Experimental And Numerical Modelling of Bottom Water Coning to a Horizontal Well
Authors: Jiang Q. , Butler R.M. 
Published: March 2010

Abstract
The displacement of oil by bottom water drive to a horizontal well was studied experimentally in a Hele-Shaw cell. The stability of the water-oil interface was investigated at different flow rates and viscosity ratios. A stable interface with higher recoveries was obtained for lower flow rates and where water and oil had the same viscosities. The effect of unstable flow conditions on the shape of interface and oil recovery was also studied. For a given viscosity ratio, higher flow rates usually resulted in a lower oil recovery at breakthrough. However, in some cases where multiple fingers formed, the oil recovery for higher flow rates was found to be higher than that for lower rates. Oil recovery at breakthrough was correlated with a dimensionless flow rate.
A novel numerical method was developed to simulate the piston type of displacement found in Hele-Shaw cells. The advancement of the water-oil interface and the corresponding oil recovery, as well as the pressure behaviour, were predicted. A single finger was identified for different flow rates when the viscosity ratio was adverse. The simulation results were in general agreement with corresponding experimental data.

Introduction
Reservoirs underlain by bottom water zones are very common and constitute a significant resource. The effective exploitation of these resources would provide an offset to the oil production decline from top quality reservoirs. Production from such reservoirs usually involves the completion of the well near the top of the reservoir so as to reduce the production of free water.
If capillary force is ignored, then there are two forces acting on the interface during production:the viscous force that results from the flowing of fluids in the reservoir andthe net gravitational force that results from the difference in density of two phases.
For upwards displacement of oil by water, the gravitational force tends to stabilize the water-oil interface. When the difference between vertical pressure gradients across the interface becomes greater than the difference of gravity pressure gradients, the water-oil interface becomes unstable and viscous fingering occurs. Otherwise, the water-oil interface is stable. Figure 1 shows schematically the shape of a stable water cone for a vertical well and a corresponding crest for a horizontal well. For vertically confined reservoirs, the cumulative oil production for isolated wells at the breakthrough depends on the volume of water cone or crest underneath the production well, (see Butler(1)). Cumulative oil production by bottom water drive can be improved by using horizontal wells in place of vertical wells because of the extended length of water crest (see Figure 1).
When the viscosity of water is less than that of oil, which is the usual case in reservoirs, the upwards displacement of oil by bottom water may cause the interface to become unstable at high production rates because of the adverse mobility ratio. The maximum production rate to maintain a stable interface is called the critical flow rate. The determination of critical production rates for various reservoir properties and production conditions has been studied by many authors(2–13).