A Fast 3-D Interface Simulator for Steam Drives
Authors: Godderij R.R.G.G. , Bruining J. , Molenaar J. 
Published: December 2007

Abstract
Here we describe a fast 3-D steam drive simulator. We use an interface model, where the single phase steam zone is separated from the two phase liquid zone by the steam condensation front (SCF) which constitutes the interface. Steady state heat balances applied at the interface reduce the steam problem to a problem of gas/oil/water flow. Heat losses are treated by a prescribed conversion of steam to water. The model incorporates gravity, viscous and capillary forces and handles arbitrary permeability distributions and well configurations.
We use a multigrid method to solve the pressure equation. The steam zone development is determined by a probabilistic method, which ensures that instability phenomena are properly treated. The oil/water flow problem in the liquid domain is solved as in conventional reservoir simulators. We validate the model with analytical models.
Example calculations for a thin medium-viscosity oil field show that a transition zone with a reduced oil viscosity just downstream of the SCF has a pronounced stabilizing effect. This, and the global heat loss effects are the reason for the high displacement efficiency of steam drives.

Introduction
Steam drive models with various degrees of sophistication are available for optimal field development and the assessment of economical risks. Fast, simple models solve the heat-balance equation and use apriori assumptions on the flow field. Examples are the frontal displacement models or the extreme gravity overlay models (a horizontal SCF). Van Lookeren was the first who combined a heat balance with mass flow. His description results in a stationary development of an inclined steam condensation front. It is, however, only applicable for favorable (pseudo) mobility ratios. Limitations of simple analytical models, and the ready availability of computers led to the development of thermal reservoir simulators. The large computational cost makes these simulators less suitable for dense gridded simulations, for many development scenarios, or reservoir heterogeneity models.
Here we describe a model that incorporates the essential features of the steam drive process but uses some assumptions to lower the computational costs. The main assumption lies in the application of steady-state heat and mass balances over the SCF to reduce the problem to the model equations of gas/water/oil flow. The essential ideas are described extensively in previous references. In these papers we use an effective viscosity in the single phase liquid zone. Therefore we could only describe the steam zone expansion and not predict oil and water production. Moreover due to the vertical equilibrium (VE) assumption we could not deal with steam underride in a low lying high permeable layer.
In this paper we present a 3-D steam drive model which includes a two-phase liquid zone and allows arbitrary injection/production well configurations. The main application of the model is to aid in the design and interpretation of steam drive projects. The model can be used:to describe the shape of the steam zone in three dimensions,to predict the time of steam breakthrough,to calculate the cumulative water and oil productions for each well, andto determine the relative importance of features related to the steam drive process such as steam override, viscous fingering, and steam and/or water cresting/coning in fine gridded homogeneous and heterogeneous reservoirs.

Physical Model
Reservoir geometry. Fig. 1 shows a 3-D representation of a tilted rectangular heterogeneous reservoir, with thickness H, width W, and length L. It is bounded by impermeable cap and base rock with constant thermal properties. The reservoir tilt can be described by two angles: P. 279^