Фрактальные характеристики многомасштабных цифровых моделей нефтяных пластов

В работе обсуждается взвешенная фрактальная размерность — характеристика нефтяных коллекторов. Показано, что эта характеристика устойчива при различных реализациях цифровых неоднородных анизотропных стохастических моделей реальных месторождений. Получена устойчивая зависимость такого параметра разработки нефтяного месторождения, как эффективность охвата, от фрактальных характеристик. На эту зависимость не влияет корреляционная функция геологической модели. Поэтому взвешенную фрактальную размерность можно использовать для решения обратных задач, когда известны параметры разработки и необходимо восстановить корреляционные функции и геологическое строение, при оптимизации параметров разработки нефтяных месторождений, где время вычислений имеет решающее значение, и при обучении нейронных сетей. This study examines the weighted fractal dimension — a fractal characteristic of petroleum reservoirs. The purpose of this paper is to demonstrate that this characteristic remains stable across various realizations of digital heterogeneous anisotropic stochastic models of actual oil fields. A robust correlation has been established between an oil field development parameter (“sweep efficiency”) and fractal characteristics. This correlation proves independent of the geological model’s correlation function. Geological and hydrodynamic modelling is an important part of oil and gas field development, which is a long and complex process. The complexity and duration of the geological and hydrodynamic modelling process are both due to the lack of sufficient information about the reservoir and the need to ensure consistency between the parameters obtained at each stage. Often, this process becomes iterative. At the same time, the timely construction of high-quality models is crucial for making effective management decisions for the field development. In this context, developing new approaches to working with geological and hydrodynamic models is an important challenge. This paper proposes a modelling approach based on geometric and topological methods. The core idea is to represent oil and gas reservoirs as three-dimensional bodies, for which topological and geometric characteristics are then analyzed. The proposed approach can be used for parameter tuning, evaluation, classification, and model generation. The obtained results demonstrate that weighted fractal characteristics, like topological characte ristics, depend on the deviation coefficient, type and range of the random field variogram. Direct correlation exists between property of a geological body (weighted fractal dimension) and an oil production parameter (volumetric sweep efficiency), which is included in the oil recovery factor formula. This dependence is unaffected by the variogramrange of the geological model. This finding is particularly valuable, as typically there is high uncertainty in estimating the variogramrange. These observations can be used during the expert evaluation of geological data to simplify sweep efficiency assessment without computationally expensive hydrodynamic modelling. The direct estimation approach for sweep efficiency reduces uncertainty in solving inverse problems and iteratively adjusting geological-hydrodynamic models, including the need to fit appropriate probabilistic characteristics.