Efficient Modelling Of Wellbore Backflow
Authors: Sharma R. , Nghiem L.X. , Siu A. , Collins D.A. , Mourits F.M. 
Published: March 2010

Abstract
Production from reservoirs with large permeability contrasts or reservoirs consisting of several non-communicating layers can result in significant crossflow between the layers through multilayer wells. This entails the backflow of reservoir fluids from the wellbore to the reservoir. Standard line source/sink methods for handling wells in reservoir simulators are unable to cope with backflow because the wellbore is assumed to have the same saturations as the reservoir. To simulate backflow accurately, the well model must keep track of the fluid saturations within the wellbore. In this work, the discretized wellbore model developed by Collins et al. (1992) is extended and applied to vertical wells exhibiting backflow. The method described calculates fluid saturations along the wellbore implicitly. Comparisons of results between the standard line source/sink well model and the discretized wellbore model are made for several field-scale cases. It was found that the standard line source/sink model can result in unphysical values compared to the discretized wellbore model, which always yielded realistic production rates for the cases considered.

Introduction
Production from highly stratified reservoirs or from reservoirs with barriers between different production zones can result in significant backflow in producing wells. This corresponds to the flow of fluids from the wellbore back into the reservoir. This process happens quite frequently when the well is completed over multiple reservoir layers with poor vertical communication. The poor communication causes the potential gradient in the reservoir to be very different from the gradient in the wellbore. As the well acts as a channel for fluid flow between reservoir regions with different potentials, backflow occurs when the difference between the reservoir pressure and the wellbore pressure (pressure drawdown) becomes negative.
Reservoir simulators where the well is represented as a line source/sink are not suitable for handling backflow. They give erroneous results, and when backflow is severe, they yield an unphysical solution. Holmes (1983) attempted to improve the source/sink representation of the well for backflow situations by including a global wellbore mass balance. In this approach, the fluid properties and saturations were assumed uniform throughout the wellbore. Modine and Coats (1990) introduced a superposition method in which fluid compositions resulting from an explicitly calculated head within the wellbore were used to determine individual layer inflow (layers producing into the wellbore) and outflow (layers receiving fluids from the wellbore).
An efficient technique for modelling wellbore dynamics in reservoir simulation was developed by Collins et al. (1992). The wellbore flow equations were cast judiciously in a form similar to the reservoir flow equations. Thus, efficient techniques that were developed to solve the reservoir flow equations can readily be applied. Since Collins et al. considered horizontal production wells only, their method required extension to the case of vertical producers and injectors. This method will be referred to as the "discretized wellbore" technique.
In this paper, the discretized wellbore technique is extended to vertical production/injection wells exhibiting backflow. Several field-scale cases are used to test the technique.