Numerical and Statistical Analyzing of the Effect of Operating

May 23, 2017 - Numerical and Statistical Analyzing of the Effect of Operating Parameters on Syngas Yield Fluctuation in Entrained Flow Coal Gasificati...
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Numerical and Statistical Analyzing of the Effect of Operating Parameters on Syngas Yield Fluctuation in Entrained Flow Coal Gasification Using Split-Plot Design Jinchun Zhang,† Jinxiu Hou,*,‡,§ Yuzhong Yang,† Qiang Zeng,† Liyun Wu,† Faquan Li,† and Jinshan Ma† †

School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China State Key Laboratory Cultivation Base for Gas Geology and Gas Control, School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China § College of Chemistry and Chemical Engineering, Taiyuan University of Technology, Taiyuan 030024, China ‡

ABSTRACT: For a coal-based production system with entrained flow coal gasification, the fluctuations in syngas yield (SY) affect the stability of downstream sections directly. The focus of this study is to analyze how some important operating parameters affect these fluctuations in SY for a typical entrained flow coal gasification, Shell coal gasification process (SCGP). In this study, we carried out a set of numerical simulation experiments in Aspen Plus simulator for a demonstration SCGP gasifier. These experiments were arranged using a special design of experiment (DoE) method, split-plot design. Then we systematically analyzed the effects of pressure (P), oxygen to coal ratio (O/C), and steam to coal ratio (S/C) on the Range and standard deviation (StDev) of SY using some statistical techniques. The results show that split-plot design is an appropriate DoE method to investigate and analyze the effects of the operating parameters on the fluctuations in SY. For the demonstration SCGP process, the fluctuations in SY are mainly affected by P and O/C. Among them, P is the dominant factor and O/C is an important factor, while S/C influences the fluctuations in SY slightly. The lowest Range and StDev of SY could be obtained only when P is at a higher level and O/C as well as S/C is at a lower level. This is the ideal condition for realizing a moderate robust syngas production.

1. INTRODUCTION Of all fossil fuels, coal is a kind of relatively cheap and abundant natural resource.1 However, clean-coal technology is more and more important and urgent with the increasing environmental concerns in the utilization of coal in recent years.2,3 Coal gasification provides a flexible and clean way to turn coal into high-value products, which help to reduce the dependence on natural gas and oil.4 The target product of coal gasification is syngas, which is a gas mixture consisting primarily of hydrogen (H2) and carbon monoxide (CO).5 The syngas is a very useful feedstock for energy generation and chemical production, such as ammonia, methanol, Fischer−Tropsch liquids, and so on.6 Generally the gasification reactors can be categorized into three groups: moving bed gasifiers, fluid bed gasifiers, and entrained flow gasifiers. Among these gasifiers, the entrained flow gasifiers have been the preferred technology for bulk syngas production due to their several advantages over other types.6 As one of the most important units of a coal-based production system, the gasifier generally locates at the forepart of the whole system and affects the following sections directly. Therefore, the realization of a successful system critically depends on the steady supply of syngas, which is mainly influenced by some operating parameters (pressure (P), oxygen/coal ratio (O/C), and steam/ coal ratio (S/C), etc.) and coal quality (contents of fixed carbon, ash, and moisture, etc.).7 In recent years, massive amounts of literature about the effects of operating parameters on the performance of an entrained flow gasifier have been reported. For instance, Park et al.8 investigated © XXXX American Chemical Society

the effects of O/C ratio and S/C ratio on the syngas contents for a 300 MWe demonstration entrained flow gasifier, a Shell coal gasification process (SCGP) gasifier, in Korea by a threedimensional (3D) computational fluid dynamics (CFD) simulation model. Chen et al.9,10 studied the influences of air/coal ratio, coal type, and particle size on product gas composition as well as other gasification performances for a two-stage air blown entrained flow coal gasification process. Guo et al.11 investigated the effects of O/C and S/C on gasification for a 15−45 ton/day pilot-scale opposed-multiburner gasifier. Kong et al.12 built a compartment simulation model using Aspen Plus process simulator for a Texaco gasifier and discussed the influences of O/C and the coal slurry concentration on gasification performance. Other similar reports can be seen in the literature.13−15 Generally, the main flows spouted into an entrained flow gasifier can be divided into two types: one is the gasifying agent (oxygen or steam); the other is coal flow (dry pulverized coal or coal−water slurry). Ideally these flows are expected to be steady to achieve a stable syngas production. However, the syngas yield (SY) usually tends to be fluctuant rather than constant in actual production, which is mainly due to the nonuniform characteristic of the granular coal flow. In practice, when analyzing the influence of some inputs on outputs for a system, there are two different objects: one is the Received: February 2, 2017 Revised: May 20, 2017 Published: May 23, 2017 A

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Energy & Fuels so-called “positional effect analysis” and the other is the so-called “dispersion effect analysis”.16,17 Figure 1 shows the difference

very suitable for the situation of the present study. A split-plot experiment is regarded as a blocked experiment, where the blocks themselves serve as experimental units for a subset of the levels of experimental units.18 Thus, there are two levels of experimental units. The blocks are regarded as whole plots, while the experimental units within blocks are called split plots or split units. Namely, the split-plot design has a nested blocking structure: split plots are nested within whole plots. Figure 2 shows the basic structure of a split-plot design with two factors.

Figure 1. Comparison of “positional effects” and “dispersion effects”.

between these two types of objects. Panel a is to compare the specific value of yA, yB, and yC to see how x affects y. Conversely, panel b is to compare the Range or standard deviation (StDev, σ) for xA, xB, and xC to see how x affects the dispersions of y. In reviewing the current studies, many of them obviously belong to positional effect analysis, because the focuses of these studies are on the specific values of some performance indexes for entrained flow coal gasification. Differing from these studies, the primary objective of the present study is to investigate how the operating parameters affect the fluctuations of SY, and we focus on the dispersion of SY rather than its specific value. Studying this problem is of significance because it would help to gain a steady syngas production and further to obtain stable reactions for downstream processes. Split-plot design is a design of experiment (DoE) method which is needed when the levels of some treatment factors are more difficult to change during the experiment than those of others.18 One of the important applications of such experiment is for reducing the variation and achieving a robust process.19,20 The split-plot designs were originally developed for use in agricultural experiments,18 and lately have drawn attention in the industry. For instance, Alexandrino et al.21 used this type of experiment method to study the homogeneity of the drug paracetamol loaded in films. Antohe et al.22 validated the optimal annealing conditions applying this type of DoE method when they analyzed thermal annealing of gold coated fiber optic surfaces for improved plasmonic biosensing. Other applications of this type of DoE method can be seen in the literature.20,23−25 However, there are still few reports on the application of this type of design in energy research, especially in coal gasification research. In brief, the motivation of this study is that we attempt to investigate how some important operating parameters (P, O/C, and S/C) affect the fluctuations of SY, which is a very vital problem for stable and safe syngas production in entrained flow coal gasification. And to realize this purpose, we used split-plot design as the main DoE method. In this study, we carried out a set of numerical simulation experiments in Aspen Plus simulator for the demonstration SCGP project reported in Park’s work8 according to its actual operational conditions. Then we systematically analyzed the effects of P, O/C, and S/C on the Range and StDev of SY using some statistical techniques.

Figure 2. Basic structure of a simple split-plot design with two factors. As shown in Figure 2, factor A is the whole-plot factor and factor B is the split-plot factor. A lot of experiments involve two types of factors, some with levels that are hard to change due to the limitations of expenses or technology and others with levels that are relatively easy to change. Split-plot designs are needed when the levels of some treatment factors are more difficult to change during the experiment than those of others. Unlike in a completely randomized experiment in which all factors are reset an equal number of times, in the split-plot design, the levels of the hard-to-change factor or factors are assigned to the whole plot and the levels of the easyto-change factor or factors are assigned to the split plot. A split-plot experiment is performed by fixing the levels of the hard-to-change factors and then running all the combinations of the easy-to-change factor levels; then, a new setting in the hard-to-change factors is selected, and the process is repeated. The nested blocking structure of split-plot design that contains both hard-to-control factors and easy-to-control factors makes such experimental arrangement of particular value not only for generally specific response analysis (positional effect analysis) but also for solving the robustness problem (dispersion effect analysis). Robustness of a product or process means that it is insensitive to some noise factors or environmental variations.26 In the product or process design practice, the noise factors (usually hard-to-control factors) could be assigned in the whole plot and the design factors assigned in the split plot; then such experiments could be employed in analyzing the robustness of a process to the noise factors by evaluating the responses’ variations that derived from the noise factors. In application of split-plot design for robust analysis, one of the earlier examples is Michael’s detergent design27 with the purpose to make its washing ability to be not much affected by some uncertainty using environmental conditions such as the hardness of the water, the temperature of the wash, and so on; even that was largely unnoticed at that time. For years thereafter, Box and Jones27 and other researchers19,28 made a series of studies on split-plot design for robust problems. However, many of them are traditional; that is, the cases discussed in these studies are that the split-plot design is constructed by factorial designs. Besides, variance analysis (ANOVA) method is used to simultaneously estimate the effects of whole plot and split plot, as well as the error of the two types of plots. The variations of responses are estimated based on the individual variations rather than combined ones of noise factors by propagation of error (POE) method. This is so complicated and, in many cases, there are insufficient degrees of freedom for the estimations. In fact, there is no sense in estimating the noise factors’ effects for robust problem because they are the sources of the responses’ variations in themselves and should be treated as whole noise environmental conditions for robust analysis. Therefore, some statisticians advise the response surface methodology (RSM) designs instead of factorial designs which should be used to arrange the split-plot units so as to gain direct solutions and be convenient to statistical analysis.18,29−31

2. METHOD AND EXPERIMENT 2.1. Spilt-Plot Design. The choice of split-plot design as the main DoE method in the present study is due to its special structure, which is B

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Figure 3. Flow scheme of a typical SCGP process. The present study focuses on the dispersion effect of operating conditions on SY for entrained flow coal gasification, which belongs to a “robust” analysis problem. In the practical operations of a Shell entrained flow gasifier, the gasifying agents are always in gaseous phases, so they are easy to control. Conversely, the coal flow is usually granular, which makes it hard to realize steady transportation. And it is wellknown that coal is not a pure component substance but one containing heterogeneous solids. The unstable coal flow and the nonuniform component of coal particles are the main cause of the fluctuations in SY. It is very hard to control these uncertainties in coal flow. This is the typical situation for applying robust split-plot design. Thus, to analyze the influences of the operating parameters on the fluctuations in SY, the split-plot design was used as the main DoE method in the present study. 2.2. SCGP Simulation Modeling. Although a number of commercial SCGP projects have been operated for many years, the practical information about the SCGP process is very little because of some technical restrictions. Besides, performing full-scale entity experiments of this process is so expensive due to its huge scale that it is impractical for many research entities. Therefore, numerical simulations have been one of most important approaches to understand the behavior of this process. This section presents the details of our simulation model for the SCGP process in Aspen Plus according to the demonstration project reported in Park’s work.8 2.2.1. SCGP Process. Figure 3 is the flow scheme of a typical SCGP process.8,32 In this process, raw coal is first ground to the suitable size and simultaneously dried. Milled and dried coal is then pneumatically transported to the pressurization and feeding system, and then it is introduced to the gasifier while oxygen and, in most cases, steam follows to the gasifier below the coal feeding zones. Furthermore, coal particles are carried out into the reactor by nitrogen. Slag, which mainly comes from the molten mineral content of the coal, flows down through the outlet at the bottom of the gasifier into a water-filled compartment, and then it is quenched and removed. Hot gas with entrained fly slag is then introduced to a syngas cooler to be cooled. Then the cooled syngas is introduced into the dry solids removal unit where the entrained fly ash is removed from the syngas. Finally, the syngas is introduced to the water washing unit to be cleaned and thereafter transported to further treating to remove gaseous pollutants such as hydrogen chloride, sulfides, and ammonia, etc. 2.2.2. Simulation Model. In this study, we built a kinetics-based model to simulate the SGCP process in Aspen Plus. Unlike a CFD-based “‘gasifier’” model33 for which the gasifier’s detailed geometry should be critically considered, Aspen Plus provides a “gasification” model,12 also called reactor network model,34,35 that simulates the coal gasification process according to the reaction stages. Generally, after the injections of the feedstock (coal, oxygen, and steam), the reaction processes undergo four stages in turn with the reactants moving up in the gasifier: coal pyrolysis (devolatilization), volatile combustion, char gasification,

and gas-phase homogeneous reactions (Figure 4). These processes were simulated by the appropriate reactor blocks in Aspen Plus

Figure 4. Reaction processes in the gasifier. (as shown in Figure 5) in the present model. Total mass balance was merely considered in the coal pyrolysis process, so it was simulated with a RYield reactor labeled as DECOM. The volatile combustion process and the char gasification process take place in the way of plug flow; therefore, both of them were modeled with RPlug reactor labeled as COMB and CHARGASF, respectively. While in the final stage, the reactions take place in gas phase and are similar to the ideal gas mixture, so they were simulated with a continuous stir reactor, RCSTR reactor, with the label of HOMORAC. Other blocks were used for helping these four reactors to simulate the above processes. Because coal, as well as char and ash, is actually a mixture of different compounds, they are always modeled as unconventional components solids in Aspen Plus. So their enthalpy and density were respectively calculated by HCOALGEN and DCOALIGT models, which are both built-in models in Aspen Plus. Moreover, the properties of mixed conventional components were calculated by RK-SOAVE method which is also a built-in method in Aspen Plus. Table 1 shows the reactions and their kinetic parameters involved in the above four processes, which are mainly from Park’s work except that about coal pyrolysis. For entrained flow coal gasification, the temperature in the gasifier is so high (>1000 °C) that the devolatilization of pulverized coal is sufficient. Therefore, the Merrick method36 based on mass balance has been recommended to determine the spices yield after coal pyrolysis by many researchers.34,37 This method was also used in our simulation model. C

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Figure 5. Simulation diagram of SGCP process in Aspen Plus. The dry pulverized coal is assumed to be fully devolatilized into the following products: char (C(s)), CO, CO2, CH4, H2, N2, S, and C6H6, where C6H6 represents the tar, which is suggested in the Aspen Plus user’s guide.38 All of the char and ash are assumed to have no organic matter. The ash was considered chemically inert, but the change of

thermodynamic properties of the particle was considered in the reaction process based on the enthalpy calculation and RK-SOAVE method. For the devolatilization process, the Merrick method can predict the spices yield based on the ultimate analysis data of coal by solving mass balance equations:

where, ωdaf,i is the ultimate analysis data. Equation 1 includes two parts: (i) five global elemental balance equations about C, H, O, N, and S and (ii) three elemental equations describing the balance of the special yields and the ultimate analysis data about hydrogen and oxygen. The yields of H2, CH4, and C6H6 are associated with the initial hydrogen content. Because the temperature in the gasifier is so high, the yields of methane and tar are very little. Thus, we supposed the proportions of hydrogen contents of the above three spices in the original hydrogen ultimate analysis data to be 0.9:0.05:0.05. Similarly, the yields of CO and CO2 depend on the initial oxygen content. We suppose their oxygen proportions in the original oxygen ultimate analysis data to be 0.5:0.5. Only two hydrogen balance equations about the proportion of CH4 and C6H6 and one oxygen balance equation about the proportion of CO were involved in eq 1 in the present model due to the consideration of the degrees of freedom for solving equations. 2.2.3. Simulation Model Validation. A validation step was performed to test our simulation model with two cases: one is the actual data from the Demkolec demo IGCC facility in the Netherlands, and the other is an Aspen Plus simulation report from the National Energy Technology Laboratory (NETL) of the United States, which are reported in Park’s work and employed to be compared with the results from their CFD model so as to verify the correctness of their model. For the two cases, Drayton Coal and Illinois No. 6 Coal were gasified, respectively (Table 2). In the present study, we also compared our Aspen Plus simulation results with the reported data about these two cases, as well as the results of Park’s CFD model (Figure 6). As seen in Figure 6, the results of our modeling have a good agreement with the reported data as well as the results of Park’s CFD model, especially that of the efficient syngas (H2 + CO). This shows that our simulations model can provide reliable predictions for the later analysis.

2.3. Arrangement of Experiments. In the present study, the splitplot designs reformed by RSM was used to arrange the experiments. The fluctuation in SY is mainly caused by the unstable feed rate and nonuniform component of coal flow which usually are hard to control in actual production. So according to the arrangement principle of splitplot design,18 these factors should be treated as noise factors and assigned to the whole plot. While, the operating conditions (P, O/C, and S/C) are the main design variables, so these factors should be assigned to the split plot. The simulation experiments were carried out basically according to the operations of the demonstration SCGP gasifier reported by Park et al.,8 for which design coal was used with a feeding rate of 2450 tons/day. The component unevenness considered in this study mainly involves the variations of moisture and ash with the assumptions that they are from 2 to 5% and from 9 to 15%, respectively, while other components change correspondingly according to their original scales. Additionally, the coal feeding rate was assumed to vary from 28 to 29 kg/s. All of the above noise factors were set up in a 23−1 III fractional factorial design for the whole plot. The description of these factors and their levels are shown in Table 3. The corresponding analysis data of design coal and its feeding rate for the whole plot are presented in Table 4. The factors assigned to the split plot (P, O/C, and S/C) were set up by a RSM design, threefactor and three-level Box−Behnken design.39 The descriptions of these factors and their levels are shown in Table 5. The structure and details of these factors assigned in the Box−Behnken design39 are shown in Table 6.

3. RESULTS AND DISCUSSION 3.1. Numerical Experiment Results. The experiment results are listed in Table 7. In statistics, the variability of a variable usually can be characterized by two statistics: Range and StDev. Of these two statistics, the former describes a variable’s D

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Energy & Fuels Table 1. Main Reactions and Kinetic Parameters Used in the Simulation Model

Table 2. Coal and Operation Conditions Used in the Validation8 Drayton coal

Illinois no. 6 coal

proximate anal (wt %) moisture fixed carbon ash volatiles

coal

2.0 51.25 12.54 34.20

11.12 44.19 9.7 34.99

ultimate anal (wt %) moisture carbon hydrogen nitrogen sulfur ash oxygen

2.0 68.01 4.82 1.33 0.99 12.54 6.88

11.12 63.75 4.5 1.54 2.51 9.7 19.53

operating conditions pressure (MPa) temperature (K) feeding rate of coal (kg/s) oxygen/coal ratio (kg/kg) stream/coal ratio (kg/kg)

2.6 1900 21.86 0.88 0.08

4.2 1432 28.35 0.798 0.103

Figure 6. Comparisons between the results of our model and that of Park’s CFD model as well as the reported literature data.

so the fluctuations in SY are described by these two statistics. Additionally, for the sake of facilitating analysis, another two statistics, minimum (Min) and maximum (Max), are also listed in Table 7. 3.2. Response Surfaces Modeling. For analyzing experiments, building a response surface model is necessary to investigate the effects of design factors on the response.40 Generally the relationship between the inputs and outputs can be described as the following equation:

dispersion spectra while the latter measures its average volatility. Because the focus of this study is to investigate the influences of operational parameters (P, O/C, and S/C) on the fluctuations in SY, which are mainly caused by the noise factors (M, A, and F),

Y = f (X) + ε E

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There are many methods to build the regression model such as polynomial, artificial neural networks (ANN), and so on. Among them, the polynomial regression model, especially the quadratic polynomial regression (QPR) model,40 is usually used in many research works because of some of its advantages such as the simplicity and feasibility to perform, the convenience for statistical analysis, and so on. A standard form of QPR model is represented by

Table 3. Description of the Factors and Their Levels for the Whole Plot levels factors

−

+

units

description

M A F

2 9 28

5 15 29

% % kg/s

moisture content in coal ash content in coal feeding rate of coal

y ̂ = β0 +

Table 4. Analysis Data of Design Coal and Its Feed Rate for the Whole Plot + −−

−−+

−+−

+++

proximate anal (wt %) moisture fixed carbon ash volatiles

5 48.13 9 37.87

2 49.8 9 39.2

2 46.15 15 36.55

5 44.77 15 35.23

ultimate anal (wt %) moisture carbon hydrogen nitrogen sulfur ash oxygen

5 64.15 4.62 0.72 0.97 9.47 20.07

2 64.65 4.65 0.73 0.97 9.23 19.77

2 60.27 4.34 0.68 0.91 15.37 18.43

5 59.66 4.29 0.67 0.89 15.79 18.68

feeding rate of coal (kg/s)

28

29

28

29

mode

levels −

0

+

units

description

P S/C O/C

2 0.05 0.1

3 0.085 0.6

4 0.12 1.1

MPa kg/kg kg/kg

pressure stream/coal ratio oxygen/coal ratio

(3)

where ŷ is the predicted response, xi or xj the design factors, β0 the intercept, βi the linear coefficients, βij the interaction coefficients, and βii the quadratic coefficients. These above coefficients in the QPR model can be determined by the ordinary least-squares (OLS) method. In addition, the validities of the regression model are usually assessed by ANOVA with some statistics including F ratio, p value, R2, and Radj2. F ratio and p value signify the significance of the founded model. A smaller p value (p < 0.05) means that the explained variance of the regression model compared with the variance of the residuals is statistically significant at the 95% confidence level. R2 and Radj2 are usually used to measure the goodness of fit of the founded regression model toward the experimental data because they estimate the proportion of variation in the response that can be attributed to the regression model rather than to the residuals. In comparison, Radj2 provides a more accurate measurement than R2 because it takes the number of parameters in the model into consideration. Generally Radj2 lies within the Range of 0−1, and the closer its value is to 1, the higher goodness of fit the founded regression model has. Moreover, a P−P plot is often employed to test whether the residuals are subject to normal distribution by the Shapiro−Wilk test.40 A test that passes indicates the correctness of the founded regression model. This study is to investigate the “dispersion effect” rather than “positional effect” of operation parameters on the SY. Thus, the Range, as well as StDev, which describes the dispersion effect of SY, was taken as the response of interest. The QPR models about the Range and StDev of SY were founded with statistical software of Jmp. Additionally, to facilitate the followed analysis, the QPR models about the Min and Max of SY were also founded. These QPR models are present as follows:

Table 5. Description of the Factors and Their Levels for Split Plot factors

∑ βi xi + ∑ βiixi 2 + ∑ βijxixj

where Y is the observation response, X the design factors, ε the residuals, and f(...) the response surface regression function.

⎧ Range = 6.43 − 2.46P + 3.96(O/C) + 2.55(S/C) + 0.28P2 − 1.55(O/C)2 + 24.5(S/C)2 ⎪ − 0.2P(O/C) − 0.21P(S/C) − 5(O/C)(S/C) ⎪ ⎪ ⎪ StDev = 3.1 − 1.25P + 1.92(O/C) + 2.12(S/C) + 0.15P2 − 0.72(O/C)2 + 9.2(S/C)2 ⎪ − 0.13P(O/C) − 0.29P(S/C) − 2.14(O/C)(S/C) ⎪ ⎨ ⎪ Min = 20.6 − 11.1P + 36(O/C) + 34.1(S/C) + 1.66P2 + 1.08(O/C)2 − 91.5(S/C)2 ⎪ − 6.33P(O/C) − 2.79P(S/C) − 3.18(O/C)(S/C) ⎪ ⎪ 2 2 2 ⎪ Max = 27 − 13.5P + 40(O/C) + 37(S/C) + 1.93P − 0.47(O/C) − 68(S/C) − 6.53P(O/C) ⎪ − 3P(S/C) − 8.18(O/C)(S/C) ⎩

The ANOVAs about the founded QPR models are presented in Table 8. It can be found in this table that all p values are much smaller than 0.05 and all the values of Radj2 are very close to 1. This manifests the precision of the founded QPR models toward the experimental data. This is further verified by the residuals’ normal tests for each QPR model (Figure 7). For P−P plot, the locations of all points that are close to the reference line and the

(4)

significant statistic of the Shapiro−Wilk test, the p value, are greater than 0.05 show a good fitness of normal distribution. It can be obviously seen from Figure 7 that all points for each QPR model are very close to the reference lines, and all p values are much greater than 0.05. This indicates the residuals of each model fit the normal distribution well and the founded QRP models are correct. F

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preliminarily judge whether they are affected by the input parameters. Figure 8 describes the distributions of SY (Figure 8a) and their corresponding Range (Figure 8b) and StDev (Figure 8c) according to the run in the split plot. Here we can preliminarily find that the fluctuations in SY are not just affected by the noise factors (M, A, and F) but by the operational parameters (P, O/C, and S/C). Because the connecting lines according to each mode in the whole plot (Figure 8a) are not parallel to each other, and the Ranges (Figure 8b) as well as the StDevs (Figure 8c) according to each run have obvious differences, especially for the Range and StDev of SY in runs 1, 2, and 11 and that in runs 5 and 10. The former runs are distinctly greater than the latter ones. This shows that different level combinations of P, O/C, and S/C indeed affect the fluctuations in SY. Further, the t-test method was performed to identify the operating parameters’ effect on the Range and StDev of SY. When effect screening, there are generally two types of parameters’ effects: main effect and interaction effect. Figure 9 presents the ordered effect screening results of P, O/C, and S/C on the

Table 6. Structure of Three-Factor and Three-Level Box− Behnken Design for Split Plot run

mode

P

S/C

O/C

1 2 3 4 5 6 7 8 9 10 11 12 13

− −0 −+0 +−0 ++0 0−− 0−+ 0+− 0++ −0 − +0 − −0 + +0+ 000

2 2 4 4 3 3 3 3 2 4 2 4 3

0.05 0.12 0.05 0.12 0.05 0.05 0.12 0.12 0.085 0.085 0.085 0.085 0.085

0.6 0.6 0.6 0.6 0.1 1.1 0.1 1.1 0.1 0.1 1.1 1.1 0.6

3.3. Discussion. 3.3.1. Effect Screening. Intuitively observing the distributions of the responses is generally helpful to Table 7. Experiment Results whole plot split plot

SY (cum/s) for given mode

statistics

mode

run

+−−

−−+

−+−

+++

Min (cum/s)

Max (cum/s)

Range (cum/s)

StDev (cum/s)

−−0 −+0 +−0 ++0 0−− 0−+ 0+− 0++ −0− +0− −0+ +0+ 000

1 2 3 4 5 6 7 8 9 10 11 12 13

20.29 21.14 10.47 10.93 5.53 22.61 6.14 23.00 8.74 4.40 34.11 17.11 14.16

23.64 24.75 12.31 12.95 7.21 25.89 8.09 26.27 11.49 5.75 38.63 19.56 16.57

24.47 25.61 12.79 13.50 7.42 25.44 8.39 25.89 11.86 5.94 38.40 19.25 17.24

24.38 25.55 12.68 13.36 7.53 25.39 8.48 25.85 12.02 6.02 38.33 19.22 17.08

20.29 21.14 10.47 10.93 5.53 22.61 6.14 23.00 8.74 4.40 34.11 17.11 14.16

24.47 25.61 12.79 13.50 7.53 25.89 8.48 26.27 12.02 6.02 38.63 19.56 17.24

4.19 4.47 2.32 2.57 2.00 3.28 2.34 3.27 3.28 1.62 4.52 2.46 3.08

1.97 2.12 1.08 1.19 0.94 1.50 1.10 1.51 1.54 0.76 2.17 1.13 1.43

Table 8. ANOVA Test for the Founded Regression Models model (response)

terms

degrees of freedom

sum of squares

mean suqare

F ratio

p value

Range

model error total R2 Radj2 model error total R2 Radj2 model error total R2 Radj2 model error total R2 Radj2

9 3 12 0.9973 0.9895 9 3 12 0.9997 0.9986 9 3 12 0.9984 0.9952 9 3 12 0.9979 0.9917

10.35 0.007 10.357

1.149 0.002

491.31

0.0001

2.41 0.001 2.411

0.267 0.0002

984.53