Analysis Of Well-to-Well Tracer Flow To Determine Reservoir Layering
Authors: Abbaszadeh-Dehghani Maghsood , Brigham W.E. 
Published: December 2007

Summary
This paper discusses tracer flow in layered reservoirs. Analytic expressions are presented describing tracer breakthrough curves from layered systems at unity mobility ratio, including rigorous treatment of tracer mixing phenomena. A nonlinear Optimization technique is introduced to analyze tracer profiles from layered reservoirs (the inversion problem). The optimization profiles from layered reservoirs (the inversion problem). The optimization algorithm generates porosity-thickness and permeability-thickness products for each layer. Also included is a field example illustrating the application of this method.

Introduction
Prior knowledge of reservoir heterogeneity is important in the design and Prior knowledge of reservoir heterogeneity is important in the design and operation of EOR projects. In any fluid injection operation, the high- permeability streaks receive substantial quantities of the injected fluid. permeability streaks receive substantial quantities of the injected fluid. This disproportionate distribution of the injected fluids reduces the volumetric sweep efficiency of the reservoir and hence lowers the process efficiency. Therefore, detection of the high-permeability zones and channels would be helpful in understanding and increasing the efficiency of injection projects. A means of tracking fluid movement in a reservoir is an important tool in directly determining reservoir heterogeneities. Radioactive and chemical tracers provide the capability of achieving this purpose. Well-to-well tracer breakthrough profiles can furnish information about the nature of reservoir layering. Often these tracer breakthrough profiles are a summation of tracer responses from several layers that constitute the formation. In practice, the number of the layers is unknown and only the tracer breakthrough curve from the multilayered system is available. This is a classic inversion problem. To analyze any of these combined tracer breakthrough profiles, they must be deconvolved into their individual layer responses. From the layer responses it is possible to compute important parameters of the layers, such as permeability- and porosity-thickness. parameters of the layers, such as permeability- and porosity-thickness. To perform the deconvolution, it is necessary to describe mathematically the tracer breakthrough curves from single-layer homogeneous systems as accurately as possible. Several works have been published on theoretical computation of tracer breakthrough curves. However, each of these includes approximations, which produce inaccurate definitions of tracer breakthrough profiles. Furthermore, only the fully developed five-spot patterns have been considered. For this work, exact analytic solutions have been derived that describe the tracer breakthrough curves from the five-spot pattern as well as several other common flooding patterns. In addition, it was necessary to derive exact expressions for the pattern breakthrough curves (displacing fluid cut vs. PV injected in immiscible displacements) of these same systems at mobility ratio of unity. These curves have been correlated into a single curve using a simple correlating parameter called "dimensionless PV." This paper presents a brief review of mathematical descriptions of PV." This paper presents a brief review of mathematical descriptions of tracer breakthrough curves along with the pattern breakthrough curves of several homogeneous developed patterns. An optimization technique is presented that generates the equivalent layering of the system. The presented that generates the equivalent layering of the system. The technique has been applied to analyze a tracer effluent profile from a field five-spot system.

Mixing Theory
Miscible fluids in a porous medium are subject to convection and dispersion. Convection is the bulk movement of fluids caused by injection and production. Dispersion results from the movement of individual fluid particles, which travel at variable velocities through the tortuous pore particles, which travel at variable velocities through the tortuous pore channels of the porous medium. As a result of this irregular movement, a transition zone (or a mixed region) forms between two miscible fluids. The size of this zone is controlled by the dispersive characteristic of the porous medium. Generally, hydrodynamic dispersion occurs in two porous medium. Generally, hydrodynamic dispersion occurs in two directions - along the mean flow (longitudinal dispersion) and perpendicular to direction of mean flow (transverse dispersion). For perpendicular to direction of mean flow (transverse dispersion). For practical purposes, transverse dispersion has little effect on the amount practical purposes, transverse dispersion has little effect on the amount of mixing between fluids. Hydrodynamic dispersion is not the only source of mixing. Molecular diffusion occurring in each pore along and across each streamline also contributes. However, it has been shown that the effect of molecular diffusion is negligible unless displacement is occurring at very low velocities. Therefore, longitudinal hydrodynamic dispersion is the major factor in establishing the mixed zone between miscible fluids flowing in porous media. porous media. The concentration of each fluid in the mixed zone can be computed as a function of position if the dispersive property of the porous medium is known.
JPT
p. 1753