271330 Optimal Synthesis for the FeedWaterHeater Network of a Pulverized Coal (PC) Power to Minimize Water Consumption
1. Introduction
Coalfired power plants contribute to almost 50% of the United States' total electric power production. At the same time, pulverized coal (PC) power plants are large water consumers to the point that construction and operability of PC power plants have started to be constrained by water availability in some regions of the country. Two process systems engineering approaches have been studied to minimize the water consumption of power plants. First, a better optimization of nonlinear uncertain systems (BONUS) algorithm has provided solutions to the minimization of water consumption under uncertain atmospheric conditions. The calculated conditions for a 550 MW PC plant predicted reductions of 6.4%, 3.2%, 3.8% and 15.4% in the average water consumption for the four different seasons from fall to summer respectively. A second approach pursues the reduction of the residual heat in the steam cycle of the PC process by formulating an optimal design of the feed water heat exchange network (HEN). The proposed methodology uses Aspen Energy Analyzer (AEA) to determine the mass flowrates of the bleeding streams while generating alternative designs that can potentially reduce the water consumption by reducing the total cooling requirement. The optimization approach to process synthesis involves the selection of an optimal solution from the superstructure with a simulated annealing (SA) capability built in Aspen Plus. Results show at least a 5% reduction in water consumption for the PC power plant via this enhanced HEN synthesis technique
2. Process Description
The PC power plant model studied in this paper is based on Case 11 referenced by the
DOE/NETL's report on cost and performance of fossil energy plants [1] . This power plant is a reheating cycle with feedwater heating. The process comprises a boiler section where coal is burned and the combustion heat is transferred to water generating steam, and a steam section where the high pressure steam is expanded through a train of high, intermediate and low pressure turbines. Steam is initially generated in the boiler and expanded in the high pressure (HP) turbine; then, it is reheated at the boiler for later expansion at the intermediate (IP) and low pressure (LP) turbines. Then, exhausted steam is condensed with liquid water and returned to the boiler while heated with bleeding streams of steam from the turbines (feedwater heater). Cooling water is sent to the cooling tower where heat from the cycle is ultimately rejected to the environment by evaporative cooling.
3. Optimization under uncertainty
3.1. Stochastic Simulation
As it was previously said, water consumption is strongly affected by weather conditions like air temperature and humidity. Detailed information about air conditions for different locations within the US can be obtained from the website (http://www1.eere.energy.gov). Histograms of the frequency distributions were fitted to the appropriate probability density functions to represent the air conditions variability of an average U. S. Midwestern urban center during each of the four seasons [7] . Stochastic simulation is carried out by efficiently sampling these distributions to generate a set of scenarios under which the plant models are evaluated and a corresponding probability distribution of water consumption (output variable) is calculated.
3.2. Stochastic Optimization
Minimization of water consumption in power plants is a
stochastic nonlinear programming (SNLP) problem where one of the moments (expected
value, standard deviation, etc.) of the water consumption's probability distribution
is the objective function, the model is the set of constraints and model
parameters are the decision variables. BONUS algorithm [4] is a “here and now” approach to solve this
problem [8] determining the process
conditions under which the expected value of the water consumption can be
reduced compared to the base case originally reported, as shown in REF _Ref319918871 \h Table 1
Season
 Optimal values of decision variables
 Savings %
 
Par 1 (%)
 Par 2 ^{0}F
 Par 3 Mass fraction
 Par 4 pressure ratio
 Par 5 pressure ratio
 
Fall
 38.9
 1160.8
 0.31
 0.49
 0.61
 6.4

Summer
 48.9
 1174
 0.42
 0.49
 0.66
 15.4

Spring
 35.5
 1096.5
 0.22
 0.36
 0.61
 3.8

Winter
 19.0
 1141.9
 0.30
 0.49
 0.79
 3.2

 Base case values of decision variables

 
All
 20
 1157
 0.3
 0.365
 0.637


4. Heat Exchange Network synthesis for water management
4.1. Modified HEN synthesis in AEA
Conventional methodology for the heat exchange network synthesis of the feed water heating system is based on equal enthalpy change on the liquid stream for each of the heaters. Mass flow rates of the bleeding streams are calculated based on such heat load distribution. AEA generates alternative designs with a mixed integer linear programming (MILP) algorithm. The solution of the MILP problem is based on the thermodynamic characteristics of the involved streams and on fixed mass flowrate of the bleeding streams. This approach was modified based on the early work by Linhoff [5] that proposes the employment of pinch technology to define mass flowrates from the bleeding streams for maximum heat recovery and improved cycle efficiency. This cycle efficiency is directly associated to the PC process water consumption through the amount of heat rejected by the cycle.
The main idea of this work is employing the AEA MILP algorithm to determine the mass flowrates of the bleeding streams while generating alternative designs that can potentially reduce the water consumption by reducing the total cooling requirement. For this purpose, the bleeding streams have been treated as utilities (instead of process streams) whose mass flowrates are determined by the calculated heat load assigned to them by the MILP algorithm.
4.2. Cost modification for alternative utility streams
Optimization algorithms based on process costs (as the
one used by AEA) yield designs that employ mostly hot streams because they
minimize heat transfer area leaving low temperature streams unused. To avoid
this situation a cost penalty was assigned to bleeding (utility) streams. The
approach assumes that feed water heating is expensive for the process when
using high pressure steam and using low pressure steam is inexpensive to the
point that some income can be generated. The main reason is that employing
large amounts of high pressure steam may decrease the process productivity and
preheating the feed water with low pressure steam will increase the process
efficiency. The drain streams are mixed and also are used to transfer sensible
heat to the feed water. The costs assigned to these drains are naturally
related to utility streams. On the
other hand the remaining drain streams are mixtures of two or three drains.
Therefore their costs have been assumed to be a weighted average of their
bleeding constituents having more weight the cost of the bleed that is more
expensive. This formulation of the problem and its solution with AEA yielded
interesting alternative designs whose cold utility consumption is lower than
that of the base case as shown in REF _Ref314440794 \h Table 2
Design
 Cooling requirement X 10 7 BTU/h

base case
 1.024

Design1
 0.627

Design2
 0.627

Design3
 0.627

5. Conclusion
This paper presents a framework for integrated water management in power systems. It has been found that water consumption depends on the weather conditions and the uncertainties in weather affect the consumption considerably. We presented an optimization under uncertainty problem for savings water consumption. The second approach is heat integration. An algorithmic framework (Figure 1) based on simulated annealing (and OA/ER/AP MINLP) for discrete decisions, BONUS algorithm for the stochastic NLP, and Hammersley sequence sampling for the sampling saved 97% of computational time to solve this problem. Optimization under uncertainty allowed us to save up to 15% in the expected value of water consumption in a PC plant and a pinch technology approach to the heat exchange network synthesis allowed a 38% in cooling requirement which will be translated in water savings as well.
Figure 1: Algorithmic Framework
References
[1]DOE/NETL, Cost and performance baseline for fossil energy plants, (2007). DOE/NETL2007/1281.
[2]DOE/NETL, Power plant water usage and loss study, (2007).
[3] U. Diwekar and E.S. Rubin, Comput. Chem. Eng. 15 (1991) 105114.
[4] K. Sahin and U. Diwekar, Annals of Operations Research 132 (2004) 4768.
[5] B. Linhoff and F.J. Alanis, ASME Advanced Energy Systems 85 (1989) 1015.
[6] J.M. Salazar, U.M. Diwekar and S.E. Zitney, Comput. Chem. Eng. 35 (2011) 18631875.
[7] J.M. Salazar, U.M. Diwekar and S.E. Zitney, Energy Fuels 24 (2010) 49614970.
[8] U.M. Diwekar, Introduction to Applied Optimization, 2nd ed., SpringerLink, New York, 2008.
[9] J. Salazar and U. Diwekar. Energy Systems 2 (2011) 263279.
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