Technoeconomic Optimization of Emerging Technologies for

Research Article Cite This: ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

pubs.acs.org/journal/ascecg

Technoeconomic Optimization of Emerging Technologies for Regulatory Analysis Daniel B. Gingerich,† Timothy V. Bartholomew,‡ and Meagan S. Mauter*,†,‡ †

Department of Engineering and Public Policy, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, United States ‡ Department of Civil and Environmental Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, United States S Supporting Information *

ABSTRACT: Evaluating sustainable technologies during the regulatory design process requires tools for rapidly assessing the cost and performance of compliance technologies that leverage process integration or are still in the development phase. This work demonstrates the use of gray-box optimization to facilitate process assessment during regulatory design, using the recent Effluent Limitation Guidelines regulating the discharge of flue gas desulfurization wastewater as a case study. We build computationally lean meta-models of an emerging ammonium-bicarbonate forward osmosis (NH4HCO3 FO) technology that is heavily integrated with heat sources at the power plant. We then compare the capital and operational costs of an NH4HCO3 FO and crystallization treatment train against that of mechanical vapor recompression and crystallization, the “Best Available Technology” for zero liquid discharge and the basis for EPA’s benefit cost analysis during the regulatory process. We estimate that the NH4HCO3 FO treatment train would reduce the cost of zero liquid discharge by $0.30−$1.20/m3 and would have reduced the cost for a stricter evaporative standard by $20−$70 million nationwide. Finally, we discuss opportunities and challenges associated with deploying gray-box optimization techniques for the rapid assessment of emerging technologies in policy analysis. KEYWORDS: Forward osmosis, Industrial wastewater treatment, Zero liquid discharge, Waste heat, Flue gas desulfurization wastewater

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INTRODUCTION Regulations are a critical driver of sustainable technology innovation, but the regulatory process itself can also stymie technology diffusion if compliance technologies and regulatory standards entrench status-quo technologies. One issue is that the U.S. Environmental Protection Agency (EPA) is statutorily required to select from existing, proven technologies when setting treatment standards or analyzing environmental regulations using benefit cost analyses under the Clean Water Act1 or the Safe Drinking Water Act.2 While emerging water technologies may be qualitatively discussed in the regulatory documentation, their potential for reduced compliance cost or increased performance is not factored into the final standards setting process, even when the proposed rule has a projected compliance deadline several years in the future.2,3 An efficient standard setting process might consider emerging technologies alongside best available technologies (BATs) when setting standards and quantifying the net benefits of the rule, rather than delegating this to the five year review process, after which large infrastructure investments have already been made. A second issue is that the BATs identified for pollution control are almost uniformly stand-alone technical solutions. © XXXX American Chemical Society

While inherently simple to analyze and implement, they eschew many of the principles of green design that advance process integration and intensification to minimize resource use.4−6 Indeed, there are several innovative green design solutions that leverage waste heat and mass flows at coal-fired power plants (CFPPs) and industrial facilities to drive pollution control processes. For example, NH4HCO3 forward osmosis7−11 (FO), and membrane distillation12 use recovered waste heat10 to reduce the carbon and emissions intensity of wastewater treatment processes. Similarly, treated wastewater can be used in FGD systems or cooling water systems to reduce process and cooling water withdrawals. One of the critical barriers to incorporating emerging green design technologies in detailed regulatory analyses is the absence of facile methods for comparing the potential of emerging, integrated technologies to existing, unintegrated technologies. The performance and cost models for integrated systems are more complex, are often highly nonlinear, and have Received: October 20, 2017 Revised: November 28, 2017

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DOI: 10.1021/acssuschemeng.7b03821 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering

components, including lead, mercury, arsenic, and selenium. The diversity of coal sources and upstream air pollution control technologies can lead to substantial variability in the concentration of these constituents within and between plants.31,32 For the 11 plants the EPA sampled during the FGD rulemaking process, the average total dissolved solids in FGD wastewater is 33,000 mg/L with an average osmotic pressure of 15 bar.24 While we assume this average FGD wastewater composition in our three power plant case studies, we also perform sensitivity analysis on this assumption by modeling FGD wastewater between 5.8 and 17.4 bar. NH4HCO3 FO and Crystallization System. NH4HCO3 FO is a two-step water treatment process (Figure 1).8,33−35 In

significantly greater uncertainty than models of stand-alone BATs already in operation. These integrated systems are also likely to have higher variability in cost and performance across facilities, depending, for example, on the quality and quantity of the waste heat recoverable at a specific power plant. The need to account for this complexity, nonlinearity, uncertainty, and variability in cost and performance modeling of emerging technologies has led to the development of a diverse set of process optimization methods. When applied to new technologies or integrated systems,13−22 optimization models are often classified as white box, black box, or gray box depending on the level of detail in the underlying mathematical model.23 White-box approaches use models that can provide a high-level of detail about the process, but can be computationally intensive. Black-box approaches rely on machine learning or flowsheet software models and can be less computationally demanding, but they also provide less mechanistic insight into the process operation. Gray-box approaches attempt to balance the two by converting a detailed process model into a computationally lean, simplified model that captures the critical relationships defining process performance. Wider adoption of these gray-box approaches in technology evaluation for regulatory analysis or regulatory compliance may address the need for rapid assessment, while still providing the high-fidelity systems models that support uncertainty and sensitivity analysis. Compliance with the recently promulgated Effluent Limitation Guidelines for the Steam Electric Generating Sector (ELGs) provides a case study in applying gray-box optimization to evaluate an emerging, integrated technology in the context of a regulatory analysis. Reducing, and ultimately eliminating, wastewater from CFPPs is an important mandate for the electricity sector, as CFPPs are the largest industrial point sources of wastewater emissions in the U.S. The EPA selected mechanical vapor compression and crystallization (MVCC) as the BAT for evaporation of flue gas desulfurization (FGD) wastewater,24 but MVCC is an energy intensive, stand-alone technology that consumes electricity rather than leveraging low temperature waste heat available at the CFPP.25,26 The EPA did not evaluate pilot-scale technologies with potential for heat or process stream integration at CFPPs, including FO processes with thermolytic (e.g., NH4HCO3) or switchable polarity solvent draw solutions.27−29 In this work, we demonstrate the use of meta-models to rapidly assess the potential of NH4HCO3 FO and crystallization to treat FGD wastewater. We begin by modeling the NH4HCO3 FO system components using detailed process models and flowsheet software. We then reduce these models into meta-models to facilitate their integration into a single NH4HCO3 FO optimization model. Finally, we apply this meta-model optimization framework to the treatment of FGD wastewater for three CFPPs case studies and compare the levelized cost of water (LCOW) for NH4HCO3 FO to that for MVCC treatment.

Figure 1. NH4HCO3 forward osmosis and crystallization process modeled in this paper. Wastewater enters the NH4HCO3FO membrane module. The dilute draw solution exiting the membrane enters a mixer and preheaters before entering the distillation column for the draw solute recovery process. The brine from the membrane enters the ammonia recovery unit and a crystallizer to produce a solid product and treated water.

the first step, the feed stream runs countercurrent to a higher osmotic pressure draw solution in a membrane module. Freshwater diffuses across the semi-permeable membrane, concentrating the feed stream and diluting a thermolytic draw solution, in this case ammonium bicarbonate. In the second stream, the draw solution enters a distillation column where it is thermally regenerated into a concentrate stream and a treated water stream with a concentration of less than 1 mg/L ammonia. For high diffusivity draw solutions or low selectivity membranes, reverse salt flux in the membrane module can lead to a significant loss of draw solute. This issue is addressed in the NH4HCO3 by passing the wastewater retentate through an ammonia recovery unit.29 Process Specifications and Constraints. We adapt the NH4HCO3 FO process for FGD wastewater treatment at CFPPs by specifying the heat integration and adding a crystallizer unit. Two preheaters (PH 1 and 2) recover heat from the streams leaving the distillation column and a third preheater (PH 3) and two reboilers (RB 1 and 3) that use waste heat from power plant exhaust gas.36,37 A crystallizer after the ammonia recovery unit enables compliance with zero liquid discharge (ZLD) standards. While our analysis does not specify or value the end use of the product water, it is of sufficient quality for internal reuse as FGD makeup water or cooling water. Finally, we assume the following specifications and constraints:

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PROBLEM STATEMENT FGD Wastewater. FGD wastewater is generated at CFPPs with wet FGD systems for sulfur dioxide air pollution control.30 The high chloride concentration in the recirculating limestone slurry can lead to corrosion of stainless steel in wet FGD systems, and so a slip stream is diverted to keep chlorides below approximately 20,000 ppm.31 In addition to chlorides, this stream contains a wide array of organic and inorganic B


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Figure 2. Optimization model.

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• Waste heat is recovered from the exhaust gas stream either upstream or downstream of the FGD system, depending on availability of composition and temperature data for each case study. • Waste heat recovery from the flue gas is limited by acid gas mist condensation, which has the potential to cause significant corrosion. In our model, the flue gas temperature is maintained above the acid gas mist condensation temperature for flue gas compositions in the three case studies by fixing the temperature drop to 10 °C. In all three case studies, the existing flue gas temperature remains safely above the acid gas mist condensation temperatures as modeled in our previous work.38 • The minimum heat exchanger approach temperature is 5 °C. • Product water has a NH4 concentration of 1 mg/L. • The osmotic pressure of FGD wastewater is 15 bar at the outlet of the FGD scrubber. Chemical precipitation pretreatment is used to reduce scaling in NH4HCO3 FO.24 We model the composition of the FGD wastewater stream as a pure NaCl stream at an osmotic pressure of 11.6 bar following the chemical precipitation process described by the EPA.32

component sizes, operating and capital expenses, and assumed discount rate and system lifespan to minimize the LCOW. We solve the optimization problem using GAMS 24.5/BARON 15.9 to a 0.1% optimality gap.39 Technical Model. The technical model determines the size and energy consumption in the five different unit processes of our NH4HCO3 FO and crystallization system: (1) the NH4HCO3 FO membrane, (2) the distillation column, (3) the heat exchangers (preheaters, chillers, and reboilers), (4) the ammonia recovery system, and (5) the crystallization unit. Below, we present the key equations in our meta-models and optimization framework. A complete discussion of the system components is reported in Supporting Information (SI), Section 1.0, and the full set of mass and energy balance equations is reported in SI Section 2.0. NH4HCO3 Forward Osmosis Membrane. To model the NH4HCO3 FO membrane process, we first build a finite element model of a CTA membrane based on water and salt fluxes across the membrane (eqs 1 and 2). Jw = A[(πfm − πdm)]

(1)

Js = B[Cfb − Cdb]

(2)

In eq 1, Jw is the water flux from the feed to the draw, A is the pure water permeability coefficient of the membrane, and π is the feed ( f) and draw (d) osmotic pressure of the solution at the membrane surface. The osmotic pressure is a function of the salt concentration, and we determine the salt concentration at the membrane surface through mass transfer equations that account for concentration polarization on both the feed and draw side. Both the osmotic pressure and mass transfer equations can be found in SI Section 1.1. In eq 2, Js is the salt flux across the membrane, B is the salt permeability coefficient, and C is the feed ( f) and draw (d) concentrations in the bulk (b) solution. Additional details on the finite element model are reported in SI Section 1.1 and Figure S1. We then simplify the NH4HCO3 FO discrete element model into a meta-model that estimates the water and salt recovery (eqs 3 and 4) based on a linear regression with fixed inlet flow rates and concentrations. We assume a draw concentration of 3 M and flow rate of 50% the wastewater flow rate. As described in SI Section 3 and Figure S4, we test the impact of these assumptions on our LCOW and find that our assumptions lead to a local minimum.

OPTIMIZATION PROBLEM Regulatory analysts typically select a BAT on the basis of cost and performance. The performance of ZLD systems are equivalent from an environmental perspective, and thus, cost becomes the primary consideration when evaluating technologies. Here, we formulate a process optimization model to minimize the LCOW by sizing the components of the NH4HCO3 FO and crystallization processes. This model also enables parametric evaluation of the effect of wastewater concentration, heat source, and system lifespan on the LCOW. Our optimization problem consists of two integrated models (Figure 2): a technical model consisting of mass and energy balance equations for the NH4HCO3 FO and crystallization system and a cost model for the process components. The technical model uses system materials and properties, FGD wastewater flow and concentration, and waste heat availability to determine energy consumption and component sizes. The cost model uses information about system flow rates and C


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ACS Sustainable Chemistry & Engineering Table 1. Cost Model Parametersa,44−47

Capital Cost Factors Cost category Chemicals Membrane Distillation

Cooling

Ammonia Recovery Crystallizer Heating a

Description

PVv

VCv

α0v

α1v

α2v

NH4HCO3 makeup [$/y] Membrane replacement [$/y] Membrane module [$] Distillation column shell [$] Distillation column packing [$] Preheater heat exchanger [$] Distillation column reboiler [$] Condenser heat exchanger [$] Chiller heat exchanger [$] Condenser cooling water [$/y] Chiller cooling water [$/y] Ammonia recovery unit [$] Ammonia recovery reboiler [$] Crystallizer [$] Crystallizer electricity [$/y] Low pressure steam [$/y] Reboiler with steam [$]

Mass of NH4HCO3 makeup [kg/y] Membrane area [m2] Membrane area [m2] Mass of steel in shell [kg] Volume of packing material [m3] Heat exchanger area of preheater [m2] Heat exchanger area of reboiler [m2] Heat exchanger area of condenser [m2] Heat exchanger area of chiller [m2] Condenser cooling water volume [m3/y] Chiller cooling water volume [m3/y] Distillate flow rate from AR unit [m3/h] Heat exchanger area of reboiler [m2] Feed flow rate into crystallizer [m3/h] Crystallizer product water flow rate [m3/y] Mass flow rate of LP steam [tonne] Heat exchanger area of reboiler [m2]

0.15 [$/kg] 8.8 [$/(m2·y)] − − − − − − − 0.025 [$/m3] 0.025 [$/m3] − − − 2.85 [$/m3] 9 [$/tonne] −

− − 0 17,400 0 57,150 57,150 57,150 57,150 − − 0 57,150 0 − − 57150

− − 44 75 7600 750 750 750 750 − − 38,040 750 606,322 − − 750

− − 1 0.85 1 1 1 1 1 − − 1 1 0.5642 − − 1

More details can be found in SI Section 2.10.

R mem , H2O = β0 + β1Am + β2Am2 + ϵ

The regression parameters in eqs 5 and 6 can be found in SI Section 1.2 and Tables S5 and S6. Both eqs 5 and 6 have an R2 greater than 0.98. Heat Exchangers. The heat exchangers in our system consist of three preheaters to raise the temperature of the diluted draw stream from 50 to 100 °C, three reboilers in the distillation column and the ammonia recovery system, and a condenser and a chiller for the distillate from the distillation column. The heat duty in a heat exchanger, Qex, is a function of the overall heat transfer coefficient, U, Chen’s temperature difference approximation, ΔTChen, (calculated using eq 7),41 and surface area of the heat exchanger, Aex (eq 8).

(3)

Equation 3 is the meta-model for water recovery, where Rmem,H2O is the water recovery in the NH4HCO3 FO module, Am is the membrane area, and β0, β1, and β2 are regression parameters reported in SI Section 1.1 and Tables S1−S4. We include a quadratic term to account for the marginal changes in the driving force that occur at higher recoveries (Figure S2). R mem , s = β0 + β1Am + ϵ

(4)

Equation 4 is the meta-model for salt recovery, where Rmem,S is the salt recovery in the NH4HCO3 FO module, and β0 and β1 are regression parameters reported in SI Tables S1−S4. The R2 of regressions in eq 3 and are greater than 0.99. Distillation Column. We use Aspen Plus40 to simulate the performance of the distillation column over a range of inlet feed flow rates, inlet concentrations, number of trays, and heat duties in order to meet a standard of less than 1 mg/L ammonia in the treated water. This treated water can be used throughout the plant as cooling water, boiler feedwater, or reused in the FGD wastewater to reduce the plant’s water withdrawals. Details of the Aspen model are reported in SI Section 1.2 and Table S5. We assume the column has a height equivalent of a theoretical plate of 0.3 m and a diameter of 1.0 m. The column is packed with a generic Goodloe structured packing.11 We use the results of the Aspen flowsheet to create a metamodel that describes the size and energy demand of the packed distillation column. The number of trays in the distillation column, Ntray, is a function of the water recovery, Rdis, and regression parameters β0 and β1 (eq 5). Ntray = exp(β0)Rdis β1 + ϵ

(7)

Qex = UAexΔTChen

(8)

For Chen’s temperature difference approximation in a counter-current heat exchanger, ΔT1 is the temperature difference between the cold stream inlet and hot stream outlet, and ΔT2 is the temperature difference between the cold stream outlet and the hot stream inlet. The overall heat transfer coefficient U for each heat exchanger42 varies based on the fluid combinations in the heat exchanger (i.e., gas−liquid, liquid− liquid, and gas-evaporating liquid). Ammonia Recovery System. Roughly 10% of the mass of NH4HCO3 back-permeates across the FO membrane, and an ammonia recovery system is used to recover a portion of this ammonia. We develop a simple performance model for the thermal vapor compression unit based on an Aspen model, where a 90% recovery of ammonium bicarbonate and 30% recovery of water is observed at a heat duty of 320 kJ/kg of distillate. Additional details on the ammonia recovery system are reported in SI Section 1.3. Crystallization. To achieve ZLD, the wastewater retentate is fed into a crystallizer unit to produce a solid stream for landfilling and a treated water stream that can be reused within the plant. The crystallizer electricity consumption is estimated from the literature at 57 kWh/m3 of inlet wastewater.43

(5)

The specific heat duty in the distillation column, Q̂ dis, is also a function of the water recovery and regression parameters β0, β1, and β2 (eq 6). 2 Q̂ dis = β0 + β1Rdis + β2Rdis +ϵ

⎛ ΔT + ΔT2 ⎞1/3 ⎟ (ΔT1ΔT2)1/3 ΔTChen = ⎜ 1 ⎝ ⎠ 2

(6) D


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ACS Sustainable Chemistry & Engineering Table 2. Case Study Parameters Case Study Available Waste Heat [kJ/s] HX Inlet Temperature [°C] HX Outlet Temperature [°C] Acid Gas Condensation Temperature [°C] Wastewater Production [m3/h]

NETL Sub PC without CCS

NETL Super PC with CCS

Plant Bowen

113,000 153 143 128 111.6

137,000 153 143 128 134.4

30,400 128 118 50 268

Figure 3. Costs for NH4HCO3 forward osmosis and crystallization. (A) Levelized cost of water for the three case studies. Note that Plant Bowen captures waste heat downstream of the FGD unit and thus relies on the use of LP steam. (B−D) Results for three different sensitivity analyses: (B) FGD osmotic pressure, (C) heat source for the FO and crystallization process, and (D) system lifespan. Results are tabulated in SI Section 4 and Tables S10−S13.

Cost Model. The objective of the problem is to minimize the LCOW [$/m3] in a NH4HCO3 FO and crystallization treatment train, as shown in eq 9. min LCOW =

specification of corrosion resistant materials and shorter-thanexpected component lifetimes (SI Section S2 and Table S9). We calculate a capital recovery factor of 0.1175 by assuming a discount rate of 10% and a 20-year project lifespan. We exclude costs that are common to both NH4HCO3 FO and the MVCC benchmark technology, including water softening costs, solids disposal, installation, site preparation, labor, and indirect capital costs. These costs constitute the majority of the total costs, in ZLD systems, ranging from $15− 30/m3 of treated water.43

CRF ∑v CCv + ∑v OCv AF

(9)

where CCv and OCv are the capital costs [$] and operating costs [$/y] of component v, respectively, CRF is the capital recovery factor, and AF is the annual flow rate of treated water [m3/y]. We calculate the capital and operating costs of each component using eqs 10 and 11 CCv = α0, v + α1, vPV vα2,v ∀v

(10)

OCv = VCvPVv ∀v

(11)

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CASE STUDIES Case Studies Description. We use the optimization model to determine the minimum costs for treating FGD wastewater to ZLD at three different CFPPs (Table 2). Two of these plants are baseline models of CFPPs developed by the National Energy Technology Laboratory (NETL).48 These models are commonly used by researchers to study the impact of retrofits on plant performance.49−51 For these plants, we assume waste

where PVv is the process variable related to the costs and VCv, and α1,v, α2,v, and α3,v are cost parameters listed in Table 1. We utilize standard engineering references44,45 for baseline cost parameters, modifying as necessary to account for the E


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withdrawn after the FGD unit at Plant Bowen. (Note that this assumption is made due to the absence of data on the precise temperature of the flue gas at Plant Bowen). This assumption results in insufficient waste heat to drive the NH4HCO3 FO and crystallization process, and requires the use of steam from the LP turbine to augment thermal energy inputs to the draw solute distillation column. The opportunity cost associated with using LP steam at Plant Bowen is $3.71/m3, making the total cost of NH4HCO3 FO and crystallization $5.66/m3. This result highlights the extent to which NH4HCO3 FO technologies require the use of waste heat to remain cost competitive. Sensitivity Analyses. FGD Wastewater Osmotic Pressure. The FGD wastewater concentration varies significantly between CFPPs31,32 and is a critical variable in the design of ZLD systems for FGD wastewater treatment (Figure 3B).54,55 For a fixed draw solution concentration, a higher osmotic pressure wastewater decreases recovery in the membrane unit and decreases the cost of heat exchangers and the distillation unit, but significantly increases the cost of the crystallization process. Specifically, we find that increasing the feed concentration after pre-treatment from 11.6 to 17.4 bar increases the LCOW by $0.45/m3 (19%), while decreasing the concentration to 5.8 bar decreases the LCOW by $0.52/m3 (22%). As FGD wastewater concentration can vary significantly depending on coal quality, air pollution control device operation, and purge frequency, this introduces considerable uncertainty into the design and costing of NH4HCO3 FO systems. Heat Source. The origin of the heat also has a significant impact on the costs of NH4HCO3 FO. The optimized design for LP steam driven NH4HCO3 FO is $7.3/m3, $5.0/m3 (220%) more expensive than the optimal design for waste heat driven NH4HCO3 FO (Figure 3C). This difference stems from the opportunity cost of reduced electricity generation at the plant, as well as significantly different process operation parameters. In the LP steam case, total heat consumption for the NH4HCO3 FO process is reduced by 2 MW (3% of heat consumed in base case) with 1.3 MW of heat reduction coming from reduced heat demand in the distillation column. System Lifespan. Regulatory analyses assign process-specific system lifespans when calculating levelized costs. For emerging technologies, this imposes significant uncertainty, as component lifespan may vary across application, and new components are unlikely to have well-defined lifespan estimates. This uncertainty is higher for systems at CFPPs given the uncertainty around lifespans for the power plants. As shown in Figure 3D, reducing the expected NH4HCO3 FO system lifespan from 20 years to 10 years increases the cost by $0.40/ m3 (17%), while increasing the lifespan to 30 years decreases the cost by $0.17/m3 (8%). These changes are due to the annualization of capital expenses, in particular, for the crystallizer and the membrane unit. For the 10-year lifespan case, the cost contribution by the crystallizer and membrane are $0.28/m3 and $0.08/m3 higher, respectively, than the 20-year lifespan case. For all three of the lifespans considered, the LCOW using NH4HCO3 FO and crystallization are lower than for MVCC. Implications for Effluent Limitation Guidelines. In establishing the ELGs, the EPA declined to mandate ZLD FGD wastewater treatment due to the high cost of the best available technology, MVCC.56,57 As noted above, using NH4HCO3 FO and crystallization instead of MVCC would have resulted in estimated cost reductions of $33−$44 million (2.5−3.3%) relative to the $1.3 billion MVCC compliance cost estimate.58

heat extraction upstream of the FGD system. We also include Plant Bowen, a CFPP located in Eularhee, Georgia. Due to limited data availability on energy flows in Plant Bowen, we assume waste heat extraction immediately before the flue gas is discharged into the environment. Uncertainty and Sensitivity Analyses. Our optimization results are sensitive to assumptions about FGD wastewater composition, energy source, and CFPP lifespan. We perform a parametric sensitivity analysis on these assumptions using the NETL 550 MW PC plant without carbon capture. FGD Wastewater Composition. FGD wastewater concentration varies both within and between plants as a result of changes in coal composition, installed air pollution control devices, or robustness of the wet FGD system design to high chloride concentration. We assess the sensitivity of the minimum LCOW to wastewater osmotic pressure by also evaluating wastewater osmotic pressures of 5.8 and 17.4 bar. Energy Source for NH4HCO3 FO. Waste heat from the flue gas is the lowest-cost option to drive the thermal processes in NH4HCO3 FO treatment, but if the waste heat is of insufficient quality or quantity, it would need to be augmented with steam from the CFPP’s low-pressure turbine. To assess the impact of extracting LP steam, we run an analysis where LP steam at a temperature of 267 °C and 5 bar is extracted and priced as described in our previous work.10 CFPP Lifespan. Cheaper natural gas and renewable energy sources lead to significant uncertainty around the remaining lifespans of existing CFPPs. To assess the impact of this uncertainty, we repeat our optimization with FGD wastewater treatment system lifespans of 10 and 30 years.

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RESULTS Cost-Minimized NH4HCO3 FO System Designs. The minimum costs for NH4HCO3 FO and crystallization systems are presented in Figure 3. Excluding pretreatment, disposal, installation, labor, and indirect capital costs, we estimate a LCOW of waste heat driven FGD wastewater treatment at supercritical and subcritical CFPPs of between $2.2/m3 and $2.4/m3 (Figure 3A). The brine crystallizer, which is powered using electricity generated at the CFPP, accounts for approximately $1.1/m3 to 1.2/m3 of this total cost. This cost for crystallization is lower than conventional industrial crystallizers because of the significant volume reduction that occurs in the NH4HCO3 FO system (>80%) and the lower internal cost of electricity at CFPPs. The cost of wastewater treatment using NH4HCO3 FO and crystallization at the subcritical and supercritical plants are lower than the benchmark cost of $3/m3 for MVCC52 (depicted as a dashed line in Figure 3) by $0.6−$0.8/m3. The EPA’s ELG analysis assumed that U.S. CFPPs produce 55 million m3 of FGD wastewater produced annually.53 If NH4HCO3 FO had been considered as a compliance technology, the estimated compliance costs would have been reduced by $33−$44 M/yr. Note that neither the NH4HCO3 FO nor MVCC cost estimates include the costs of pretreatment to remove heavy metals and divalent cations, solid disposal, labor, or indirect capital costs.24 In contrast, the cost of NH4HCO3 FO and crystallization treatment at Plant Bowen is significantly higher than the MVCC benchmark technology. This difference stems from the location at which we model the withdrawal of waste heat. While we assume waste heat is withdrawn upstream of the FGD for the NETL model power plants, we assume waste heat is F


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reductions would have resulted in a positive benefit−cost analysis for ZLD.

Although the EPA did not specify an acceptable cost for ELG compliance with a ZLD standard in their regulatory documentation, it is unlikely that these reductions in compliance costs would have led the EPA to consider a ZLD standard for FGD wastewater given that total ZLD costs were so large. However, this analysis does suggest that when standards are set using benefit−cost analyses, as is the case for Clean Water Act and Safe Drinking Water Act rules, emerging technologies may be cheaper, and cheaper technologies may facilitate tighter standards on wastewater discharges.

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CONCLUSIONS Gray-box approaches to process optimization modeling, including the work presented here, have several advantages as a tool for regulatory design. First, gray-box approaches use process information that is likely to be available or can be readily derived, such as flowsheet models and cost data from similar technologies. Second, these approaches are inherently flexible and can be used to evaluate a wide variety of design configurations. Finally, these models have sufficient process fidelity to enable uncertainty and sensitivity analysis. Despite these advantages, there are several limitations associated with implementing meta-model optimization in the regulatory design space. Most importantly, the meta-modeling approach may introduce errors and additional uncertainty into process representation. While the meta-models in this study have high R2 values, the fits represent regression-to-process model fidelity rather than a regression-to-measurement fidelity. As such, the meta-modeling approach is likely to be better suited for first pass screening of emerging technologies, rather than for the final rule making process.

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DISCUSSION Incorporating emerging technologies into regulatory assessments poses a legitimate challenge for regulators. While established technologies have well-documented performance and cost data across a range of applications and system scales, the data on emerging technologies may be limited to lab- or pilot-scale demonstrations, may be proprietary or otherwise restricted, and may not reflect the application being considered under the regulatory assessment. In these cases, process models of technology performance are the only viable tool for simulating efficacy and cost and incorporating these estimates into the regulatory assessment process. This simulation process is further complicated for emerging technologies that leverage the green design principle of process integration. In these cases, process performance and cost are likely to be highly nonlinear and exhibit significant uncertainty around design parameters. Developing appropriate modeling tools for benchmarking emerging technologies to established ones through rapid exploration of different design configurations and facile sensitivity analysis will facilitate the consideration of emerging technologies in regulatory design. This paper demonstrates the use of gray-box optimization techniques as one such rapid, facile method for estimating the costs and performance of emerging, integrated technologies during regulatory assessment processes. Gray-box techniques, which leverage meta-models of stand-alone process performance to simulate an integrated process, are especially well suited for exploring the large design decision space inherent when developing regulatory standards that span multiple installations. Gray-box techniques are also well suited to performing sensitivity analysis on these design assumptions, which is critical in environmental control processes where composition and flow may be highly variable. In short, we propose that the balance of simplicity and process fidelity provided by a gray box optimization approach enables emerging, integrated technology assessment and its incorporation into the regulatory design process. To demonstrate the value of this approach, we augment the analysis of FGD wastewater treatment regulations under the recent ELGs with a cost assessment of the NH4HCO3 FO plus crystallization treatment process that is powered using waste heat at the CFPP. We began by developing simplified process and flowsheet models of NH4HCO3 FO and crystallization units to identify the minimum cost process configuration for integrating NH4HCO3 FO with CFPPs. We then used this optimization framework to identify system design parameters and the installation conditions to make NH4HCO3 FO and crystallization cost competitive with the current best available technology. We demonstrated that considering NH4HCO3 FO would have reduced the costs of the ZLD regulatory option, though the EPA’s omission of an estimate of ZLD benefits precludes a definitive assessment about whether these cost

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.7b03821. Descriptions of (1) process meta-models, (2) optimization problem formulation, (3) additional sensitivity analyses on draw loop design, and (4) tabulated results presented in Figure 3 of the main manuscript. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (412) 268-5688. ORCID

Meagan S. Mauter: 0000-0001-6946-7213 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Department of Energy (DEFE0024008) and the National Science Foundation (CBET1554117). D.B.G. and T.V.B. also individually acknowledge support from The Pittsburgh Chapter of the ARCS Foundation (Achievement Rewards for College Scientists). This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily G


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(10) Gingerich, D. B.; Mauter, M. S. Retrofitting the Regulated Power Plant: Optimizing Energy Allocation to Electricity Generation, Water Treatment, and Carbon Capture Processes at Coal-Fired Generating Facilities. ACS Sustainable Chem. Eng. 2018. (11) Zhou, X.; Gingerich, D. B.; Mauter, M. S. Water Treatment Capacity of Forward-Osmosis Systems Utilizing Power-Plant Waste Heat. Ind. Eng. Chem. Res. 2015, 54 (24), 6378−6389. (12) Lokare, O. R.; Tavakkoli, S.; Rodriguez, G.; Khanna, V.; Vidic, R. D. Integrating membrane distillation with waste heat from natural gas compressor stations for produced water treatment in Pennsylvania. Desalination 2017, 413, 144−153. (13) Moradi-Aliabadi, M.; Huang, Y. Multistage Optimization for Chemical Process Sustainability Enhancement under Uncertainty. ACS Sustainable Chem. Eng. 2016, 4 (11), 6133−6143. (14) Ruiz-Mercado, G. J.; Carvalho, A.; Cabezas, H. Using Green Chemistry and Engineering Principles To Design, Assess, and Retrofit Chemical Processes for Sustainability. ACS Sustainable Chem. Eng. 2016, 4 (11), 6208−6221. (15) González-Bravo, R.; Nápoles-Rivera, F.; Ponce-Ortega, J. M.; ElHalwagi, M. M. Multiobjective Optimization of Dual-Purpose Power Plants and Water Distribution Networks. ACS Sustainable Chem. Eng. 2016, 4 (12), 6852−6866. (16) González-Bravo, R.; Ponce-Ortega, J. M.; El-Halwagi, M. M. Optimal Design of Water Desalination Systems Involving Waste Heat Recovery. Ind. Eng. Chem. Res. 2017, 56 (7), 1834−1847. (17) Bartholomew, T. V.; Mauter, M. S. Multiobjective Optimization Model for Minimizing Cost and Environmental Impact in Shale Gas Water and Wastewater Management. ACS Sustainable Chem. Eng. 2016, 4 (7), 3728−3735. (18) Garibay-Rodriguez, J.; Rico-Ramirez, V.; Ponce-Ortega, J. M. Mixed Integer Nonlinear Programming Model for Sustainable Water Management in Macroscopic Systems: Integrating Optimal Resource Management to the Synthesis of Distributed Treatment Systems. ACS Sustainable Chem. Eng. 2017, 5 (3), 2129−2145. (19) Sánchez-Bautista, A. d. F.; Santibañez-Aguilar, J. E.; You, F.; Ponce-Ortega, J. M. Optimal Design of Energy Systems Involving Pollution Trading through Forest Plantations. ACS Sustainable Chem. Eng. 2017, 5 (3), 2585−2604. (20) Wang, B.; Gebreslassie, B. H.; You, F. Sustainable design and synthesis of hydrocarbon biorefinery via gasification pathway: Integrated life cycle assessment and technoeconomic analysis with multiobjective superstructure optimization. Comput. Chem. Eng. 2013, 52, 55−76. (21) Gao, J.; You, F. Shale Gas Supply Chain Design and Operations toward Better Economic and Life Cycle Environmental Performance: MINLP Model and Global Optimization Algorithm. ACS Sustainable Chem. Eng. 2015, 3 (7), 1282−1291. (22) Yue, D.; Kim, M. A.; You, F. Design of Sustainable Product Systems and Supply Chains with Life Cycle Optimization Based on Functional Unit: General Modeling Framework, Mixed-Integer Nonlinear Programming Algorithms and Case Study on Hydrocarbon Biofuels. ACS Sustainable Chem. Eng. 2013, 1 (8), 1003−1014. (23) Tay, D. H. S.; Kheireddine, H.; Ng, D. K. S.; El-Halwagi, M. M.; Tan, R. R. Conceptual Synthesis of Gasification-Based Biorefineries Using Thermodynamic Equilibrium Optimization Models. Ind. Eng. Chem. Res. 2011, 50 (18), 10681−10695. (24) Technical Development Document for the Effluent Limitations Guidelines and Standards for the Steam Electric Power Generating Point Source Category; U.S. Environmental Protection Agency: Washington, DC, 2015. (25) Aybar, H. S. Analysis of a mechanical vapor compression desalination system. Desalination 2002, 142, 181−186. (26) Zhou, Y.; Shi, C.; Dong, G. Analysis of a mechanical vapor recompression wastewater distillation system. Desalination 2014, 353, 91−97. (27) Stone, M. L.; Rae, C.; Stewart, F. F.; Wilson, A. D. Switchable polarity solvents as draw solutes for forward osmosis. Desalination 2013, 312, 124−129.

state or reflect those of the United States Government or any agency thereof.

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NOMENCLATURE A: Pure water permeability coefficient [m/Pa s] B: Salt permeability coefficient [m/s] πf m: Osmotic pressure at the feed-side membrane surface [Pa] πdm: Osmotic pressure at the draw-side membrane surface [Pa] Cf b: Concentration in the feed-side bulk solution [kg/m3] Cdb: Concentration in the draw-side bulk solution [kg/m3] Jw: Water flux in NH4HCO3 FO module [m/s] Js: Salt flux in NH4HCO3 FO module [kg/m2 s] Rmem: Recovery in the NH4HCO3 FO module [%] Amem: Area of membrane [m2] Rdis: Water recovery in distillation column [%] Ntray: Number of trays in distillation column [-] Q̂ dis: Specific heat duty in the distillation column [J/m3] β: Regression parameters [-] ε: Regression error term [-] ΔTChen: Chen’s temperature difference approximation [°C] ΔT1: Temperature difference between cold stream inlet and hot stream outlet [°C] ΔT2: Temperature difference between cold stream outlet and hot stream inlet [°C] Qex: Heat exchanger heat duty [kW] Aex: Heat exchanger area [m2] U: Overall heat transfer coefficient [kW/m2-°C] LCOW: Levelized cost of water [$/m3] CRF: Capital recovery factor [1/y] CC: Capital costs [$] OC: Operating costs [$/y] AF: Annual flow rate of treated water [m3/y] α: Capital cost parameters [-] VC: Variable cost parameter [$/process unit] PV: Process variable related to the costs [process unit]

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