# A Comprehensive Wellbore/Reservoir Simulator

**Paper Number: **18419-MS

**Authors**: Stone, T.W., Alberta Research Council; Edmunds, N.R., Alberta Oil Sands Technology and Research Authority; Kristoff, B.J., Saskatchewan Research Council

**Source**: SPE Symposium on Reservoir Simulation, 6-8 February, Houston, Texas

**Copyright**: Copyright 1989, Society of Petroleum Engineers

**Preview **This paper describes a fully implicit, three dimensional thermal numerical model for simulating flow through a porous media and through a wellbore. Darcy's law is used together with conservation of energy and mass to model flow in the porous media. The wellbore simulator is a time dependent, thermal, three-phase, one dimensional model which conserves energy, momentum of all phases and mass. Wellbore grid blocks are embedded in reservoir grid blocks. Variables in the reservoir and wellbore are solved for simultaneously. Many options are included in the wellbore simulator including the ability to model parallel flow in inner tubing and outer annuli and specification of slant angles or other parameters per wellbore grid block. This coupled model is targeted mainly at horizontal well or other applications in which a high degree of dynamic interaction occurs between the wellbore and reservoir.

**Introduction **In field operations which employ vertical wells, completion of those wells may extend several meters. Horizontal wells, for example, may extend several hundred meters and be perforated along the entire length. Recovery processes that do not involve high pressure gradients within the reservoir will be sensitive to the wellbore dynamics of these long horizontal wells and adequate modelling of flow down the wellbore is important. Flow regimes, inner tubing/outer annuli, stagnant zones, undulations in the trajectory of the horizontal well need to be resolved within the model in order to adequately predict the system. One of the applications the model described in this paper was designed to handle is gravity drainage. In this process, gravity provides the driving force enabling steam to flow upward and hot fluids to flow downward. Economics for the process are enhanced by using a pair of long horizontal wells. The upper well injects high quality steam and the lower well acts to collect hot fluids. Both wells may be used initially in circulation mode to heat the reservoir in order to start the process. Because the motivating forces within the reservoir are small, dynamics of the wellbore need to be adequately represented in order to predict the reservoir/wellbore system.

A drive process in which injection may initiate from a vertical well completed over several meters and production may occur from a long horizontal well can also be predicted and analyzed. A scaled experiment of this process is described in this paper together with a numerical prediction.

In this paper, model equations are presented together with boundary conditions and solution techniques. Stability of the coupled model is then discussed. Finally, applications of the model are presented including the simulation of the scaled experiment and an idealized field scale prediction.

**Model Description **

**Basic Equations**: Reservoir

The reservoir model consists of four equations satisfying conservation of energy, conservation of mass and phase equilibrium constraints. The mass conservation equations involve two components, water and oil. Addition of other distillable components is straightforward and is not presented here.