Linear Scaling in Slug-Type Processes Application to Micellar Flooding
Authors: Parsons Robert W. 
Published: December 2007

Abstract
A relaxed scaling technique, "linear scaling," has been employed in such single-fluid injection processes as waterflooding. This paper develops processes as waterflooding. This paper develops theory and applications of linear scaling for such multiple-fluid injection processes as micellar/ polymer flooding. polymer flooding. Linear scaling demands that saturation profiles and related properties be completely defined by specifying the number of pore volumes of each fluid injected at any time in the injection history. Mobility and saturation profiles can be constructed from over-all pressure measurements and production data, respectively, from linear cores. Detailed micellar flooding experiments, in which saturation profiles, differential pressures, and production histories were measured, demonstrate production histories were measured, demonstrate that these laboratory multiple-fluid injection displacements are linearly scalable to a good approximation. We employed two micellar slugs that were used in field tests of the Maraflood oil recovery process.

Introduction
Rigorous mathematical scaling of displacement processes and relaxed scaling techniques have processes and relaxed scaling techniques have been discussed extensively. "Linear scaling" specifies direct correspondence among experiments when equal pore volumes of fluids have been injected, and is a special relaxed-scaling situation. It requires geometric similarity and identical rock and fluid properties for both model and prototype, but assumes that most of the dimensionless groups normally employed for scaling are unimportant for describing a displacement process. Calculation of relative permeability as presented by Welge and Johnson et al. are examples of single-fluid linear scaling applications. In multifluid chemical injection schemes, linear scaling will have limited application and must be employed with caution. In particular, fluid dispersion may not be expected to follow a linear law; this would be important in field applications. Nonlinear gravity effects could also be influential in certain geometries. In organizing saturation and pressure data from several micellar flooding experiments, it became apparent that these systems might be linearly scalable. This observation prompted clarification and better definition of linear scaling relationships for multiple-fluid injection processes. This paper is an outgrowth of that work. Its purpose is to develop linear scaling theory for multiple-fluid injection processes and demonstrate that our laboratory micellar floods scale linearly to a good approximation.

THEORY

Basic Considerations
For a given porous medium and fluid system, a displacement process is said to be linearly scalable if fluid concentration (saturation) at any point and time is a function of only the number of pore volumes of each fluid injected with respect to that point. This is a fundamental definition. The key to applying linear scaling is understanding the concept of relative pore volumes injected with respect to a point. In one-dimensional systems (linear, radial, or spherical), this is easy to define and the practical consequences of being able to do so will be expanded later. For experimental models having heterogeneity, anisotropy, and/or non-one-dimensional boundaries (such as five-spot patterns), it is impossible to assign a fixed pore volume to a given point, since streamlines change configuration during nonunit mobility ratio displacements. Even so, by assigning an appropriate pore volume history to each point, the basic definition will still hold. One consequence of the linear scaling definition is that, in geometrically similar rocks of different size but at the same point in their relative injection history (same number of pore volumes of each given fluid injected into each rock), the saturation or concentration profiles (or contours) in all the rocks will be similar different by only a linear magnification or reduction.
SPEJ
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