(2018) Identification of Fractal Properties of Oil Reservoir. Hyperparameters of Hydrodynamic Model Optimization Problem. Dimension Reduction (Upscaling)

Project Type: Work project, Mathematical Modeling, Applied Research
Programming Language: Maple 18, Python 3
Project Сode: Main Script.pdf
Project Full Description: En Machine Translate, in Russian
Company: math. model. lab. GAMMETT

I. Motivation

Coarsening of computational spatial grids is one of the main ways to reduce the cost of computing resources in geological and hydrodynamic modeling of hydrocarbon reservoirs. The procedure of overriding reservoir properties in an upsized cell of the computational grid is called upscaling (averaging). The quality of this procedure is determined by degree of prognostic capability decreasing of applied models. The traditional way for determining the average value as the arithmetic mean is not always applicable in practice, since it does not take into account the spatial heterogeneity of the averaged values distribution. In this paper, we consider the case of a reservoir with formation reservoir properties (permeability and porosity) values close to power functions of the spatial variable. Proximity of reservoir properties to power function indicates to a fractal inhomogeneity of the porous medium. The power-law up-scaling procedure is proposed for this case. An initial-boundary-value problem for a one-dimensional fractal model of unsteady-state filtration is considered. The identification procedure of fractal quantities of this model is proposed and investigated. The proposed methods tested on data from one of the fields in Western Siberia. A comparative analysis with the arithmetic mean method is performed on permeability data. The proposed techniques have a potential for use in reservoir engineering and monitoring.

II. Problem

The main purpose of this work is attempt to application modern type of hydrodynamic models (accounting to fractality) to industrial tasks. Project tasks:

• hyperparameters (fractality) of hydrodynamic model optimization problem;
• dimension reduction (Upscaling).

III. Key Results

• The method of empirical identification filtration model parameters in a fractal medium based on the minimum of the proximity functional to a solution with a piecewise constant function of permeability bridges (field data);
• The task of identifying parameters using the proposed technique is equivalent to a simpler problem of identifying parameters based on the best approximation of a piecewise constant function by a power function on the entire interval;
• A modified procedure for averaging (upscaling) FES is proposed, which takes into account their power (fractal) distribution law;
• When testing the proposed procedure on the field data of one of the wells in Western Siberia, it was found that the modification of upscaling led to an improvement in the correspondence of the flow value to the actual value by 20%. This indicates a great potential for the application of this technique in the design and monitoring of field development.

IV. Content

The project code contains 1 scripts:

1. Main Script.pdf (hyperparameters of hydrodynamic model optimization problem).

License:

Russian Government Registration.