Abstract:

Most oil and gas reservoirs are naturally heterogeneous. The description of a reservoir is challenging because the measurement data are limited spatially. Various studies have been conducted to extract the heterogeneous permeability from well test pressure data. A periodic pumping test is one category of well test that has been utilized to estimate reservoir permeability. So far the technique has proven useful in estimating average permeability by utilizing the dominant sourcing frequency. In terms of describing a more comprehensive heterogeneous permeability distribution, heavy computational effort in matching the entirety of the pressure history data was required. This also requires us to know the flow rates. It is of much interest how to best design and control the pressure pulsing technique to reveal the heterogeneous nature of reservoirs efficiently.

We propose a new inverse framework for obtaining the permeability distribution by utilizing frequency contents. This work investigated how to utilize multiple frequency components of pressure pulse testing data in estimating the horizontal permeability and vertical permeability distributions between an injection point and an observation point. Models of a radial multicomposite reservoir and a partially penetrating well in a multilayered reservoir with crossflow were examined. Attenuation and phase shift information acquired from pressure pulse tests at multiple frequencies was used to estimate the permeability distribution of reservoirs. A semianalytical solution was derived for the two reservoir models for single-phase flow in a periodic steady state.

Nonlinear optimization was used to infer the permeability distribution that satisfies the given frequency response data. Quasi-Newton line search optimization with gradient information was used for both methods. Synthetic homogeneous and heterogeneous reservoir cases were examined under periodic steadystate conditions with multiple sinusoidal inputs and multiple frequencies contained in square pulses. The estimation performance of the frequency method was investigated and compared to straightforward pressure history matching and the wavelet compression method.

The study also examined the benefits and limitations of using multiple frequencies in estimating the permeability distribution. In addition, the sensitivity of the permeability estimation to perturbation in both pressure data and frequency attributes was investigated. A heuristic method for detrending was devised which helps with obtaining accurate attenuation and phase shift information. Cases with different values of storage, skin, and boundary conditions were considered. The impact of varying the number of periods and the sampling rate was analyzed to determine the sensitivity of Fourier transformation to these factors.

By matching attenuation and phase shift at various harmonic frequencies, which are the multiples of the fundamental sourcing frequency, the results were found to be in good agreement with the actual permeability distribution trend. Attenuation and phase shift provide an ‘indicator characteristic’ which can reveal reservoir heterogeneity. The pressure pulse testing with multiple frequencies is useful in describing the heterogeneity of the reservoir parameters quantitatively, when the radius of cyclic influence is covered by the sourced frequencies. By processing the time series pressure data effectively, the amount of both the time and frequency conditioning data is reduced, and there is no need to utilize the flow rate data. Thus the frequency method proved more efficient computationally than matching the full history pressure data. However, the accurate extraction of the frequency parameters is essential for determining the permeability distribution. The successful pulse test design relies heavily on the choice of sourcing frequency which depends on the factors such as permeability range of inspection, the distance between the two points, and the mechanic precision of the measurement device. The quality of the permeability estimate improves with more pulses, an increased sampling rate, and processing pulses from later time.

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Copyright 2012, Sanghui Ahn: Please note that the reports and theses are copyright to their original authors. Authors have given written permission for their work to be made available here. Readers who download reports from this site should honor the copyright of the original authors and may not copy or distribute the work further without the permission of the author, Sanghui Ahn.