Abstract 
Introduction
The response surface methodology (RSM) is an efficient way of optimizing chemical processes when one or more responses are influenced by multiple variables [1]. This methodology uses experimental data to fit a polynomial equation with mathematical techniques. RSM is able to take into account interactions between variables and quadratic variables [1]. To apply the RSM, a design of experiment (DOE) has first to be carried out in the range of interest of the variables for the studied response(s). There are different types of DOE: factorial, Doehlert, central composite and BoxBehnken. The choice of the DOE depends on the purpose of the study [1].
Various software can be used to generate the DOE and calculate the RSM. One of those is R and its package “rms”. The “rms” package is specific to DOE and RSM [2]. The advantage of R is of being opensource, having access to a huge amount of statistical packages, being easy to use and to customize.
In the present study, the optimization of subcritical water pretreatment of wheat straw (Triticum aestivum L.) has been assessed with a RSM using R. It has been optimized in the context of glucose production for its conversion into a cellulosic biofuels or biochemicals. For such productions, a thermic and/or chemical pretreatment of the biomass is needed to be able to enzymatically hydrolyze the cellulose to glucose. Without any biomass pretreatment, lignin prevents this hydrolysis [3].
Material and methods
The subcritical water pretreatment of wheat straw (Triticum aestivum L.) has been realized with a 1.3 liters batch reactor (4540 reactor of Parr). The cellulose, hemicelluloses and lignin content of the solid residue after pretreatment has been estimated based on the Van Soest method. A rotatable central composite design has been chosen as DOE to have a RSM with isovariance of the predicted response, and a secondorder polynomial quadratic equation made of an intercept, a linear, a quadratic and an interaction component.
R script for cellulose:
 Generate design of experiment (DOE):
doe < ccd(2, n0 = c(4,0), alpha="rotatable")
# 2 ? 2 variables
# n0 = c(4,0) ? 4 replicates of the central point
 Generate response surface (RSM) and statistical analysis of the response surface:
rsm.cel < rsm(formula = Cellulose ~ SO(Time, Temperature), data = doe)
# SO ? Second order polynomial equation
summary(rsm.cel)
# Value of the coefficients of the RSM and their significance
 Generate plots (2D and 3D):
contour(rsm.cel, ~ Time + Temperature, atpos = 3, main="Cellulose (g/100g)",
image = TRUE, img.col = terrain.colors(40), xlabs = c("Temperature (°C)", "Time (min)", "Time..min.", "Temperature...C."))
persp(rsm.cel, ~ Time + Temperature, atpos = 0, theta = 60, phi = 15, zlab="Cellulose (g/100g)", main="Cellulose (g/100g)", contour="colors", col = terrain.colors(40),
xlabs = c("Temperature (°C)", "Time (min)", "Time..min.", "Temperature...C."))
Results and discussion
Temperature of subcritical water pretreatment has a significant effect on the solid residue chemical composition (cellulose, hemicelluloses and lignin). The temperature effect is quadratic for cellulose and hemicelluloses content. Time of subcritical water pretreatment has no significant effect on the solid residue chemical composition.
The solid residue after subcritical water pretreatment has:
 increasing cellulose content until 190°C of pretreatment;
 decreasing hemicelluloses content with increasing temperature of pretreatment;
 increasing lignin content with increasing temperature of pretreatment.
R2=0.911 ; SEC=2.5 ; RPD=SDy/SEC=2.5 R2=0.955 ; SEC=3.8 ; RPD=SDy/SEC=3.5 R2=0.977 ; SEC=0.8 ; RPD=SDy/SEC=4.9
Figure 1. Cellulose, hemicelluloses and lignin content of the solid residue
after subcritical water pretreatment
Conclusions
Temperature is an important parameter to optimize and control for the subcritical water pretreatment of fibrous biomass. For wheat straw, the maximum cellulose content after pretreatment is obtained at 190°C of subcritical water pretreatment. This temperature of pretreatment will also enable to have a high yield of enzymatic hydrolysis to get glucose for the production of cellulosic biofuels or chemicals.
References
[1] M. Bezerra, R. Santelli, E. Oliveira, L. Villar, L. Escaleira, « Response surface methodology (RSM) as a tool for optimization in analytical chemistry ». Talanta Vol. 76, pp. 965977, 2008
[2] R Core Team, « A Language and Environment for Statistical Computing ». Vienna, Austria, 2012
[3] L. da Costa Sousa, S.Chundawat, V.Balan, B. Dale, « Cradletograve assessment of existing lignocellulose pretreatment technologies ». Curr Opin Biotechnol Vol. 20, pp. 339347, 2009

Authors 
Gofflot, S., Godin, B., Goffin, I., Nyssen, N., Delcarte, J., Sinnaeve, G. 