Negative-order production

The negative-order production reaction is a production reaction whose rate depends inversely on the concentration of the product species. Consequently, the production rate will decrease as the concentration of the product species increases. Negative-order production kinetics can be used to model self-limiting production processes in which accumulation of a species reduces its own production rate.

The reaction equation is,

\[ \emptyset \to P \]

The reaction rate is defined by,

\[ r = r_0 + \frac{k}{\left( c_P + \epsilon \right)^{n}} \]

Here, \(k\) is the rate constant. The rate offset \(r_0\) provides a constant contribution to the production rate and may be positive or negative. The concentration offset \(\epsilon\) prevents the reaction rate from becoming singular as the concentration approaches zero. The order \(n\) may be any non-negative real number. Setting \(n=0\) reduces the reaction to a constant-rate production process with rate \(r=r_0+k\).

The following table lists the input parameters for this type of reaction.

Name	Description	Default	Range
rate_offset	rate offset \(r_0\)	0	\(\in \mathbb{R}\)
rate_constant	rate constant \(k\)	0	\(\ge 0\)
concentration_offset	concentration offset (\(\epsilon\))	0	\(\ge 0\)
order	reaction order \(n\).	1	\(\ge 0\)
product	The name of the product species