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TABLE OF CONTENTS
The overall goal of your work is to develop an economic and environmental evaluation model for selecting an optimum scheme for produced water desalination. Regarding the environmental evaluation:
- What are the expected constituents of the produced brine, and in what relative quantities? How does the source of brine (including type of unconventional extraction considered) impact these constituents?
- The multi-objective portion seeks to reduce environmental impact by calculating the carbon footprint. What other environmental impacts, if any, will be considered within the first objective?
- Within the section on “Brine Management” in your white paper, you mention several options: injection of brine into deep wells, processing for disposal into landfills, and power generation from brine using pressure-retarded osmosis or reverse electrodialysis. What additional environmental impacts, other than those captured by carbon footprint, are presented by these different options?
The term produced brine may refer to the produced water or it may refer to the brine resulting form produced water desalination. In either case the constituent would be the same, except for some material that could be added (e.g. chemical added for chemical reactions) or removed (e.g. suspended solid removal through filtration) during pretreatment processes (depending on desalination pretreatment need), added anti-fouling and anti-scaling material (depending on desalination system fouling and scaling tendency), and volatile components. In the following sections, water constituent analysis is organize consistent with the time of operation stages and starts from the fracing fluid preparation and continues to produced water production.
Fracturing fluid is a fluid which is injected into the well at high pressures in order to create cracks in the rock formations to allow the gas and brine flow. 
There are different types of fracturing fluids which can be used in different scenarios.in most of the cases, water-based fluids (Viscosified or Nonviscosified water-based fluids) are used. In some cases, foam generated with N2 or CO2 can be used to stimulate shallow, low-pressure zones. In other cases, Gelled oil-based fluids are used for water sensitive formations. Acid-based fluids also can be used in carbonate formations. In “slickwater” treatments, low-viscosity fluids created which usually contain 98-99% of water, 1-1.9% sand and less than 1% of additives this combination can be different in various geographical locations. for example in Germany, Damme 3, drilled by ExxonMobil in 2008 and the fluid which was used had 94.6% water, 5.23% sand, and 0.17% additives. 
Chemical additives- A variety of Additives can be mixed with the injecting water, this is based on the depth of the target shale and the geological characteristics of the location. For example, Biocides such as Terpenes, isothiazolinones, are added to prevent the growth of bacteria in the produced water. Inorganic acids and bases are added for pH control. Breakers such as Sulfates, peroxides (e.g. Ammonium persulfate, calcium peroxide) are mixed with the injecting water for Reducing viscosity. To Protect equipment from Corrosion, Inhibitors such as Acids, alcohols, sulfites, (e.g. 2-butoxyethanol, amine bisulfite) are combined with the water. The crosslinker is another important additive which is used to support the formation of the gel, and to increase viscosity for a better transportation of sand. Polyacrylamide, petroleum distillates, e.g. aromatic hydrocarbons (benzene, toluene) are added in order to reduce the friction and avoid creating turbulent flow. Guar gum, hydroxyethylcellulose, polymers (e.g. acrylamide copolymers, vinyl sulfonates) are added as gelling agents to increase the viscosity for better transportation of sand. Scale Inhibitors such as acids, phosphonates, (e.g. dodecylbenzene, sulfonic acid, calcium phosphonate) are mixed with the injecting water to prevent precipitation from mineral scaling. 
Flowback and produced waters – After injecting Fracturing fluid with different mixture of additives into the well, about 8 to70% of this water eventually will come back to the surface. This wastewater can be categorized according to the time of the comeback and components of the fluid into Flowback water and produced water. 
Flowback water comes to the surface in days after the fracturing operation starts, with a very high flow rate at the beginning and gradually drops in the following months of starting the operation, therefore it contains mainly the components of injecting water mixed with additives and chemicals, metals and organic compounds which come from the shale formation. The volume of injected water is much higher than the absolute volume of flowback water, for the reason that majority of the water will be isolated into the shale formations through imbibition especially in the first 3 months of starting the operation.
The proppant (sand) in injecting water plus particles from rocks create suspended solids in the flowback water with the concentration rage of 300 to 3000 mg/L. The geological variability in components of rocks has an important role on the level of Total dissolved solids(TDS) in the wastewater. For example, in Germany, the TDS was reached to the maximum of 180,000 mg/l with an average of 100,000mg/l and in the Marcellus Shale in Pennsylvania, USA , the TDS range was between 8000-360,000 mg/l. And in the UK another study reported, the maximum TDS was 130,000 mg/l. [1,5]
Produced water is the next phase of wastewater comeback. High concentration of salt is the characteristics of produced water which comes from underground brines and salts from rock formation. Other important components of produced water are dispersed oil compounds, dissolved organic compounds, inorganic salts, treatment chemicals, production solids (formation, corrosion, scale, bacteria, waxes, and asphaltenes), dissolved gases and metals. 
Phenols, BTEX (benzene, toluene, ethylbenzene, and xylene), and Polyaromatic hydrocarbons are categorized as dissolved and dispersed oil (hydrocarbons) in the produced water. These hydrocarbons in high concentrations can be dangerous for the environment and nature.
Dissolved ions, compounds or minerals are categorized in cations, anions, naturally occurring radioactive materials and heavy metals.
Cations (mainly Na+) and anions (mainly Cl–) play a significant role in the salinity of produced water. Other ions such as [CO3] 2-, [SO4] 2-, [HCO3] –, K+, Mg2+, Fe2+, Ca2+ and Ba2+ have an important effect on the level of conductivity and scale formation potential in produced water. 
In the study on Marcellus Shale in Pennsylvania which was done in 2011, Flowback Water Characteristics were analyzed in the 1, 5, 14, and 90 days after fracturing operation. About 25% of the injected water came back to the surface as flowback water over 90 days. The total dissolved solids concentrations in flowback water were from 8000 to 360,000 mg/l, sodium with the concentration of 30,000 mg/l was the dominant cation, followed by calcium and magnesium. Chloride was the most common anion with the concentration of 80,000 mg/l. 
The Ra-226 and Ra-228 isotopes have been reported as the most common naturally occurring radioactive elements in produced water. As an example, in the Marcellus shale, the content of radium-226 is significantly higher than the standard for drinking water 10,000 pCi/l vs. 5 pCi/l.  it can be significantly dangerous when absorbed and accumulate on iron oxides inside of brine tanks . It is demonstrated in another study that higher levels of salinity correlate with lower radium adsorption. 
The presence of heavy metals (barium (Ba), cadmium (Cd), chromium (Cr), copper (Cu), lead (Pb)in produced water has been reported in different studies and its level depends on the age and geology of the formation. 
Production chemicals such as corrosion inhibitors and Scale inhibitors can also enter the produced water in small to significant amounts. carbon dioxide is the major dissolved gas followed by oxygen, and hydrogen sulfide in the produced water, these gases are produced by bacteria or by chemical reactions. 
The main goal of the multi-objective optimization process is the comparison between different desalination systems and management options. This comparison includes economic and environmental assessments simultaneously. While carbon footprint is the main environmental impact assessment element of the model, other environmental impacts could be potentially added to the function by the methods that would be explained further in this section.
Other environmental impacts that helps the comparison between different choices of produced water management are as follows:
- Environmental impacts of desalination: soil, groundwater, and air pollution, noise emission, adverse effects of chemical additives and corrosion products release (explained in the next question), contaminant release through leakage and failure of storage tanks, pumps, and pipes, treating the sensitive habitats and rare animal lives 
- Environmental impact-difference between different desalination methods: Thermal desalination systems brine usually have higher temperature in comparison to membrane-based ones, while membrane desalination brine usually contains more anti-scaling and anti-fouling chemicals. 
- Environmental impact of crystallization and disposal into landfill: Risk of leakage form the landfill to the water reservoirs. 
- Environmental impact of deep well injection: a) Risk of leakage from the wells and groundwater reservoir pollution. b) increasing the earthquake occurrence probability 
- Operators health and safety risk: Although this option might not be directly related to environmental impact, but it is related to human health, and should be assessed along with other environmental risks. Any method of managing the brine is accompanied by a relative risk of exposing human health to danger. Desalination plant operations have certain safety and health limit, and brine transport by truck also impose human health to the risk of accident.
Methods to include the environmental impacts in the model (multi-objective function):
- Analytic hierarchy process [AHP]: The application of this method is in the complex decision-making procedures. AHP process will prioritize the available decisions through some pairwise comparisons and helps the decision maker to choose the best option. AHP sets works with a set of criteria and a set of options for each criterion. The criteria here could be different environmental impacts. Based on the pairwise comparison different weights would be assigned to each criterion; the more important the criterion, the higher the weight. Then, different scores would be assigned to each option based on their importance, the higher score, indicates the better performance of the option. For example, risk of polluting the aquifer and inducing earthquake are two criteria for which the decision maker could give higher weigh to the aquifer pollution, because of it might have higher probability of occurrence. Direct injection of the brine into deep wells, and crystallization are two options of both criteria. In this case, crystallization would have a higher score for both criteria in comparison to deep well injection; since, it has a lower probability of polluting the aquifer and causing earthquake. Finally, the option with higher product of score and weight would be the best decision . The work done by Balfaqih et.al is good example of applying this method to assess the economic and environmental performance of desalination supply chain (including feedwater and chemical acquisition, desalination, fresh water storage, distribution to the consumers). In their model cost, revenue, leverage, profitability, and water loss are defined as economic metrics, eco-toxicity potential, airborne emissions, and health and safety of the staff are considered as economic metrics. Note that, the decision maker determines the relative importance of the criterion. 
- Sustainability analysis: Sustainability analysis integrates environmental, economic and social impact of a project, here produced water management option. The basis of this method is somehow similar to AHP method, but with more details enabling the model to be written as an objective function for the optimization procedure. Metrics, system parameter, metric weights, system parameter weights, system component variables, are the elements of a sustainability index model. Metrics (indicators) are the measure of the impact of a project on one of the suitability aspects (environmental, economic, or social). The weights are the relative importance of the metrics, and system parameters and their relative weights which are in fact subgroup of each metric. Each system parameter could be expressed as function of system variable. The sum of the product of the system parameters and their weight for all metrics will result in sustainability index.  For example, environmental impact is a metric with a weight, and impact on soil contamination is a system parameter (subgroup of the environmental metric) with its relative weight, and type of desalination could be the component variable. This example is not accurate and is just provided for the sake of better explanation of the analysis procedure.
The are four major way to deal with the desalination brine: 1) direct injection into deep wells, 2) crystallization and disposal into landfills,  3) Power generation through reverse electrodialysis and power retarded osmosis. . 4) application in industry (e.g. producing Cl2 and NaOH through Electrolytic cells require NaCl brines with concentration near saturation 
The main environmental impact difference between the mentioned options lies within the energy consumption and their resulting emissions and carbon footprint. For example, PRO and RED are the source green power generation [18, 19], unlike crystallizer that are consumer of the energy. Disposal into deep wells consume fuels for transportation. Industrial application could be assumed as neutral in the sense of energy consumption.
As other environmental impact than emission and carbon footprint are concerned, brine injection into deep wells could be compared against all three latter options. Since the main difference between those options are their energy consumption which is not the focus of this question. One can argue the positive effect of the PRO and RED, and brine industrial application on the environment through decreasing the load of extracting fuel and minerals and help to save the environment and ecosystem. Yet, the magnitude of this positive effect is not as large as the other environmental impacts.
All three methods of PRO, and RED, industrial application, remove the need for brine disposal and its negative environmental impacts due to its high concentration, high temperature, and chemical constituents. The brine is a result of water pretreatment and desalination, and thus, it might contain chemicals such as corrosion products, anti-fouling, anti-scaling, anti-foaming, halogenated organic compounds, oxygen scavengers, and acids. These contents could negatively alter the physical and chemical properties of the receiving environment and be a treat for the ecosystem. 
It should be noted that crystalizing and disposing solids into landfill are also accompanied with the risk of leakage from the landfill as mentioned in the previous section, but the magnitude of the risk of aquifer contamination is lower in comparison of injection of high volume of brine into deep wells.
Some examples of adverse environmental impacts of some of the brine constituent are as follows :
- High Salinity and high temperature could decrease the vitality and biodiversity
- Biofouling control additives are highly toxic for majority of organism
- Halogenated organics have carcinogenic effects
- Coagulants might increase the local turbidity and thus prevent the effective photosynthesis
- Antiscalants acids are poorly degradable have chronic effect
- Antifoaming chemicals are accompanied with high risk of accumulation and long-term effects, and low acute toxic effects
- highly acidic or alkaline cleaning solutions that may cause toxicity without neutralization,
- disinfectants and detergent have high and moderate toxic effects, respectively.
- corrosion inhibitor which could have low toxic effect
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Please provide a critical review of the attached manuscript. Your review should be 6-8 pages (number of pages listed for each question are just suggestions) and should include the sections listed below. Please include the references that helped you formulate your conclusions and support your answers and focus your response on critical analysis with fundamental insights rather than a simple recap and summary of the work.
- Brief overview of the scope and goals of the work described in the manuscript (Chen et al. published in Journal of Membrane Science) with particular emphasis on the novelty of the approach described in this study (1 page).
- Critical analysis of theoretical approach with special emphasis on modeling assumptions and potential for errors in data interpretation. Also, you should discuss shortcomings and possible improvements in the approach for the follow-on studies (2 pages).
- Discuss the results and conclusions offered in this manuscript. Do the results support the conclusions of the study? Are there other conclusions that can be made based on the results reported in the manuscript? (3 pages).
- Discuss practical relevance of the key findings of this study and compare this integrated approach to other technical solutions that can achieve similar outcome (e.g., MVR followed by a separate crystallizer) (2 pages).
The main goal of this paper is to analyze the efficiency of a CMDC (continues membrane distillation crystallization) system to reduce the desalination brine volume. The analysis is conducted through running several experiments to find the local optimum values for operating variables, consisting of temperatures and flow rates of feed and permeate streams. The efficiency metrics applied in this study are pure water and solid salt (NaCl) production rates.
The experiments are conducted to find the flux change trend with the mentioned factors and to analyze the underlying reasons of the obtained trends. Then these trends and obtained results of experiments are further analyzed to find the principal principal factors influencing the flux.
Considering the obtained results, this paper emphasizes the dominant mechanism governing the CMDC process is the deposition and crystallization which cause the system to demonstrate different performance under varying operating conditions. This finding of this paper is consistent with the operating feed salinity which is near saturation that make the solute more prone to deposition on membrane surface.
The novelty of this paper lies in systematic analysis offered for continues membrane distillation crystallization system. Most of the published papers prior to the present paper were dealing with running experiments and analyzing the challenges (including crystallization on membrane surface, and blockage of the tube connecting membrane and crystallizer. of CMDC applications and its performance efficiency, yet this paper is the one to offer a method to optimize the operating conditions of CMDC.
The CMDC configuration in this paper consist of a direct contact membrane distillation (DCMD) module and a cooling crystallizer. The analysis process and the results are discussed in the next sections.
In the present CMDC analysis, the optimization process is conducted through design of experiments (DOE). DOE analysis helps to understand the effect of different combination of influencing factors (with multiple levels) on the response variables. In this paper, temperatures and flow rates of the streams on both feed and permeate sides, each with three levels, are considered as the influencing factors to be studied. The response variable to measure the efficiency of the system is chosen to be pure water production rate, considering the fact that solid salt production rate is directly related to pure water production rate through overall mass balance in the system. Pure Nacl solutions is used for the experiments.
For full factorial design with four factors each with three levels, 81 different combination is possible to run the experiment. Considering the time and cost to run this large number of experiments, orthogonal fractional factorial (OFF) is applied to decrease the number of experiments to nine with one replication. OFF method does not analyze all possible combination, and instead analyze the most important ones judged by the experimenter and normal probability plots. Finally, the range analysis method is adopted to analyze the results of experiments, and to determine the most influencing factors, and local optimum value for each factor. The presented optimization process of CMCD is analyzed further in the following:
- Influencing factors are limited to just four operating variables (temperature and flow rates of the feed and permeate streams), while there are other factors such as feed salinity, temperature difference across the membrane, membrane area, membrane permeability, membrane structure and morphology, etc. that could affect the membrane performance significantly [1-4]
- Crystallizer characteristics is not analyzed. Crystallizer characteristics such as size directly impact the residence time in the crystallizer and thus, it would impact the system performance and quality of the produced solid salts.
- Response variable or objective function (in optimization terminology) is chosen to be pure water production rate. Considering the importance of economic reliability of each desalination system, energy consumption and final water production cost might be better criteria for efficiency measurement of a system.
- Factors interactions are not analyzed through OFF analysis. Generally factorial designs are meant to analyze the individual factors effect along with their interactions impacts on the response variable; yet, in the present OFF, the analysis is simply carried on the average response of each level for each factor individually. This way of analysis could somehow be similar to experiment on different levels of a factor with three number of replication for each level, while other factors are kept constant. Although, in the OFF method, other factors are not kept constant and are changed in each replication for each factor and also their combination is changed within each level. This even might be the source of minor inaccuracy in the analysis, in comparison to the simple individual experiment, if only individual effect analysis is the purpose of DOE.
As a case in point, Onsekizoglo et. Al. studied the membrane distillation operating condition with two level factorial experiment and concluded that the feed salinity and temperature difference have significant interactive effect on evaporation flux. 
- Range analysis is used to analyze the experiments results. Although, range analysis is computationally faster than variance analysis, the latter is statistically more efficient . This is because the range is not an effective representative of the variability in the data. For instance, consider a situation in which 4 datapoint (of total 5 datapoint) are near upper extreme of the whole data range, and only one is near the lower extreme of the whole data range. In this case, expected mean value obviously lies near the upper extreme, and the variance is less affect by the only 1 data point far from the mean. But, in range analysis, the range (difference of the maximum and minimum distance from the mean) would be larger than variance. Hence, range analysis might overestimate the variability and cause error in determining the principal influencing variables.
- Pure NaCl is used for the experiments. In real industrial problems, different salts exist in the solution, and their crystallization condition and order might affect the performance of the system. [4,6]
The designed OFF experiments are conducted for three level of each factor and the results are as follows:
- Effect of feed temperature: The experiments results shows that the maximum flux occurs at the median level. The reason for this trend is explained as follows: Increase in the feed temperature first increases vapor pressure at the feed side, and thus increases the driving force for the vapor pass through the membrane. Increased permeation rate leads to higher supersaturation state of the stream to the crystallizer and results in higher solid production rate. By further increasing the temperature, the cooling load on the crystallizer increases, and less crystal would be formed. As a result, the recycled mother liquor stream to the feed tank would have higher salinity and decreases the water production flux by increasing the boiling point elevation.
- Effect of feed flowrate: Similar to feed temperature, a maximum flux occurs by increasing the feed flowrate followed by a decrease in flux by further increasing the feed flowrate. This could be explained by the fact that increasing the feed flow rate would increase the Reynold number and create turbulent near the membrane surface reducing the boundary layers thickness. This enhances the mass and heat transfer which results in a higher permeate flux. Higher supersaturation state would be created as a result of higher permeate flux, and solid salt production rate would be increased. By further increasing the feed flowrate, the residence time in the crystallizer would be decreased and less crystals would form. Therefore, the mother liquor would be recycled with higher concentration and decrease the vapor pressure by boiling point elevation which will cause reduction in evaporation rate.
- Effect of permeate side temperature: Pure water production rate shows an ascending trend by increasing the temperature on the permeate side. By increasing the permeate side temperature, the driving for permeate flux will be decreased which decreases the flux. But, it also decreases the conduction heat transfer loss which result in higher feed temperature side that in turn increases the driving force and decrease the crystal deposition on the membrane surface. Both mechanisms would increase the flux by increasing permeate side temperature.
- Effect of permeate side flowrate: By increasing the permeate side flowrate, flux would be decreased. This phenomenon is explained as follows: By increasing the permeate side flowrate, the turbulent flow will decrease the boundary layer thickness and enhance the permeate flux. On the oth er hand, this turbulent will increase the conductive heat loss and decrease the feed side temperature. Reduction in feed side temperature would promote deposition on the feed side and will decrease the permeation. As a result, retentate concentration would be decrease, and solid salt production rate is reduced.
- Optimum result by range analysis: By applying range analysis, feed flow rate and permeate side flowrate are the principal influencing factors showing the largest range. The optimum values are obtained by comparing the largest distance from the average of each level. Running the experiment with optimum values shows the best performance of the system.
- Crystal quality analysis: Feed flowrate has the largest impact on both mean crystal size and its distribution which a result of decreased residence time in the crystallizer. Feed temperature also demonstrate significant influence on the crystal size. Increased temperature will increase the cooling load on the crystallizer and hamper the crystal growth.
The main conclusion of this paper is that the CMDC process is mainly controlled by deposition of salt on the membrane surface. Although this conclusion and offered explanation regarding the reason of such flux trend (with varying levels of factors) seem logical, but the demonstrated result might not fully support the conclusion. Since there are limited number of data point and further analysis might be needed to ensure the results. Additionally, the range analysis does not reveal whether a factor has significant impact on the response variable or not. It states that flowrates of both side are principal factors but does not explain anything about the temperatures. If the temperature is not principal so the explanation regarding the observed trend might not be valid. On the other hand, all explanations are valid by some probability and no proof is provided.
I reviewed different papers to validate the result of this paper experiment and found some, for example references number  and  both demonstrated the same result for the relation between the feed temperature and mean crystal size as the presented paper. Reference  also demonstrated the same result for the effect of feed flowrate on the mean crystal size, and flux.
One of the main effective factors on crystallization in CMDC is the nucleation enhancement on the membrane surface, because heterogenous nucleation energy barrier is lower than the homogenous energy barrier in the bulk. [7,8]. It allows nucleation on membrane surface and crystal growth in separate environment that prevent membrane fouling and accelerate the crystallization process. . Hence, analysis of nucleation might help interpret the obtained trend better. For example, in ref  it is demonstrated that nucleation and growth rate are directly and adversely related to temperature rise. This kind of analysis crystallization kinetic parameters could possibily be used in explanation of the crystal size variations, and other trends which shows maximum in the median level. Flowrate affect the
The results of this study could be used to analyze the possibility of CMDC and ZLD (zero liquid discharge) application in the shale gas produced management.
There are different desalination systems (e.g. MD and MVR) and different crystallization types (cooling, evaporating, vacuum, forced circulation). Thus, different combination of desalination system and crystallization could be considered for treating the produced water to prevent the mentioned environmental problems in previous chapter. Mechanical vapor recompression systems are mostly coupled with thermal or forced circulation crystallizers , whereas membranes could be coupled with both type of cooling and heating crystalizers. 
Different combination could have different performance, energy consumption, and practical limitation. For example, membrane is more prone to deposition on membrane surface in comparison to thermal evaporation and crystallization systems, on the other hand the membrane surface helps the heterogenous nucleation and crystallization.
Crystallizers also show different crystallization performance based on their types and under different operating conditions such as the one discussed in the previous sections. Generally cooling crystallizer generate larger crystals in comparison to heating crystallizers.
Solute type and its solidity variation with temperature affect the crystallization type and temperature. For example, for a solute with negative solubility, thermal crystallization might work more efficiently. et.al have analyzed the MDC system with integration of MD with a thermal crystallizer. For instance, Zhong et. al combined a vacuum membrane distillation with a thermal crystallizer to crystalize calcium carbonate which has an adverse solubility relation with temperature . It should be noted that thermal crystallizers have higher temperature than feed tank, and cooling crystallizers have lower temperature than the feed.
It is worth to note that, MCr or membrane crystallization is also an emerging technology to not only produce nucleates on the membrane surface, but also to grow them on this surface. No separate crystallizer is added in this system. [superfobisity]
To date, there is no published comprehensive analysis on comparison among different desalination and crystallizer combination economic and technical performance. Membrane based studies mostly deal with experimental analysis of operating conditions and mechanical vapor compression-based systems are mostly analyzed through exergy and energy separate from crystallizer.
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- Briefly summarize the attached article by Onishi et al. published in Journal of Cleaner Production. Your summary should include an overview of the main goals of the paper, modeling approach (especially uncertainty quantification), and the critical findings. Finally, discuss ways to incorporate uncertainty in your future work focused on Zero Liquid Discharge (ZLD) technologies for shale gas produced water treatment.
- You are planning to use multiobjective optimization methods, discuss the relative merits of at least three multiobjective optimization techniques and discuss the relative advantages/disadvantages of those methods versus Data Envelopment Analysis.
The main goal of the present paper is to find an optimum design for a backward feed MEE-MVR (multiple effect mechanical vapor recompression) desalination plant for shale gas flow back water under uncertainty. The fluid to be desalinated is the shale gas flowback water, and the uncertainty included in the optimization process arises form feed (produced water) flowrate and salinity. Other objective of this paper is to set the plant configuration so that it could be able to be integrated with zero liquid discharge (ZLD) technologies. Note that this paper does not include the crystallization process in the model, and just set the brine concentration near saturation so that it could potentially work with ZLD technologies.
The MEE/MVR desalination plant configuration mainly consist of falling film horizontal tube evaporators, a mechanical vapor compressor, a feed-distillate preheater, mixers, and pumps. However, the cost of pump and mixers are not accounted in the final model because they constitute only a small fraction of the total cost of fresh water production.
The primary model to be optimized is developed by heat and mass balance equations, heat transfer coefficient equations and heat transfer area calculations, correlation for physical properties of the streams using the state parameters (temperature, pressure, and concentration) using OLI software, constraints on working temperatures and pressures of the system, and non-linear and non-convex cost functions. The primary objective function here is to minimize the total annual cost of fresh water production near brine saturation condition, given a specific feed water flow rate and concentration. The decision variables, are the operating conditions (system pressure and temperatures) which affects both operating and capital costs.
It should be noted that this model does not include heat transfer coefficient calculation for evaporator and preheater; Instead, it uses an experimental correlation for both evaporator and preheater heat transfer coefficients.
The uncertainty is added to the optimization process by converting the primary model to a stochastic multiscenario model. As mentioned earlier, the uncertainty in this analysis is due to unknown or varying feed water flow rate and concentration. In order to account for these uncertainties, multiple pairs of feed flow rate and concentration are generated. Each of these pairs is a distinct scenario for the optimization process. Then, the primary objective function would be modified so that it encompasses all the scenarios at the same time instead of considering just one specific scenario for the feed water. This work is done through weight average of total annual cost of all scenarios. The weight of each scenario is its probability of occurrence which is considered equal for all scenarios in this study.
As in the primary model, the decision variables are operating conditions for each scenario which determine the capital costs (through transfer areas and equipment capacities) and operating costs (through energy consumption). Capital costs are categorized as scenario-independent element and operating costs are considered as scenario-dependent element of the objective function. This means the different operating condition for different scenarios would be optimized simultaneously so that they all have same equipment capacity, but with probably different energy consumption. This kind of modeling might push to the model to have the biggest capacity for the extreme condition to be able to work with all scenarios, which might result in equipment oversizing. To prevent oversizing problem, external steam is added to the model as secondary source of energy to prevent the compressor oversizing.
Scenario generation is done through assuming multivariate normal correlated distribution functions for uncertain variables. Then, random values will be generated using Monte Carlo sampling technique within the defined boundaries. Two main elements in the multivariate normal distribution functions are the expected value of the uncertain variables, variance of each uncertain variables, and covariance of these variables. In this study this value is estimated roughly based on the available data for flow back water rate of generation, and its salinity. The flowrate expected value is estimated using the number of simultaneous wells in exploration step, amount of water required for hydraulic fracturing, and the assuming average 25 percent flow back water. The expected value for salinity is estimated based on Barnett and Marcellus shale plays data. The covariance between flow rate and salinity is considered -0.8, as this paper states that the salinity will be increased with the flowback water flow rate reduction after first two weeks of hydraulic fracturing.
The optimization process of the proposed nonlinear programming model is done using the interior-point solver IPOPT under GAMS.
Critical finding and result of running the model: The optimization process is first done to compare the deterministic approach (i.e. a single scenario) and multiscenario stochastic approach. For this purpose, the model is first run by a single scenario and the obtained equipment capacities are set fixed for the multiscenario stochastic approach. The result shows higher average total cost for stochastic model compare to the optimum total cost for the deterministic model. This is due to the fact that only small fractions of the scenarios will result in lower total annual cost and the rest of them will result in higher costs with steam added as external energy source to compensate for the extra energy required.
In the next step the multiscenario stochastic model is optimized and the cumulative curve of total annual cost distribution is generated to account for the risk associated with each cost estimation. The resulted average total annual cost of this optimization is lower in comparison to the previous first step. This is because it has accounted for all scenarios instead of just one scenario to optimize the mode. Additionally, the stochastic optimization is done with different variance and covariance for the uncertain variables. The results of this step show that, as the more conservative cost estimations will result in higher probability of occurrence since larger number of scenarios will result in the estimated or lower than estimated cost. Also, based on the cumulative curves, increase in variance will increase the risk, since there is more variation in data. Likewise, increase in covariance will increase the risk, the scenario generation will include the extreme conditions in which two uncertain variables both occurs at extreme levels at the same time.
The sensitivity analysis is done for different brine salinities. For this purpose, the whole stochastic model is run multiple times with setting different brine salinity limit for each run. The results of this sensitivity analysis show that the total annual cost would be increased by increasing the brine concentration.
To develop optimization procedure under uncertainty for the ZLD operation, following steps should be taken:
- Primary model development: a model would be build based on system configuration, mass and heat transfer balances, energy requirement calculations, and other thermodynamic correlations. In the future work, ZLD operation will be included in the model by not only setting the constraint on brine salinity, but also adding the selected type crystallizer (cooling, evaporative, etc.) to the configuration. Hence, the decision variables (operating conditions, and equipment characteristics) in the primary model would be optimized by considering a continuous process consisting of brine concentrator (MD or MVR) and crystallizer.
- Choosing Uncertain parameters: Recognizing the uncertainty source in developing a model is an important step in developing the model.In shale gas produced water desalination, uncertainty arises from different input variables or correlations in the model like: a) uncertainties related to feed water (flow rate, salinity), b) uncertainties related to inflation and amortization rate c) uncertainties related to individual equipment costs. For example when there are limited datapoint available to estimate the cost function, boost wrapping technique would be used to generate other data points and regression is used to create a correlation between size and cost of the equipment. In this case if the variance of the parameter of the obtained model is high, the parameter itself become an uncertain variable. 
- Choosing scenario dependent/independent elements of the model: As explained in the summarized paper, some elements of the model are scenario (a vector of uncertain parameters) dependent, and some of them are scenario independent. The discussed paper, assume the operating costs as scenario dependent, and capital cost as scenario independent; since, it is considering one fixed equipment set up for the plant which could not be changed after initial decision. But, the present MVR technologies, in the oil and gas shale plays, are modular and they could be designed in multiple skids [1’]. In this way the capital also could be assumed as semi-scenario dependent and the model become more flexible. It is semi-dependent, because the capacity of each individual module is same for different scenarios, but the number of modules could be different. For example, we could consider that higher capacities require larger number of modules, and lower capacities require lower number of modules. The optimum solution could result in an average number of modules. For smaller capacities, some modules could be excluded from the system and for larger capacities some modules could be added to the system.
- Modeling the uncertainty: There are different modeling philosophy for uncertainty [2’], which would be briefly discussed in this section.
- Stochastic programming: a) Programming with recourse: the uncertain variables are divided into two parts; one part should be determined before the realization of the random event, and the second part could be chosen after random even occurred. The second group are call corrective variables. (e.g. linear, non-linear, integer, robust stochastic programming) b) Probabilistic Programming: this method assign cost to recourse activities to make sure that the second-stage problem is feasible and tries to minimize the penalty or recourse cost functions. [2’]
- Fuzzy mathematical programming: a) Flexible Programming, b) Possibility programming. The difference of fuzzy with uncertainty analysis is that instead of using probability distribution for uncertain variables, it uses random parameters and constraint (fuzzy sets) [2’]
- Stochastic dynamic programming consider that decision process is taken place through different stages through time. [2’]
Multi-objective optimization methods could be categorized into four different groups, based on the decision maker (DM) preference. Preference indicates the relative importance of an objective function among other objective functions.
- No preference methods are used when decision maker has no preference. An example of “No preference method” is genetic algorithm (GA). Genetic algorithm is evolutionary algorithm which investigate the search space to find the optimum solution through improving a set of data points (populations) by mutation, crossover, and reproduction. This kind of algorithm are dependent to the function continuity and derivatives and could work with any type of objective functions (including non-convex) functions to find a global solution. It also has the potential to converge on a pareto optimal set. Disadvantages of the GA methods include: 1- It might be trapped in a local optimum. 2- Its programming is complex, and 3- Computationally costly.
- Posteriori methods are used when decision make is not sure about his/her preference. Here the model is first run through different pareto optimal solutions, and then decision maker will choose the most preferred one. Weighting method is an example of posteriori methods. This method is easy to solve and implement and is perfect for models with two objective functions, since the solution could be visualized for decision maker. The sum of weighting method is able to work with both posterior and priori methods. If weighted are unknown varying weight would be analyzed in the model and result in a set of pareto optimal solutions. This method cannot work with non-convex function, and pareto optimal solution is not necessary based on the preferred weight, since it is varying through the optimization process.
- Priori methods are used when decision maker knows his/her preference. In this method, decision maker enters his/her preferences and in this he/she put a constraint on the model. Pareto optimal solution are produced based on the decision maker preference. In addition to weighting sum average method (explained earlier), Lexicographic ordering and global programming. In the Lexicographic ordering method, the objective function with highest importance (preference) is optimized first, and the second important function in optimized within the first obtained pareto optimal solution, and this process will continue. In global programming method the sum of weighted standard deviation of all objective function from their goal is optimized. This method is easy to implement and understand and helps the decision maker to capture the important element of the problem and convert them to goal and constraint for the model. This method might not result in optimum solution and might not converge toward the global optimum.
- Interactive methods require the decision maker decide whether the solution of a run is satisfactory or not. This method actively is in interaction with decision maker, and decision maker could define the direction of the optimization in each iteration (i.e. only solution that of DM preference are generated). Reference point method which is an intuitive way to express preference is one example of the interactive methods. This method consumes so much time from the decision maker, and he/she might lose the track of the procedure.  , 
Data envelope analysis (DEA) is method to measure the efficiency and benchmarking. It determine the efficiency of Decesion Making Units (DMU) by pairwise comparison of the data points, determine the pareto front which is the optimum efficiency. This pairwise comparsion is done by comparing individuatl unit or mixing them by volume and comparing the mix against another one. DEA is able to compute the cost and resource saving that can be made by modifying an inefficient system to efficient system. In this way DMUs approach the best perormace DMU.
DEA process in run using varying number of input and output to the DMUs. It could work without limitation concerning the input and output numbers. Additionally, the input and output units does not need to be consistent for running the analysis. Also, it does not require a function to operate and it directly calculate the efficiency based on the number of input (resources) to the outputs (gains).
Main disadvantage of DEO is that noises are not tolerable in this model, since this model works with extremes. Another disadvantage of DEO is that although it is suitable for relative efficiency estimation, it converges very slowly to the absolute best efficiency. Indeed, it compares the DMUs with its peers, and not with the theoretical maximum. DEA programming consist of formulating each DMU as a line, and therefore, when the problem becomes large, the computational aspect of the problem would be a major concern. , 
DEA comparsion with MOO might not be proper, since one deals with functions, and one deals with input and outputs, one deal with finding the optimum solution, one deal with finding the performance efficiency to improve the situation, DEA is noise sensetive and MOO methods are less sensetive.
These two methods could be applied based on the context or could be merged to result in a powerful and robust model. For example, Rung et.al combined the DEA and GE to combine the power of GE to search the design space and the power of DEA to guide mode toward efficient frontiers.