Analysis of oil displacement by water in oil reservoirs with horizontal wells Paulo Dore Fernandes, Thiago Judson L. de Oliveira and Rodrigo A. C. Dias
Problem Description This work involves near-well reservoir simulations. Typical reservoir simulations are interested on the general behavior of a entire field. An analysis of oil displacement by water in a oil reservoir with a single horizontal well is the focus of this work. It is also interesting to present a study of fluid displacement in porous media. This study was done to show the importance of relative permeability curves to predict the water breakthrough in producing wells.
Goals The main objective of this work is to analyze in detail the displacement of oil by water in horizontal wells. Different relative permeability curves are proposed in order to understand the impact of this curves in the water front. The body forces are neglected in the first simulation and then added in order to understand its impact.
Methodology Oil Displacement by Water - Porous Media Typical reservoirs simulators use Darcy's law. The use of the average theory is relatively new in reservoir simulations. The inertia and Brinkman terms are neglected when Darcy's law is used. The interaction between the phases is given by the relative permeability curves. Darcy Law - Saturation Average Theory Fluent Equations Where: Fractional Flow: f w kw w ko k w o w
Methodology Relative Permeability Curves Corey Model for Relative Perm k k rw ro kk kk rw ro Sw Swi 1 Swi S 1 S 1 S w w S S or or or nw no Corey Model - Linear The displacement of oil by water depends on permeability curve chosen. Linear Model: There isn t a defined advancement front. Linear Model: The water breakthrough is anticipated due to the interaction between the fluids Linear Model: Easier convergence Linear Model: Not physically real
Methodology Relative Permeability Curves Corey Model - Nonlinear k k rw ro kk kk rw ro Sw Swi 1 Swi S 1 S 1 S w w S S Corey Model - Nonlinear or or or nw no The displacement of oil by water depends on permeability curve chosen. Nonlinear Model: There s a well defined water advancement front. Nonlinear Model: Water front close piston behavior. Nonlinear Model: Difficult convergence. Nonlinear Model: Behavior more real. Pattern experimentally measured.
Methodology Relative Permeability Curves A courant number study was made in order to validate the simulations. The one-dimensional displacement of oil by water has analytical solution. The numerical solution was compared with the analytical Linear Model: Good answer for any Courant number. Nonlinear Model: Good behavior depending on the Courant number.
Methodology Real Case The modeling will be applied to real cases of near well reservoir simulation. The pressure transient behavior will be neglected. The well pressure drop is considered. The effect of body forces are neglected in the first simulation and then considered. Initial condition: S w0 = 0.1 Inlet: 100% of water, Pressure Outlet: Pressure Wall Symmetry Inlet Detail level - CFD Outlet
Methodology - Mesh The mesh was generated using the Cut Cell technique. The mesh has 4.556.731 elements. Well details: Reservatório Mesh refining close to the well region.
Inside the horizontal well
Results Uniformly Perforated (without gravity) The pressure drop in the well is considered. In this case a uniformly perforated screen is applied in the well. The well pressure drop increases with time. This is because more mobile fluid occupies more space in the reservoir leading to higher flow rates (pressure-pressure BC). The absence of body forces has a consequence in simulation. The water does not flow preferentially to the lower region of reservoir.
Results Unevenly Perforated (without gravity) The pressure drop in the well is considered. In this case a unevenly perforated screen is applied in the well. The well pressure drop increases with time. This is because more mobile fluid occupies more space in the reservoir leading to higher flow rates (pressure-pressure BC). The absence of body forces has a consequence in simulation. The water does not flow preferentially to the lower region of reservoir. The annulus (well-screen) pressure drop is almost equalized.
Results Real Case (With Gravity) Right at the initial instant, we can already see the effect of gravity in the simulation. Despite all outer contour is a inlet condition, the water enters firstly where the pressure gradient is larger. The main objective of this simulation is to understand the behavior of the displacement of oil by water when the body forces are taken into account.
Results Real Case (With Gravity) It is easy to see through the planes that are transverse to the well length that water firstly enters in reservoir from the bottom and displaces oil there. A important behavior happens in well plane. The water moves faster through this plan than by transverse planes due to the smaller distance between the well and water inlet.
Results Real Case (With Gravity) The arrival of water from the bottom well plane form an aquifer there. If we look at the transverse planes we realize that the water front in these plans is relatively far from the well. An aquifer is generated by the arrival of water coming from the well parallel planes. This conclusion is important and can only be found using detailed CFD solutions.
Results Real Case (With Gravity) The top view helps the visualization of the water zone formed due to early arrival of water in parallel planes to the well length. The water zone can be seen at already 10 months of simulation..
Results Real Case (With Gravity) The use of CFD simulations of reservoir allows us to analyze in detail what occurs in the reservoirs. Calculation of body forces is critical to get a more realistic behavior of the reservoir.
Results Real Case (With Gravity) We can see through the transverse planes that lot of oil remains trapped in the reservoir
Conclusions The study of relative permeability curves was fundamental to understanding the interaction between the phases in the displacement of water by oil. Unevenly perforated screen equalizes the pressure drop in the well and could impact significantly the arrival of water. It is important take into account the body forces on simulations of the reservoir. On the present simulation, the early arrival of water in the well is due to two factors: the accounting of body forces and the linear relative permeability curve.
Next Steps Develop a solution to obtain a consistent behavior with the use of a real relative permeability curve. Perform simulations with a pair of horizontal wells (producer and water injector) to study the effect of its position on the water breakthrough.