Aspects of Discretized Wellbore Modelling Coupled to Compositional/Thermal Simulation
Authors: Oballa V. , Coombe D.A. , Buchanan L. 
Published: March 2010

Abstract
The practical advantages and limitations of discretized well- bore modelling when coupled to full field compositional and/or thermal simulations are presented in detail The implementation of an efficient, strongly, coupled discretized wellbore model is irst discussed, with emphasis on wellbore hydraulic options and run-time-saving features such as pseudo-steady state initialization. The impact of these various aspects are shown on typical isothermal and thermal compositional field scale processes. The traditional sink/source modelling approach to fully coupled wells is used as a reference case in these comparisons where, applicable. By doing so, this paper, presents guidelines for the simulation engineer on the use and possible misuse of discretized wellbore model.

Introduction
In the past decade the use of horizontal wells increased rapidly due to improved drilling techniques as well as more efficient application to reservoirs where production from vertical wells was not economical. Reservoirs with vertical fractures, gas caps and/or bottom aquifers or heavy oil and tar sands reservoirs were the major contenders. New processes were used to deplete these reservoirs and numerical simulation became a tool in understanding these processes. Initially horizontal wells were modelled by the traditional sink/source approach. In this method only the hydrostatic pressure distribution along the well is known. Compositional, energy and frictional pressure drop effects are neglected. In the course of history matching the performance of these reservoirs, it was realized that wellbore flow characteristics may impact on reservoir behaviour in terms of different breakthrough time, uneven communication between wellbore and a reservoir, etc. Therefore, several approaches were tried by different authors(1, 2) to include hydraulics in the modelling of wellbore flow. In this work the approach of Collins et. al(3) was extended and implemented in a thermal/compositional simulator.

Implementation of Strongly Coupled Well Model
CMG's simulator STARS is an advanced simulator that can handle a wide range of processes such as steam drive, steam cycling, combustion, polymer, foam and emulsion flow, etc. In STARS two well models are available. The first one is a standard sink/source approach. The second one, Discretized Wellbore model (DW) is more sophisticated and attempts to overcome some deficiencies of the first model. It also considers fluid and heat flow in the wellbore. The focus of this paper is on the second model, however, a brief description of a sink/source model is also furnished for completeness.
Sink/Source Model
In a sink/source (SS) model, flow from/to a reservoir is represented by a single term in reservoir flow equations. Steady state flow is assumed to be in the wellbore, i.e., there is no wellbore storativity. Only one equation per completion (layer) is solved with a bottom hole pressure as a primary variable. It means that only the pressure distribution due to gravity is known in the wellbore, but not the composition nor the temperatures distribution. This poses numerical difficulties when some layers in a well are producing and some injecting. Heat conduction between a wellbore and a reservoir is also neglected. Fluid flow from/to a reservoir is calculated from Equation (1)