BIOPLUME IIIntroduction to Solution Methods and

Model Mechanics

What does it do?

• Two dimensional finite difference model for simulating natural attenuation due to:

– advection

– dispersion

– sorption

– biodegradation

How Does BPIII Solve Equations?

• Contaminant transport solved using the Method of Characteristics

• Particles travel along Characteristic lines determined by flow solution.

• Particles carry mass

• Advection solved via particle movement

• Dispersion solved explicitly

• Reaction solved explicitly

– First order decay

– Instantaneous Biodegradation

Initial location of particleNew location of particleFlow line and direction of flowComputed path of particle

Particle Movement

Limitations/Assumptions

• Darcy’s Law is valid

• Porosity and hydraulic conductivity constant in time, porosity constant in space

• Fluid density, viscosity and temperature have no effect on flow velocity

• Reactions do not affect fluid or aquifer properties

• Ionic and molecular diffusion negligible

• Vertical variations in head/concentration negligible

• Homogeneous, isotropic longitudinal and transverse dispersivity

Limitations of Biodegradation

• No selective or competitive biodegradation of hydrocarbons (lumped hydrocarbons)

• Conceptual model of biodegradation is a simplification of the complex biologically mediated redox reactions that occur in the subsurface

End of

Simulation?

End ofPumpingPeriod?

End ofTime Step?

Start

Read Geologic, Hydrogeologic& Chemical Input Data

Generate Uniformly Distributed Particles

Make New/Remove Old Particles @ Edges

Compute Explicitly Conc. at Nodes

Compute Dispersion Coefficients

Determine ∆t for Explicit Calculations

Move Particles

Calc. Avg. Conc. in Each Cell

Compute Hydraulic Gradients

Adjust Concentration of Each Particle

Compute Ground Water Velocities

Compute Mass BalanceStop

Summarize and Print Results

YN

Y

N

NY

BIOPLUME II Flowchart

HOW TO SET UP A MODEL

1. Data Collection & Analysis

2. Modeling Scale

3. Discretization

4. Boundary Conditions

5. Parameter Estimation

6. Calibration

7. Sensitivity Analysis

8. Error Estimation

9. Prediction

SOURCE DATA

• Mass of contaminant

• Q, C0

• Discrete vs. Continuous

Nature of contaminant

• Chemical stability

• Biological stability

• Adsorption

PARAMETER ESTIMATION

1. Porosity

2. Dispersivity

3. Storage coefficients

4. Hydraulic conductivity

5. Thickness of unit

6. Recharge rates

REGIONAL SCALE - QUANTITATIVE

• Aquifer characteristics

• Background gradients

• Geology

• Recharge sources

LOCAL SCALE - WATER QUALITY

• Site history

• Site characterization

• Source definition

• Nature of contamination

• Plume delineation

MOC TIMING PARAMETERS

Total Simulation Time

1st pumping period 2nd

NPMP = 2

For Each Pumping Period

PINT = pumping period in yrs

NTIM = # of time steps in pumping period

MOC BOUNDARY CONDITIONS

Two types

• Constant Head

– Water Table = constant

• Constant Flux

– Flow rate Q

– Concentration C0

MOC BOUNDARY CONDITIONSSpecifications of NCODES

For Each Code in NOEID map

• LEAKANCE (s-1)– vertical hyd. conduct. / thickness

• CONCENTRATION OF CONTAMINANT

• RECHARGE RATE (ft/s)

NOTEFor constant head cells set LEAKANCE to 1.0

MOC SOURCE DEFINITION

Injection well• Flow rate - Q

• Concentration - C0

Constant Head Cell

• C=C0

Recharge Cell• Flow rate - Q

• Concentration - C0

PHYSICAL AQUIFER CHARACTERISTICS

1. Transmissivity (ft2/s) – VPRM

2. Thickness (ft) – THCK

3. Dispersivity (ft)

Longitudinal – BETA

Ratio – DLTRAT = Txx/Tyy

4. Porosity – POROS

5. Storativity – SNOTE

For transient problems

TIMX – increment multiplier

TINIT – size of initial time step

MOC REACTION PARAMETERS

NREACT

Flag to instruct MOC to expect reaction data0 - no reactions

1 - reactions taking place

expect card # 4 free format

Two types of reaction:

RETARDATIONKD - Distribution coefficient

RHOB - Bulk density

RADIOACTIVE DECAYTHALF - Half life of solute

INPUT PARAMETERS AFFECTING ACCURACY FOR HYDRAULIC

CALCULATIONSITMAX

Maximum allowable number of iterations: 100-200

Increase ITMAX if hydraulic mass balance error is > 1%

NITP

Number of iteration parameters

USE 7

TOL

Convergence criteria: <0.01

Decrease TOL to get less hydraulic mass balance error

PARAMETERS AFFECTING ACCURACY OF TRANSPORT

NPTPND - Number of particles in a cell

NPMAX - Maximum number of particles

= NX • NY • NPTPND

STABILITY CRITERIA FOR MOC

MOC may require dividing NTIM or PINT into smaller move time steps

t minimum of

– Dispersion

– Mixing

– Advection

( ) ( )22

5.0

dy

D

dx

D yyxx +

( )

kji

kji

W

nb

,,

,,

( )maxxV

xΔγ

( )maxyV

yΔγ

INPUT PARAMETERS AFFECTING STABILITY OF MOC

CELDIS - max distance per move– If CELDIS < space between particles MOC will oscillate for

N yrs BUT gives smallest Mass Balance errors for T>N

– If CELDIS = Stability Criteria DO a sensitivity analysis on CELDIS

NPTPND - initial # of particles– Accuracy of MOC directly proportional to NPTPND

– Runtime inversely proportional to NPTPND

RULE OF THUMB– Initially set NPTPND=4 or 5 and CELDIS=0.75 or 1

– For final runs use NPTPND=9 and CELDIS=0.5

Output control

NPNTMVNumber of particle moves after which output is requested. Use 0 to print at end of time steps

NPNTVLPrinting velocities

0 - do not print

1 - print for first time step

2 - print for all time steps

NPNTDPrint dispersion equation coefficients

NPDELCPrint changes in concentration

NPNCHVDo not use this option. Always set to 0. It is used to request cards to

be punched.

Output control (cont.)