minimization of water consumption under uncertainty for a...

Published: April 25, 2011

r 2011 American Chemical Society 4645 dx.doi.org/10.1021/es1043062 | Environ. Sci. Technol. 2011, 45, 4645–4651

ARTICLE

pubs.acs.org/est

Minimization of Water Consumption under Uncertaintyfor a Pulverized Coal Power PlantJuan M. Salazar,† Stephen E. Zitney,‡ and Urmila M. Diwekar*,†

†Vishwamitra Research Institute: Center for Uncertain Systems Tools for Optimization and Management, Clarendon Hills,Illinois 60514, United States‡Collaboratory for Process & Dynamic Systems Research, National Energy Technology Laboratory, Morgantown, West Virginia 26507,United States

bS Supporting Information

’ INTRODUCTION

The US Department of Energy (DOE) and its NationalEnergy Technology Laboratory (NETL) have extensively stu-died the characteristics and conditions of coal-fired power plantsto ensure the availability of clean technologies to fulfill theincreasing demand of electricity.1 Water consumption is one ofthe characteristics that need to be addressed when assessing thecapabilities of clean production of coal-fired power plants.2

Makeups, blowdowns, process water, and cooling system areresponsible for water consumption, with the cooling systemrepresenting the largest water consumer in power plants.3 R&Dactivities have been carried out to find alternative sources ofcooling water. Important efforts have been made in advancedcooling technologies, advanced recycling techniques, and ad-vanced wastewater treatment processes.4 Additionally, compre-hensive models of pulverized coal (PC) power plants have beenbuilt employing the Aspen Plus process simulator to evaluate thecost and performance of the systems.2 Performance evaluationwith these models includes the determination of water consump-tion based on a rigorous mass balance of the power generationplant as suggested by the DsOE/NETL guidelines for energysystems analysis.5 However, these models still require detailedsimulations for an appropriate estimation of the cooling towerevaporation losses. This paper complements those research

efforts with a less simplified model of the cooling tower addedto the original power plant simulation and a computational toolthat can determine the conditions which minimize the waterconsumption in PC plants. Cooling tower evaporation losses arethe most significant ones within the cooling system and areaffected by fluctuating environmental parameters like airhumidity.3 This implies that computational tools of integratedprocess and water network analysis should include the influenceof uncertain parameters. Process modeling under uncertainty, orstochastic modeling, has been employed for process analysis inpower systems in the past.6 When including the optimizationtechniques, the resulting nonlinear stochastic programming(NLSP) can become highly computationally demanding.7 Thesecomputational expenses have been drastically decreased with thebetter optimization of nonlinear uncertain systems (BONUS)algorithm.7 The BONUS solver has been integrated with AspenPlus simulations using the CAPE-OPEN interfaces (www.colan.org) and the Advanced Process Engineering Co-Simulator(APECS).8�11 The advantages of BONUS are exploited to

Received: December 23, 2010Accepted: April 12, 2011Revised: April 11, 2011

ABSTRACT: Coal-fired power plants are large water consumers. Water consumption inthermoelectric generation is strongly associated with evaporation losses and makeup streamson cooling and contaminant removal systems. Thus, minimization of water consumptionrequires optimal operating conditions and parameters, while fulfilling the environmentalconstraints. Several uncertainties affect the operation of the plants, and this work studies thoseassociated with weather. Air conditions (temperature and humidity) were included asuncertain factors for pulverized coal (PC) power plants. Optimization under uncertainty forthese large-scale complex processes with black-box models cannot be solved with conventionalstochastic programming algorithms because of the large computational expense. Employmentof the novel better optimization of nonlinear uncertain systems (BONUS) algorithm,dramatically decreased the computational requirements of the stochastic optimization.Operating conditions including reactor temperatures and pressures; reactant ratios andconditions; and steam flow rates and conditions were calculated to obtain the minimum waterconsumption under the above-mentioned uncertainties. Reductions of up to 6.3% in water consumption were obtained for the fallseason when process variables were set to optimal values. Additionally, the proposed methodology allowed the analysis of otherperformance parameters like gas emissions and cycle efficiency which were also improved.

4646 dx.doi.org/10.1021/es1043062 |Environ. Sci. Technol. 2011, 45, 4645–4651

Environmental Science & Technology ARTICLE

calculate the conditions in which a reduction on the averageconsumption of water for a PC plant can be reached.

The goal of the paper is to show a newmethodology to reducewater consumption in power plants. This paper concentrates onoptimizing the operating conditions of the PC plant in the face ofuncertainty in order to reduce water consumptions. It has beenfound that with the use of BONUS algorithm the water con-sumption for the fall season can be reduced by 6.3% withsignificantly reduced computational effort. Additionally, otherperformance parameters including gas emissions and processefficiency have shown significant improvements

’PULVERIZED COAL (PC) PLANT MODEL

The PC plant model employed in this work is described indetail as Case 11 by the report on cost and performance offossil energy plants.1 A scheme of the process is shown inFigure 1. Particularly, this is a supercritical steady-state PCmodel that does not include carbon sequestration technologyand is intended to generate 548MWof electricity. The processis divided into two main sections: boiler section and steamgeneration section. The boiler is modeled as a series of tworeactors which take into account the stoichiometry of chemi-cal reactions and thermodynamic equilibrium of combustionreactions (a stoichiometry reactor and a Gibbs equilibriumreactor) and gas cleaning section comprising an ash removalunit and a flue gas desulfurization (FGD) unit that is attachedto the boiler effluent. The steam section comprises the typicalhigh (HP), intermediate (IP), and low pressure (LP) turbinetrain and is a steam reheating scheme with feedwater heatingfrom turbine extracted steam.

’WATER SYSTEM IN THE PC PLANT

Water consumption is associated with the FGD section aslimestone slurry preparation and makeup. In the steam sectionwater consumption is mainly associated with the amount of heatrejected at the condenser since it determines the circulating waterthrough the cooling tower and therefore the amount of waterevaporated (Figure 1). The calculation of water consumption wasoriginally performed outside the Aspen Plus software environment.1

Therefore, this calculation was integrated into the original PCmodels by including different calculating blocks (Fortran codes)along with unit operation blocks (Aspen simulations of equilibriumseparation units) to estimate the water consumption.

The estimation of the evaporation rate strongly depends on thecooling tower model employed. The original estimation wasperformed according to a simplified empirical model reported inthe literature12 and suggested to be used only in the absence ofinformation about air and tower operation conditions; it has beencalled Empirical Model in this work. However, in order to employ aless simplified model, an equilibrium-based model for the coolingtower was employed in this work for the estimation of theevaporation rates. This model is based on a simple scheme reportedin literature,13 and it was implemented in Aspen Plus as a unit-operation-based model. Other transport-based models ofcooling towers have been reported in the literature14 whereexperimental data were fitted to the model to estimate themass transport parameters and from air and water enteringconditions (temperature and flow rates) the model can deter-mine the outlet water temperature and evaporation, blowdownand drift losses are estimated through empirical correlations. Thetwo models employed in this study are described in the Support-ing Information.

Figure 1. Schematic representation of a PC process, turbines are labeled as LP: low pressure, IP: intermediate pressure, HP: high pressure. Adaptedfrom ref 1.



’UNCERTAIN VARIABLES INWATER NETWORK FOR APC PROCESS

NETL’s systems analysis reports onPCplantwater consumptionmake several assumptions that could become important sources ofuncertainty since they are directly related to the water consumptionand can be fairly variable.1�3 Air temperature and humiditycontinuously fluctuate throughout the US with the changingseasons, and their influence on water consumption was mentionedabove. The effect of the variability of these atmospheric conditionson some performance parameters including water consumption forPC plants was studied through a stochastic simulation.15

The main source of information for cooling tower designconditions, including air humidity considerations, is the text byHensley on cooling tower fundamentals.12 The author suggestsusing average measurements of the wet-bulb temperature todetermine the temperature range and approach temperature thatguarantee the appropriate cold water conditions at peak demand.However, for more complex processes or more accurate designs(as those required for the PC case in this study), the referencesuggests the inclusion of wet-bulb temperature during criticalmonths (summer) and in some case in the entire year. Therefore,if design activities require this level of accuracy, simulationpurposes will additionally require detailed data for the particularlocation of the plant.

Data for the air temperature and humidity can be obtainedfrom DOE’s energy efficiency and renewable energy program(EERE) Web site (http://www1.eere.energy.gov) as describedin previous works.15 In ref 15, to perform stochastic simulationsthe authors organized data in four seasons, starting at September2005 and finishing at August 2007 and histograms of thefrequency distributions were fitted to the appropriate probabilitydensity functions as log-normal and uniform* (segmented uni-form distribution) distributions to represent the air conditionsvariability of an average midwestern urban center during each ofthe four seasons of a year. Results of the characterization of theuncertainty are included in the Supporting Information.

Once these probability density functions have been created,stochastic simulation and optimization can be carried out toaccount for the influence of uncertainty associated with weatherfluctuations in water consumption. The first step of this approachis efficiently sampling the probability functions of dry-bulbtemperature and relative humidity to generate a set of scenariosthat accurately represent the potential uncertainty realizations.The second step is propagating the uncertainty by executing thewhole plant simulation for each of these scenarios and recordingthe results of the water consumption based on the cooling towermodel and the FGD performance. Finally, the resulting distribu-tion from the recorded data is analyzed as the output variable ofthe stochastic simulation, and one of its moments (expectedvalue or standard deviation) becomes the objective function forthe stochastic optimization.

’NOVEL STOCHASTIC OPTIMIZATION ALGORITHM

As noted in the previous section, stochastic optimizationpursues the minimization of one of the moments of the distribu-tion calculated after each stochastic simulation. Therefore, onestochastic simulation per set of decision variables consideredduring the optimization algorithm or outer loop is required asshown in Figure 2. As the stochastic simulation is located at theinner loop, several visits to it are expected during the solution ofthe optimization problem requiring a large number of model

runs. For complex models such as the PC plant model, each runmay require several minutes making the multiple evaluationscomputationally intensive if not prohibitive.

The excessive number of model calculations required todetermine the probabilistic objective function and constraintsin stochastic programming problems has been considerablyreduced by the BONUS algorithm. The algorithm makes useof a reweighting method using Kernel density estimation toapproximate the function and its derivatives. These probabilisticapproximations are fed to the nonlinear optimizer at the outerloop of the stochastic programming. A brief description of theprocedure is reported below:7

1 Generate a set of scenarios for the stochastic simulation.Data for decision variables are sampled from uniformdistributions and data for uncertain variables are withdrawnfrom the corresponding probability distributions.

2 Run the model for the number of scenarios previouslygenerated.

3 Select the starting point for the estimation of the objectivefunction with the weights calculated by Gaussian Kernelestimator for the probability density function of decisionvariables (eq 1, where f(u) is the probability densityfunction of uncertain variable u, Nsamp is the number ofsamples taken, and h2 is the variance of the data set).

4 Perturb the decision variables, estimate the objective func-tion, and estimate the derivative using the reweightingapproach.

5 Repeat step 4 until allowed Kuhn-Tucker error is reached.

f ðuiÞ ¼ 1Nsamph

∑Nsamp

i¼ 1

1ffiffiffiffiffiffi

2πp e�

12

u � uihð Þ2 ð1Þ

where f(u) is the probability density function of the uncertainvariable u, h is the standard deviation of the sampled values ofuncertain variable u, Nsamp is the number of sampled values ofuncertain variable u, ui is the ith sampled value of the uncertainvariable u, and u is the mean of samples values of uncertainvariable u.

The BONUS algorithm employs a sequential quadratic pro-gramming (SQP) method for the solution of the nonlinearprogramming problem. The model is a nonconvex functionwhose minima depend on the starting point for the SQP routine.Therefore, different values of the initial point were evaluated todetermine local minima that could represent any improvementfrom the base case.

The selection of decision variables for the optimizationproblem was based on the parameters that could be changed in

Figure 2. Stochastic Optimization Framework, SQP: sequential quad-ratic programming.



the process model. Thismodel is described in detail by theNETLreport on cost and performance baseline for fossil energy plants.1

A set of variables that were described in the report as assumptionsor assigned parameters were selected to be considered as decisionvariables. To quantify the influence of these variables in the waterconsumption, a stochastic simulation tool integrated in AspenPlus (similar to that described above for the integration of theBONUS algorithm) was employed as described in the literature.6

This tool samples the ranges of the potential decision variablesfrom uniform distributions. Then, it runs the model for each ofthe generated combinations to calculate the consumed waterwhich is the output variable. During the analysis of the results,partial rank correlation coefficients (PRCC) were used. Theabsolute value of PRCC is directly proportional to the influenceof the deterministic variables on the water consumption as PRCCare a measure of the relationship between the output and inputvariables for a nonlinear function.6 A stochastic simulation wasrun for 500 scenarios of ten potential decision variables, and the fivemost influential ones were selected to be used in the BONUSalgorithm. The ten potential decision variables were selected basedon the feasibility to be changed in the model and their role as designvariables. For instance, variables such as boiler temperature orpressure drops in turbines can be easily modified within thesimulation; reactant ratios such as air excess or water contents inthe FGD slurry can be part of a design or operational policy andgenerator loss is a design variable that depend on the particulartechnology employed for the generator (this variable was assumedas 0.015 in the base case). Air excess, reheater temperature, watercontent of the limestone slurry to the FGD, pressure drop at thehigh pressure turbine 1, generator losses, and pressure drop at thehigh pressure turbine 2 were chosen as decision variables.Implementation of BONUS Algorithm in Aspen Plus Mod-

els. To take full advantage of the BONUS algorithm, a CAPE-OPEN (CO) compliant stochastic optimization tool was built foruse in CO-compliant steady-state simulators via the APECScosimulation technology. Calculator blocks were used to manip-ulate a sensitivity analysis that performs the stochastic simulation.The sequential quadratic programming (SQP) algorithm was

coupled with the reweighting estimation to do the optimizationand added to the simulation. Under these conditions, the modelis required to run the number of selected samples (600 for thisparticular case) once and not every time that a modification tothe NLP solver is required (different starting points, decisionvariable bounds or perturbation size).

’RESULTS AND DISCUSSION

Optimization under Uncertainty Using BONUS. Due to thenonconvexity of the water consumption function, different startingpoints for the BONUS algorithm were evaluated by changing theinitial values of reheater-temperature and air excess. Each of theoptimization runs yielded a local minimum (design and operatingconditions, and objective function value) as shown in Table 1.In Table 1, BONUS estimations are considered guidelines that

are verified with the values calculated by rigorous stochasticsimulation; therefore, the lowest value of 2.481E6 lb/h is notselected as the minimum possible for this set of estimationsbecause the stochastic simulation calculates 2.619E6 lb/h underthis policy. The calculations started at 20% and 40% air excessand 1157 �F reheater temperature defined really similar estima-tions and errors; implying that about 2.62E6 lb/h is theminimumconsumption that can be calculated for this particular range of thedecision variables. This value represents a reduction of 4.5% inthe average water consumption of the process; however, for mostof the cases, the BONUS algorithm calculated the optimalpressure ratios for the high pressure turbines as the upper boundsof the established range (0.39 forHP1 and 0.69 forHP2) whichwereconsidered arbitrarily and can be widened to estimate more localminima that can provide lower values of average water consumption.

Table 1. Local Minima and Corresponding Policies for the Minimization of Water Consumption under Uncertainty for DifferentStarting Points of the Boiler Air Excess and Reheater Temperature

policy for local minima

local minima of water

consumption (1E3 lb/h)

starting point:

(%) and (oF)

air

excess

(%)

reheater

temperature

(�F)water contents of FGD

slurry (mass fraction)

pressure drop

ratio at HP1

generator loses (fraction of

the total generation)

pressure drop

ratio at HP2

bonus

estimation

stochastic

simulation

estimation

bonus

estimation

error (%)

20-1157 35.938 1158.1 0.25606 0.39 1.38 � 10�2 0.69 2581 2621 1.5

30-1157 29.02 1156.9 0.21 0.35343 6.47 � 10�3 0.69 2481 2640 6

40-1157 35.583 1164.2 0.25801 0.39 1.38 � 10�2 0.69 2579 2619 1.5

50-1157 22.422 1156.4 0.28208 0.39 1.09 � 10�2 0.69 2581 2676 3.5

40-1050 33.86 1049.5 0.30359 0.39 2.12 � 10�2 0.69 2638 2697 2.2

40-1100 51.755 1102.1 0.24333 0.39 9.03 � 10�3 0.69 2591 2629 1.4

Figure 3. Sequential quadratic programming (SQP) BONUS iterationsfor the minimization of water consumption starting from different valuesof the boiler air excess (%) and reheater temperature (in �F).



The ranges of the pressure drop for the high pressure turbineswere changed, and the bonus algorithm was run again. Results fordifferent starting points are presented in Figure 3.The most significant reduction is calculated when the SQP

routine is started at 1157 �F and 50%. The optimal conditionscalculated to accomplish this reduction is compared to the basecase in Table 2. Interestingly, the deterministic estimation ofwater consumption for the optimal conditions from the stochas-tic simulation is larger than the deterministic estimation for thebase case; which suggests that a conventional deterministicoptimization technique would not predict this policy. Instead,the stochastic optimization algorithm suggests a realistic policythat considers the weather variations achieving a reduction in theexpected value of water consumption of 6.3%.Table 2 includes a column that shows the expected values for

water consumption when only one of the decision variables is setat its optimal value. The values that affect the water consumption

at the highest level are the pressure drop at the first high pressureturbine, the air excess to the boiler, and the efficiency of thegenerator. This information is useful since it provides guidancefor the operation when not all parameters can be set at theiroptimal values. However, it can be seen that the interaction ofthese parameters is highly nonlinear and cannot be extrapolatedwith this experiment.Cumulative probability of the water consumption, efficiency,

CO2 emissions, and SO2 emissions from the stochastic simula-tion under the optimal and the base case are shown in Figure 4.The 6.3% level of average savings can be complemented with thewater consumption cumulative probability, the plot shows thatunder the optimal conditions there is about 80% of probabilityfor the water consumption to be less than or equal to theexpected value (2.57E6 lb/h). For the base case conditions, theexpected value or lower values of water consumption only haveabout 60% of probability to occur. The cumulative probability of

Table 2. Results of BONUS Optimization of Water Consumption Compared to the Base Case

variable base case optimal

estimate of water consumption with corresponding variable at its

optimal value (�106 lb/h)

reheater temperature (0F) 1155 1160.8 2.73

air excess (%) 20 38.9 2.63

ΔP HP1 0.385 0.49 2.61

generator losses (fraction of the total generation) 0.015 0.005 2.63

ΔP HP2 0.637 0.61 2.74

slurry preparation ratio 0.3 0.24 2.74

deterministic estimation (�106 lb/h) 2.63 2.719

BONUS estimation water consumption (�106 lb/h) 2.81 2.43

water consumption from stochastic simulation (�106 lb/h) 2.74 2.57

Figure 4. Cumulative probability of performance parameters for base case and optimal conditions of a pulverized coal (PC) plant under weatheruncertainty.



the other performance parameters show how the increment ofthe overall efficiency of the cycle is suspected to be one of thecauses for the reduction in water consumption; the effect of thechange on the turbine pressure drops significantly reduces theamount of heat that needs to be removed by the condenser,increases the productivity of the turbines, and increases thetemperature of the water entering the boiler. This improvementreduces the fuel consumption and therefore the carbon and sulfuremission levels of the whole process.As it was said before, the water consumption is calculated

based on different parameters that include the FGD consump-tion, cooling tower evaporation, cooling tower draft, and coolingtower blowdowns. The cumulative probability of these para-meters under weather uncertainty is shown in Figure 5. Theevaporation, drift, and blowdowns are calculated based onthe condenser duty, which is lower for the optimal conditions;the variability is similar for the three of them since it comes fromthe weather uncertainty. The FGD water makeup has lowervariability in the optimal conditions than under the base caseconditions. The deviations from the expected value are char-acteristic of hot and humid air conditions; these deviations arecompensated by the increment of air excess which helps to cooldown the FGD reactor and guarantee the adiabatic operation.Optimal policy can be analyzed as follows: The reheater

temperature needs to be increased to improve the processefficiency; however, excess increment in this temperature willincrease the condenser duty. As it was said before, the air excessneeds to be increased to improve the FGD water consumption.Air excess increments are normally associated with efficiencyreduction, which intuitively seems to be detrimental for the waterconsumption; however, boiler’s efficiency depends on the airenthalpy which is defined not only by its flow rate but also by itstemperature and humidity. As air temperature and humidity areuncertain parameters the effect of air excess modifications on theefficiency can be mitigated by atmospheric changes. Therefore

the air excess increment may not be reflected as strongly in anefficiency reduction. The increment in the pressure drop of theHP1 reduces the amount of heat to be rejected by the condenserbecause the bleeding streams are hotter and the feedwaterreaches the boiler at higher temperature; this change needs tobe compensated by a reduction in the pressure drop of the HP2turbine to keep the generation levels. Generator losses evidentlyare forced to be reduced (by a technological improvement) dueto their influence on the process efficiency.It should be noted that the deterministic results at optimal

values are worse than the base case. This shows that uncertaintiescan change designs significantly.Optimization of the PC plant simulation employing the

purely empirical model was also carried out using the sensi-tivity analysis tool to determine the decision variables and theBONUS algorithm; the results are shown in the SupportingInformation.The BONUS algorithm drastically reduced computational

expenses of this analysis. A total of 62 iterations were performedby SQP with different initial points for the first bonus run and 80for the second run. A conventional stochastic simulation wouldrun 120 samples per iteration of SQP which would involve102240 runs of the model. BONUS only required 1212 runs, areduction of 99% in computational time. Each model runrequires approximately 9 to 10 min of CPU time.The aim of this paper is to show a new methodology for

reducing water consumption in power plant by consideringoptimization under uncertainty and a new algorithm to solvethe large scale problem. The case study here shows that the waterconsumption was reduced by 6.3% for the fall season for the PCplant described here. These results are accompanied by improve-ments in efficiency and emissions also. For other seasons, we carriedout similar case studies and found that the water consumption isreduced by 3.2% in winter to 15.4% in summer. However, it is notpossible to analyze and present the detailed analysis of these case

Figure 5. Cumulative probability of water consumption factors for the base case and the optimal conditions.



studies in this single paper. A follow up paper which includes thesecase studies is under review for the Journal Energy Systems.

’ASSOCIATED CONTENT

bS Supporting Information. Details of the cooling towermodels, sensitivity analysis of these models, and optimization ofthe empirical model. This material is available free of charge viathe Internet at http://pubs.acs.org.

’AUTHOR INFORMATION

Corresponding Author*Phone: (630)-655-0866. Fax: (630)-655-0866. E-mail:[email protected]. Corresponding author address: 36856-th Street, Clarendon Hills, IL 60514, USA.

’ACKNOWLEDGMENT

This technical effort was performed with financial support ofthe National Energy Technology Laboratory’s ongoing researchin Process and Dynamic Systems Research under the RDScontract DE-06-485AA-VRI.

’REFERENCES

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