ThomAlysis

The problem

The mean isn't the answer.
The band around it is.

Flow rate, sorbent mass, inlet concentration. Every measurement carries error. ThomAlysis turns that uncertainty into a credible interval on the breakthrough time.

Typical combined error

0%

Enough to shift a fitted breakthrough time by hours.

The model

The Thomas equation, in three forms.

Thomas — linear

\dfrac{C_{out}}{C_{in}} = \dfrac{1}{1 + \exp\!\left[\dfrac{k_{Th}\,q_0\,m}{Q} - k_{Th}\,C_0\,t\right]}

Breakthrough time

t_b = \dfrac{q_0\,m}{C_0\,Q} - \dfrac{\ln\!\left(\dfrac{1-c}{c}\right)}{k_{Th}\,C_0}

Log-form (Yan)

\dfrac{C_{out}}{C_{in}} = \dfrac{1}{1 + \left(\dfrac{q_0\,m}{C_0\,Q\,t}\right)^{k}}

k_Th rate constant
q₀ sorption capacity
m sorbent mass
Q volumetric flow
C₀ inlet concentration
c breakthrough fraction

Three steps

Noisy curve in. Confidence band out.

Step 1

Upload

An Excel sheet with t, in, out.
Step 2

Fit

Linear or log-form Thomas. Non-linear least-squares with R² and RMSE.
Step 3

Propagate

Monte Carlo refits the curve a thousand times under your reported instrument error.

The team

PM AH TH

Universität Wien

philipp.martin@univie.ac.at

For academic users

Please cite if it supports your work.

Recommended citation

Martin, P., Herbst, A. & Hofmann, T. (2026).

ThomAlysis

The mean isn't the answer. The band around it is.

The Thomas equation, in three forms.

Noisy curve in. Confidence band out.

Upload

Fit

Propagate

Please cite if it supports your work.

The mean isn't the answer.
The band around it is.