hougen

Hougen–Watson model

Syntax

rate = hougen(beta,X)

Description

rate = hougen(beta,X) returns predicted reaction rates as a function of the Hougen–Watson model coefficients beta and reactant concentrations X. The Hougen–Watson model has the form

$$rate=\frac{{\beta }_1{X}_2-X_3/{\beta }_5}{1+{\beta }_2{X}_1+{\beta }_3{X}_2+{\beta }_4{X}_3}$$

where X₁, X₂, and X₃ are the concentrations of hydrogen, n-pentane, and isopentane, respectively.

hougen is a utility function for the Response Surface Demonstration Tool.

Examples

Compute Hougen–Watson Reaction Rate

Compute a predicted reaction rate according to a Hougen–Watson model with coefficients β = [1.2, 0.1, 0.01, 0.1, 1.5] and the following reactant concentrations: hydrogen = 100, n-pentane = 80, and isopentane = 120.

rate = hougen([1.2 0.1 0.01 0.1 1.5],[100 80 120])

rate =

    0.6723

The predicted reaction rate is 0.6723 grams per hour.

Input Arguments

beta — Hougen–Watson model coefficients

numeric vector with five elements

Hougen–Watson model coefficients, specified as a numeric vector with five elements.

Data Types: single | double

X — Reactant concentrations

numeric matrix with three columns

Reactant concentrations, specified as a numeric vector with three columns. The columns of X contain the concentrations of hydrogen, n-pentane, and isopentane, in that order.

Data Types: single | double

Output Arguments

rate — Reaction rates

numeric vector

Reaction rates, returned as a numeric vector.

References

[1] Bates, D. M., and D. G. Watts. Nonlinear Regression Analysis and Its Applications. Hoboken, NJ: John Wiley & Sons, Inc., 1988.

Version History

Introduced before R2006a