RSM is performed for the gasification of eucalyptus wood sawdust. We plot the Pareto chart. This chart indicates that only x1, x2, x3 and x4 are significant in agreement with the conclusions reported in Ref. 1
Experiment design matrix with model responses
​​
In[]:=
tbl=Join[{{"run #",Style["ER",Darker@Red],Style["dp (μm)",Darker@Red],Style["T (K)",Darker@Red],Style["SBR",Darker@Red],Style["H2 (vol%) ",Darker@Blue],Style["CO2 (vol%)",Darker@Blue],Style["Utility",Darker@Blue],Style["H2 (vol%) ",Darker@Green],Style["CO2 (vol%)",Darker@Green],Style["Utility",Darker@Green]}},{{1.,0.2,550.,1050.,1.5,35.16,28.84,4.29,36.06,28.66,4.36},{2.,0.,550.,1050.,1.5,46.77,17.69,7.59,41.55,20.25,6.03},{3.,0.4,100.,900.,0.5,27.08,39.10,1.51,29.62,39.22,2.06},{4.,0.,100.,900.,0.5,46.45,19.21,7.39,46.27,18.73,7.38},{5.,0.4,1000.,900.,0.5,36.23,41.26,3.97,32.5,42.32,2.96},{6.,0.,100.,900.,2.5,32.87,21.81,4.16,30.83,22.86,3.61},{7.,0.4,100.,1200.,0.5,38.44,33.78,4.82,38.29,33.11,4.78},{8.,0.4,100.,1200.,2.5,39.58,34.96,5.01,35.81,37.31,3.85},{9.,0.,1000.,1200.,2.5,51.83,15.95,8.65,48.57,16.24,7.97},{10.,0.2,100.,1050.,1.5,31.35,30.29,3.21,32.91,28.85,3.71},{11.,0.,1000.,1200.,0.5,52.19,14.37,8.88,54.92,13.76,9.4},{12.,0.4,1000.,1200.,0.5,38.45,33.79,4.82,39.76,33.14,5.23},{13.,0.2,1000.,1050.,1.5,39.54,27.34,5.41,37.68,28.84,4.89},{14.,0.4,100.,900.,2.5,23.25,42.57,0.03,21.32,42.76,0.34},{15.,0.2,550.,1200.,1.5,47.03,24.01,7.14,45.22,24.39,6.85},{16.,0.2,550.,1050.,2.5,27.85,32.24,2.07,32.54,29.49,3.44},{17.,0.4,550.,1050.,1.5,24.29,42.38,0.43,29.21,39.89,1.96},{18.,0.4,1000.,1200.,2.5,39.57,34.97,5.01,40.55,35.02,5.17},{19.,0.,100.,1200.,2.5,37.39,20.83,5.36,41.92,19.35,6.51},{20.,0.2,550.,1050.,0.5,44.86,23.67,6.75,39.87,26.48,5.35},{21.,0.,100.,1200.,0.5,52.10,14.21,8.89,51.53,14.56,8.82},{22.,0.4,1000.,900.,2.5,27.62,43.48,1.51,27.46,43.53,1.44},{23.,0.,1000.,900.,2.5,37.94,22.55,5.36,38.89,22.8,5.53},{24.,0.2,550.,900.,1.5,34.54,31.04,4.02,36.05,30.73,4.27},{25.,0.,1000.,900.,0.5,48.02,22.93,7.39,51.07,20.99,8.42}}];
In[]:=
tbl//TableForm
Out[]//TableForm=
In[]:=
low={0,100,900,0.5};high={0.4,1000,1200,2.5};
In[]:=
mid=0.5(low+high)
Out[]=
{0.2,550.,1050.,1.5}
In[]:=
halfrange=0.5(high-low)
Out[]=
{0.2,450.,150.,1.}
In[]:=
codedvar=Table[(tbl[[i,j+1]]-mid[[j]])/halfrange[[j]],{i,2,26},{j,1,4}]
Out[]=
{{0.,0.,0.,0.},{-1.,0.,0.,0.},{1.,-1.,-1.,-1.},{-1.,-1.,-1.,-1.},{1.,1.,-1.,-1.},{-1.,-1.,-1.,1.},{1.,-1.,1.,-1.},{1.,-1.,1.,1.},{-1.,1.,1.,1.},{0.,-1.,0.,0.},{-1.,1.,1.,-1.},{1.,1.,1.,-1.},{0.,1.,0.,0.},{1.,-1.,-1.,1.},{0.,0.,1.,0.},{0.,0.,0.,1.},{1.,0.,0.,0.},{1.,1.,1.,1.},{-1.,-1.,1.,1.},{0.,0.,0.,-1.},{-1.,-1.,1.,-1.},{1.,1.,-1.,1.},{-1.,1.,-1.,1.},{0.,0.,-1.,0.},{-1.,1.,-1.,-1.}}
Coded variables (The central composite design (CCD) technique is employed to conduct the optimization analysis).
In[]:=
codedvar//TableForm
Out[]//TableForm=
0.
0.
0.
0.
-1.
0.
0.
0.
1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
1.
1.
-1.
-1.
-1.
-1.
-1.
1.
1.
-1.
1.
-1.
1.
-1.
1.
1.
-1.
1.
1.
1.
0.
-1.
0.
0.
-1.
1.
1.
-1.
1.
1.
1.
-1.
0.
1.
0.
0.
1.
-1.
-1.
1.
0.
0.
1.
0.
0.
0.
0.
1.
1.
0.
0.
0.
1.
1.
1.
1.
-1.
-1.
1.
1.
0.
0.
0.
-1.
-1.
-1.
1.
-1.
1.
1.
-1.
1.
-1.
1.
-1.
1.
0.
0.
-1.
0.
-1.
1.
-1.
-1.
Forming MD (the Computation Matrix)
In[]:=
M=codedvar;
In[]:=
x1=Transpose[M][[1]]
Out[]=
{0.,-1.,1.,-1.,1.,-1.,1.,1.,-1.,0.,-1.,1.,0.,1.,0.,0.,1.,1.,-1.,0.,-1.,1.,-1.,0.,-1.}
In[]:=
Dimensions[x1]
Out[]=
{25}
In[]:=
x2=Transpose[M][[2]]
Out[]=
{0.,0.,-1.,-1.,1.,-1.,-1.,-1.,1.,-1.,1.,1.,1.,-1.,0.,0.,0.,1.,-1.,0.,-1.,1.,1.,0.,1.}
In[]:=
x3=Transpose[M][[3]]
Out[]=
{0.,0.,-1.,-1.,-1.,-1.,1.,1.,1.,0.,1.,1.,0.,-1.,1.,0.,0.,1.,1.,0.,1.,-1.,-1.,-1.,-1.}
In[]:=
x4=Transpose[M][[4]]
Out[]=
{0.,0.,-1.,-1.,-1.,1.,-1.,1.,1.,0.,-1.,-1.,0.,1.,0.,1.,0.,1.,1.,-1.,-1.,1.,1.,0.,-1.}
In[]:=
MD=Transpose[{Table[1.0,{i,1,25}],x1,x2,x3,x4,x1x1,x2x2,x3x3,x4x4,x1x2,x1x3,x1x4,x2x3,x2x4,x3x4}];
In[]:=
Dimensions[MD]
Out[]=
{25,15}
In[]:=
Grid[MD,Frame->All]
Out[]=
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
-1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
1.
-1.
-1.
-1.
1.
1.
1.
1.
-1.
-1.
-1.
1.
1.
1.
1.
-1.
-1.
-1.
-1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
-1.
-1.
1.
1.
1.
1.
1.
-1.
-1.
-1.
-1.
1.
1.
-1.
-1.
-1.
1.
1.
1.
1.
1.
1.
1.
-1.
1.
-1.
-1.
1.
1.
-1.
1.
-1.
1.
1.
1.
1.
-1.
1.
-1.
-1.
1.
-1.
1.
1.
-1.
1.
1.
1.
1.
1.
1.
-1.
1.
1.
-1.
-1.
1.
1.
-1.
1.
1.
1.
1.
1.
1.
1.
-1.
-1.
-1.
1.
1.
1.
1.
0.
-1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
1.
-1.
1.
1.
-1.
1.
1.
1.
1.
-1.
-1.
1.
1.
-1.
-1.
1.
1.
1.
1.
-1.
1.
1.
1.
1.
1.
1.
-1.
1.
-1.
-1.
1.
0.
1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
1.
1.
-1.
-1.
1.
1.
1.
1.
1.
-1.
-1.
1.
1.
-1.
-1.
1.
0.
0.
1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
-1.
-1.
1.
1.
1.
1.
1.
1.
1.
-1.
-1.
-1.
-1.
1.
1.
0.
0.
0.
-1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
-1.
-1.
1.
-1.
1.
1.
1.
1.
1.
-1.
1.
-1.
1.
-1.
1.
1.
1.
-1.
1.
1.
1.
1.
1.
1.
-1.
1.
-1.
1.
-1.
1.
-1.
1.
-1.
1.
1.
1.
1.
1.
-1.
1.
-1.
-1.
1.
-1.
1.
0.
0.
-1.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
-1.
1.
-1.
-1.
1.
1.
1.
1.
-1.
1.
1.
-1.
-1.
1.
H2 (vol %)
Using LinearModelFit to get the model

Statistical and ANOVA analyses

A small p - value (typically < 0.05) means the variable significantly contributes to explaining the outcome . A large p - value suggests the variable may not be important in the model and should be dropped from the model equation .
Predicted responses
Pareto Chart of Standardized Effects with significance threshold (dotted red line).
This chart confirms that only x1, x2, x3 and x4 are significant.

References

◼
  • [1] A. Sharma and R. Nath, H2-rich syngas production from gasification involving kinetic modeling: RSM-utility optimization and techno-economic analysis, RSC Adv., 13 (15) 2023, pp. 10308-10321, DOI: https://doi.org/10.1039/D3RA00287J

    • CITE THIS NOTEBOOK

    Pareto chart for gasification of eucalyptus wood sawdust​
    by Housam Binous and Ahmed Bellagi
    Wolfram Community, STAFF PICKS, November 13, 2025
    ​https://community.wolfram.com/groups/-/m/t/3574355