In-situ bioremediation is based on the use of bacteria to degrade the contaminant directly
in the polluted soils, and can be seen as a way to improve and accelerate natural
decontamination processes. As it is usually based upon the use of indigenous bacterial
strains, it is environmentally safe and less expensive than other decontamination
techniques.
Generally speaking, there are some problems in order to predict the outcome of field
scale operations from laboratory or pilot plant data and to reliably evaluate the times and
the costs of the intervention; the COLOMBO model is developed to describe the time
evolution of the relevant variables during bioremediation and to solve this kind of topics.
We often have to deal with contaminants not miscible with water or only slightly soluble, as
mineral fuels (e.g., petrol, fuel oil) or solvents. For this reason, the COLOMBO model can
simulate a whole bioremediation process in a three-phase water-oil-air system.
The model is based on a straightforward discrete scheme, namely that of cellular automata
(CA), which rely upon discrete space cells, discrete time steps and discrete state space. In
this approach, the interactions are local, the state of each cell at time t+1 - x(t+1) depends upon its own state and those of its neighbours at time t and a transition function
leads from the old cell_state to the new cell_state.
The model has a layered structure:
In the fluid dynamical layer, we deal with the phase movements inside the soil. The basic
idea is that the pressure waves (and the relative potential distribution) reach the steady
state “suddenly” with respect the phase flows, and so they can be computed before
everything else; then the flows of each phase in the porous media is calculated following
the gradient of potential. In order to follow a real experiment or field intervention, the model
is able to simulate saturated or unsaturated zones, external forced condition like wells with
fixed infiltration (exfiltration) rate and physical boundaries like surfaces or impermeable
walls.
An example of fluid dynamical layer simulation, in which one injection well
(left side) and one extraction well (right side) are present into a saturated
soil; water is introduced from the injection well to a constant pumping rate.
Once the pressure field has reached a steady state, the model computes
the water potential distribution (on the left) and then the water flow (on the
right).
Once the flows of each phase have been determined, the chemical layer can simulate the
fate of the contaminants. The model computes the changes in concentration over time due
to advection, (in which dissolved chemicals are moving with the flowing phase where they
are present), hydrodynamic dispersion (in which molecular diffusion and small scale
variations in the velocity of flow through the porous media cause spreading of the
contaminant front), exchange among phases (e.g. adsorption/desorption phenomena) and
chemical reactions. In the last case, we simulate the dissociation of hydrogen peroxide in
oxygen and water. The exchange among different phases can be modeled both assuming
an instantaneous equilibrium and dynamically modeling a couple of matter flows through
each interface between different phases, to reach a steady state.
An example of chemical layer simulation. The fluid dynamical configuration is
the same of the previous example; two contaminant zones are present in the
soil matrix. We can observe two kind of phenomena: first, the soluble
components of the contaminant pass from the soil matrix to the water and
second, they are transported from the water flows towards the extraction well.
The contaminant concentration in the soil decreases as time passes.
In the biological layer the model simulates the growth of the biomass and its interaction
with nutrients and contaminants. We suppose that, potentially, the bacteria could utilize the
contaminant presents in each phase of the ground; the electrons acceptor is the oxygen
dissolved in the water.
The model can simulate a biodegradation process by both aerobic and anaerobic
reactions. In the first case, it uses an oxygen-limited reaction following a Monod kinetic to
describe the growth of the biomass. In addition to oxygen, other nutrients, such as nitrogen
and phosphorous, may limit the biodegradation of the contaminants: the model takes
account of this fact. In the second case it is assumed a time constant decay of the
interested chemical.
In the figures we can see a case study of application of the whole model, in which we deal
with a soil portion of a real intervention. The field is been divided in hexagonal zones with
a side of 20 meters; on the vertexes of each hexagon and on its center there are extraction
wells while inside the hexagons there are 18 injection wells. We have simulated one
hexagon: water enriched with hydrogen peroxide is introduced by means of the injection
wells. The oxygen, produced from the hydrogen peroxide dissociation, is carried by the
water flows (which follow gradient of the water potential distribution). It should be noted
that, where the oxygen presence is bigger, we have the highest bacteria growth and the
smallest contaminant concentration.
Fluid dynamical layer
The multiphase flow in a porous medium is governed by Darcy law:
q  
k r k

 p   gz
(1)
where q (m/s) is the volumetric flow, k (m2) is the permeability of the solid matrix, kr is the
relative permeability of the phase , ma (Pa s), p (Pa) and  (kg/m3) are the viscosity,
pressure and density of phase  respectively. kr takes into account the presence of
different phases in the soil and depends of the saturation S (defined as the ratio between
the volume of the phase  and the pores volume in a reference volume).
The phases present into the soil can have different affinity with the soil matrix: they could
tend to stay near the surface of the soil particles (wetting phase), or they could tend to stay
far from the surface of the soil particles, in the middle of the pores of the soil (non wetting
phase). In a two-phase system there is a correlation between the pressures of the wetting
(pw) and the non-wetting phases (pnw), expressed in terms of the capillary pressure pcnw (the
pressure discontinuity at the interfaces between the wetting (w) and the non-wetting (n)
phases):
pn = pw+ pcnw(Sw)
(2)
The capillary pressure can be itself be expressed in terms of the saturation of the wetting
phase Sw, following the Van Genuchten model.
In a three-phase gas-NAPL-water system we can write:
pn = pw+ pcnw(Sw)
pg  pn = pcgn(Sg) = pcgn(Sw , Sn)
(3a)
(3b)
where pn (Sn), pw (Sw) and pg (Sg) are the saturation pressures of the non-wetting phase
(NAPL, non aqueous phase liquid), water (the wetting phase, in this case) and gas
respectively.
The relative permeability too depends on the presence of the different phases.
In a two-phase system the relative permeability of each phase can be expressed in terms
of the effective saturation Se of the wetting phase, following the approach of Mualem and
Van Genuchten (MVG).
In a three-phase water-oil-gas system, the preliminary experiments for the determination of
the relative permeability show that the relative permeability of water depends only on the
saturation of the water itself: due to its highest affinity to the solid matrix, the water fills the
smallest pore space, no matter how the remaining pore space is subdivided between oil
and gas. The relative permeability of oil and gas in a three-phase system, however,
depends on the saturation of all three phases. The reason is that, in a two-phase system
with water, oil fills the larger pores, whereas, in a two-phase system with gas, it fills the
smaller pores. Based on these considerations, different authors have developed methods
for determining the relative permeability-saturation without measuring the three-phase
system. In the COLOMBO model, we have followed the model of Stone II.
The transition function
The basic idea is to consider as reference pressure the water pressure: the pressures of
the other phases are obtained by applying relations (3a) and (3b).
Pressure waves move faster than phase flows so we can suppose that phases moves only
after that the pressure field has reached a stationary state (that depends on the phases
distribution in the soil).
Therefore, the following procedures define the global evolution of the system:
a) the update of state variable values imposed from outside (e.g. the flow rate of the
pumps);
b) the computation of the phase potentials (it involves the application of the transition
function for the pressure several times to CA);
c) the computation of the flows;
d) the computation of the remaining state variables.
Particularly, mass conservation requires that the algebraic sum of the flows in a cell
vanish:
f
6
k 1
i
k

 f ko  0
(4)
where f ki means the incoming flux of any kind of phase, and f ko means the outcoming
flux of any kind of phase; the possible flux direction are six (k ranges from 1 to 6) because
of the topology of the neighbourhood.
By inserting equation (1) and (3a) in (4) (and assuming, for simplicity, that only air and
water are present inside the soil), we can derive:
 k 0rw k p wj   w gz j k 0ra k p wj  p cwa
   a gz j
j




cell _ size
a
cell _ size
j 1   w
6

0


(5)
with:
p wj  p wj  p0w
z j  z j  z 0
(6)
where the subscripts w and a means, respectively, water and air; p is the pressure,  the
density,  the viscosity. This equation depends only upon the values of the water
pressure; we can derive the value of the water pressure of the central cell as a function of
the pressures of water in the neighbouring cells. This is exactly the definition of transition
function: the value of a state of a cell depends upon the values of the neighbouring cells.

p w0  f p w1 , p w 2 , p w3 , p w 4 , p w5 , p w6

(7)
This transition function is iterated over the whole cellular automata until a stationary
condition is reached. From the potential distribution we can compute the pressure
distribution by subtracting the gravitational potential and the phase flows which follow the
gradient of the potential.
Return to the COLOMBO model
Chemical layer
The most relevant phenomena that can involve chemicals are:

advection, due to the motion of the phase in which it is present;

hydrodynamic dispersion and molecular diffusion within the phase that contains the chemical;

exchange among phases (e.g. adsorption/desorption, transpiration);

chemical reactions.
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Biological layer
The biodegradation of an organic compound is the result of many different processes that
can be affected by many different factors: the presence of other microorganism's (fungi,
actynomicetes etc), different kinds of bacteria (that can cooperate or compete), chemical
compounds, chemical and physical characteristics of soil, temperature etc. etc.
The main factors that describe the behavior of a bacteria population are:



Spontaneous growth and death;
Decrease due to the presence of poisonous chemicals;
Growth due to the degradation of a specific compound.
COLOMBO model describes aerobic biodegradation in a contaminated soil.
The proposed model can describes the behavior of three kinds of bacteria: degrading
bacteria (which are able to degrade the contaminant), resistant bacteria (which can survive
in presence of the contaminant) and non resistant bacteria, for which the contaminant is
poisonous.
Of course, the behaviour of the degrading bacteria is the most relevant in bioremediation.
We suppose that, potentially, the bacteria could utilize the contaminant presents in each
phase of the ground; the electrons acceptor is the oxygen dissolved in the water.
Bacteria
Contaminant exchange
Oxygen exchange
We can show the biological transition functions that describes the evolution of a bacterial
population X and the relative consumption of contaminant.
If the degradation phenomenon is not aerobic, we can model the decrease of the pollutant
concentration by means of a time constant decay.
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