## Problem with parameter fitting (CXTFIT)

A discussion forum for STANMOD users. STudio of ANalytical MODels is a software package for evaluating solute transport in porous media using analytical solutions of the convection-dispersion solute transport equation.

leboeg
Posts: 8
Joined: Thu Mar 26, 2009 8:47 am

### Problem with parameter fitting (CXTFIT)

Hello,

I've made some colloid transport experiments and now I would like to model the resulting breakthrough curves with CXTFIT to obtain retardation factors and first-order deposition coefficients. For most of the BTC fitting was fine, however, with one BTC I've got a problem because CTXFIT couldn't find the accurate parameter value and consequently fitting was very bad (R2 = 0.5961).
The experimental data come from a breakthrough experiment with carboxylated polystyrene microspheres (1 µm) in a fully saturated quartz sand matrix (column length: 20 cm) with 0.1 mM CaCl2 as a background electrolyte. The breakthrough of the microspheres is strongly retarded with first arrival after approx. 2 pore volumes (for details please find the ctxfit.out file below).

I would be very grateful if you could help me with this problem.
Many thanks in advance,

Marc
------------------------------------------------------------

Model description
=================
Deterministic equilibrium CDE (Mode=1)
Flux-averaged concentration
Reduced time (T), Position(Z)
(All parameters except D and V are dimensionless)
Characteristic length = 20.0000
for dimensionless parameters

Initial values of coefficients
==============================
Name Initial value Fitting
V........ .2262E+01 N
D........ .1000E+01 Y
R........ .1000E+01 Y
mu....... .3500E+00 Y
Cin...... .1000E+01 N
T2....... .7206E+01 N

Boundary, initial, and production conditions
===========================================
<Initial estimate of b.c.>
Single pulse of conc. = 1.0000 & duration = 7.2060
Solute free initial condition
No production term

Parameter estimation mode
=========================
Maximum number of iterations = 100

Iter SSQ D.... R.... mu...
0 .4412E+01 .100E+01 .100E+01 .350E+00
1 .1432E+01 .186E+01 .130E+01 .833E+00
2 .1136E+01 .251E+01 .174E+01 .101E+01
3 .1001E+01 .764E+01 .245E+01 .106E+01
4 .9244E+00 .246E+02 .461E+01 .122E+01
5 .9006E+00 .148E+02 .428E+01 .100E+01
6 .8982E+00 .195E+02 .473E+01 .106E+01
7 .8978E+00 .188E+02 .459E+01 .106E+01
8 .8976E+00 .171E+02 .437E+01 .105E+01
9 .8976E+00 .170E+02 .437E+01 .104E+01
10 .8976E+00 .170E+02 .437E+01 .104E+01

Covariance matrix for fitted parameters
=======================================
D.... R.... mu...
D.... 1.000
R.... .990 1.000
mu... .880 .859 1.000

RSquare for regression of observed vs predicted = .59618517
(Coefficeint of determination)

Mean square for error (MSE) = .2896E-01

Non-linear least squares analysis, final results
================================================

95% Confidence limits
Name Value S.E.Coeff. T-Value Lower Upper
D.... .1704E+02 .4002E+02 .4259E+00 -.6458E+02 .9867E+02
R.... .4366E+01 .5167E+01 .8450E+00 -.6173E+01 .1491E+02
mu... .1044E+01 .3476E+00 .3005E+01 .3354E+00 .1753E+01

------------------Ordered by computer input-------------------
Concentration Resi-
No Distance Time Obs Fitted Dual
1 1.0000 .1221 .0000 .0000 .0000
2 1.0000 .3664 .0000 .0002 -.0002
3 1.0000 .6107 .0000 .0064 -.0064
4 1.0000 .8550 .0000 .0265 -.0265
5 1.0000 1.0992 .0000 .0584 -.0584
6 1.0000 1.3435 .0000 .0961 -.0961
7 1.0000 1.8320 .0100 .1721 -.1621
8 1.0000 2.0763 .0200 .2063 -.1863
9 1.0000 2.3206 .0400 .2371 -.1971
10 1.0000 2.5649 .0700 .2643 -.1943
11 1.0000 2.8091 .1000 .2882 -.1882
12 1.0000 3.0534 .1200 .3090 -.1890
13 1.0000 3.2977 .1700 .3272 -.1572
14 1.0000 3.7862 .2600 .3566 -.0966
15 1.0000 4.0305 .3000 .3684 -.0684
16 1.0000 4.5190 .3500 .3876 -.0376
17 1.0000 4.7633 .4100 .3953 .0147
18 1.0000 5.0076 .4700 .4020 .0680
19 1.0000 5.2519 .4900 .4078 .0822
20 1.0000 5.7404 .5400 .4173 .1227
21 1.0000 5.9847 .5600 .4211 .1389
22 1.0000 6.4732 .5900 .4274 .1626
23 1.0000 6.7175 .5800 .4300 .1500
24 1.0000 6.9618 .6100 .4322 .1778
25 1.0000 7.2060 .6400 .4341 .2059
26 1.0000 7.4503 .6500 .4359 .2141
27 1.0000 7.6946 .6500 .4355 .2145
28 1.0000 7.9389 .6400 .4240 .2160
29 1.0000 8.4274 .3500 .3639 -.0139
30 1.0000 8.6717 .0200 .3261 -.3061
31 1.0000 8.9159 .0000 .2887 -.2887
32 1.0000 9.1602 .0000 .2535 -.2535
33 1.0000 9.4045 .0000 .2217 -.2217
34 1.0000 9.6487 .0000 .1932 -.1932

Z= 1.0000 (Flux conc. vs. time)
Sum(C*dT)= 3.1776
Time C
.0000 .00000E+00
.1000 .97533E-13
.2000 .25665E-06
.3000 .37475E-04
.4000 .46213E-03
.5000 .21055E-02
.6000 .58080E-02
.7000 .12008E-01
.8000 .20710E-01
.9000 .31631E-01
1.0000 .44356E-01
1.1000 .58435E-01
1.2000 .73452E-01
1.3000 .89039E-01
1.4000 .10490E+00
1.5000 .12078E+00
1.6000 .13650E+00
1.7000 .15191E+00
1.8000 .16690E+00
1.9000 .18141E+00
2.0000 .19538E+00
2.1000 .20878E+00
2.2000 .22158E+00
2.3000 .23380E+00
2.4000 .24541E+00
2.5000 .25645E+00
2.6000 .26691E+00
2.7000 .27683E+00
2.8000 .28621E+00
2.9000 .29508E+00
3.0000 .30346E+00
3.1000 .31138E+00
3.2000 .31886E+00
3.3000 .32591E+00
3.4000 .33256E+00
3.5000 .33884E+00
3.6000 .34476E+00
3.7000 .35035E+00
3.8000 .35561E+00
3.9000 .36057E+00
4.0000 .36526E+00
4.1000 .36967E+00
4.2000 .37383E+00
4.3000 .37776E+00
4.4000 .38146E+00
4.5000 .38495E+00
4.6000 .38824E+00
4.7000 .39135E+00
4.8000 .39428E+00
4.9000 .39705E+00
5.0000 .39966E+00
5.1000 .40212E+00
5.2000 .40445E+00
5.3000 .40665E+00
5.4000 .40872E+00
5.5000 .41068E+00
5.6000 .41253E+00
5.7000 .41428E+00
5.8000 .41593E+00
5.9000 .41749E+00
6.0000 .41896E+00
6.1000 .42036E+00
6.2000 .42168E+00
6.3000 .42292E+00
6.4000 .42410E+00
6.5000 .42521E+00
6.6000 .42627E+00
6.7000 .42727E+00
6.8000 .42821E+00
6.9000 .42910E+00
7.0000 .42995E+00
7.1000 .43075E+00
7.2000 .43151E+00
7.3000 .43222E+00
7.4000 .43290E+00
7.5000 .43352E+00
7.6000 .43374E+00
7.7000 .43278E+00
7.8000 .42976E+00
7.9000 .42424E+00
8.0000 .41617E+00
8.1000 .40584E+00
8.2000 .39365E+00
8.3000 .38006E+00
8.4000 .36548E+00
8.5000 .35030E+00
8.6000 .33481E+00
8.7000 .31926E+00
8.8000 .30385E+00
8.9000 .28872E+00
9.0000 .27398E+00
9.1000 .25972E+00
9.2000 .24598E+00
9.3000 .23279E+00
9.4000 .22018E+00
9.5000 .20816E+00
9.6000 .19672E+00
9.7000 .18585E+00
9.8000 .17554E+00
9.9000 .16577E+00
10.0000 .15653E+00
10.1000 .14779E+00
10.2000 .13954E+00
10.3000 .13174E+00
10.4000 .12438E+00
10.5000 .11743E+00
10.6000 .11088E+00
10.7000 .10470E+00
10.8000 .98875E-01
10.9000 .93381E-01
11.0000 .88200E-01
11.1000 .83317E-01
11.2000 .78712E-01
11.3000 .74371E-01
11.4000 .70278E-01
11.5000 .66419E-01
11.6000 .62780E-01
11.7000 .59349E-01
11.8000 .56113E-01
11.9000 .53060E-01
12.0000 .50180E-01
12.1000 .47464E-01
12.2000 .44900E-01
12.3000 .42481E-01
12.4000 .40198E-01
12.5000 .38043E-01
12.6000 .36008E-01
12.7000 .34087E-01
12.8000 .32272E-01
12.9000 .30558E-01
13.0000 .28939E-01
13.1000 .27410E-01
13.2000 .25965E-01
13.3000 .24599E-01
13.4000 .23308E-01
13.5000 .22087E-01
13.6000 .20933E-01
13.7000 .19842E-01
13.8000 .18810E-01
13.9000 .17833E-01
14.0000 .16910E-01

ntoride
Posts: 74
Joined: Fri May 21, 2004 12:50 pm
Location: Japan
Dear Mark,
I am sorry for my late reply. I also made a cxtfit project and confirmed your results. The observed concentration increased gradually from T=2 to T=8 and dropped drastically at T=8. The shape of BTC is obviously different form the CDE prediction. The BTC needs to be symmetrical in case of the CDE assumption. There seems to be different mechanisms for the colloid transport from the CDE assumption. I also noticed the amount of solute in effluent was 2.63 although the input amount was 7.206. Is it possible to consider the colloid still remained in the soil? Is there any possibility that the colloid clogged locally at a certain location?
Nobuo

leboeg
Posts: 8
Joined: Thu Mar 26, 2009 8:47 am
Dear Nobuo,

many thanks for your reply. I also thought about pore clogging as a possible explanation. This would agree with results from another BT experiment with a hydrophobic sand matrix. Using a 0.1 mM CaCl2 background solution we found virtually no colloid breakthrough and a clearly visible colloid retention within the top 2 or 3 cm of the column. So it seems that fitting with CXTFIT should no be possible!?

Many thanks again and best wishes from Germany,

Marc