TY - JOUR
T1 - Closed-Form Solution to the Problem of Reaction with Fixed- Bed Adsorption Using Delay-Differential Equations
AU - Xia, Shu
AU - Hodge, Nichole
AU - Wiesner, Theodore
N1 - Funding Information:
S. Xia was supported by the Department of Internal Medicine at the Texas Tech University Health Sciences Center and the Office of the Vice-President for Research at Texas Tech University. This research was also supported in part by a Howard Hughes Medical Institute grant through the Undergraduate Science Education Program to Texas Tech University.
PY - 2009/5/1
Y1 - 2009/5/1
N2 - Delay-differential equations (DDEs) can describe many chemical engineering models. However, the formalism of DDEs appears to be underutilized in chemical engineering. We have recast the canonical chemical engineering problem of batch reaction with fixed bed sorption into the form of a delay-differential equation, obtaining a more intuitive model and a simpler closed form solution than those previously reported. Considerable model reduction is possible through the use of DDE formalism when one considers that chemical processes can be partially represented by networks of transportation and state delays. Analytical and numerical methods for solution, as well as controllability and stability theory for systems of DDEs, are nearly as rich and developed as those for ordinary differential equations. Significant progress thus may be possible in areas such as the modeling, synthesis, and control of chemical processes, if the governing equations can be expressed in the form of delay-differential equations.
AB - Delay-differential equations (DDEs) can describe many chemical engineering models. However, the formalism of DDEs appears to be underutilized in chemical engineering. We have recast the canonical chemical engineering problem of batch reaction with fixed bed sorption into the form of a delay-differential equation, obtaining a more intuitive model and a simpler closed form solution than those previously reported. Considerable model reduction is possible through the use of DDE formalism when one considers that chemical processes can be partially represented by networks of transportation and state delays. Analytical and numerical methods for solution, as well as controllability and stability theory for systems of DDEs, are nearly as rich and developed as those for ordinary differential equations. Significant progress thus may be possible in areas such as the modeling, synthesis, and control of chemical processes, if the governing equations can be expressed in the form of delay-differential equations.
KW - Chemical reactors
KW - Delay-differential equations
KW - Dynamic simulation
KW - Mathematical modeling
KW - Organic acids
KW - Packed bed
UR - http://www.scopus.com/inward/record.url?scp=63449116172&partnerID=8YFLogxK
U2 - 10.1016/j.ces.2009.01.025
DO - 10.1016/j.ces.2009.01.025
M3 - Article
VL - 64
SP - 2057
EP - 2066
JO - Chemical Engineering Science
JF - Chemical Engineering Science
IS - 9
ER -