Conditional Simulation Method for Reservoir Description Using Spatial and Well-Performance Constraints

Abstract

Summary This paper describes a conditional simulation technique that constrains areal permeability fields to typical statistical information and indirectly to waterflood well performance. Near-well effective permeability and reservoir connectivity characteristics are used as indirect well-performance constraints. Results are validated by examining simulated waterflood performance of a five-spot pattern. This technique can be used to reduce the uncertainty of future well performance significantly. Additionally, the effect of alternative operating scenarios, such as infill drilling, can be evaluated more realistically. Introduction Existing geologic, petrophysical, and geophysical conditioning data are always sparse in comparison with reservoir size and complexity. Although conditional simulation techniques have been developed to account for such information, the resulting "equally probable" realizations of reservoir properties can result in simulated well performance that varies widely under normal waterflood conditions. This is true even when the variogram captures reservoir spatial correlation adequately. Reservoir descriptions must account for individual well performances before they can be considered realistic. However, the inverse problem of determining detailed spatial descriptions of reservoir properties from dynamic well-performance data is extremely complex and currently has no practical solution. Simulated annealing is considered to be one of the most flexible conditional simulation methods.1–7 Various desirable characteristics of an image can be accounted for with simulated annealing. These characteristics can be totally unrelated to each other, be of different magnitudes, and have different units of measurement. Applicability of simulated annealing to constraining images of permeability to waterflood performance is demonstrated with one-quarter of a five-spot waterflood pattern. Reservoir connectivity parameters are defined and used as additional conditional simulation constraints within the simulated annealing framework. Benefits of flexibility in specifying near-well effective permeability constraints are demonstrated; advantages and disadvantages of these parameters are identified and illustrated. Results are validated by comparing simulated waterflood performance based on permeability fields generated by use of typical constraints with those obtained that include connectivity and near-well effective permeability constraints. Background Several investigators have studied connectivity as related to stochastic reservoir characterization.8–10 Most work has focused on modeling the connectivity of fluvial sand bodies or shales. Stochastic geologic models, based on empirical relationships of sand-body geometry and deposition, have been used to generate 2D and 3D reservoir descriptions of facies that are conditioned to geologic models and well data. The facies are usually defined as reservoir rock (sand) or nonreservoir rock (shale). Well-density and location sensitivities have been conducted to determine the sand fraction that is drainable (accessibility factor) as a function of well spacing.10 Another study11 applies two measures of connectivity to the characterization of a crossbedded sandstone outcrop by use of high- and low-permeability binary indicators. Boolean techniques have been used to distribute sand bodies within a reservoir and to determine sand connectivity as a function of well spacing.12 Stochastic indicator simulation was developed to account for the connectivity of extremes (high-permeability streaks and shale barriers).13 Indicator simulation and a random-walk procedure have been used to determine the probability distribution of connected PV for a nine-spot pattern.14 All these conditional simulation techniques use a combination of geologic and statistical data to investigate connectivity and associated parameters. None of these methods use well-performance data as conditioning constraints. Reservoir engineers consider geologically sound "equally probable" realizations to be improbable if simulated well performance does not approximate historical well performance. In this study, near-well effective permeability and connectivity characteristics are used as indirect performance constraints to improve the reservoir description. Near-well permeabilities typically are estimated from transient pressure data.7,15–17 These methods estimate the type of permeability averaging represented by the pressure response at the well. Because radial symmetry is assumed, these techniques are best for estimating effective permeability of near-well radial volumes. In this case, "near-well" indicates the radial volume centered at the well that is large enough so that directional pressure-gradient effects have dissipated (e.g., those created by hydraulic fracturing) but small enough not to be distorted by regional heterogeneities. In this paper, near-well permeability is the effective permeability of the region surrounding the well that has the greatest effect on initial productivity or injectivity. The other parameter, connectivity, possibly can be estimated from tracer tests.18 However, we did not consider tracer applications. Instead, we attempted to relate connectivity to commonly measured production parameters. Connectivity Measurements In this study, reservoir connectivity is characterized by two methods: the fractional connectivity function and the flow-pattern permeability coefficient. Both techniques define connectivity on the basis of the spatial arrangement of permeability. This approach was used because permeability typically has a stronger influence on flow characteristics than any other variable. Additionally, both techniques quantify reservoir connectivity relative to specific well locations. Although existing definitions of connectivity may be used to improve predictions of overall field rates and recoveries, local connectivity measurements are required to predict interactions between specific wells and interwell permeability spatial distributions better. p. 145–152

Stratigraphic and structural connectivity

“…As mentioned previously, this provides a measure of reservoir compartmentalization. This definition was previously used by Allen (1978), King (1990), and Hird & Kelkar (1994). Bulk reservoir connectivity can first be explained by percolation theory (King 1990;Hovadik & Larue 2007).…”

Fault Block Modelling-An Alternative Simulation Tool for Strongly Compartmentalized Gas Reservoirs

“…Uncertainty analysis also includes suggestions on how to reduce reservoir uncertainty and recommendation for an optimum well location strategy. typical reservoir characteristics, as presented by Hird and Kelkar (10) , in conditional simulation. Uncertainty about reservoir characteristics by putting error bars on important parameters has been discussed and recommended by øvreberg et al (11) , and Meling et al (12) introduced uncertainties in stochiastic geological models using distribution functions.…”

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.…”