Optimization of IGCC Processes with Reduced Order CFD Models

Yidong Lang1,2, Stephen E. Zitney2 and Lorenz T. Biegler* 1,2

1Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 2Collaboratory for Process & Dynamic Systems Research, National Energy Technology

Laboratory, Morgantown, WV

Abstract Integrated gasification combined cycle (IGCC) plants have significant advantages for efficient power generation with carbon capture. Moreover, with the development of accurate CFD models for gasification and combined cycle combustion, key units of these processes can now be modeled more accurately. However, the integration of CFD models within steady-state process simulators, and subsequent optimization of the integrated system, still presents significant challenges. This study describes the development and demonstration of a reduced order modeling (ROM) framework for these tasks. The approach builds on the concepts of co-simulation and ROM development for process units described in earlier studies. Here we show how the ROMs derived from both gasification and combustion units can be integrated within an equation-oriented simulation environment for the overall optimization of an IGCC process. In addition to a systematic approach to ROM development, the approach includes validation tasks for the CFD model as well as closed-loop tests for the integrated flowsheet. This approach allows the application of equation-based nonlinear programming algorithms and leads to fast optimization of CFD-based process flowsheets. The approach is illustrated on two flowsheets based on IGCC technology. Keywords: Co-simulation, PCA, Reduced Order Modeling, IGCC, Process Optimization, CFD

1. Introduction It is critical for the energy industries to reduce carbon emissions from power generation. For fossil fuel plants, integrated gasification combined cycle (IGCC) processes have been recognized as a core technology that allows more efficient capture of carbon dioxide. The main components of IGCC include air separation, coal gasification, synthesis gas cleanup, electricity generation with combined cycles, and carbon capture and storage. Using these components, IGCC processes produce electricity more efficiently than conventional plants and convert almost all carbon into carbon dioxide and hydrogen-rich fuel, which makes it easier to capture CO2 for sequestration. Consequently, simulation and optimization of IGCC processes have become more important, and it is expected that optimization of process design and operation for IGCC will lead to significant economic and environmental benefits. As shown in Figure 1-1, the gasfier and the gas-turbine-combustor are key units of the IGCC process, but these cannot be modeled accurately with conventional process

simulation models (Zitney and Syamlal, 2002). With few exceptions, process simulation models consist of lumped parameter descriptions with a number of ideal assumptions (e.g., perfect mixing, plug flow, equilibrium behavior and shortcut models). To capture spatially distributed phenomena that include multi-phase fluid flow, multi-phase reaction kinetics, and interfacial heat and mass transfer, computational fluid dynamics (CFD) models are required to evaluate the performance of these units, and to provide accurate descriptions of process behavior for process simulation and optimization (Sloan et al., 2007). These phenomena can be observed when we investigate the gasifier and the gas-turbine-combustor in an IGCC flowsheet. In this investigation, we choose an entrained-upflow, coal-slurry gasifier with a CFD model from Shi et al. (2006). For the combustor, a CFD model is able to compute the shape of the flame and corresponding field variables (Zitney et al., 2006). These features are strongly related to equipment geometries of the equipment and cannot be handled by process simulation models. With distributed parameter multiphysics models of these units, there is greater scope to improve their design and operation.

Figure 1-1: Schematic of IGCC Process Flowsheet However, CFD models do not integrate well with steady-state process simulation models for two reasons: data interfaces and transfer between these models, and widely different computational requirements for these models. To address these issues, the National Energy Technology Laboratory (NETL) sponsored a series of projects to implement co-simulation with process simulation tools (such as Aspen Plus or HYSYS) and CFD tools (such as FLUENT or CFX). This led to the Advanced Process Engineering Co-Simulator (APECS) (Zitney, 2006), a commercial tool set that offers a CAPE-OPEN compliant platform for the seamless integration of steady-state process simulation with high-fidelity CFD-based simulations of key equipment. Because CFD models can become

prohibitively expensive when integrated within a process flowsheet, especially when embedded in recycle and optimization loops, APECS offers a systematic reduced order modeling (ROM) approach developed in a previous study (Lang et al., 2009) and based on experimental designs, Principal Component Analysis (PCA) and input-output mapping. Once accurate ROMs are developed, the CPU time needed to solve the ROM typically reduces to only a few CPU seconds, and the ROM-based simulation yields approximately the same fidelity as the CFD model. This study extends the development of this ROM-based framework to process flowsheet integration and optimization. For flowsheet integration, the ROM must be “wrapped” to fit the modular framework of the simulator. Once this interface is developed, advanced simulation and optimization algorithms related to equation-oriented flowsheeting can be applied directly. To demonstrate this approach we use the USER3 protocol (Aspen Technology, 2009), similar to the CAPE-OPEN standard, to convert the ROMs into process simulation modules for use in an Aspen Plus process simulation. In addition, “closed-loop” tests are performed to evaluate the performance of the ROM and validate the CFD model at the process optimum. This procedure either confirms that the ROM can replace the CFD model without loss of fidelity, or allows the construction of a more refined ROM with additional process information. This closed-loop test is demonstrated on a gasifier ROM integrated with a combined cycle. In addition, we integrate two ROMs derived from CFD models into a large-scale IGCC process. With this integration, a 7% increase in power output can be achieved, thereby showing the benefit of our ROM-based optimization. In the next section, we briefly present the methodology of PCA-based ROM, and discuss the application and validation of this ROM-based strategy for the gasifier and combustion units in the IGCC. Section 3 describes building the ROM interface as a USER3 model in Aspen Plus. Section 4 presents two cases studies for ROM-based optimization. First, the gasifier ROM is coupled to a combined cycle optimization and a closed-loop test is performed. Second, we present the process optimization of an IGCC process with two ROMs and discuss its results. The final section concludes the paper and discusses topics for future work.

2. ROMs from CFD models

This section presents the background for creating the ROMs of the two IGCC equipment items based on CFD models: the gasifier and the combustor. The methodology is described first followed by the application to the units.

2.1 Background

For a given equipment unit, we assume that the relationships of the state and output variables corresponding to its input variables can be expressed by the following state space model in steady state:

x

y

!

"##

$

%&&=

B

D

!

"#

$

%&u or

x

y

!

"##

$

%&&=

B(u)

D(u)

!

"##

$

%&&

(2-1)

where u is the input vector; y is the output vector containing the output variables of interest; the state vector x is any variable of interest in the fluid field, such as temperature, pressure, or velocity, bounded by the geometry of the equipment. Finally, the coefficient matrices B and D can be derived using the methodology of PCA-based ROM. In order to obtain a ROM with high fidelity and integrate it into a flowsheet for process simulation and optimization, considerable effort is required to obtain a data set from a series of CFD simulations of the equipment. The cases are obtained through space-filling experimental designs, such as Latin Hypercube Sampling (LHS) over specific domain of the inputs, the operating window. The two kinds of ROMs: xROM and yROM, are illustrated in Figure 2-1. The first displays the field profiles of state variables of interest, such as the temperature profile inside the equipment. The second is the mapping from the input to the output of the equipment through field calculations. The methodology of PCA-based ROM is described in Lang et al. (2009). For process optimization, only the yROMs are required to compute the output stream information leaving the equipment, while xROMs are usually invoked for further flow field investigation after the optimization is solved. In this paper, we focus on yROMs for the gasifier and the gas-turbinecombustor and further develop them as ‘process modules’ used for process optimization. During the developments of the yROMs, two types of methods are used for input-output mapping. For this purpose, neural networks (NNET) (Demuth et al., 2005) and Kriging (Lophaven et al., 2002) have been explored and compared. In our previous study we found no significant difference in accuracy between the two for input vectors of low dimension (e.g., the gasifier with three inputs), but the Kriging method has more robust interpolations and is easier to implement. For example there is no need to determine the number of the neurons that balance the accuracy and overfitting as in NNET. Also it is much faster to obtain the parameters of the model than to train the neural net. For larger input dimensions more design points are necessary to build the mapping model. In the case of the combustor, the dimension of the input domain is nine and we chose 128 design points for the Kriging mapping. We observed that the prediction error increases with the distance from the design point. Therefore increasing the density of the number of design sites in the input domain reduces the distance between unknown and design points, and increases the accuracy of the prediction. Usually, the dimension of the input domain is usually no more than 9 or 10 in process studies (Caballero and Grossmann, 2008).

Figure 2-1. PCA-based ROM scheme Following our previous work, we explicitly express input-output mappings as a set of equations from either NNET or Kriging, which allows the evaluation of analytic derivatives of the process module in sparse form. This is important for integration of the process model within the simulator for simulation and optimization. It also allows us to select advanced NLP solvers other than those offered by the process simulators.

• For the NNET model we choose one hidden layer, one output layer and the sigmoid function as follows:

!

u'i =2(ui " umin,i)

ui,max " umin,i

"1 i =1,...n (2 - 2a)

a' j = IW j,iu'i +B1, j

i=1

n

# j =1,...ns (2 - 2b)

a j =1

1+ exp("a' j ) j =1,...ns (2 - 2c)

y'k = LW j ,ku' j +B2,k

j=1

ns

# k =1,...q (2 - 2d)

yk =1

2(y 'k +1)(ymax,k " ymin,k ) + ymin,k k =1,...q (2 - 2e)

where n is dimension of the input vector; ns is number of neurons in the hidden layer of the NNET; q is dimension of output vector.

!

IW " #ns$n ,

!

LW " #ns$q ,

!

B1" #ns and

!

B2" #q are parameters of NNET obtained by training it. u and u’ are the original and

scaled inputs, respectively; a’ and a are the intermediate outputs from neurons; y’ and y are scaled and original outputs, respectively.

• For the Kriging model we choose a first degree polynomial and Gauss correlation as follows:

!

u'i =ui " u i

# i

"1 i =1,...n (2 - 3a)

dxi, j = u'i "S j ,i i =1,...n, j =1,...m (2 - 3b)

rj = exp("$idxi, j )i=1

n

% j =1,...m (2 - 3c)

y'k = f i&k,i

i=1

n +1

' + ( k, j rj

j=1

m

' k =1,...q (2 - 3d)

yk = y'k ˆ # k + y k k =1,...q (2 - 3e)

where n is dimension of the input vector; m is number of design sites for the regression; q is dimension of output vector; S is the input matrix of design sites; θ, β and γ are parameters from the Kriging regression; f is the basis of the first degree polynomial with 11 =f , fi =ui-1’, u is the input vector of current trial point,

!

u and σ are the mean and variance, respectively, among the design sites S ; dx is the distance matrix between scaled current input vector u’ and the design sites S ; and r is the correlation between u’ and S ; y, y’ are scaled and original output vectors at the trail point u , respectively;

!

y , ˆ " are the mean and variance vectors of the output matrix corresponding to the design site S .

2.2 Validation test

We expect that the ROM would perform quite well at known points with either NNET or Kriging. However, the true measure of a ROM’s performance is described by how well it can predict interpolated points. The second step in the evaluation of a ROM’s performance is to validate the ROM’s predictions at unknown points. Without extra design points, we apply the technique of ‘cross validation’ or ‘rotation estimation’ used in statistics. The method of cross validation creates m ROMs, each with one case missing, and then uses these ROMs to predict the eliminated cases. The differences between the prediction by ROM and the original CFD model are used to calculate relative errors for all cases and all variables in output vectors, with:

!

rlerri, j =| ˆ y i, j " yi, j |

yi, j i=1,…n; j=1,…q (2-4)

where

!

ˆ y i, j is the ROM prediction and yi,j is the value from the CFD model, the subscript i is the index of the design point and j denotes the j-th element in the output vector. When the rlerr matrix is available after cross validation is completed, we use data fitting tools to analyze its statistics. This is shown later in this section for the cross validations of the yROMs of the gasifier and the combustor. The data fitting provides a statistical distribution of relative errors as well as confidence intervals for the ROM approximation. Results of cross validations are also presented in the next two subsections on the gasifier and the combustor, respectively.

2.3 Entrained-flow coal gasifier

Gasification technology is a key component of today’s IGCC power plants and is expected to be the centerpiece of tomorrow’s high-efficiency, zero-emission systems. The gasifier provides a means for converting coal to a hydrogen-rich synthesis gas, ideally suited for power generation, refining, and chemical applications. In order to realize the full potential of this technology, researchers are using CFD modeling to better understand the complex physical and chemical phenomena, including fluid flow, heat and mass transfer, and chemical reactions, that impact gasifier performance and efficiency. These high-fidelity CFD models are also used within overall process simulations for improving the design, analysis, and optimization of gasification-based power plants. Recent technologies have not only implemented turbulence and particle physics but have also utilized stochastic processes to ensure accurate capture of particle dynamics. Details can be found in Shi et al. (2004), Kobayashi et al. (1976), Wen and Chuang (1979), and Syamlal and Bissett (1992). The entrained-flow, coal-slurry gasifier model developed in Shi et al. (2006) is considered here. This is a two-stage, upflow gasifier consisting of a horizontal first stage and a vertical second stage as shown in Figure 2-2. All of the oxidant and 78% of the coal slurry are evenly divided between the left- and right-hand inlets of the first stage. The horizontal stage is mainly a coal combustor, which provides hot gases through the connection to the second stage where the remaining 22% of the coal slurry is injected. Most of the coal gasification process occurs in the second stage. The total volume of the gasifier is 45.5 m3; the particle volume fraction is estimated to be around 4%; and the average particle residence time is estimated to be 10 seconds. The operating pressure is 28 atm and the coal slurry and oxygen are fed into the gasifier at temperatures of 450 K and 411.4 K, respectively. It is important to note here that this is a prototype gasifier design and is not intended to represent any existing gasifier designs, commercial or otherwise. The CFD model utilized here is a steady-state 3-D FLUENT model (Shi et al., 2004). The Eulerian-Lagrangian modeling approach is applied whereby the gas phase is treated as continuous and the coal particles are handled using the discrete phase model (DPM). The continuous gas phase conservation equations include the continuity equation, momentum equations, energy equation, turbulence equations, species transport equations, and radiation transfer equation. The gas phase reactions are modeled using the eddy dissipation model along with an Arrhenius rate law. Using DPM, the particle trajectories, along with mass and energy transfer to/from the particles, are computed with a Lagrangian formulation. The coal slurry flow is simulated as two separate particle types, namely water droplets and coal particles, which are injected into the gasifier through the carrying gas with a particle diameter distribution. The assumption of only two particle types is reasonable given that the water evaporates quickly after the slurry enters the gasifier. The physical and chemical modeling of the coal slurry is implemented by using user-defined functions (UDFs). In this discrete phase the coal particles undergo the processes of moisture release, vaporization, devolatilization, char oxidation, and gasification. In the

continuous phase, two combustion and two water gas shift reactions are modeled. Finally, the coupling between the continuous phase (gas) and the discrete phase (particle) is solved by tracking the exchange of mass, momentum, and energy. The geometry of the gasifier and its typical temperature profile are shown in Figure 2-2.

Figure 2-2. Entrained-flow gasifier and its typical temperature profile (K). We invoke NNET during development of ROMs for the gasifier. In Figure 2-3, we present a physical comparison of the contours obtained by the CFD model and xROMs of the gasifier for Case 29 out of a total of 30 simulated cases (Lang et al., 2009). The left figure in each set is the result of the FLUENT model and the right is predicted by its ROM, respectively. For simplicity, we consider a rectangular portion from the geometry for xROM development, which captures the main characteristics of the field and does not lose generality. The figure illustrates that all seven monitored states are computed to high accuracy at designed cases. This is consistent with our numerical error analysis.

Coal Slurry & O2

Figure 2-3. Contour plots of seven variables for Case 29. The left figure in each set

is the FLUENT result, while the right is the ROM prediction.

Figure 2-4. Statistical results of cross validation for yROM of gasifier

The statistical results of cross validation for seven outputs variable of the gasifier with 28 cases are shown in Figure 2-4. From the plots we observe that the mass fraction of H2S and the temperature in the output space have a very accurate interpolation, 100% of them

H2S Mass Fraction H2O Mass Fraction H2 Mass Fraction Temperature

CH4 Mass Fraction CO2 Mass Fraction CO Mass Fraction

are within 1.0%. The majority of the errors occur in the CO2 mass fraction; 15% of its prediction is within 1.0% and 60% within 5.0%.

2.4 Combustor In advanced gasification-based power plants, gas-turbine combustors burn a mixture of synthesis gas (mainly carbon monoxide and hydrogen) and air to deliver high-temperature gases to the gas turbine for power generation. Such combustors involve complex turbulent and reacting flows requiring the use of high-fidelity CFD models to provide an accurate calculation of the inlet temperature for the gas turbine. The combustor model used here is based on a turbulent, lean-premixed, swirl-stabilized research combustor at NETL (Sidwell et al., 2005). The CFD model is scaled up to represent a single combustor can in a 250MW gas turbine with 16 combustor cans used in an advanced gasification-based power plant. As shown in Figure 2-5(a), the 2D axisymmetric combustor geometry has nearly 6000 computational cells which are used to solve the CFD model in FLUENT.

(a)

(b) (c)

Figure 2-5. (a) 2-D Geometry of a single axisymmetric combustor can

Rotational axis

0.105 2.62

5 1.68

0.28

0.098

0.2485

0.2366

0.4851

0.3241

0.0875

All dimensions in meters ssMetermeters

and its mesh; (b) typical temperature field of the combustor; (c) detail of studied portion of the geometry

The flame is anchored by careful scaling and design of the combustor and the nozzle velocity is matched to the research combustor at NETL. In the FLUENT model of the combustor, the finite rate/eddy dissipation model is selected (Zitney et al., 2006). The reaction rate is defined by taking the minimum of the chemical reaction rate and the turbulent mixing rate. The overall reactions in the combustor are: 2CO + O2 2CO2 2H2 + O2 2H2O (2-5) CH4 + 2O2 CO2 + 2H2O To develop the ROM, we can vary the input variables that represent operating conditions and boundary conditions in the CFD-based combustor model. These cases provide corresponding state fields and output stream(s). Figure 2-5 (b) shows a typical temperature field displayed as filled contours, from which we can see that the temperature in a large portion of the geometry is uniform; therefore we only focus on a rectangle as shown in Figure 2-5(c) during xROM development. In addition, we developed xROMs for seven monitored states. Kriging is used for the input-output mapping. Figure 2-6 presents the contours of the six monitored states in the rectangle obtained by the FLUENT model and the developed xROMs for Case 1. Comparing these contours we conclude that the xROM maintains high accuracy and only a small distortion of the contours can be observed in the total pressure and the temperature fields. It is also hard to find differences for mass fractions of the monitored components in these plots.

Figure 2-6. Contours of six monitored states in combustor. The top figure in each set is from the FLUENT model, while the bottom is predicted by xROM.

Figure 2-7. Statistics of relative errors of yROM of the combustor compared with FLUENT results We also implement cross validation of the input-output ROM (i.e., yROM) and the statistical results for 128 cases of the combustor are shown in Figure 2-7. The combustor case shows much better predictions, i.e. all of 128x7 = 896 relative errors are less than 1.0%, except one that is up to 1.7%. These results, along with those in Section 2.3, provide reasonable confidence that the yROMs of the gasifier and the combustor can be developed further as process modules that can be integrated within an IGCC process for optimization. 3. Development of ROMs as Process Modules

Because the inputs of the CFD model usually are different from those of the process simulator, some additional variable transformations are needed. Moreover, the ROM itself needs to be incorporated within a process module in the flowsheet simulator.

3.1 Wrapping the gasifier ROM as a process module

We now describe the procedures to convert the ROM to a process module that is integrated within steady-state process simulators. The procedures are implemented with two simulation tools: GAMS (Brooke et al., 1998) and Aspen Plus at different stages. First, in order to explore how to use the ROM for process simulation as well as process optimization, we implement the “closed loop” test with GAMS for the integration of the

developed ROM of the gasfier with a flowsheet of a steam cycle process illustrated in Figure 4-1. We found that the ROM must be wrapped so that its outputs correspond to the stream variables of the flowsheet. Figure 3-1 (a) shows the gasifier ROM described in section 2.3 while Figure 3-1 (b) shows in more detail how to wrap the ROM as a unit integrated within the flowsheet. These wrapping procedures are implemented here with GAMS. In our previous work, the rigorous 3-D FLUENT model with a discrete phase method (DPM) for the gasifier has been used and we derived PCA-based xROMs and yROM. In this investigation, we apply these ROMs to implement two sets of procedures for process optimization with GAMS and Aspen Plus. Table 3-1. Inputs and outputs of yROM of gasifier Inputs Outputs (s82)

R1 = Ratio of s84 to s83 [w/w%] Mass fraction of H2S Mass fraction of H2O

R2 = water in coal slurry [w/w %] Mass fraction of H2 Mass fraction of CH4

R3 = Ratio of oxygen to carbon [w/w%]

Mass fraction of CO2 Mass fraction of CO Temperature [K]

(a) (b) Figure 3-1. (a) yROM of gasifier (b) its flowsheet topology as process module.

Gasifier

water

Coal

O2

InterfaceInterfac

e

Coal

water

O2

s41 s81

s82

s83

s84

s85

s86

s87

s88

s89

Gasifier

GFpost

Splitter

Mixer 1

Mixer 2

The inputs of the yROM of the gasifier are its three operating parameters, while the outputs are the mass fractions of six components and the temperature, as listed in Table 3-1. The initial yROM does not integrate with any flowsheet. Additional work is needed so that inputs and outputs of the gasifier ROM are compatible with the process streams of a process module, and the module has the ability to receive input streams and provide output streams from the process simulator. Within GAMS, this transformation is illustrated in Figure 3-1 (b) where “Gasifier” represents the yROM and stream (s82) is the output leaving the gasifier as primary syngas. After this stream, a mass balance/splitter block represents post-gasification treatment so that syngas s81 is obtained and ready to be used as fuel. The “Interface” in Figure 3-1(b) consists of a set of equations, which equates stream s81 in the process module to stream s41 in the combined cycle. The entire flowsheet including the gasifier process module is shown in Figure 4-1. Note that the three input variables R1, R2 and R3 remain with the ROM of the gasifier. They dominate the gasifier performance, because of their physical representations in Table 3-1, and appear in Equation (3-1), which must be considered during “wrapping”. Their influence is ensured by adding (3-1) as constraints in the optimization formulation or as equations in the unit module, as implemented with [NLP 1-6] in Section 4. 3.2 Linking the process module in Aspen Plus Our goal is to use the equation oriented (EO) mode in process simulation. In EO mode, all equipment models (or blocks) in the flowsheet are formulated as a complex set of explicit equations with residuals in the form of f(x) = 0. The set of equations is then solved simultaneously during simulation and optimization. Our choice of the EO mode allows us to consider even more efficient NLP solvers to solve these optimization problems in the future. With Aspen Plus as the modular simulator, we choose the built-in USER3 modeling protocol to accommodate the yROM as a process module. To create this user-defined block, we write a set of FORTRAN subroutines, which are then integrated into the flowsheet. In the converted process module, a complete set of utility functions provides information to respond to task flags raised by Aspen Plus during simulation or optimization. Also the sparsity pattern and the number and values of non-zero elements in the Jacobian are determined and transferred to provide the requirements of most NLP large-scale solvers. Since the input of the equipment model in Aspen Plus is different from that of the CFD model and its ROM, information of the inlet streams in Aspen Plus must be translated. For the three feeds entering the gasifier, only the coal feed is independent while the other two are dependent on it by their own ratios. Thus, the converted process module of the gasifier must take care of two input steam constraints, FeedH2O = R2 Feedcoal (3-1)

FeedO2 = R3 Feedcoal Massout = Feedcoal +FeedH2O +FeedO2 where Feed denotes mass flowrate of the feed streams and its subscripts are the names of feed streams. R2 and R3 are the ratios determined by module of the gasifier and Massout represents the mass flowrate of the output stream. Figure 3-2 illustrates the constraints in the module.

Figure 3-2. Scheme of gasifier module and the special constraints (3-1) Finally the USER3 model from the ROM plus necessary peripheral modules leads to the complete model of the gasifier in Aspen Plus.

Figure 3-3. Flowsheet topology of gasifier Figure 3-3 shows how the gasifier is wrapped and simulated in Aspen Plus. Three feed streams enter the USER3 model, GASIF, and produce output stream, RAWSYNG. This stream is separated into 5% ASH with the remainder going to a turbine CMP-1000 and a heat exchanger HE-1000 to become SYNGAS at T = 315.3 K and P = 19.7 bar, which enters the rest of the IGCC flowsheet.

Figure 3-4. Flowsheet topology of gas-combustor-turbine The same wrapping procedures are implemented for the combustor and the resulting flowsheet topology of gas-combustor-turbine is shown in Figure 3-4 to illustrate how the gas-combustor-turbine is simulated with Aspen Plus. Stream 300 is the hydrogen-rich synthesis gas that mixes with nitrogen as fuel gas. Stream 301 is the oxygen-rich supply compressed to 10 bar (Stream 302) by a single stage compressor (JC3101) which is

driven by the gas turbine directly. Stream 302 is split into streams 302A and 304 according to a specific ratio. Stream 300 mixes with Stream 302A and forms Stream 303 that enters the combustor (CMBSTR USER3 model). The combusted gas is then cooled to about 1050 ºC by mixing with remaining air, Stream 304, which forms Stream 304B. This stream drives gas turbine JC3104 to produce electricity, measured in work Stream W04. Then exhaust Stream 305 goes through a series of heat exchangers to release its heat energy which is recovered by the combined cycle. 4. ROM-based IGCC Optimization This section describes two optimization case studies that incorporate ROMs developed from CFD models of the gasifier and combustor. We first consider the integration of the gasifier with a combined cycle superstructure modeled in GAMS, and then proceed with an Aspen Plus-based optimization of the IGCC process with carbon capture that contains both ROMs. The steam cycle is developed using the superstructure optimization models from Bruno et al. (1998). The flowsheet of this combined cycle is an important part of IGCC process. Here the flowsheet receives a syngas stream consisting of CO, H2, CH4 and CO2, which is the outlet of the gasifier. Modeled in GAMS the yROM of the gasifier is shown in Figure 4-1.

Figure 4-1. Combined cycle optimization integrated with gasifier module 4.1 Combined cycle optimization case studies

AIR

FUEL

LP CONS . MP

CONS . HP CONS .

CW

DW

High Pressure ( HP ) Header

Vacuum Header

Condensate Header

Medium Pressure ( MP ) Header

Low Pressure ( LP ) Header

Deaerator

HRSG

Gas Turbine

S 1 S 58

S 2

S 3

S 59

S 4

S 60

S 61

S 5

S 6 S 7

S 8

S 9

S 15 S 20

S 16 S 12

S 11 S 17

S 10 S 37 S 38

S 34 S 35 S 36

S 41

S 46

S 43

S 42

S 45

S 40

S 39 S 47 S 54

Gasifier

water

Coal

O2

We consider four optimization cases with different objective functions with problem formulations that satisfy the 500 MW energy demand. In all four cases, the independent variables are the three ratios in the yROM that are also the operating conditions of the gasifier. The NLPs contain 851 variables and 4 degrees of freedom: the flowrate of coal feed, the three operating ratios of the gasifier. The NLP formulation and the optimal solution are presented as follows. • Case 1: To minimize heating value of the syngas, equivalent to minimizing the cost of

the syngas, the optimization problem is expressed as [NLP 1]

DemandyElectricitOutputPowerNetbalancesenergyandmasscycleSteam

equationsNNET

FeedMassFeedRFeedFeedRFeedts

FcHHVtH

jjout

coalO

coalOH

jjj

00

0 ..

cosmin

32

22

≥

=−

=⋅−

=⋅−

⋅⋅=

∑

∑

[NLP 1]

where HHVj and Fcj are the heating value and the mole flowrate of j-th component, respectively. There are three components with positive heating values, i.e. HHVH2 = 0.269258, HHVCH4 = 0.0.839671 and HHVCO = 0.269558 [MBtu/kmol]. NNET_Equations, represents the yROM derived with a neural network. • Case 2 is the same as Case 1, but with additional lower and upper bounds on output

temperature of the stream leaving the gasifier, as described in [NLP 2].

KTKDemandyElectricitOutputPowerNetbalancesenergyandmasscycleSteam

equationsNNET

FeedMassFeedRFeedFeedRFeedts

FcHHVtH

out

jjout

coalO

coalOH

jjj

16701660

00

0..

cosmin

32

22

≤≤

≥

=−

=⋅−

=⋅−

⋅⋅=

∑

∑

[NLP 2]

• Case 3: Minimize the flowrate of coal feed as [NLP 3]

DemandyElectricitOutputPowerNetbalancesenergyandmasscycleSteam

equationsNNET

FeedMassFeedRFeedFeedRFeed

tsFeedH

jjout

coalO

coalOH

coal

00

0..

min

32

22

≥

=−

=⋅−

=⋅−

=

∑ [NLP 3]

• Case 4 is the same as Case 3, but with additional lower and upper bounds of output

temperature of the stream leaving the gasifier, expressed as [NLP 4]

KTKDemandyElectricitOutputPowerNetbalancesenergyandmasscycleSteam

equationsNNET

FeedMassFeedRFeedFeedRFeedts

Feed

out

jjout

coalO

coalOH

coal

17001660

00

0.. min

32

22

≤≤

≥

=−

=⋅−

=⋅−

∑ [NLP 4]

The optimal solutions of the four NLPs are obtained using the CONOPT3 solver and listed in Tables 4-1(a) and (b). We observe that optimal values of R1, R2 and R3 in [NLP 1] are all at their upper bounds. In [NLP 3], R1, R2 and R3 are all at their lower bounds. For the remaining two cases, the additional temperature constraints force R3 to leave its bounds. In [NLP2] the optimal value of R3 decreases from its upper bound and in [NLP4] it increases from its lower bound. Table 4-1(a) Optimal solutions of [NLP1] and [NLP2] Starting Optimal

NLP 1 NLP 2 Objective [$/hr] Min syngas cost

37081.55 35767.468 35791.737

Variables R1 [%] 80 84.6928 84.6928 R2 [%] 30 34.9266 34.9266 R3 [%] 80 84.8813 82.7162 Feedcoal [kg/hr] 5500 1.7637e+5 17481e+5 CONOPT Iter 110 104 CPU time (sec) 0.09 0.08

Table 4-1(b) Optimal solutions of [NLP 3 and 4] Starting Optimal

NLP 3 NLP 4 Objective[kg/hr] 5500 1.5513e+5 1.5561e+5 Variables R1[%] 80 70.3411 70.3411 R2 [%] 30 25.2085 25.2085 R3 [%] 80 75.2154 75.9128 Feedcoal[kg/hr] 5500 --- --- CONOPT Iter 120 99 CPU (sec) 0.25 0.08 Having obtained the four optimal solutions, we validate the ROM with FLUENT CFD cases of the gasifier model at the four optimal solutions. The relative errors from the outputs of these FLUENT runs are listed in Table 4-2 (a) and (b). The smallest error, less than 1.0% occurs in the outlet temperature and the mass fraction of H2S and CO in output stream of the gasifier. The largest error is in the mass fraction of CO2. These characteristics are the same as in the yROM evaluation in our previous study (Lang et al., 2009), where we showed similar relative errors due to the stochastic and dynamic nature of the discrete phase model. As a result, we observe that the process module inherits the properties of the yROM derived from the 3-D FLUENT model with DPM. These closed-loop tests show that the ROM derived from the CFD model performs well. The ROM maintains the essential input-output behavior of the CFD model, provides accurate derivatives for equation-oriented optimization, and leads to very efficient optimization strategies. Table 4-2 (a) Error evaluation of closed-loop test for Cases 1 and 2 (NLP 1 and 2) min Heat value Case 1 Case 2 (with additional constraints) R1 R2 R3 R1 R2 R3 84.6928 34.9266 84.8813 84.6928 34.9266 82.7162 yROM Fluent error (%) yROM Fluent error(%)

H2S 0.01317 0.01315 0.20311 0.01328 0.01327 0.02011 H2O 0.30540 0.30657 0.37995 0.30438 0.30248 0.62983 H2 0.01157 0.01136 1.84072 0.01154 0.01159 0.48576 CH4 0.02502 0.02513 0.41165 0.02748 0.02812 2.27500 CO2 0.06784 0.06754 0.44552 0.06143 0.06757 9.08430 CO 0.55210 0.55083 0.23151 0.55701 0.55184 0.93594

Temp 1709.29 1716.34 0.41060 1670.00 1670.62 0.03693 Table 4-2(b) Error evaluation of closed-loop test for Cases 3 and 4 (NLP 3 and 4)

min Coal Feed Case 3 Case 4 (with additional constraints) R1 R2 R3 R1 R2 R3 70.3411 25.2085 75.2154 70.3411 25.2085 75.912813

yROM Fluent error (%) yROM Fluent error (%) H2S 0.01509 0.01511 0.17401 0.01504 0.01506 0.09924 H2O 0.20786 0.20417 1.80365 0.20626 0.21256 2.96652 H2 0.01751 0.01801 2.76817 0.01784 0.01656 7.73165 CH4 0.03106 0.03108 0.06850 0.02985 0.03230 7.59190 CO2 0.06599 0.07499 11.99523 0.07312 0.06378 14.65133 CO 0.63573 0.63109 0.73518 0.63110 0.63322 0.33569

Temp 1644.08 1636.56 0.45936 1660.00 1668.07 0.48395

4.2 Description of the MTNO-IGCC process We now consider the integration of both the gasifier and combustor ROMs within a process optimization for the IGCC process with carbon capture. Here we adopt an IGCC process described in a detailed case study prepared by TNO (Kessel et al., 1998). The scale of the original IGCC plant is 500 MWe with two trains shown in Figure 1-1 and described as follows. The gasifier converts feeds for coal, water and oxygen into syngas; then the CO in the syngas is converted into H2 and CO2 in two cascaded water-shift reactors. The syngas becomes an H2-rich stream, with 90% of all CO2 in the stream captured by a temperature swing adsorption (TSA) unit. The CO2 is compressed for subsequent storage and sequestration. On the other hand, after mixing with nitrogen and oxygen, the H2-rich gas enters the combustor of the gas turbine to produce electricity. The energy in the turbine exhaust is recovered by driving the steam turbines in the steam cycle. For this study, we modify the flowsheet (and the plant capacity) to be consistent with our gasifier and combustor process modules. We use the developed USER3 module of the gasifier as the initial unit to accept the water, coal and oxygen feeds. We replace a reactor block that previously simulated the combustor with the yROM developed as a USER3 module. Correspondingly, some auxiliary blocks are added to integrate the module into the flowsheet. We denote this as the MTNO-IGCC flowsheet. The flowsheet is simulated with Aspen Plus in EO Mode, where the gasifier and the combustor are simulated with the USER3 models described above. The detailed process flowsheet in Aspen Plus is shown in Figure 4-2 with the main sections indicated for gasification, water-gas-shift, TSA and CO2 compression, gas-combustor-turbine and the steam cycle; the USER3 models of the gasifier and the combustor modules are idicated by arrows. More detail of the steam cycle is provided in Figure 4-3, where the turbines for power output are identified.

4.3 Optimization of MTNO-IGCC with CFD-based ROMs First, we focus on the performance of the two process modules developed from the gasifier and combustor CFD models. We select four independent variables that relate to the gasifier and the combustor, i.e. the ratios R1-R3 of the gasifier and the split fraction of splitter MC301 (see Figure 3-4) that determines the flowrate of the oxidant supplied to the combustor. We denote this basic problem as [NLP 5].

Second, we add three independent variables selected from the other process variables: 1) mass flowrate feeding into the water gas shift (WGS) reactors; 2) mass flowrate of the makeup stream recycling within the steam cycle and 3) heat allocation ratio of the high pressure turbine to the medium pressure turbine (see Figure 4-3). These lead to [NLP 6]. Both [NLP 5] and [NLP 6] can be stated as below:

!

max Enet = W j

j= turbine

" # Wk

k= consumer

"

= (W04#WCMP ) + (W

07+W

09+W

10#1 +W10#2 #Wpump )

s.t. FeedH2O = R2 Feedcoal [NLP 5, 6] FeedO2 = R3 Feedcoal

NNET Equations for gasifier Kriging Equations for Combustor Model Equations for all equipment where W04 is work produced by the gas-turbine, WCMP is the energy consumed by the compressor in the gas-combustor-turbine for compressing the air from 1 to 10 bar. W07 and W09 are the work produced by the high and medium pressure steam turbines in the steam cycle, respectively. W10-1 and W10-2 are the work produced by the two low pressure steam turbines and Wpump is the energy used by the water pump in the steam cycle for recycling the water in the steam cycle. The objective function is to maximize the power output of the plant subject to a set of equations that model the MTNO-IGCC flowsheet, implicitly expressed in the EO mode of Aspen Plus. These problem formulations consist of 3747 EO variables. [NLP5] and [NLP6] are solved with no more than 15 iterations and less than 3 CPU seconds by DMO, the default solver available in Aspen Plus. The optimal solutions of these problems are listed in Table 4-3. Table 4-3 Optimal solutions Starting point Optimal solution

[NLP 5] [NLP 6] Net-work-of-gas- turbine[MWe] 225.338 228.143 228.270 WCMP -73.846 -73.843 -73.844 W04 299.184 301.986 302.114 SC-w-tot [MWe] 116.095 129.626 136.382 W07 23.828 26.832 30.045 W09 27.383 30.227 31.059 W10-1 37.130 41.239 42.579 W10-2 31.678 35.252 36.475 Wpump -3.925 -3.925 -3.775 Power output of plant [MWe] 341.433 357.768 364.652 No. of iterations 8 15 CPU time [sec] 1.37 2.38

Independents Gasifier_Ratio (R1) [%] 80.2601 70.3411 70.3411 Gasifier_Ratio (R2)[%] 26.2087 31.4308 30.7035 Gasifier_Ratio (R3)[%] 84.8813 84.8813 84.8813 Split ratio of MC301[%] 24.0000 24.0036 24.0047 Split ratio of Q8 [%] 60.0 --- 70 Mass flow of Stream 413 [kg/hr] 750,000 --- 721,417 Mass flow of WGS Feed [kg/hr] 245,023 --- 239,500 In Table 4-3, Net-work-of-gas-turbine = (W04 – Wcmp) is the net power output from the gas turbine only, where W04 is the output power from the gas-turbine, Wcmp is the consumed power by the compressor inside the gas-combustor-turbine. SC-w-tot = (W07+W09+W10-1+W10-2 -Wpump) represents the total power recovered by steam cycle facilities, where W07 and W09 are output powers from the high and medium pressure steam turbines, respectively; W10-1 and W10-1 are the power produced by the two low pressure steam turbines; Wpump is the energy consumed by the water pump to maintain water cycling within the steam cycle. The objective function, i.e. power output of plant = Net-work-of-gas-turbine + SC-w-tot is the total net power output obtained from MTNO-IGCC. In [NLP5] we consider decision variables for the gasifier and the combustor only; for this optimization the power output of the plant increases by 16.34 MWe or 4.8% from its original operation. By including the three additional variables from the MTNO-IGCC flowsheet in [NLP 6], the objective function improves by an additional 6.88 MWe; the total increase is 23.22 MWe or 6.8%. This result demonstrates the advantages of co-simulation for process optimization through conversion of ROMs from CFD models into process modules. With the process module, the process optimization clearly improves the objective function, and provides greater process accuracy over conventional steady-state simulations. Moreover, the CPU time used to solve NLP problems with almost 4000 variables is no more than 3 seconds; this result shows that process modules derived from yROMs overcome the prohibitive computational requirements of CFD models and are effective surrogate models in process simulation and optimization. 5. Conclusions

The objective of co-simulation is to simulate processes modeled with both process simulators and CFD tools, for example Aspen Plus and FLUENT. Over the past decade, co-simulation has been demonstrated to link high fidelity models of key process equipment with process simulators. To overcome the burden of excessive computational requirements of CFD models, a PCA-based methodology has been verified to generate reduce order models (ROMs). Co-simulation with ROMs retains all of the advantages and removes the computational barriers for process simulation with CFD-based tools. This study extends co-simulation from process simulation to process optimization and demonstrates the benefit of this extension for large-scale process optimization problems

for IGCC. In this investigation we adopt CFD models of the gasifier and the combustor developed at NETL and we define the input domains for them in the MTNO-IGCC process. The ROMs from the CFD models were integrated into the process flowsheet as user-defined blocks within the simulator. Finally, EO-based process optimization is performed and significant improvements are realized. CFD models were incorporated into this process optimization through the following procedures:

• Solve CFD model at a set of points from an experimental design to obtain a database of snapshots.

• Develop the ROMs using the database through the application of PCA-based data reduction and input-output mapping.

• Convert the yROM into a user-defined model, for instance, the USER3 model in Aspen Plus.

• Replace the corresponding conventional models in the flowsheet with the user-defined process module.

• Perform the EO-based process optimization. These procedures were implemented for gasifier and combustor CFD models. The results of the optimization for the MTNO-IGCC process (with carbon capture) show that the power output of the process can increase by 5-7% compared to the case with conventional models. This implies that ROM-based flowsheet optimization can significantly increase the efficiency of energy processes. Future work will continue the improvement of methods to develop accurate and efficient ROMs from CFD models, along with their integration and validation within process optimization environments. This implementation will also be extended to the CAPE-OPEN software standard and to integration within the APECS system. Acknowledgements This research was performed in support of the National Energy Technology Laboratory's on-going research in Process and Dynamic Systems Research under the RDS contract DE-AC26-04NT41817. Thanks to Ravindra Kamath for setting up the steam cycle model in Figure 4-1. References Aspen Technology, Inc. Aspen Plus User Models, Version 7.1, 2009 Brooke, A., D. Kendrick, A. Meeraus, and R. Raman. GAMS - A User's Guide. http://www.gams.com, 1998.

Bruno, J.C., F. Fernandez, F. Castells and I.E. Grossmann, "MINLP Model for Optimal Synthesis and Operation of Utility Plants", Chemical Engineering Research and Design, 76, pp.246-258 (1998) Caballero, J. A. and I. E. Grossmann, “An Algorithm for the Use of Surrogate Models in Modular Flowsheet Optimization,” AIChE Journal, 2008, 54, 10, 2633-2649 Demuth, H, M Beale and M. Hagan, Neural Network Toolbox, MATLAB (2005) Kamath, R. S.; PhD Thesis, Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 2010 Kessel, L.B.M. van, J.C.P.L. Saeijs, V. Lalbahadoersing, A.R.J. Arendsen, M. Stavenga, A.B.M. Heesink and H.M.G. Temmink, IGCC Power Plant: CO2 removal with high temperature adsorbents, TNO-Report R98/135, Netherlands Organization for Applied Scientific Research, 1998 Kobayashi, H., J. Howard and A. Sarofim, Coal devolatilization at high temperature, Proc. of the Combustion Institute, 16 (1976) Lang, Y-D, A. Malacina, L. T. Biegler, S. Munteanu, J. I. Madsen and S. E. Zitney, “Reduced Order Model Based on Principal Component Analysis For Process Simulation and Optimization," Energy and Fuels, 23, 1695-1706 (2009) Lophaven, S. N., H. B. Nielsen and J. Sondergaard, DACE A Matlab Kriging Toolbox, Technical Report IMM-TR-2002-12, Technical University of Denmark, Denmark, 2002 Shi, S., S.E. Zitney, M. Shahnam, M. Syamlal, W.A. Rogers, Modeling Coal Gasification with CFD and the Discrete Phase Method, Journal of the Energy Institute, 79, 4, pp. 217-221 (2006) Shi, S., M. Shahnam, M. Syamlal, W.A. Rogers, Coal Gasification for Future Power Generation, FLUENT News, p. S11, Fall (2004) Sidwell, T., Casleton, K., Straub, D., Maloney, D.,Richards, G., Strakey, P., Ferguson, D., and Beer, S., Development and Operation of a Pressurized Optically-AccessibleResearch Combustor for Simulation Validation and Fuel Variability Studies, Proceedings of ASME Turbo Expo 2005, Paper GT2005-68752 (2005) Sloan, D., W. Fiveland, S.E. Zitney, and M.O. Osawe, “Plant Design: Integrating plant and equipment models,” Power Magazine, Vol. 151, Issue 8, August (2007). Syamlal, M. and L.A. Bissett,. METC Gasifier Advanced Simulation (MGAS) Model, Technical Note, NTIS report No. DOE/METC-92/4108 (DE92001111) (1992)

Wen, C. Y. and T.Z. Chuang, Entrainment Coal Gasification Modeling, Ind. Eng. Chem. Process Dev., 18 (4), 684-695 (1979) Zitney, S.E., “CAPE-OPEN Integration for CFD and Process Co-Simulation,” Proc. of the AIChE 2006 Annual Meeting, 3rd Annual U.S. CAPE-OPEN Meeting, November 12-17, San Francisco, CA (2006). Zitney, S.E., M.O. Osawe, L. Collins, E. Ferguson, D.G. Sloan, W.A. Fiveland, and J.M. Madsen, “Advanced Process Co-Simulation of the FutureGen Power Plant,” Proc. of the 31st International Technical Conference on Coal Utilization & Fuel Systems, May 21-25, Clearwater, FL (2006). Zitney, S.E. and M. Syamlal, "Integrated Process Simulation and CFD for Improved Process Engineering," Proc. of the European Symposium on Computer Aided Process Engineering –12, ESCAPE-12, J. Grievink and J. van Schijndel, Eds., May 26-29, The Hague, The Netherlands, 2002, pp. 397-402 (2002).

Figure 4-2 Process flowsheet of modified TNO-IGCC in Aspen Plus

Figure 4-3 Detail of Steam Cycle for modified TNO-IGCC in Aspen Plus