Reservoir Modeling

1. Saleh_Farag_SAAD
Single Phase Pressure Equation
Reservoir Simulation

2. Saleh_Farag_SAAD

3. Sign Convention:
In (+)
Out (-)
Block Center
Timestep
t, t+Δt
Units
Control Volume
Saleh_Farag_SAAD

4. Saleh_Farag_SAAD
Now divide by (Δ𝑋𝑋)𝐴𝐴∆𝑡𝑡
Sign Convention:
In (+)
Out (-)
Block Center
Timestep
t, t+Δt
Units

5. Saleh_Farag_SAAD
Differential Form of the
conservation Equation

6. Saleh_Farag_SAAD
Differential Eq:

7. Saleh_Farag_SAAD
Expanding LHS using Chain Rule: ρ(P) and 𝝓𝝓 (P)
𝒅𝒅𝒅𝒅
𝒅𝒅𝒅𝒅
=
𝒅𝒅𝒅𝒅
𝒅𝒅𝒅𝒅
𝒅𝒅𝒅𝒅
𝒅𝒅𝒅𝒅
The Single Phase Pressure Equation
The Conservation Equation

8. Saleh_Farag_SAAD
Cf

9. Saleh_Farag_SAAD

10. Saleh_Farag_SAAD
RHS RHS

11. Saleh_Farag_SAAD
0

12. Saleh_Farag_SAAD
𝑪𝑪𝒇𝒇
𝟏𝟏
𝝆𝝆
Multiply by

13. Saleh_Farag_SAAD
Dh is a constant known as Hydraulic Diffusivity – it is a diffusion constant describing how
fast the pressure wave “diffuses” across the reservoir. Faster pressure communication if
Dh is larger i.e. if
Diffusivity Eq:

14. Saleh_Farag_SAAD

15. Saleh_Farag_SAAD
Thanks

16. Saleh_Farag_SAAD

17. Saleh_Farag_SAAD