Reservoir Description by Integrating Well-Test Data and Spatial Statistics

Abstract

Summary We present a method to integrate log, core, and well-test pressure data to describe reservoir heterogeneities. The conditional simulation method of simulated annealing is used to incorporate diverse sources of data. We use analytical solutions for radially heterogeneous reservoirs to define an equivalent radial permeability and a corresponding region of investigation. By numerical experimentation on drawdown well-test simulations in heterogeneous permeability fields, we determine that a weighted-area-based geometric average of the gridblock permeabilities within the region of investigation best defines the equivalent radial permeability. This information, along with the spatial statistics from core/log data, is coded into the overall objective function of the simulated annealing algorithm to yield a consistent reservoir description. Introduction Integration of all available data in describing a reservoir will yield a more accurate prediction of reservoir performance. The conventional approach to reservoir description by use of geostatistics can readily accommodate the use of static (core and log) data, specifically permeability and porosity data. The statistics of the sample data can be defined, and the support volume is a function of the size of the retrieved core or the depth of investigation of the logging instrument. Permeability and porosity values can be upscaled to represent gridblocks for the purpose of reservoir simulation studies. Well-test interpretation techniques provide useful information on a scale larger than core or log data. On this scale, we can determine faults, drainage boundaries, and an average reservoir permeability. On a smaller scale, we can determine wellbore damage and whether the system is single or dual porosity. Conventional geostatistical methods are unable to incorporate well-test data. The support volume represented by a well-test permeability needs to be determined, as well as a procedure that relates the well-test derived permeability to the distribution of small-scale permeabilities within the reservoir. We present a methodology to include well-test data for the description of small-scale heterogeneities.

Modeling the Interfering Effects of Gas Condensate and Geological Heterogeneities on Transient Pressure Response

“…Therefore, this instantaneous-permeability concept should be used with great care. Feitosa et al (1994) and Sagar et al (1995) indicated that the instantaneous permeability can be numerically approximated as a weighted harmonic average of the radial permeabilities in the model. This is defined as follows:…”

Fast and Efficient Modeling and Conditioning of Naturally Fractured Reservoir Models Using Static and Dynamic Data

“…Even average well-test permeabilities need flowbased evaluations of models (Sarda 2001), the strong and spatially varying anisotropy of permeability making inappropriate other elsewhere successful forward modeling methods as those based on power averaging, multiple-point proxy or well-test response approximations (Gautier and Noetinger 2004, Srinivasan and Caers 2000, Sagar 1993). This paper presents an integrated approach that has been developed as a workflow for modeling naturally fractured reservoirs ( Figure 1).…”

Numerical Estimation of the Degree of Reservoir Permeability Heterogeneity Using Pressure Drawdown Tests

“…Inversely, one can use production data (Houseworth, 1988;Newley and Begg, 1992;Alvarado, 1994;Hird and Kelkar, 1994;Hallford and Hegeman, 1995;Hird and Dubrule, 1995;Vasco and Gupta, 1997;Babadagli, 1999) or pressure change in time (Alabert, 1989;Oliver, 1992;Feitosa et al, 1993;Sagar et al, 1993;Deutsch and Journel, 1994;Yadavelli et al, 1994;Herweijer and Dubrule, 1995;Kamal et al, 1995;Pecher et al, 1995;Yadavalli et al, 1995;Campozana et al, 1996;Oliver, 1996;Rosa and Horne, 1997;Ceyhan, 1998) to describe the permeability heterogeneity. This would be a desirable application but still a challenging task as a unique solution to the problem cannot easily be obtained.…”

“…Permeability distributions can be generated using stochastic methods (Sagar et al, 1993;Yadavelli et al, 1994Yadavelli et al, , 1995, simulated annealing (Deutsch and Journel, 1994) and fractal geometry (Chang and Yortsos, 1990;Babadagli, 1999). In a quantitative description of these distributions, the fractal dimension of the distribution (Hewett, 1986;Hewett and Behrens, 1990;Chang and Yortsos, 1990;Berta et al, 1994;Babadagli, 1999) and Dykstra-Parson's coefficient (Sagar et al, 1993;Yadavelli et al, 1994) have been used previously. Once the permeability distribution is quantified one way or another, it can then be correlated to the pressure response.…”