An optimization technique to calibrate the biodegradation ...€¦ · An optimization technique to calibrate the biodegradation rate in a first order decay chain Presented by Alvaro

Goldsim User conference 2004

Goldsim User conferenceLas Vegas 11 – 12 October 2004

An optimization technique to calibrate the biodegradation rate

in a first order decay chain

Presented by Alvaro BUORO Equinocio – France - [email protected]


To what extent the natural degradation can control the plume spreading?

“Natural Attenuation” refers to naturally-occurring processes in soil and ground-water environments that act without human intervention to reduce the mass, toxicity, mobility, volume, or concentration of contaminants in those media.

These in-situ processes include biotransformation, dispersion, dilution, adsorption, volatilization, and chemical or biological stabilization or destruction of contaminants

Biotransformation can often be a dominant process in the natural attenuation of chlorinated solvents such as DNPLs.


Really need to treat a contaminate site?We Need modeling and measurements to define !Biotransformation rate constants are site-specific and

dependent on :• the size of the of dechlorinating microbial population, • the availability of electron donors, • and environmental conditions (i.e. aerobic or anaerobic)

Biotransformation processes are integrated in the decay rate

and values reported from the literature may vary orders

magnitude.

An appropriate biotransformation rate is vital to get a model calibrated to field data


kinetics of Biotransformation

PCE = Perchloroethene TCE = Trichloroethene DCE = Dichloroethene VC = Vinyl Chloride

Reductive dechlorination of DNPLs can be modeled as a sequential first-order decay process.

This means that a parent compound undergoes first-order decay to produce a daughter product and that product undergoes first-order decay and so on.

PCE TCE DCE VC Ethene

Using degradation rates in the model integrates all biotransformation processes in an unique parameter


Footprints of DNPLs

Reductive transformation of DNPLs

Dense non-aqueous phase liquids (DNAPLs), such as PCE and TCE, usually act as continuing sources of groundwater contamination.

They have a small solubility in water and degrade under anaerobic conditions in the soil


How to obtain the site specific decay rate?

The best approach for determining degradation rate constants is to calibrate field data for a given sampling event.

One possible approach is sequential:1. To simulate several degradation rates values until

the PCE predicted concentrations of the model “match” the PCE field data.

2. Then, find the TCE rate until the TCE predicted concentrations match the field data,

3. Then continue estimating rate constants for the other constituents.


Proposed approach 1We propose to get the calibrated degradation rates based on a

simple interactive stochastic approach:

1. Define an optimization function like the rooted mean squared error (√ (measured-calculated)2) for each chemical for all observation points,

2. Generate a set of 50 realization of the degradation rates

3. Screen a sub-set of degradation rates with reduced variation based on the zone of the minimum function value

4. Generate a new set of realizations based in these new distributions limits (=back to step 2 until good agreement)

5. Select the best degradation rate interval for each chemical component


Example of DNPL pollution

Schema of model simplification

Constant source C0

Actual plumelimit <C1 mg/l

Well 1 Well 2 Well 3

future plumelimit <C2 ?

Constant source C0

D1 D2 D3

Available information


Goldsim Model layout


Definition of the observation positions

1. Definition of a row label with the number of observation wells

2. Definition of a data set with a vector of distances


Definition of the constant concentration for the source term

Term used to get a constant concentration in the source: (mass_input_instantaneous/2)/half_life


Implementation of the spreading of possible decay-rates variation

Literature data


How the decay-rate was implemented in GS


Definition of the field measurements used in the objective function

Here simply defined as a matrix of species by distance


Objective function definition

The aim is to minimize the difference field data (measured) and modeled at all the observation wells.

The Objective function is defined as Root Mean Square error :

at each observation position sqrt((Transport_well1.Concentration[CV]-

mesured_concentration[CV,D1])**2+ (Transport_well1.Concentration[TCE]-mesured_concentration[TCE,D1])**2+ (Transport_well1.Concentration[DCE]-mesured_concentration[DCE,D1])**2)

Or by chemical component (i.e.: TCE, DCE, CV)at all wells sqrt((Transport_well1.Concentration[TCE]-

mesured_concentration[TCE,D1])**2+(Transport well2.Concentration[TCE]-


The objective function in Goldsim


0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22Fobj_tce [mg/l]

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

TCE

_dr

[1/y

r]

Degradation rate TCE x Objective function TCE

Analysis of the results

Results of the first screening TCE


Results first screening DCE

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.510.010.511.0Fobj_DCE [mg/l]

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

DC

E_d

r [1

/yr]

Degradation rate DCE x Objective function DCE


Results first screening VC

2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6Fobj_CV [mg/l]

1

2

3

4

5

6

7

8

9

10

11

12

CV

_d

r [1

/yr]

Degradation rate VC x Objective function VC


Objective function first screening

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Sum_fobj


Results second screening TCE

0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22Fobj_tce [mg/l]

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

TC

E_d

r [1

/yr]



Results second screening DCE

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4Fobj_DCE [mg/l]

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

0.60

DC

E_d

r [1

/yr]



Results second screening VC

2.62.83.03.23.43.63.84.04.24.44.64.85.05.25.45.65.86.06.26.46.66.87.07.27.47.67.8Fobj_CV [mg/l]

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

CV

_dr

[1/y

r]

Degradation rate CV x Objective function CV


Objective function second screening

3

4

5

6

7

8

9

10

11

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Sum_fobj


Results final screening TCE

0.0755 0.0760 0.0765 0.0770 0.0775 0.0780Fobj_TCE [mg/l]

0.391

0.392

0.393

0.394

0.395

0.396

0.397

0.398

0.399

0.400

0.401

0.402

0.403

0.404

0.405

0.406

0.407

0.408

0.409

TC

E_

dr

[1/y

r]



Results final screening DCE

1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58 1.60Fobj_DCE [mg/l]

0.300

0.305

0.310

0.315

0.320

0.325

0.330

0.335

0.340

0.345

0.350

DC

E_

dr

[1/y

r]



Results final screening VC

2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5Fobj_VC [mg/l]

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

CV

_d

r [1

/yr]

Degradation rate VC x Objective function VC


Global results

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Sum_fobj

Percentiles

Upper Bound 75% Percentile 25% Percentile Lower Bound Mean Median


Composed results Objective Function for well 1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Fobj_d1

Percenti les




0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Fobj_d2

Percentiles




2.3

2.4

2.5

2.6

2.7

0 1 2 3 4 5 6 7 8 9 10 11

(mg/

l)

Time (yr)

Fobj_d3

Percenti les

Upper Bound 75% Percenti le 25% Percentile Lower Bound Mean Median


Measurements and modeling results

0.001

0.010

0.100

1.000

10.000

100.000

0 200 400 600 800 1000

Distance From Source (ft)

Co

nce

ntr

atio

n (m

g/L

)

DCE Field Data

TCE Field Data

VC Field Data

DCE GS model

VC GS model

TCE GS model


Another approach : The Optimization module of GS

Using the same definition of objective function and changing the decay rate element to data type

With a simple setting at two places the optimization can be done in a single shot


1. Inside the optimization module definition of the bounds of variation for each element


2.Link the optimization variable to the “local”model element previously set in the optimization module


3. Optimize!

The results are in the same range


Conclusion

Two approaches were proposed to calibrate field data to natural biodegradation rates.

1. A stochastic approach

2. An optimized approach more direct and fast

Goldsim can in a simple and efficient way find the best decreasing rate calibration of DNPLs Biodegradation


Alvaro BUORO Equinocio – [email protected]

Documents

An optimization technique to calibrate the biodegradation ...€¦ · An optimization technique to calibrate the biodegradation rate in a first order decay chain Presented by Alvaro