# Geometry two

For the second geometry,the case of two caves of different sizes connected by a fracture is considered, with water injection from the bottom, thus oil is displaced towards the upside, as shown in the figure below.

The parameters such as Reynolds numbers, viscosity of the fluids, interfaces tension, as shown in the table below, will be varied to see the effects on the oil recovery, sweeping efficiency, distribution of the remaining oil,flow rate, etc. The CFD softwares Jadim and fluent, are used separately to simulate this case. The sensitivity of mesh density is also tested.

Simulation parameters

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) $$dt_{min}/dt_{max}$$(s) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) mesh size (cells) inlet Re 1000;800 2;20 0.487 0.1e-7;0.1e-4 0.02;0.05 2 0.45*0.35 90*70 20 1000;800 2;20 0.487 0.1e-7;0.1e-4 0.02;0.05 5 0.45*0.35 90*70 50 1000;800 0.1;1 0.1;1 0.1e-7;0.1e-4 0.02;0.025 5 0.45*0.35 90*70 200 1000;800 2;20 2;20 0.1e-7;0.1e-4 0.02;0.025 2 0.45*0.35 360*280 20 1000;800 0.01;0.1 0.01;0.1 0.1e-7;0.1e-4 0.02;0.025 1 0.45*0.35 360*280 2000

# Similation with jadim - coarse mesh

Firstly, a coarse mesh and real parameters of fluids  are applied to simulate the flow with VOF method by jadim software.

However, the simulation is not reasonable because the water and oil is mixed.  This could be caused by the high Reynolds number or the density of mesh. Therefore, the inlet velocity is decrease and the viscosity is raised for the simulation.

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) $$dt_{min}/dt_{max}$$ (s) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) mesh size (cells) inlet Re 1000;800 0.1;1 0.025 0.1e-7;0.1e-4 0.02;0.05 5 0.45*0.35 90*70 200

This time, the phenomenon of diffusion is not as severe. But the mixture of the two phase still happens.

Thus, to avoid the diffusion, we need to use:

-a higher value of viscosity (100 times) to avoid this situation.

-a refine mesh.

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) $$dt_{min}/dt_{max}$$ (s) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) mesh size (cells) inlet Re 1000;800 2;20 0.487 0.1e-7;0.1e-4 0.02;0.05 2 0.45*0.35 90*70 20 1000;800 2;20 0.487 0.1e-7;0.1e-4 0.02;0.05 5 0.45*0.35 90*70 50

With the viscosity of the fluids 1000 times of the initial values and Reynolds within 100, the calculation finally reaches convergence. Below is the initial and final state for the Reynolds 50.

# Similation with jadim - refine mesh

As mentioned before, to solve the problem of convergence during calculation and test the sensitivity of results to the mesh density. A mesh of density 16 times compared with the former one is applied.

To achieve the above objectives, two group of parameters are used for the refine mesh:

A. A group of parameters same with one of those used for the coarse mesh, which is:

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) $$dt_{min}/dt_{max}$$ (s) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) mesh size (cells) inlet Re 1000;800 2;20 0.487 0.45*0.35 0.2;0.025 2/5 0.45*0.35 360*280 20/50

B. The interface tension as initial values. Viscosity 10 times and 100 times to the initial values.

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) $$dt_{min}/dt_{max}$$ (s) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) mesh size (cells) inlet Re 1000;800 0.01;0.1 0.025 0.1e-7;0.1e-4 0.02;0.025 1 0.45*0.35 360*280 2000 1000;800 0.1;1 0.025 0.1e-7;0.1e-4 0.02;0.025 1 0.45*0.35 360*280 200

When the viscosity is 10 times, the problem of convergence still exists. However, for the case where viscosity is 100 times, the calculation achieves convergence.  For the group of parameters same with one of those adopted with the coarse mesh, the calculation converges; however it take almost 14 times to finish the simulation.

For case B, the movement of the fluids is similar with what we have obtained from the coarse mesh. Also, the interface between the two fluids is clearer.

# Geometry two - simulation with fluent

To compare the differences results given by fluent and jadim. Firstly, same parameters with one group which is adopted by jadim in utilized, as shown in the table below.

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) inlet Re 1000;800 2;20 0.487 0.02;0.05 5 0.45*0.35 50

With fluent, we have more dispersed phase due to the high viscosity. The differences for the results of jadim of fluent will be discussed later.

Then the real parameters of the fluids is used to see the differences.

 $$\rho_{water} /\rho_{oil}$$ (kg/m3) $$\nu_{water} /\nu_{oil}$$ (Pa.s) $$\sigma_{oil/water}$$ (N/m) inlet/outlet lenght (m) inlet velocity (m/s) mesh size (m) inlet Re 1000;800 0.001;0.01 0.025 0.02;0.05 0.066 0.45*0.35 1320

For the real parameters of the fluids, the viscosity is much smaller, the velocity is small, The weber number is very small, so the interface tension plays an important role in the process, so the interface does not change.

# Post treatment and results analysis

1. Evolution of flow rate and oil recovery

In the very beginning before the dimensionless time reaches 0.3, the outlet oil flow rate equals with the inlet flow flow, because of mass conservation and that water has not reached the outlet. Afterwards, water reaches the outlet, the outlet oil flow rate starts to slow down, and the gradient for the oil recovery rate starts to slow down.

2. Parameters sensitivity

A. Inlet Re

Re=20                                                                                Re=50

To evaluate the effects of Reynolds number on the oil recovery, all other parameters are set the same value except that the Re number are different at the inlet. For a high Re, water reaches the outlet earlier, and the value of oil recovery is higher. This could lead by the recirculation caused by a higher Re.

B. mesh density (0.00125m/cell & 0.005m/cell)

Coarse mesh (Final state)                                                           Refine mesh(Final state)

From the figures of oil recovery ratio and flow rate, for the simulation with the refine mesh, the water reaches the outlet later, because the water diffuses less with the refine mesh. Therefore, we have a lower oil recovery ratio. And the interface in clearer with the refine mesh.  However, it take about 14 times to finish the calculation with the refine mesh. Thus, both calculation duration and the precise requirements should be taken into consideration when choosing the mesh density.

3.  Comparison for fluent and jadim

To compare the the differences of the softwares jadim and fluent, all parameters are set as the same value. From the figures, by using software fluent, water reaches the outlet with a shorter time. One possible reason is that there is more diffusion with fluent. Another reason for the difference could be the method used to calculate the flow rate at the outlet. In jadim, the oil outlet oil outlet velocity  is calculated by the average of the multiplication of the velocity and oil ratio in every cell by every time step. However, for fluent, this velocity is calculated by the average velocity and average oil ratio by every time step.