A Type-Curve Approach to Analyzing Two-Well Tracer Tests

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Abstract
Summary The traditional approach to analyzing field tracer data generally involves a history matching procedure that is time-consuming and frequently results in a nonunique solution. In this work we use theoretical frequency response functions to build type curves of 'transfer function' and 'phase spectrum' that have a dimensionless heterogeneity index as a parameter to characterize a stochastic permeability field. The 'transfer function' contains information regarding the amplitude attenuating characteristics of the Heterogeneous medium and the 'phase spectrum' provides information about the spacing between the frequency components of the input and output tracer pulses. In a manner analogous to type curve matching for well testing, we can analyze field tracer history by comparing the theoretical and field observed 'transfer function' and 'phase relations'. This analysis leads to an estimate of the heterogeneity index and pore volume. We demonstrate the technique by analyzing field tracer data from the Big Muddy field, Wyoming, and compare the use of parameters so obtained in scaling up. Results show very good agreement with the field data. Introduction Two-well tracer tests, injecting a tracer into a well and analyzing its breakthrough response in a second well, have been commonly used as a part of reservoir surveillance and management programs. Less common are rigorous means of analyzing the tracer response. Analysis of field tracer response has largely been limited to qualitative evaluations of flow patterns in the reservoir (e.g., detection of preferential flow paths, well to well communication, fluid drift, faults etc.). The classical streamline approach is quantitative but is restricted to simple flow geometries with homogeneous flow properties or to non-communicating layers. A more general approach is to use a numerical simulator to match the tracer production data since arbitrary heterogeneity can be modeled and more complex fluid flow included as needed. However, such a procedure is time consuming and can lead to non-unique reservoir parameters. Field evidence indicates that permeability frequently varies randomly throughout the reservoir on several scales and exhibits spatial correlation. Since it is impractical, if not impossible, to describe heterogeneity in deterministic detail, in this paper we adopt a stochastic approach based on statistical characterization of reservoir heterogeneities. Interpretation of tracer response for parameter estimation can be classified into two broad categories -- the time domain approach and the frequency domain approach. The former involves estimation of temporal and spatial moments from the observed tracer history and areal breakthrough patterns. Analysis of tracer tests in the petroleum literature has largely been limited to the time domain approach. The frequency domain approach, on the other hand, applies Fourier analysis to the theoretical and experimental response functions. A comparison of these methods for analysis of laboratory data has been given by Duffy and Al-Hassan. The main advantage of the frequency domain analysis is that the impact of noise in the data is reduced. In frequency analysis, the noise content of an experiment is more or less uniformly distributed over all harmonics in the experimental frequency response function. This is of particular importance in flow through heterogeneous media where dispersive mixing causes attenuation of high frequency amplitudes, resulting in so called 'low pass' filtering effects.