Designing Horizontal Wells Using a Coupled Wellbore to Reservoir Flow Simulator
Authors: Thuren J.B. , Bass J.M. , Baker A.J. 
Published: December 2007

Abstract
The new Texaco finite element reservoir simulator, UNISIM, has been applied to model water injection in a long horizontal well located in a North Sea reservoir. The simulator has some unique advantages over typical finite difference simulators used in the industry:the model has adaptive gridding which refines grids automatically where required most,the horizontal wellbore is treated as porous media and is uniquely tied directly to the reservoir,the inherent errors for PI prediction in finite difference simulators for horizontal wells are avoided andtransient conditions (not semi-steady state) are modelled.
Since this is a new simulator, at present, it is primarily applied to research applications. In the future, wellbore flow models other than porous media will be investigated.
For this study, the wellbore is treated as a very high permeability porous media with porosity set approximately equal to 1. The reservoir is considered as containing 2 fluid phases.
Five simulations were performed under this project, 4 with a cylindrical wedge mesh and 1 with a flat 70ft thick reservoir sector. For the wedge, results were calculated with constant wellbore permeability (assuming laminar wellbore flow) and varying wellbore permeability (assuming turbulent wellbore flow). Two simulations were run to demonstrate the effect of partially closing the wellbore to the reservoir. The run using the 70ft reservoir sector applied unstructured meshing to place the offset well 15ft from the bottom of the reservoir.
The results show that openhole completions for long horizontal wells result in very large flow from the heel of the well. Partial completions can push injection water further down the wellbore towards the toe end. It is also observed that horizontal injector flow is a completely transient phenomenon.
The simulator is jointly developed by Texaco EPTD and Computational Mechanics Co., Austin, Texas. This simulator is based upon a new generation of finite element techniques which are hp-adaptive. The h refers to the local mesh size and p refers to the order of the local polynomial approximation. The adaptivity means that h and p can be changed at any simulation time step to capture the movement of saturation fronts or locally increase the solution accuracy at any point. The solution field generated is continuous across grid blocks for pressure, saturation and flow. For further technical details on UNISIM, see Reference 1.
The capability of generating continuous solution fields is vital in the modeling of coupled wellbore to reservoir flow. This is because flow must turn within a grid block. When an injector fluid (water) flows down the wellbore it must turn before exiting through the perforations. This will cause an additional flow pressure drop along the wellbore.
Wells consist of a refined mesh usually with a higher order p polynomial approximation. This approach is natural and allows the correct pressure and flow rates to be developed at the well boundaries without any apriori specification of productivity or well indexes. Flow out of the injector well is calculated from first physical principles.
For purposes of this study, adaptive meshing will be controlled by the gradient of saturation, thereby maintaining a highly accurate calculation of saturation fronts and the time such fronts arrive at critical boundaries.
The simulator has a complete pre/post processing capability, unique in that it can handle the display of continuous solution fields. Most illustrations in this report were generated interactively using post processor displays.

Fundamental Data
The starting point for this project is in the original data. The desired well length is to be 4750ft. The well lies horizontally in a region of high permeability unconsolidated sandstone.
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