The Problem of the Combined Use of Filtration Theory and Machine Learning Elements for Solving the Inverse Problem of Restoring the Hydraulic Conductivity of an Oil Field

Kosyakov, V. P.; Legostaev, Dmitry Yu.; Musakaev, E. N.

doi:10.21684/2411-7978-2021-7-2-113-129

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…В качестве моделей будут использоваться физически содержательные модели, основанные на законе сохранения массы. Первая модель -это модель материального баланса (МБ) для группы связанных участков в однофазной постановке [9], вторая -модель емкость-сопротивление (СRM) [10] и третья -однофазная двумерная фильтрационная модель (ФМ) [2].…”

Section: методыunclassified

“…Так, диапазон изменений КПЗ за последний год, согласно проведенному многовариантному расчету, равен 𝑘 𝑡=2030 ∈ [0.77, 0.9], что, с практической точки зрения, является значительной величиной. Существует семейство моделей емкость-сопротивление [2], в настоящей работе используется модель CRMP. В основе рассматриваемой модели лежат уравнения материального баланса, записанные для контрольного объема, представляющего собой дренируемый объем скважины: , где q j (t n ) -добыча жидкости на скважине j; I i (t k ) -закачка рабочего агента на скважине i; N I , N Jколичество нагнетательных и добывающих скважин соответственно.…”

Section: параметрическая идентификацияunclassified

“…Для решения в качестве фильтрационной модели будет использоваться двумерная математическая модель фильтрации слабосжимаемой жидкости [1,2]:…”

Section: двумерная фильтрационная модельunclassified

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Applying proxy-modeling tools to estimate the effective injection factor for an oil field

Kosyakov

Musakaev

Gaydamak

2022

TSU Herald. Phys Math Model. Oil, Gas, Energy

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This work is devoted to the joint use of physically based proxy models of different levels of complexity to determine the effective injection ratio factor. Effective injection factor is a parameter that reflects the proportion of injected fluid that enters the reservoir and does useful work to maintain reservoir pressure and displace oil from the reservoir. The selection of the effective injection factor when using a full-scale hydrodynamic simulator is difficult due to the high requirements for computational and time resources. Therefore, to calculate this coefficient, it is justified to use the simplified proxy modeling approach, which allows to evaluate the desired parameter in an acceptable time frame. The task of finding the effective injection ratio is related to inverse problems. The following were used as proxy models: a material balance model for the field as a whole and for a system of hydrodynamically connected blocks, a capacitance-resistance model (CRM) and a two-dimensional filtration model. The order of the models corresponds to the hierarchical principle "from simple to complex". Based on the history of oil field development (production, fluid injection, reservoir and bottomhole pressure), the effective injection coefficients were obtained, they were compared, and the analysis of the results was carried out.

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Section: методыunclassified

Section: параметрическая идентификацияunclassified

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Applying proxy-modeling tools to estimate the effective injection factor for an oil field

Kosyakov

Musakaev

Gaydamak

2022

TSU Herald. Phys Math Model. Oil, Gas, Energy

Self Cite

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“…In fact, it is similar to the approach of choosing a "suitable" solution within the hydrodynamic function domain based on "expert" assessments of previous options. The problem is solved by minimizing the quality functional between the defined and given parameters (hydrodynamic, filtration, capacitive), for example, according to the least squares criterion [9]. The significant disadvantage of ML algorithm implementation is the availability of a substantial "training" data set (actual data or previously obtained solutions).…”

Section: Introductionmentioning

confidence: 99%

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

Dieva,

Aminev,

Kravchenko

et al. 2024

Computation

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To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation.

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Using elements of machine learning to solve the inverse problem of reconstructing the hydraulic conductivity field for a filtration problem

Kosyakov

Legostaev

2022

TSU Herald. Phys Math Model. Oil, Gas, Energy

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In the modern world, machine learning methods are widely used. In the oil industry, there is also a noticeable trend to use these methods in the context of digitalization and intellectualization of the entire production process. The present work is devoted to the development of a technique for solving the inverse problem of restoring the permeability field of an oil reservoir with the combined use of machine learning elements and a filtration model. A computational algorithm has been implemented, which implies close mutual integration of the filtration part and the machine learning block, the results of which are used to parameterize the physically meaningful model. A network of radial basis functions is used as a machine learning model. The proposed solution search procedure includes the numerical solution of the direct and adjoint problems for the filtration model. Solving the adjoint problem allows one to apply gradient optimization methods widely used in machine learning methods. The paper presents the results of a numerical experiment. On the example of a symmetrical two-dimensional development element, a solution was obtained for the problem of restoring the permeability field for a set of zonal-heterogeneous oil reservoirs. For the reconstructed fields, the characteristic sizes of inhomogeneities coincide with the initial ones with sufficient accuracy. The fundamental possibility of a qualitative restoration of the porosity-permeability characteristics of the interwell space is shown, which is impossible when using classical interpolation methods without involving additional data. The paper studies the influence of the choice of the type of control parameter on the behavior of the objective function and its derivative, which affects the process of solving the inverse problem. As a result of the study, the use of hydrodynamic resistance as an adaptable parameter in solving the inverse problem is proposed.

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The Problem of the Combined Use of Filtration Theory and Machine Learning Elements for Solving the Inverse Problem of Restoring the Hydraulic Conductivity of an Oil Field

Cited by 4 publications

References 6 publications

Applying proxy-modeling tools to estimate the effective injection factor for an oil field

Applying proxy-modeling tools to estimate the effective injection factor for an oil field

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

Using elements of machine learning to solve the inverse problem of reconstructing the hydraulic conductivity field for a filtration problem

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