Application of uncertainty quantification methods for coal devolatilization kinetics in gasifier modeling

PTEC-09952; No of Pages 10 Powder Technology xxx (2014) xxx–xxx

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Application of uncertainty quantification methods for coal devolatilization kinetics in gasifier modeling Aytekin Gel a,b,⁎, Kiran Chaudhari a,c, Richard Turton a,c, Philip Nicoletti a,d a

National Energy Technology Laboratory, Morgantown, WV, United States ALPEMI Consulting, LLC, Phoenix, AZ United States West Virginia University, Morgantown, WV, United States d URS Corporation, Morgantown, WV, United States b c

a r t i c l e

i n f o

Available online xxxx Keywords: Coal gasification kinetics Kinetics software Uncertainty quantification Propagation of input uncertainties Sensitivity analysis

a b s t r a c t The focus of this research is to study sensitivity of input parameters in terms of chemical reaction kinetics of coal devolatilization using non-intrusive uncertainty quantification (UQ) methods. The effects of heating rate, pressure, and temperature on coal devolatilization have been considered. Variations in coal devolatilization kinetics and product yields were captured via Carbonaceous Chemistry for Computational Modeling (C3M) for operating conditions similar to the transport gasifier using PC Coal Lab (PCCL) kinetic package. Temperature, pressure and heating rate were considered as three input parameters, while the quantities of interest or response variables were mass fractions of CO, CO2, H2, tar, H2O, and CH4 along with total volatile yield. A direct Monte Carlosimulation-based approach was employed to perform the UQ analysis. The correlations among the response variables were investigated by computing a correlation matrix that supports the findings of yield of devolatilization reported by various experiments in the literature. Sensitivity study of the input parameters was analyzed by using the Sobol Total Indices methodology implemented in PSUADE, an open source UQ toolbox. These findings clearly demonstrate the pronounced effect of temperature on coal devolatilization product yields, and hence will be considered as a key parameter in future studies. The preliminary study presented in this paper paves a path for incorporating uncertainty caused by chemical reaction kinetics in computational fluid dynamics based modeling of coal gasifier systems and scale-up studies. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Non-intrusive parametric input uncertainty propagation is one of the uncertainty quantification techniques employed in numerical or mathematical models to predict the effect of the uncertainty on output due to variations in input parameters. Many assumptions are made by the user when simulating a physical problem as it is very difficult to model exactly all the complex phenomena taking place. Some of these assumptions are directly related to the model parameters or inputs, and the remaining are embedded with the selected model (e.g., the drag model used in multiphase flows). These assumptions can make a significant difference between the model predictions and reality. The discrepancy between the result of the model and the true physical scenario is referred to as predictive uncertainty, and the degree of this uncertainty is often a function of the ability of the model to capture the phenomena in the physical scenario of interest [28]. Therefore, as part of any uncertainty quantification activity it becomes necessary to understand the change in model predictions based on the variations in the user prescribed parameters (e.g., boundary conditions) employed in the set-up of the problem, which is also known as input uncertainty ⁎ Corresponding author at: NETL, Morgantown, WV, 26505. E-mail address: [email protected] (A. Gel).

propagation. In a previous UQ study, the uncertainty issues relating to the hydrodynamics model in a computational fluid dynamics code for gasifiers were addressed [11]. The current study addresses the input parameter uncertainties affecting the chemical reactions taking place during coal conversion by employing non-intrusive input parameter uncertainty propagation techniques. Other sources of uncertainties such as model form uncertainty and numerical approximation uncertainty are disregarded for the scope of the current work. The uncertainty quantification (UQ) for coal gasification processes can be used to predict the variations in product yields and reaction rates given the uncertainties/variations in operating conditions and fuel properties. The gasification of coal at moderate temperatures goes through 4 stages: (1) primary devolatilization; (2) pyrolysis of secondary volatiles; (3) homogeneous reforming of non-condensables, and (4) char conversion via oxidation and gasification [23]. Among all of the reactions in coal conversion, coal devolatilization can account for up to 70% of the loss in weight of the coal [33]. This process depends on the organic properties of the coal. The quantity of volatiles released during pyrolysis impacts the char's heterogenous and gas phase homogeneous reaction chemistry. Various studies [5,18,21] have reported that operating conditions such as temperature, pressure, heating rate, particle diameter, residence time, and coal rank can affect the coal devolatilization reaction kinetics. Hence, it is crucial to obtain kinetics

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Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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and product yields for devolatilization by considering the effects of these parameters. Kinetic software packages such as PC Coal Lab (PCCL), Chemical Percolation Model for Coal Devolatilization (CPD), Solomon's Functional-Group, Depolymerization, Vaporization, and Cross-linking (FGDVC) predict the effect of operating conditions on coal devolatilization kinetics and product yields, so they have been considered for this UQ study. These kinetic packages are accessed via the recently developed Graphical User Interface (GUI) known as Carbonaceous Chemistry for Computational Modeling (C3M) [47]. This study focuses on predicting the effect of operating conditions on coal devolatilization kinetics and product yields predicted by PCCL. Based on the results of various experiments available in the literature, effects of heating rate, pressure, and temperature on coal devolatilization have been considered in this study. 1.1. Effect of heating rate on coal devolatilization Heating rate has a significant effect on coal pyrolysis such that primary devolatilization reaction rate and yield increase with an increasing heating rate [10,14]. Various experimental and analytical studies have reported that an increase in heating rate during coal devolatilization can lead to a decrease in coal particle swelling ratio, an increase in the amount of tar produced, an increase in total volatile yield released causing a decrease in char yield, and an increase in particle size along with an increase in devolatilization rate [5,7,40,41]. In the literature, different coal types were tested showing the effects of heating rate on coal devolatilization. Work performed by Gibbins and Kandiyoti [12] on coal samples of Pittsburgh No.8, Illinois No. 6, Wyodak-Anderson, and Pocahontas No.3 used heating rates from 1 to 1000 °C. Experiments were performed by Griffin et al. [13] on samples of Pittsburgh No.8 at heating rates between 10 to 20,000 K/s and data reported by Freihaut and Seery [9] on Ben and Utah bituminous coal samples at heating rates ranging from1.0 to 105 K/s. These studies for coal devolatilization provided the evidence for an increase in the tar and total volatile yield at higher heating rates. Hayashi et al. [15] reported that when brown coal was pyrolyzed at slow and high heating rates, it affected the selectivity to tar, CO, CO2, and gaseous hydrocarbons (GHC) on a carbon basis. Fletcher and Shurtz in their studies [10,34] observed an increase in swelling ratio when Pittsburgh No. 8 and Illinois No.6 coal were pyrolyzed at heating rates between 1 to 106 K/s. Findings of studies carried out by Roberts et al. [29] on Australian coal and by Serio et al. [33] on North Dakota (Zap) lignite, Gillette and Montana Rosebud subbituminous coals, and Pittsburgh No. 8, Kentucky No. 9, and Illinois No. 6 bituminous coals, report an increase in devolatilization rate with respect to heating rates. These findings confirm the importance of heating rate as an input parameter in this study. 1.2. Effect of temperature on coal devolatilization Temperature has a similar effect as heating rate on coal devolatilization. Reaction rate of primary pyrolysis/devolatilization along with total volatile yield increases with an increase in temperatures [33,37]. Total tar yield depletes when temperature is increased beyond 650 °C because of the onset of secondary tar cracking reactions [9,24,46]. Ismail [17] reported that the particle swelling ratio increases with temperature during coal devolatilization for plastic coals such as bituminous and sub-bituminous coals but does not change significantly for non-plastic coals such as lignite and anthracite. In a similar way, the study performed by Zhong et al. [46] on bituminous coal showed the effect of changing temperature (700–950 °C) on devolatilization yield and rate along with experiments done by Matsuoka et al. [22] on Taiheiyo coal at temperatures 600–850 °C. The latter reported an increase in H2, CH4, CO and CO2 yields, while the yields of H2O and tar decreased with respect to increasing temperature. The results of these studies confirm the significant effect that temperature has on volatile

yields and reaction rates for devolatilization and that temperature is a key input parameter for this study. 1.3. Effect of pressure on coal devolatilization The effects of pressure on coal devolatilization have been observed for different coal ranks over a wide range of operating conditions. Multiple studies have reported that the devolatilization rate decreases as pressure increases [20,25,27,39,43]. Increasing pressure inhibits tar release that ultimately reduces the total volatile gas yield and promotes secondary tar reactions [10,20,22]. Serio et al. [33] observed the reduction in tar yield with increase in pressure and the reduction in char reactivity when pyrolysis experiments were carried out on three subbituminous and one lignite coal at pressures between 3 and 13 atm. The reduction in tar and total volatile yields appear to be most significant for bituminous coals and less pronounced for lignite. However, according to Zeng and Fletcher [45], the effect of pressure on the tar and total volatile yields appears to be less pronounced at high pressure. Sun et al. [36] examined the pyrolysis of two Chinese coals (0.4–4 mm) as a function of pressure (1 to 13 atm), their results showed that the yield of total volatiles decreased with increasing pressure when temperature was above a certain temperature (560 °C for a Chinese bituminous coal and 680 °C for a Chinese anthracite coal). Arendt and van Heek [2], Griffin et al. [13], Anthony and Howard [1], and Bautista et al. [4] confirmed this trend while studying a variety of coals. The Matsuoka et al. [22] study, mentioned earlier, reported increases in yields of CH4 and CO2 with increasing pressure, whereas C2–C6 product yields monotonically decreased with increasing pressure. Fletcher and Shurtz in two different studies [10,35] reported a decrease in particle swelling ratio with an increase in pressure. The sensitivity of pressure on coal devolatilization makes it a suitable choice for an input parameter for this study. 2. Software packages 2.1. Carbonaceous chemistry for computational modeling (C3M) The Department of Energy's National Energy Technology Laboratory (NETL) has developed a Graphical User Interface (GUI) known as Carbonaceous Chemistry for Computational Modeling (C3M) that creates a seamless connection between the computational fluid dynamic (CFD) software codes such as Multiphase Flow with Interphase Exchanges (MFIX) developed at NETL, ANSYS-FLUENT by ANSYS Inc., and BARRACUDA by CPFD and available kinetic packages such as, METC Gasifier Advanced Simulation (MGAS), PC Coal Lab (PCCL), Chemical Percolation Model for Coal Devolatilization (CPD), Solomon's FunctionalGroup, Depolymerization, Vaporization, Cross-linking (FGDVC). Fig. 1 shows the basic framework of C3M. C3M is used to access and analyze a variety of kinetic processes and reaction mechanisms typically found in coal/biomass/petcoke gasification, gas clean-up, and carbon capture processes [47]. The GUI provides a platform for the user to conduct virtual kinetic experiments to evaluate kinetic predictions as a function of fuel and sorbent type and/or operating conditions before using it in a CFD code of interest for simulating a process. C3M's unique features provide a way to compare simultaneously the graphical outputs of all kinetic packages (in terms of reaction rate constants and product yields). C3M can export the reaction kinetics of interest in the acceptable input-file format for the chosen CFD code. Currently, several UQ analysis methods are being implemented within C3M through a direct integration with an open source UQ toolbox as part of the effort to offer basic UQ analyses capability within C3M. Because of the low computational cost of all the kinetic packages, C3M can be utilized for multiple operating conditions and fuel types very cheaply and quickly, which also enables direct Monte Carlo simulation without the need for a surrogate model during UQ analysis.

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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Fig. 1. C3M architecture.

2.2. PC Coal Lab (PCCL) PCCL was developed by NIKSA ENERGY ASSOCIATES LLC, and is a set of mathematical models to predict a fuel's (mainly coal, petroleum coke and biomass) devolatilization and gasification behavior by simulating processes as they would occur in simple laboratory test facilities [26]. Input data is based on proximate and ultimate analysis of the coal. PCCL predicts the devolatilization, combustion, and gasification behavior of a wide variety of coals (more than 2000 types worldwide). The software can simulate two types of tests, namely, an electrically heated wire grid experiment and a laminar flow drop tube furnace experiment. The predictions give the yields of all major primary devolatilization products – CO2, H2O, CO, CH4, C2H4, C2H6, C3H6, C3H8, H2, H2S, HCN, tar, and char – as well as the elemental compositions of tar and char and the tar molecular weight distribution. It also predicts the subsequent secondary pyrolysis of primary volatiles into CO2, H2O, CO, H2, CH4, C2H2, and soot. PCCL v4.1 predicts char combustion from ignition throughout the later stages of burnout based on the expanded version of Hurt's Carbon Burnout Kinetics (CBK) Model [16]. It also describes char gasification by H2O, CO2, H2, and CO with a newly expanded version of CBK called CBK/G. PCCL was employed in this study to predict the effects of temperature, pressure and heating rate on pyrolysis of coal. In the remainder of this study, C3M term will refer to C3M/PCCL use as described above. 3. Uncertainty quantification methodology In this study, non-intrusive uncertainty quantification methods were employed for parametric model input uncertainty propagation.

One of the major advantages of this approach is the treatment of the application simulation code (i.e., C3M) as a black box without any structural changes within the simulation code itself. Ideally, Monte Carlosimulation-based random sampling approaches are preferred for investigating input uncertainty propagation or performing other UQ analysis. However, for applications such as computational fluid dynamics simulations requiring a transient 3D device-scale gasifier model, the prohibitive computational cost does not permit a Monte Carlo simulation approach. Instead, surrogate models characterizing the system behavior for the select response variables need to be constructed separately. In order to build an adequate surrogate model, a certain number of carefully chosen sampling simulations must be performed, and the quality of the surrogate model needs to be assessed to quantify the additional uncertainty introduced by employing the surrogate model instead of the actual application code. In this study, the computational cost of running many samples of C3M simulations were quite cheap so direct Monte Carlo-simulation-based approach was employed. Fig. 2 illustrates the integrated UQ analysis framework and workflow that has been employed in this study. The framework was developed at NETL with external collaborators and consists of two main software components, i.e., a UQ toolbox (PSUADE from LLNL, https:// computation.llnl.gov/casc/uncertainty_quantification/) and an application model (C3M from NETL, https://mfix.netl.doe.gov/members/ download_C3M.php). A brief overview of the workflow between these software components is described before providing additional details in this section. In a separate input file for PSUADE, the user prescribes the variables to be treated with uncertainty and a range of values to determine the upper and lower bounds. Quantities of interest or response variables

Fig. 2. Schematic illustration of the UQ framework and workflow.

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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with the type of UQ analysis to be performed are also specified in this input file. This is shown as Step 1 in Fig. 2. PSUADE creates separate work directories for each independent run (called ‘samples’) and modifies the input file for C3M by substituting new sets of values for the variables that were prescribed by the user to be treated as uncertain or varied if employing a design-of-experiments approach. The values for these variables are determined based on several factors such as the sampling method chosen, the number of samples, the upper and lower bounds, and the probability distribution function prescribed for the uncertain variables in the PSUADE input file. These are shown as Steps 2 and 3 in Fig. 2. In Step 4, under normal workflow procedures, PSUADE would launch the application code executable for each sample independently. This can be done either in serial mode (i.e., one simulation is performed at a time and the next sample run does not start until the previous one is finished) or in parallel mode (i.e., simulations are performed concurrently, with the number of running samples depending on the number of processors allocated). However, for C3M application, this step was performed manually as C3M was originally developed under a Windows operating system based environment and PSUADE was not ported initially. In the most recent implementation, this issue has been resolved by porting PSUADE to the Windows operating system and creating a GUI from C3M for PSUADE setup [6]. Once the simulations for all the samples are completed, PSUADE triggers the postprocessing steps, which can be coded in a python script to extract the data for quantities of interest from results and saves them in the database file for PSUADE. However, in this study this task was also performed manually due to operating system difference and results were saved into a PSUADE database file. This file is later used for uncertainty analysis, such as for building surrogate models based on response surface methods, sensitivity studies, or propagating uncertainties to determine their effect on the quantities of interest. The analysis tasks are usually performed in the interactive mode of PSUADE using the command line to enter PSUADE's UQ analysis commands and review the text-based results. PSUADE also provides an interface to Matlab for further post processing and visualization of the results. Additional details on the UQ framework and workflow can be found in Gel et al. [11] and Tong and Gel [38]. In order to build a data-fitted response surface as a surrogate model within PSUADE, the sampling points need to be carefully determined within the allowable input parameter space in order to extract the maximum information for the responses with a minimal number of simulations. Several sampling methodologies are available for this purpose; e.g., full factorial or fractional-based approaches, central composite design (CCD), and space-filling methodologies such as Latin Hypercube (LH) and Monte Carlo (MC) sampling.

3.1. Identify and characterize all sources of input uncertainty and quantities of interest as responses The first step of the UQ process requires identification of all sources of uncertainties and their adequate mathematical characterization. Usually this is achieved through the information provided by domain experts and/or available data in the literature. In order to capture the

Table 2 List of quantities of interest (QoI) or response variables based on the output from C3M. Quantities of Interest (QoI) or response variables 1 2 3 4 5 6 7

CO species mass fraction CO2 species mass fraction Tar species mass fraction H2 species mass fraction H2O species mass fraction CH4 species mass fraction Volatile matter (daf) species mass fraction

desired information from domain experts in a systematic way, a survey was developed to aid the identification and characterization of all sources of uncertainties among model input parameters. The survey asks participants to list all the sources of uncertainties known to them and to answer various questions for each of these parameters such as the most likely value of the parameter, lower and upper bounds for the parameter, justification for the provided most likely value with references, etc. Additionally, the domain experts are requested to characterize the listed uncertainties as aleatory, epistemic or mixed. These are defined by Roy and Oberkampf [30] as “aleatory – the inherent variation in a quantity that, given sufficient samples of the stochastic process, can be characterized via a probability density distribution, or epistemic – uncertainty due to lack of knowledge by the modelers, analysts conducting the analysis, or experimentalists involved in validation.” For aleatory uncertainties, the domain experts are asked to provide a probability distribution function (PDF) to characterize this type of uncertainty. Finally, the input parameters that might be correlated with each other are identified because they need to be analyzed as a special case. The domain experts are also asked to prioritize the importance of the source of uncertainty based on their own experience. Although this feedback might introduce some bias, additional screening studies and simulations can be performed to minimize the effect of bias introduced by the participants. Table 1 shows a consolidated version of the survey for the current study. The objective of the survey is to capture the knowledge and prior information about the parameter from the domain experts to document it in a systematic way. This will facilitate open discussions about the uncertain parameters and also the importance of their knowledge for the identification and characterization of uncertainties. Further details on the survey and complete version can be found in Gel et al. [11]. For the scope of this study, the first three input parameters shown in Table 1 were considered to be uncertain parameters to be used in the UQ analysis. Generally pressure of the gasifier system stays constant with little variations. But for demonstrating the effect of pressure on coal devolatilization and capability of C3M, pressure has been considered as an input uncertainty. In a given gasifier reactor system, one can have different temperature zones, also at times it's difficult to measure the exact temperature of the particle inside the reactor. Along with that, the coal particle can experience range of heating rates in an actual gasifier, hence it is hard to predict the exact heating rate for the coal particle. However, for the demonstration purposes of this study all uncertainties were considered as aleatory.

Table 1 Survey for the identification and characterization of all sources of uncertainty for the problem in consideration. Importance rank

Uncertain input parameters (units)

Variable name

The most likely value (n) or the nominal value

Minimum (value or % of n)

Maximum (value or % of n)

Justification for the provided “most likely value” and lower/upper bounds (provide reference citations)

Classification of uncertainty

1 2 3 4 5

Heating rate (°C/s) Temperature (°C) Pressure (kPa) Particle diameter (μm) Residence time (s)

HR Tp P dp T

5000 926 1500 100 5

200 500 861 50 1

9727 1010 3447 200 10

Domain expert experience [3,42] [3,19,42] [19,44] Domain expert experience

Aleatory Aleatory Aleatory Aleatory Aleatory

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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Fig. 3. Histogram for (a) heating rate and (b) temperature showing the distribution of the 10,000 sample values used in the Monte Carlo simulation.

Uncertainty quantification analysis often employs propagation of uncertainties to better understand their effect on the quantities of interest through a Monte Carlo simulation. When the computational models are expensive, a surrogate model is employed to perform the Monte Carlo simulation. As the computational cost (in terms of wall clock time required for solution) of C3M was insignificant, direct Monte Carlo simulation was employed for propagating the uncertainties without the need to construct a surrogate model and perform the MC on it. An example of surrogate model based Monte Carlo simulation can be found in Gel et al., [11]. The input uncertainties were assumed to be of the aleatory type, hence they can be characterized with probability distribution functions. For the scope of this study, a Normal distribution with a prescribed mean and standard deviation was used for all three input parameters (temperature, pressure, and heating rate) consistent with the typical operating ranges for a transport gasifier. Fig. 3(a) shows the histogram of the heating rate values used in Monte Carlo simulation with 10,000 samples. The histogram was generated by sampling from a Normal distribution with a mean of 3000 °C/s and a standard deviation of 1000 °C/s, which is truncated between the lower and upper bounds of 200 °C/s

and 9727 °C/s, respectively. Fig. 3(b) shows the histogram of temperature based on a Normal distribution with a mean of 800 °C and standard deviation of 100 °C, which was bounded between 500 °C and 1010 °C. Finally, the third uncertain input parameter, i.e., pressure was also characterized with a Normal distribution (mean = 2000 Pa, standard deviation = 500 Pa) as shown in Fig. 4. The UQ toolbox, PSUADE was used to generate 10,000 samples for each of the three input parameters with random drawings from the prescribed distributions. Then direct Monte Carlo simulation was performed by using samples obtained from random drawings for the input parameters and running C3M model with these sample values. Along with these three input parameters, residence time of 5 s (so that complete devolatilization occurs), particle diameter of 100 μm were chosen for Powder River Basin (PRB) coal (Fuel type). As a result for each of the response variables 10,000 outputs were generated. A histogram and empirical cumulative distribution function (eCDF) can be used to visualize the effect of the input uncertainties considered. Figs. 5 to 11 show the histogram of the response variables, i.e., CO, CO2, Tar, H2, H2, CH4 and Volatile Matter species. The Monte Carlo simulations show that with the prescribed variability in input parameters (heating rate, temperature and pressure), the mean CO species mass fraction will be 0.1244 and there will be some variability with standard deviation of 0.0086. Similarly, the variability observed for CO2 species mass fraction is shown in Fig. 6. On the other hand, for the same prescribed uncertainty in input parameters, less variability is observed in tar species mass fraction as it can be observed from the

Fig. 4. Histogram for pressure showing the distribution of the 10,000 sample values used in the Monte Carlo simulation.

Fig. 5. Histogram of CO species.

Eight response variables or quantities of interest were selected from C3M output, which are shown in Table 2.

3.2. Propagate input uncertainties with direct Monte Carlo simulation

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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Fig. 6. Histogram of CO2 species. Fig. 8. Histogram of H2 species.

narrower distribution in Fig. 7. However, H2 species mass fraction shows substantially larger variation with a skew as shown in Fig. 8. Figs. 9 to 11 show the histogram plots for the remaining species, H2O, CH4 and Volatile Matter, respectively. Although H2O and CH4 histograms exhibit similar and typical Normal distribution, the volatile matter yield exhibits a skewed distribution similar to H2 but in the opposite direction. The solid line represents the fitted distribution provided by the statistical analysis software for the data obtained from 10,000 sample run Monte Carlo simulation. The empirical cumulative distribution function plots for each of the histogram plots are given in Figs. 12 to 18. Empirical CDF plots can provide more practical information for engineers and researchers as they assess the probability of a certain event occurring given the prescribed input uncertainties. For example, from Fig. 12, one can read the probability of CO species mass fraction being less than equal to 0.135 is 90%. Alternatively, the probability of CO species mass fraction being less than 0.135 and greater than 0.12 is about 60%. Another practical interpretation on how to use the information gained from uncertainty propagation may be gained by considering another response variable, i.e., CO2 species mass fraction eCDF as seen in Fig. 13. The probability for CO2 species mass fraction being less than or equal to 0.21 is 80%. If a design engineer is constrained due to some regulations with coal kinetics requiring the CO2 species to be ≤ 0.21 then 80% of the time could be achieved based on the current model prediction and with the prescribed input uncertainties. However, if the allowable limit is to achieve a mean value of the histogram, i.e., 0.205 then the probability reduces to slightly less than 50%. To increase

Fig. 7. Histogram of tar species.

this probability, the uncertainty in the input parameters needs to be reduced. This will require adequate assessment of which input parameter has the most significant influence on the CO2 species mass fraction, and a sensitivity analysis, which is presented in Section 3.4 attempts to answers this question quantitatively. Comparing the histogram and eCDF plots shown in Figs. 5 to 18, one can develop several practical insights. For example, the tar species mass fraction appears to be the least sensitive to uncertainty for the variability observed in the three input parameters. On the other hand, the H2 species mass fraction appears to be the most sensitive (as seen from Figs. 8 and 15 due to the skew of the right tail). Similarly, the effect of skewed distribution observed in Volatile Matter (Fig. 11) can be observed in the empirical CDF plot in Fig. 18 with a longer lower tail. These types of insights can play a crucial role in achieving robust design where the process is tolerant or less sensitive to fluctuations in inputs. 3.3. Correlation of quantities of interest The investigation of correlation between response variables is another useful analysis that can be performed as part of the UQ process in order to gain better insight into the uncertainty in predicted results. Given the prescribed input uncertainties, the correlation matrix shows how each species are correlated with each other. In other words, the correlation is a measure of the strength of linear association between two numeric variables. Table 3 shows the correlation matrix computed for the quantities of interest based on the 10,000 sample Monte Carlo simulation results. When the absolute values of the correlation matrix

Fig. 9. Histogram of H2O species.

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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Fig. 10. Histogram of CH4 species.

are close to 1, this shows a strong correlation between variables, e.g., H2 and CO, H2O and CO2, CH4 and H2O. Values closer to zero indicate no correlation whereas values in between reflect weak correlations. Negative values indicate inverse correlation, e.g., CO and CO2 are weakly and inversely correlated, i.e., when CO increases then CO2 decreases. Table 3 shows that there is a positive correlation between the devolatilization yield of CO and H2 along with CO2 and H2O, similar positive trends between these devolatilization gas species yield were reported by Weiland et al. [42] with PRB coal and Serio et al. [33] with Pittsburgh No.8 at similar operating conditions. This serves as a strong evidence of the positive correlation reported in Table 3, i.e., 0.9836. The scatter plot shown in Fig. 19 is simply the visual representation of the correlation matrix provided in Table 3 obtained by plotting the data from Monte Carlo simulations. The diagonal with response variable name shows the histograms for each variable (as shown in Figs. 5 to 8). The colored ellipses in each plot would contain about 95% of the data if both X and Y were normally distributed (as seen from histograms this may not be the case all of the time). Skinny, tilted ellipses are a graphical depiction of a strong correlation. Ellipses that are almost circles are a graphical depiction of a weak correlation.

Fig. 12. Empirical CDF for CO.

Fig. 13. Empirical CDF for CO2.

3.4. Sensitivity analysis Sensitivity Analysis (SA) is an important component of the UQ analysis as it can identify the input parameters that contribute the most to the variability observed in the response variables and can enable engineers to allocate their limited resources to measure those parameters more accurately or try to reduce the uncertainty. The primary goal of

Fig. 11. Histogram of VM species.

sensitivity analysis is to answer questions like “which of the uncertain input parameters is more important in determining the uncertainty in one of the output factors”, or “if the uncertainty in one of the input

Fig. 14. Empirical CDF for tar.

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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Fig. 15. Empirical CDF for H2.

Fig. 17. Empirical CDF for CH4.

parameters can be eliminated, which parameter should be chosen to reduce most of the variance in the output?” Saltelli [31]. In this study, PSUADE was used to conduct Sobol's total sensitivity analysis using 1000 numerical integrations Saltelli et al. [32]. The results of the sensitivity analysis are summarized in Fig. 20. Most of the experimental studies done in the literature were performed by changing one parameter (temperature/pressure/heating rate) in a run, where in this UQ study the effect on devolatilization product yield is the combination of all three together. Temperature appears to have the most influence on the response variables among the three input parameters deciding devolatilization yield. This sensitivity relates to the findings of Matsuoka et al. [22] where they reported an increase in H2, CH4, CO and CO2 yields, along with decrease in the yields of H2O and tar with respect to increasing temperature. Chen et al. [7] and group also reported the devolatilization product yield of low rank coal between temperature 400 and 1100 °C at 1 bar and 50 bar pressure. They observed that the yield of CO and H2 are majorly affected by temperature rather than the pressure tested. A similar effect of temperature on the yield of H2 was reported by Chen et al. [8]. A study performed by Gibbins and Kandiyoti [12], on Pittsburgh No. 8 reported the increase in total volatile yield as a major function of temperature compared to heating rate that supports the finding of sensitivity study shown by our model. All surveyed literature

concludes that with an increase in temperature, more volatiles are emitted from the coal. The majority of the variability observed in H2 species mass fraction can be associated with the uncertainty in temperature (i.e., nearly 100% due to temperature). So to reduce the variability in H2 (as observed with skewed histogram in Fig. 8), reducing the uncertainty in temperature will have the highest impact as opposed to the other two input parameters. On the other hand, tar species is the least sensitive response variable to the fluctuations in temperature but quite sensitive to heating rate in the chosen range of input variation.

Uncertainty quantification in chemically reacting multiphase flows plays a critical role in robust design and optimization of fossil fuel based energy production systems such as coal gasifiers. In a previous UQ study, uncertainties in a computational fluid dynamics code for gasifiers were addressed [38,48]. The current study addresses the uncertainties affecting the chemical reactions taking place during coal conversion and specifically focuses on coal kinetics. As part of this study, the effect of uncertainty in three key input parameters (heating rate, temperature and pressure) of C3M based computational coal kinetics model was investigated through non-intrusive parametric

Fig. 16. Empirical CDF for H2O.

Fig. 18. Empirical CDF for VM(daf).

4. Summary and conclusions

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

A. Gel et al. / Powder Technology xxx (2014) xxx–xxx

9

Table 3 Correlation matrix for quantities of interest 1 to 6. Multivariate Correlations

CO CO2 tar H2 H2O CH4

CO

CO2

tar

H2

H2O

CH4

1.0000 −0.4990 −0.3964 0.9087 −0.4965 −0.5003

−0.4990 1.0000 −0.5844 −0.6626 0.9836 0.9802

−0.3964 −0.5844 1.0000 −0.1835 −0.5870 −0.5804

0.9087 −0.6626 −0.1835 1.0000 −0.6586 −0.6615

−0.4965 0.9836 −0.5870 −0.6586 1.0000 0.9802

−0.5003 0.9802 −0.5804 −0.6615 0.9802 1.0000

uncertainty propagation. PSUADE, a UQ toolbox from Lawrence Livermore National Laboratory was employed to perform UQ analysis. Due to the low cost of the computational model, a direct Monte Carlo simulation with 10,000 samples was performed. The response variables were species mass fractions such as CO, CO2, H2, tar, H2O, and CH4. The preliminary results show that tar species appear to be least sensitive to the prescribed uncertainties in input parameters, whereas H2 appears to be the most sensitive one. The correlation among the response variables was also investigated by computing the correlation matrix. The correlations demonstrate the findings of yield of devolatilization. The positive correlation trends between CO and H2, CO2 and H2O along with CH4 and CO2 support findings in the literature. Additional data from experimental observations are needed to support the negative correlation between CO and CO2. As part of the UQ process, a sensitivity analysis was performed based on Sobol Total Indices methodology implemented in PSUADE. The sensitivity analysis clearly demonstrates the pronounced effect of temperature on H2, VM and CO species mass fractions compared to the other two input parameters. Tar species appear to be the least affected

Fig. 20. Sensitivity analysis results based on Sobol Total Sensitivity Indices.

by temperature as heating rate seems to have more impact on the variability observed for tar. Although temperature was found to be the dominant input parameter, it should be kept in mind that in this UQ study the effect on devolatilization product yield is the combination of all three together. Also temperature is easier to regulate, control and predict in the reactor setting than heating rate, hence in the future it will be a key parameter for UQ studies. In order to use the presented methodology in computational modeling of coal gasifiers, several enhancements need to be incorporated. For this purpose, the preliminary study presented in this paper will be extended to include uncertainty in coal characteristics such as proximate and ultimate analysis with additional response variables such as

Fig. 19. Scatter plot showing the correlations between response variables 1 to 6.

Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024

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A. Gel et al. / Powder Technology xxx (2014) xxx–xxx

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Please cite this article as: A. Gel, et al., Application of uncertainty quantification methods for coal gasification kinetics in gasifier modeling — Part 1: Coal devolatilization, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.01.024