Application of Lévy Random Fractal Simulation Techniques in Modelling Reservoir Mechanisms in the Kuparuk River Field, North Slope, Alaska

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIncorporating a suitable level of heterogeneity into reservoir simulations is necessary for accurate prediction of production rates and final recoveries. Spatial correlation of petrophysical properties, particularly permeability extrema, exerts a profound influence on flow underlying reservoir displacement and depletion processes. Common modelling techniques are founded on Gaussian assumptions for statistical distributions. Such Gaussian-based approaches can inadequately model the permeability extrema that can dominate reservoir performance. However, optimal reservoir management strategies at the Kuparuk River Field require that significant efforts be made to correctly model reservoir behaviour.This study utilises a new method, Lévy fractal simulation, for interpolating permeability at a former gas injection area now being targeted for oil production. The main producing interval is a diagenetically and mineralogically complex clastic unit. The diagenetic complexity causes difficulties in the lateral modelling of large changes in petrophysical properties observed in nearvertical wells, particularly permeability. Prior efforts at modelling the movement of gas, at typical interwell scales, have met with limited success. In this study, the Lévy technique employs automatic calibration with log and core data for the interwell interpolation of the spatially complex reservoir properties. The Lévy fractal simulations preserve the sharp jumps in reservoir properties observed at stratigraphic boundaries and within reservoir sub-zones. The spatially correlated petrophysical properties are consistent with geologic experience.A fine-scale permeability model incorporating well conditioning data was built using the Lévy fractal interpolation technique. This model encompassed not only the gas injection area but drillsite patterns immediately adjacent. The model preserves the geometry of the reservoir units so that truncation and onlap relationships are preserved. The permeability extrema in the model are characterised by lateral continuities extending over many grid blocks away from control locations. Porosity was modelled using sequential Gaussian simulation (SGS) in which well porosity logs were used as the primary conditioning data, and the modelled permeability used as secondary conditioning data. The fine-scale model was then used as input in an upscaled dynamic simulator built to test reservoir mechanisms. The model was also useful for prognosing porosity and permeability at proposed well locations. Early drilling results indicate that substantial quantities of producible oil remain in the former gas injection area.

Stochastic fractal‐based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions

“…This might be a practical option for individuals who are Mathematica users. Gaynor et al [2000] used a version of a code called LevySim that was developed previously by Painter [1996b], but the code is not readily available (S. Painter, personal communication, 2002). (The Gaynor et al [2000] application, involving 3.9 million permeability values generated on a complex, faulted, 3‐D grid, which are then upscaled for a multiphase reservoir simulator, is one of the largest to date.)…”

“… Gaynor et al [2000] used a version of a code called LevySim that was developed previously by Painter [1996b], but the code is not readily available (S. Painter, personal communication, 2002). (The Gaynor et al [2000] application, involving 3.9 million permeability values generated on a complex, faulted, 3‐D grid, which are then upscaled for a multiphase reservoir simulator, is one of the largest to date.) More recently, Painter [2001] described a code that is available for research purposes from the Southwest Research Institute (S. Painter, personal communication, 2002).…”

Conditioning of Lévy-Stable Fractal Reservoir Models to Seismic Data

“…seismic amplitude as a function of time t , depth z w seismic wavelet a k ,ā wavelet coefficients Φ well log property k z Fourier wavenumber for depth S, S synth Synthetic seismic χ 2 mismatch error in optimisation C, C ij , i, j = 1, 2 Covariance matrices between true and synthetic seismic a, b coefficients in covariance model l 2 sum-of-squares norm of vector The rejection distribution of the l 2 norm in the case of a correlated seismic/synthetic-seismic field with a = 0.63, b = 0.48, compared to the case if the two fields had the same self correlation but zero cross correlation. Probabilities developed by Monte Carlo, using a plausible Ricker power spectrum model for the covariance C, averaged on a column height of about 1 1 2 seismic wavelengths.…”