A mathematical model for identifying the fractional derivative parameter and predicting the results for the fluid flow equation in the well

В данной статье рассматривается идентификации параметров математической модели, основанной на дифференциальном уравнении с дробными производными. С помощью этой модели описывается установившееся течение в скважине в трещинном деформированном пласте. Рассматриваемая модель может быть использована и при разработке нефтяных месторождений с трещиноватыми коллекторами. Идентификация параметра осуществлялась с помощью оптимизации показателя качества адекватности математической модели - коэффициента детерминации. Также была представлена технология прогнозирования результатов давлений, для области, в которой не проводились экспериментальные измерения. Предлагаемая технология сопровождена расчетами. This article discusses the identification of the parameters of a mathematical model based on a differential equation with fractional derivatives. This model is used to describe the steady-state flow in a well in a fractured deformed formation. The considered model can be used in the development of oil fields with fractured reservoirs. The identification of the parameter was carried out by optimizing the quality indicator of the adequacy of the mathematical model the coefficient of determination. The technology for predicting the results of pressures was also presented, for an area in which no experimental measurements were carried out. The proposed technology is accompanied by calculations.

Internal DLA for Cylinders

This chapter discusses the continuum limit of internal Diffusion-Limited Aggregation (DLA), a random lattice growth model governed by a deterministic fluid flow equation known as Hele-Shaw flow. The internal DLA model was introduced in 1986 by Meakin and Deutch to describe chemical processes such as electropolishing, etching, and corrosion. The chapter focuses primarily on fluctuations, and seeks to prove the analogous results for the lattice cylinder. In the case of the cylinder, the fluctuations are described in terms of the Gaussian Free Field exactly. The main tools used in the proofs are martingales. As the chapter shows, the martingale property in this context is the counterpart in probability theory of well-known conservation laws for Hele-Shaw flow.

Numerical Investigation of Unsteady Laminar in Oscillated Lid–Driven Cavity Flow

This article reports the flow characteristics in an oscillated lid–driven cavity. The mesoscale numerical scheme of the multiple relaxation time lattice Boltzmann method is applied to solve for the fluid flow equation. Our predicted results revealed that the flow behavior is critically dependent on the dimensionless Reynolds number and frequency of the oscillated top lid of the cavity.