Spatially continuous regularization of the parameters of the capacitance

Spatially continuous regularization of the parameters of the capacitance–resistance model

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Egor Illarionov^a^,^b^,^*, Elizaveta Gladchenko^c, Anton Voskresenskii^a^,^d, Sergey Safonov^a, Klemens Katterbauer^e

Petroleum Research | 2026, 11(2) : 431 - 440

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Petroleum Research | 2026, 11(2): 431-440

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Spatially continuous regularization of the parameters of the capacitance–resistance model

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Egor Illarionov^a^,^b^,^*, Elizaveta Gladchenko^c, Anton Voskresenskii^a^,^d, Sergey Safonov^a, Klemens Katterbauer^e

Affiliations

^aAramco Innovations, Moscow, Russia

^bMoscow State University, Moscow, Russia

^cCenter for Petroleum Science and Engineering, Moscow, Russia

^dITMO University, Saint-Petersburg, Russia

^eSaudi Aramco, Dhahran, Saudi Arabia

Published: 2026-06-10 doi: 10.1016/j.ptlrs.2025.09.001

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Abstract

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The capacitance–resistance model (CRM) is a widely-used model for predicting well production rates because it requires the estimation of only a small number of parameters to describe production wells and the connectivity between injection and production wells. However, CRM parameters are not inherently spatially constrained, which can lead to unnatural results. In this research, we conducted spatially continuous regularization of CRM parameters and investigated how it affected model accuracy. A related goal was to investigate how this regularization improved the spatial interpolation of CRM coefficients. For regularization, we considered CRM parameters as values for a spatially continuous function, implemented this function using a neural network, and fited it using production history data. We employed two benchmark datasets—the egg and Costa datasets—to compare two models: the unconstrained conventional CRM and the proposed spatially regularized CRM. We concluded that the spatially regularized CRM yielded accuracy close to that of the conventional CRM; however, it provided a more interpretable spatial distribution of the CRM parameters.

Key words

Capacitance-resistance model / Machine learning / Neural networks / Petroleum

Cite this Article

Egor Illarionov, Elizaveta Gladchenko, Anton Voskresenskii, Sergey Safonov, Klemens Katterbauer. Spatially continuous regularization of the parameters of the capacitance–resistance model[J]. Petroleum Research, 2026 , 11 (2) : 431 -440 . DOI: 10.1016/j.ptlrs.2025.09.001

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Year 2026 volume 11 Issue 2

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Article Info

doi: 10.1016/j.ptlrs.2025.09.001

Receive Date：2025-02-26
Online Date：2026-07-29
Published：2026-06-10

Article Data

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History

Received：2025-02-26
Revised：2025-08-30
Accepted：2025-09-11

Affiliations

^aAramco Innovations, Moscow, Russia

^bMoscow State University, Moscow, Russia

^cCenter for Petroleum Science and Engineering, Moscow, Russia

^dITMO University, Saint-Petersburg, Russia

^eSaudi Aramco, Dhahran, Saudi Arabia

Corresponding:

Aramco Innovations, Moscow, Russia. E-mail address: egor.illarionov@math.msu.ru (E. Illarionov).

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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