### inverse fitting problem: no link between data and estimation

Posted:

**Wed Nov 19, 2014 2:13 pm**Hallo dear STANMOD-friends,

I am having quite huge problems in fitting concentration curves to my experimental data breakthrough-curves. This will be a basics problem I still did not understand, so I am already sorry for asking stupid questions here, but I just don`t get it by studying all those examples and papers from the inventors Toride and van Genuchten, so could you please help me?

I obtained beautiful breakthrough curves from surfactant solutes passing sand columns, the CXTFIT 2.1W module also draws these data perfectly (red circles).

My goal is estimation of pore-velocity, Distribution factor and Retardation factor (v, D, R) with a non equilibrium CDE model.

No matter what I try in STANMOD, my estimated curves never link to the data, so the mathematical least-squares analysis is doing things I don`t understand at all.

To help you understand, I will describe my config step by step and attach the files as well.

CXTFIT-module:

1. inverse problem

2. deterministic equilibrium CDE (just because non equilibrium CDE ALWAYS leads to: "not enough data")

3. time and position are dimensional (because I want to estimate velocity, v)

4. units are mm for length, min for time and dimensionless concentration

5. concentration mode: resident concentration, third type inlet Cr (as found as suggestion of Toride) [I am pumping solute constantly with 0,5ml/min]

6. inverse parameter: used min and max, no mass estimation, max 150 iterations

7. v D R enabled for fitting with starting values and min/max values as expectable

- v: fitted (0,5; min:0,000001 max:10)

- D: fitted (10; min:0 max:100)

- R: fitted (1; min:0 max:1)

- Mu: 0 [I donâ€™t have information about this]

9. BVP: pulse input at application time: input concentration: 1, application time: 70 [measuring starts with first pore volume of surfactant-solute pumped into the column, after time 70 relative concentration reached 1 and degradation is initialized by inserting purified water - is this BVP the right coice?]

10. IVP: zero initial concentration

11. PVP: zero production

12. inverse data structure: T,C,fixed depth BTC; 18 data points, position of the BTC 1 [what is meant by a position of BTC, the BTC starts at time 0 but no estimation possible with this value]

13. data in format of time in min and relative concentration

14. output structure: tried various values.. just don't understand, why i can generate so many output positions, no one fits to my data..

I always have the opinion, that CXTFIT is calculating its own BTC based on my information I give, but it doesn't fit the estimation to the data I inserted.

If you could please have a look on my file and give me some hint, I would be extremely graceful!

Thank you kindly for your attention already for reading this!!

Let me know, if I can give you more information.

Regards,

David

I am having quite huge problems in fitting concentration curves to my experimental data breakthrough-curves. This will be a basics problem I still did not understand, so I am already sorry for asking stupid questions here, but I just don`t get it by studying all those examples and papers from the inventors Toride and van Genuchten, so could you please help me?

I obtained beautiful breakthrough curves from surfactant solutes passing sand columns, the CXTFIT 2.1W module also draws these data perfectly (red circles).

My goal is estimation of pore-velocity, Distribution factor and Retardation factor (v, D, R) with a non equilibrium CDE model.

No matter what I try in STANMOD, my estimated curves never link to the data, so the mathematical least-squares analysis is doing things I don`t understand at all.

To help you understand, I will describe my config step by step and attach the files as well.

CXTFIT-module:

1. inverse problem

2. deterministic equilibrium CDE (just because non equilibrium CDE ALWAYS leads to: "not enough data")

3. time and position are dimensional (because I want to estimate velocity, v)

4. units are mm for length, min for time and dimensionless concentration

5. concentration mode: resident concentration, third type inlet Cr (as found as suggestion of Toride) [I am pumping solute constantly with 0,5ml/min]

6. inverse parameter: used min and max, no mass estimation, max 150 iterations

7. v D R enabled for fitting with starting values and min/max values as expectable

- v: fitted (0,5; min:0,000001 max:10)

- D: fitted (10; min:0 max:100)

- R: fitted (1; min:0 max:1)

- Mu: 0 [I donâ€™t have information about this]

9. BVP: pulse input at application time: input concentration: 1, application time: 70 [measuring starts with first pore volume of surfactant-solute pumped into the column, after time 70 relative concentration reached 1 and degradation is initialized by inserting purified water - is this BVP the right coice?]

10. IVP: zero initial concentration

11. PVP: zero production

12. inverse data structure: T,C,fixed depth BTC; 18 data points, position of the BTC 1 [what is meant by a position of BTC, the BTC starts at time 0 but no estimation possible with this value]

13. data in format of time in min and relative concentration

14. output structure: tried various values.. just don't understand, why i can generate so many output positions, no one fits to my data..

I always have the opinion, that CXTFIT is calculating its own BTC based on my information I give, but it doesn't fit the estimation to the data I inserted.

If you could please have a look on my file and give me some hint, I would be extremely graceful!

Thank you kindly for your attention already for reading this!!

Let me know, if I can give you more information.

Regards,

David