Application of Le´vy Random Fractal Simulation Techniques in Modeling Reservoir Mechanisms in the Kuparuk River Field, North Slope, Alaska

Summary Incorporating 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 modeling 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 behavior. This study utilizes a new method, Le´vy 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 modeling of large changes in petrophysical properties observed in near-vertical wells, particularly permeability. Prior efforts at modeling the movement of gas, at typical interwell scales, have met with limited success. In this study, the Le´vy technique employs automatic calibration with log and core data for the interwell interpolation of the spatially complex reservoir properties. The Le´vy fractal simulations preserve the sharp jumps in reservoir properties observed at stratigraphic boundaries and within reservoir subzones. The spatially correlated petrophysical properties are consistent with geologic experience. A fine-scale permeability model incorporating well conditioning data was built using the Le´vy 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 characterized by lateral continuities extending over many gridblocks away from control locations. Porosity was modeled using sequential Gaussian simulation in which well porosity logs were used as the primary conditioning data, and the modeled 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. Introduction The Kuparuk River field1 was discovered in 1969 on the North Slope of Alaska (Fig. 1) and is the second largest producing field in North America after the Prudhoe Bay field. The field was put on production in 1981, with a field-wide waterflood recovery development initiated in 1983. Recoverable reserves in the field are in excess of 0.32×109 m3 (2 billion bbl) with the first billion barrels having been produced by 26 May 1993.3 Oil in the Kuparuk River field is trapped in Lower Cretaceous marine sandstones in a low-relief, faulted anticlinal structure that has an area in excess of 518 km2 (200 sq miles).4 Within the anticlinal closure, both stratigraphic and unconformity-related trapping mechanisms are operative. The Kuparuk River formation is divided into upper and lower members separated by a regional unconformity (Fig. 2). The lower member consists of Units A and B; the upper member comprises Units C and D. The main reservoir sands are found in the A and C units along with minor sands in the B unit. The C sand is the most productive interval. Although the C sand has about one third of the field's reserves, it has produced over half of the oil to date. Thus, the Kuparuk C sand is an obvious target for sweep improvement and enhanced recovery processes. The Kuparuk C sand is a glauconitic, siderite-cemented sandstone locally interbedded with mudstone. Extensive bioturbation and secondary diagenesis have destroyed or masked primary sedimentary structures. The more significant post-depositional modifications of the C sand include early siderite cementation and multiple phases of dissolution of siderite and glauconite. These diagenetic events have resulted in a reservoir with complex distributions of petrophysical properties that have proven to be extremely difficult to model. The Gas Recapture Project's goal is to reclaim, for oil production, that area within two drillsite locations (1C and 1D) and immediately adjacent but undeveloped, that had been used for gas injection. Gas injection was necessary because field rules preclude the flaring of produced or associated gas and only a relatively small amount of gas had been used for fuel or enhanced oil recovery processes. Approximately 50×106 m3 (300 MMSTB) of oil is considered to be accessible in this area, and a depletion mechanism was sought that could produce some of this resource. Key outcomes of this study bear upon the distribution of gas-invaded zones, the possibility of diverting gas with water injection, and re-pressurization and sweep of the area through waterflooding. In-house simulations in nearby Kuparuk 1A and 1F drillsite areas, based on Gaussian geostatistical static models, did not correctly predict the migration of gas from the injection area. Because these studies were primarily done for infill screening, this shortcoming was not considered to be critical or important. Those simulation studies required the boosting of permeability using well multipliers in order to match primary liquid rates. In addition, deterministic intervention, through the inclusion of a high-permeability "thief" zone, was necessary in these reservoir descriptions. Although the liquid volumes were generally consistent, the gas/oil ratio (GOR) history would not match. This mismatch indicated that, because permeability heterogeneity in the interwell region was being inadequately rendered, the dynamics of gas migration were not being captured.