the recovery ratio, which is the ratio of permeate to inlet feed flow rates. A novel performance parameter, the effectiveness of an RO exchanger, is defined as a ratio of the recovery ratio to the maximum recovery ratio. A one-dimensional numerical model is developed to correct for the effects of feed-side external concentration polarization and nonlinearities in osmotic pressure as a function of salinity. A comparison of model results to experimental data found in the literature resulted in an average error of less than 7.8%. The analytical ε-MTU model can be used for design or performance evaluation of RO membrane mass exchangers. Keywords