Download Modelling Biogrout

Modeling Biogrout
Miranda van Wijngaarden
29 June, 2009
Biogrout: a new soil improvement method
• Bacteria are flushed into the soil.
• Subsequently, reactants are flushed through the soil.
• Microbial induced calcium carbonate precipitation.
• The calcium carbonate crystals form bridges between the sandgrains.
• Loose sand is transformed into sandstone:
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29 June, 2009
Applications
• Reinforcement of the soil underneath railway-tracks;
• Reinforcement of dunes (decrease wave erosion);
• Circumvention of liquefaction (earthquakes)
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Model
bacteria
CO(NH2 )2  2H2O 
 2NH4 +  CO32
urea
water
ammonium carbonate
Ca 2+  CO32  CaCO3 (s)
calcium carbonate
calcium carbonate
• Flow
• Concentration of urea, ammonium, calcium and calcium carbonate
• Bacteria
• Reaction rate (exponential decay)
• Fluid
NH4
urea
Ca2
• Density:    (C
,C ,C
).
• Viscosity: assumed to be constant
• Properties of the subsoil
• Geometry
• Porosity: decreases due to calcium carbonate precipitation
• Permeability k=k()
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Model – flow
k x p
qx  
,
 x
k y p
qy  
,
 y
k z  p

qz      g  .
  z

q  

t
 k


    p   gez     .
t
 

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Model – urea

  C urea
t
     DC

urea

C urea

    DC urea   q  C urea   r 
t
 

     q  C urea ,
 t

C urea

    DC urea   q  C urea   r .
t
r is a formula for the (chemical) reaction rate.
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
urea




q
C
r,

Model – urea, calcium en ammonium
urease
2H2O  CO( NH2 )2  Ca2 
 2 NH 4  CaCO3
(s)
C urea
urea
urea


 

D

C

q


C
r,


t
Ca 2 
C

t
    DC Ca   q  C Ca


2

2
r,


C NH4

    DC NH4   q  C NH4  2 r .


t
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Model – calcium carbonate and porosity
urease
2 H 2O(l )  CO( NH 2 ) 2 (aq)  Ca 2 (aq) 
 2 NH 4 (aq)  CaCO3 ( s)
C CaCO3
  r mCaCO3 .
t
mCaCO3

  r
.
t
CaCO3
 (t ) 
C CaCO3 (t )  C CaCO3 (0)
CaCO
3
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.
Numerical simulation with the model
•
•
•
System of coupled non-linear equations
Finite Element Method
IMEX scheme:
1. Solve pressure, the flow and the concentrations implicitly
> using Newton iterations in case of non-linearities
> taking the porosity, permeability and density from the
previous time step
2. Update the porosity, permeability, density and boundary
conditions
•
Matlab
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Experimental system
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Initial and boundary conditions
Initial conditions:
C
urea
(0,x)=C
NH4
Ca 2+
(0,x)=C
(0, x)  CCaCO3 (0, x)  0,
 (0, x)  initial .
Boundary conditions (during flow):
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Flow strategy
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Numerical results 2D
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Numerical results 2D
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Numerical results 3D
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Numerical results 3D
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Conclusion and Discussion
• By rewriting the differential equations for the concentrations and
substituting the differential equation for the flow these equations
could be simplified.
• We solved is a non-linear system of equations, which converges
and is stable.
• Most calcium carbonate precipitated in the vicinity of the injection
wells.
• In the lower part of the domain more calcium carbonate is
precipitated. The reason is density flow.
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Further research
• Validation of the assumptions
• Find a better relation for the (decreasing) reaction rate
• Comparison with data from the container experiment and other
‘real life’ experiments
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Questions??
29 June, 2009