A Fast Procedure for Upscaling in Compositional Simulation
Authors: Christie M.A. , Clifford P.J. 
Published: December 2007

Abstract
Single phase upscaling techniques have been in use for a number of years now to incorporate sub-grid reservoir description information into reservoir simulation. There have also been a number of approaches to developing two-phase upscaling algorithms suitable for black oil simulation.
The key barrier to the development of compositional upscaling techniques is algorithm speed. A straightforward extension of existing two-phase upscaling approaches would consume enormous amounts of cpu time due to the number of additional components modelled and the need to perform flash calculations. This paper describes an upscaling method for simulations in which compositional processes play a key role, such as miscible gas injection or gas cycling schemes. We will describe the method to generate upscaled compositional fluxes in 2 or 3 dimensions, and the way in which the upscaled fluxes are incorporated into a compositional simulator.
Our approach uses a streamline technique which provides a tremendous gain in speed for the loss of a small amount of accuracy. The streamline technique produces upscaled fluxes almost identical to those obtained from post processing conventional compositional model runs in a fraction of the time.
The results of applying these upscaled fluxes in a realistic example show that we can obtain close agreement between fine and coarse grid models of lean gas injection into oil at residual saturation. For an example problem with a 12 component equation of state, the component recovery curves using upscaled fluxes on a 5 × 5 grid agree well with the original 100 × 20 fine grid

Introduction
The industry has put a significant amount of effort into developing single phase and two-phase upscaling algorithms (see [1] for a review). The purpose of these algorithms is to take a fine scale geological description and to produce effective properties appropriate for coarser scale simulation which "preserve" the key fine scale features. The upscaled properties reproduce behaviour "on average", and do not reproduce fine details.
All upscaling procedures work in essentially the same way: remove a section of the fine detailed model; assume boundary conditions; calculate an effective property.
Single phase upscaling is becoming used more widely; it is fast, and generally its limitations are known.
Two phase upscaling has had limited use to date, but is reasonably fast and our understanding of it is developing. The two-phase upscaling work and work on pseudo functions has shown that upscaling multi-phase flow is fast enough to be realistic for black-oil models.
There have been limited attempts at any form of pseudoisation of compositional flows. One example is the alpha-factor approach of Barker and Fayers. Their alpha factor approach allowed a fine grid model to be upscaled - providing one had run the fine grid model in the first place. The recent development in streamline techniques has improved the speed of compositional modelling sufficiently for compositional upscaling to be considered, and the alpha-factor method of Barker and Fayers provides a way for compositional upscaling to be incorporated into a full-field simulator.

Compositional Upscaling
In compositional modelling, oil described by n pseudo components eg, C1, C2, C3-4, C5-8, etc. An Equation of State determines the split into liquid or gas phase, and provides liquid and gas densities. The equation of state is determined by fitting against laboratory data.
The key characteristic of compositional simulation is that the components are conserved, but they flow by phases.
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