# Team:NKU China/Model

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Modelling
Introduction
Oil recovery is quite a huge project that requires a lot of manpower and material resources every time there is a new method to test. So it’s important to find a way to simulate the process and get the results. Fortunately, nowadays mathematics is developed enough to construct a model like a machine,putting the known parameters into it and getting the simulated results without conducting the whole experiment,which is likely to be rather complex.In our project, we just use mathematical models to have a general govern and better understand of our system’s efficiency.

The device we constructed works in a dynamic environment and compared with the diameter of the water injection well where the microbes are transported into the oil reservoir and water channel where they function,they are small enough to obey the law applied to water flow which carries them.That’s what we refer constructing the transmission mode,which helps us determine when to “wake up” our engineered microbes.And we also need to know how to “wake them up”- the behavior of fim switch is simulated.By connecting the models together, we can run the microbes virtually with no worry of time,safety and cost,which should be considered when conducting on the spot.
General Model
We employed Darcy’s Law to estimate the time cost on the arrival of microbes at the water channel.Upon arriving at the spot, we put inducer like IPTG to activated the complemented gene Bcs A,which is a gene controlling the production of cellulose knocked down in our device and operated by an operon.With the effect of cellulose,the water channel is blocked and the fim switch is activated by adding another inducer like Ara artificially.Then the switch make it possible to produce rhamnolipid in our engineered bacteria,which helps driving oil flow out with water.Thus, the efficiency of oil recovery is increased.
Governing expressions & equations
Fig1. Governing expressions & equations
Fig2. General Scan
Fig3. Microbes’ transportation & plugging effect
Fig4. The fim S switch
Fig5. Functions enhancing oil production
Fig 6. Result of the general model
The Transmission Model
To have a closer look at the process microbes are transported in the oil reservoir, we constructed a model under the condition of a porous rock media underground ,similar as the transmission of underground used water.
Governing equation[1]
Fig7. Governing equation
Initial conditions & Boundary conditions
Fig8. Initial conditions & Boundary conditions
where C is the fluid phase concentration, D is the effective dispersion coefficient, x is distance, t is time, v is the interstitial fluid velocity, and k is a reaction constant. A function similar to the gamma distribution is used as the initial condition, and a time-dependent boundary condition is applied at x=0, and Ci, Ca, Cb, β, μ, and λ are constants.
Here we designed an interactive part to show the result dynamically. As space is limited in this wiki, there are four short film to show how it functions.
 General Column Length Diffusivity Growth Costant Pore Velocity
The Fim Switch Model
With limited data, a stochastic model is powerful enough to give results from unsteady bio-systems.That’s what we apply in our model.To make it easy to understand, we just explain the “on” and “off” state and the switch itself with three small models as follows:
Overlook
Fig9. Overlook of the switch model
Switch On
Fig10. State: Switch on
Result(Stochastic TAU-LEAP)[switch on]
Fig11. Result(Stochastic TAU-LEAP)[switch on]
Switch Off
Fig12. State: Switch off
The switch
Fig13. The S switch
Result(Stochastic TAU-LEAP)[switch]
Fig14. Result(Stochastic TAU-LEAP)[switch off]
Reference
P. Sivasankar, A. Rajesh Kanna, G. Suresh Kumar, Sathyanarayana N. Gummadi，Numerical modelling of biophysicochemical effects on multispecies reactive transport in porous media involving Pseudomonas putida for potential microbial enhanced oil recovery application，Bioresource Technology，211 (2016) 348–359.