1. SIMULATION EXAPLES OF WATER INJECTION NTNU Author: Professor Jon Kleppe Assistant producers: Farrokh Shoaei Khayyam Farzullayev

2. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards  The water can apparently travel through a coarse grid model more quickly than a fine grid model.  The water front becomes smeared causing a prematurely water break through in the coarse grid model.  This effect is called numerical dispersion.  In practice there are other factors contributing to numerical dispersion such as the averaging of relative permeabilities and of saturations. Characteristics of this model:  A simple quarter five-spot model of oil displacement by water injection.  The oil producer well at the corner was controlled by constant bottom hole pressure (BHP) and the water injector well at the centre was controlled by constant injection rate.  Case 1 : geometry of 5 x 5 x 1  Case 2 : geometry of 50 x 50 x 1 Five spot model, water injection simulation

3. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Case 1 Animation of Oil Saturation 5 x 5 x 1

4. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards  The movement of water front through the model can be seen better in this view. Animation of Iso-Surface Oil Saturation

5. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Animation of Oil Saturation  The model structured with large number of gridblocks would be an obvious way to overcome the inaccuracy of numerical dispersion. Case 2 50 x 50 x 1

6. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Animation of Iso-Surface Oil Saturation  In the case with a large number of grids we achieve better sweep efficiency and sharper developed front.

7. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Effect of permeability distribution  As a result of gravity forces, the heavier fluid flows downwards. Since the density of water is normally greater than oil’s, it will always tend to flow to the layers below.  As a general rule of fluid flow in porous media, fluids always flow to the higher permeability layers. Characteristics of this model:  Two-phase cross-sectional linear simulation model  Geometry: 50 x 1 x 10  Water injection well is located on the left side of the model  Producer is on the right hand side of the model.  Case 1 : Permeability increases downwards  Case 2 : Permeability increases upwards

8. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Case 1  The injected water tends to flow towards the bottom layers as a result of gravity and increase of permeability downwards, this leads to early water break through. Animation of Oil Saturation Permeability increases downwards

9. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Water mass flow  As the water displaces oil from the bottom layer, it may leave some zones not displaced due to fast movement of water along the bottom towards the producer well.

10. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Case 2  The injected water tends to be in the upper layers because of the high permeability.  On the other hand, gravity also plays its role by pushing the water downwards  The effect of both factors create balance in the sweep of the reservoir Animation of Oil Saturation Permeability decreases downwards

11. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Water mass flow  From this diagram it is possible to see the movement of water to the bottom by gravity from the top layers, while displacing oil.

12. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards Oil saturation profile, highest permeability layer at bottom. Oil saturation profile, highest permeability layer at top.  Water sweeps the oil with greater efficiency in Case 2 than in case 1.  In this slide both examples discussed before are simulated at the same grid distribution and time interval in order to illustrate the difference in sweep efficiency.

13. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards References  Kleppe J.: Reservoir Simulation course Kleppe J.  Snyder and Ramey: SPE 1645 Snyder and Ramey

14. Simulation Examples of Water Injection Five spot model, water injection simulation Case 1 Coarse grid model Case 2 Fine grid model Effect of permeability distribution Case 1 Permeability increases downwards Case 2 Permeability decreases downwards  Title: SIMULATION EXAPLES OF WATER INJECTION  Author:  Name: Prof. Jon Kleppe  Address: NTNU S.P. Andersensvei 15A 7491 Trondheim  Website Website  Email Email  Size: 650 Kb  Software required: About this module