Horizontal well and near-well region simulation using coupled axial-radial productivity models

Cao, Jie (2016) Horizontal well and near-well region simulation using coupled axial-radial productivity models. Doctoral (PhD) thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (9MB)

Abstract

Directional drilling technologies have dramatically increased the application of advanced wells in reservoir development since the 1990s, including horizontal, deviated, multilateral and smart wells. The great demand for highly accurate and efficient well models arrives from the fact that drilling technology has outpaced simulation techniques. The well model, usually coupled with the reservoir model, is crucial for productivity estimation and prediction. The main objectives of this research are to develop a well/near-well model and associated simulation techniques using coupled axial-radial productivity models for advanced wells. The analytical coupled axial-radial flow models were recently developed and described in research notes. These ideas originate from the observation that the axial reservoir pressure gradient cannot be ignored since pressure gradients exist in horizontal wellbores. The analytical models consider both axial reservoir flow and radial well inflow in the near-well reservoir, physically representing a two dimensional problem. These models were solved under both steady state and semi-steady state conditions, using external boundary pressure and average reservoir/grid block pressure, thereby generating the coupled axial-radial productivity (CARP) models. The main focus in this work is to apply the CARP models in the construction of a numerical scheme for horizontal well and near-well region simulation (i.e. the well/near-well model), in which wellbore hydraulics are included. In steady state and semi steady state flow, the pressure solutions are analytical in each grid block and result in curved surfaces of near-well reservoir pressure, contrary to the constant pressure distribution used in the finite difference method. Hence, the new numerical scheme is demonstrated, and proved in the steady state case, to be a higher order method than the standard finite difference method. The simulation results show that the new method requires less grid block refinement to achieve the same accuracy compared to the finite difference method. The CPU time needed for the same grid blocks to achieve the same accuracy is greatly reduced using the new method compared to the finite difference method. This reduces the need for grid block refinement in the near-well region. Furthermore, the numerical well/near-well models are applied in heterogeneous reservoirs and special cases where cross flow occurs. Wide permeability ranges can be dealt with in these models in a stable manner without special treatment. Both the axial and radial flow directions are solved as unknowns in these models; hence the cross flow between the well and the near-well reservoir can be represented. Besides, the new well/near-well model can be coupled with standard finite difference reservoir simulators such that both the well completion effects and remote reservoir effects are taken into consideration. An iterative coupling scheme is used in this research, and calculated examples considering unevenly distributed skin factors also demonstrate the application of the new well/near-well model and the stability of the coupling scheme. The well/near-well model is also developed for anisotropic reservoirs using average reservoir pressure. Based on previous research notes, this is achieved through a permeability tensor used for axial reservoir flow and well inflow equations. This permeability tensor is generated using a unique transformation that converts the anisotropic media into a virtually equivalent isotropic media in the axial and radial directions. This transformation is only applied in the near-well region without changing boundary conditions, and it preserves volume, flow rates and pressure. The cylindrical near-well region is transformed into elliptical cylinders; consequently, Dietz shape factors for ellipses are used in productivity models.

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