TY - JOUR
T1 - Headspace diffusion limitations on heterogeneous catalysis in unstirred batch reactors
AU - Peters, Baron
N1 - Funding Information:
We thank Susannah Scott, Brad Chmelka, Brian Vicente, and Anthony Fong for many helpful discussions and suggestions. This work was funded by the US Department of Energy, Basic Energy Sciences, Catalysis Science Grant no. DE-FG02-03ER15467 .
PY - 2012/3/26
Y1 - 2012/3/26
N2 - Headspace gas diffusion can affect measurements of catalytic rate constants in unstirred batch reactors when the reaction occurs in a small pile of catalyst within the reactor. To quantify these effects, the governing equations for catalysis in a round-bottom flask were solved numerically in a toroidal coordinate system. We also introduce a simpler model reactor geometry that preserves the essential characteristics of a typical bench-scale flask-reactor. The preserved characteristics include the reactor volume, an averaged diffusion length scale, and the area of the catalyst pile. An eigenfunction expansion solution for the model reactor closely parallels the full numerical solutions in the round-bottom flask reactor, thus confirming the validity of the simplified model reactor. Solutions for the model reactor show that concentrations measured above the catalyst pile decay exponentially to equilibrium even when transport limitations are important. Therefore, exponential decay rates in these reactors should not be equated to first order (or pseudo-first order) reaction rate constants without first checking carefully for diffusion limitations. Two dimensionless parameters govern the reactor performance. Effectiveness factors are computed for unstirred catalytic batch reactors over a wide range of the two dimensionless parameters. Our findings show quantitatively when headspace stirring is and is not necessary. When stirring is inconvenient or impossible, the tabulated effectiveness factors can be used to design reactors that are small enough, with kinetics that are slow enough, and with the catalyst dispersed over a large enough area to avoid headspace diffusion limitations.
AB - Headspace gas diffusion can affect measurements of catalytic rate constants in unstirred batch reactors when the reaction occurs in a small pile of catalyst within the reactor. To quantify these effects, the governing equations for catalysis in a round-bottom flask were solved numerically in a toroidal coordinate system. We also introduce a simpler model reactor geometry that preserves the essential characteristics of a typical bench-scale flask-reactor. The preserved characteristics include the reactor volume, an averaged diffusion length scale, and the area of the catalyst pile. An eigenfunction expansion solution for the model reactor closely parallels the full numerical solutions in the round-bottom flask reactor, thus confirming the validity of the simplified model reactor. Solutions for the model reactor show that concentrations measured above the catalyst pile decay exponentially to equilibrium even when transport limitations are important. Therefore, exponential decay rates in these reactors should not be equated to first order (or pseudo-first order) reaction rate constants without first checking carefully for diffusion limitations. Two dimensionless parameters govern the reactor performance. Effectiveness factors are computed for unstirred catalytic batch reactors over a wide range of the two dimensionless parameters. Our findings show quantitatively when headspace stirring is and is not necessary. When stirring is inconvenient or impossible, the tabulated effectiveness factors can be used to design reactors that are small enough, with kinetics that are slow enough, and with the catalyst dispersed over a large enough area to avoid headspace diffusion limitations.
KW - Batch reactor
KW - Catalyst screening
KW - Diffusion limitations
KW - Heterogeneous catalysis
KW - Reaction engineering
KW - Reactor modeling
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U2 - 10.1016/j.ces.2011.12.013
DO - 10.1016/j.ces.2011.12.013
M3 - Article
AN - SCOPUS:84856579527
VL - 71
SP - 367
EP - 374
JO - Chemical Engineering Science
JF - Chemical Engineering Science
SN - 0009-2509
ER -