Optimal inflammable operation conditions for maleic anhydride production by butane oxidation in fixed bed reactors

Abstract

Flammability of butane in air restricts the butane concentration intake to produce maleic anhydride (MA) by partial oxidation in fixed bed reactors. In this work, the triangle flammability diagram for butane–air mixture is established. This graphical tool is transformed into analytical functions, which are imposed as constraints in the reactor design equations. The analytical function acts a predictive model for fire and explosion hazards using only the reaction temperature and fuel mixture anywhere in the reactor. The simulation analysis revealed the existence of safe optimal operations that do not compromise the reaction conversion and MA yield. These optimal operating conditions can be obtained at the low butane feed concentration of 1.4%, which coincides with that reported in the literature, or at a higher concentration of 8%. The latter increases the molar percentage of MA in the product, leading to easier product purification. The findings of this study may assist in minimizing the fire hazards associated with the presence of hydrocarbon vapors derived from MA production.

Appendix

Coordinate transformation The three-axis coordinates $Z = \langle A,B,C\rangle$ can be transformed into two-axis coordinates $X = \langle x,y\rangle$ by the following mapping operator:

$$ X = MZ^{\prime} $$

where the matrix M is defined as follows:

$$ M = \left[ {\begin{array}{*{20}l} 0 \hfill & 1 \hfill & {0.5} \hfill \\ 0 \hfill & 0 \hfill & {\sqrt {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}} } \hfill \\ \end{array} } \right]. $$

Line function generation Given any two points on the x–y space, e.g., $\langle x_{1} ,y_{1} \rangle$ and $\langle x_{2} ,y_{2} \rangle ,$ a straight line in the form of y = ax + b that passes through the two points can be developed by simple linear algebra as follows:

$$ a = \frac{{y_{2} - y_{1} }}{{x_{2} - x_{1} }} $$

$$ b = y_{1} - \frac{{y_{2} - y_{1} }}{{x_{2} - x_{1} }}x_{1} . $$

Therefore, a line function can be expressed as: $f(x,y) = y - ax - b.$

Coordinates of the line’s intersection The x–y coordinates of two intersecting lines, e.g., $y_{1} = a_{1} x + b_{1}$ and $y_{2} = a_{2} x + b_{2} ,$ can be found as follows:

$$ x = \frac{{a_{2} - a_{1} }}{{b_{1} - b_{2} }} $$

$$ y = b_{1} + \frac{{a_{2} - a_{1} }}{{b_{1} - b_{2} }}a_{1} . $$

Inverse coordinate transformation The two-axis coordinates $X = \langle x,y\rangle$ can be transformed back into three-axis coordinates $Z = \langle A,B,C\rangle$ by the following mapping operator:

$$ Z = NX^{\prime} $$

where the matrix M is defined as follows:

$$ N = \left[ {\begin{array}{*{20}c} {\frac{21}{79}} & { - \frac{21}{79}(1/\sqrt 3 )} \\ 1 & { - 1/\sqrt 3 } \\ 0 & {2/\sqrt 3 } \\ \end{array} } \right]. $$