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

## Problem with parameter fitting (CXTFIT)

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

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