The Fractal Model of Fractured Reservoirs Based on Pareto Distribution and Integrated Investigations

Abstract

AbstractHorizontal wells and hydraulic fracturing made a significant contribution to the US unconventional oil and gas production. However, due to complex fracture networks forecasting oil and gas production is a challenging task. This paper derives characteristic distribution of block patterns and fractures that are located between the blocks in traditional and unconventional reservoirs. By analyzing historical well production data on tens fields in different basins using distribution of initial and cumulative production and decline curve analysis of thousands wells from 1960 to 2019 we show that the Hyperbolic model, Pareto and Arps Laws can apply on the well-by-well production data on traditional and unconventional fields including shale and tight reservoirs. Physical and mathematical modeling and studies conducted in many oil and gas fields show that multi-scale rock fractures divide productive rocks into blocks of various sizes, which are complex self-similar fractal structures, and their behavior is described by a power law distribution and a general universal Pareto law. The generator of power law distribution and Pareto’s Law is an algorithm for cascading splitting of the continuum. It was found that the linear dimensions of different-scale blocks in fractured reservoirs asymptotically approach the value of the Golden Sect. (1.618). Based on this law has been developed fractal model of fractured reservoir. It includes several hierarchical levels of matrix blocks and fractures, sometimes ten and more. In the proposed model, not only the sizes of the blocks are in the ratio of 1.618, and permeability of the fractures changes in the ratio of 1.618, which allows to reproduce the daily and cumulative oil and gas well production according to power law distribution and Pareto’s law. The proposed model not only contributes to a more accurate mathematical description of the development of fractured oil and gas reservoirs in hydrodynamic modeling, but also allows us to explain in a new way the appearance of ring structures and vortex spiral objects in the earth’s crust, the formation of which is still debatable. Using of the special developed AVP program allows you to significantly improve the accuracy of hydrodynamic calculations of reservoir development and obtain all three types of Decline Curve wells in accordance with the Arps law.