High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

AbstractNumerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

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Numerical calculation of unstable immiscible fluid displacement in a two-dimensional porous medium or Hele-Shaw cell

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000004653 ◽

1985 ◽

Vol 26 (4) ◽

pp. 452-469 ◽

Cited By ~ 3

Author(s):

M. R. Davidson

Keyword(s):

Porous Medium ◽

Numerical Procedure ◽

Immiscible Fluids ◽

Boundary Integral ◽

Immiscible Fluid ◽

Two Dimensional ◽

Time Step ◽

Fluid Displacement ◽

Numerical Errors ◽

Hele Shaw Cell

AbstractA numerical procedure for calculating the evolution of a periodic interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell is described. The motion of the interface is determined in a stepwise manner with its new velocity at exach time step being derived as a numerical solution of a boundary integral equation. Attention is focused on the case of unstable displacement charaterised physically by the “fingering” of the interface and computationally by the growth of numerical errors regardless of the numerical method employed. Here the growth of such error is reduced and the usable part of the calculation extended to finite amplitudes. Numerical results are compared with an exact “finger” solution and the calculated behaviour of an initial sinusoidal displacement, as a function of interfacial tension, initial amplitude and wavelength, is discussed.

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Numerical Solution of the Time-Depending Flow of Immiscible Fluids with Fuzzy Boundary Conditions

International Journal of Mathematical Engineering and Management Sciences ◽

10.33889/ijmems.2021.6.5.079 ◽

2021 ◽

Vol 6 (5) ◽

pp. 1315-1330

Author(s):

Rajesh Kumar Chandrawat ◽

Varun Joshi

Keyword(s):

Fluid Flow ◽

Boundary Conditions ◽

Newtonian Fluid ◽

Differential Quadrature Method ◽

Immiscible Fluids ◽

Immiscible Fluid ◽

Velocity Change ◽

Flow Problems ◽

Rotation Vectors ◽

Fuzzy Boundary

Fluid flow modeling using fuzzy boundary conditions is one of the viable areas in biofluid mechanics, drug suspension in pharmacology, as well as in the cytology and electrohydrodynamic analysis of cerebrospinal fluid data. In this article, a fuzzy solution for the two immiscible fluid flow problems is developed, which is motivated by biomechanical flow engineering. Two immiscible fluids, namely micropolar and Newtonian fluid, are considered with fuzzy boundary conditions in the horizontal channel. The flow is considered unsteady and carried out by applying a constant pressure gradient in the X-direction of the channel. The coupled partial differential equations are modeled for fuzzy profiles of velocity and micro-rotation vectors then the numerical results are obtained by the modified cubic B - spline differential quadrature method. The evolution of membership grades for velocity and microrotation profiles has been depicted with the fuzzy boundaries at the channel wall. It is observed that Micropolar fluid has a higher velocity change than Newtonian fluid, and both profiles indicate a declining nature toward the interface.

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High-resolution large time-step schemes for inviscid fluid flow

Applied Mathematical Modelling ◽

10.1016/j.apm.2019.12.006 ◽

2020 ◽

Vol 81 ◽

pp. 263-278

Author(s):

Sigbjørn Løland Bore ◽

Tore Flåtten

Keyword(s):

Fluid Flow ◽

High Resolution ◽

Large Time ◽

Inviscid Fluid ◽

Time Step ◽

Large Time Step

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Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

Acta Geophysica ◽

10.1007/s11600-018-0132-3 ◽

2018 ◽

Vol 66 (3) ◽

pp. 243-266 ◽

Cited By ~ 3

Author(s):

Eric Thompson Brantson ◽

Binshan Ju ◽

Dan Wu ◽

Patricia Semwaah Gyan

Keyword(s):

Numerical Simulation ◽

Porous Media ◽

Fluid Flow ◽

High Resolution ◽

Immiscible Fluid ◽

Flow Transport ◽

Immiscible Fluid Flow ◽

High Resolution Schemes

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Artificial Neural Network Models and Predicts Reservoir Parameters

Journal of Petroleum Technology ◽

10.2118/0121-0044-jpt ◽

2021 ◽

Vol 73 (01) ◽

pp. 44-45

Author(s):

Chris Carpenter

Keyword(s):

Neural Network ◽

Artificial Intelligence ◽

Artificial Neural Network ◽

Fluid Flow ◽

Capillary Pressure ◽

Relative Permeability ◽

Immiscible Fluids ◽

Flow In Porous Media ◽

Phase Saturation ◽

Artificial Neural

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19854, “Modeling and Prediction of Resistivity, Capillary Pressure, and Relative Permeability Using Artificial Neural Network,” by Mustafa Ba alawi, SPE, King Fahd University of Petroleum and Minerals; Salem Gharbi, SPE, Saudi Aramco; and Mohamed Mahmoud, King Fahd University of Petroleum and Minerals, prepared for the 2020 International Petroleum Technology Conference, Dhahran, Saudi Arabia, 13–15 January. The paper has not been peer reviewed. Copyright 2020 International Petroleum Technology Conference. Reproduced by permission. Capillary pressure and relative permeability are essential measurements that affect multiphase fluid flow in porous media directly. The processes of measuring these parameters, however, are both time-consuming and expensive. Artificial-intelligence methods have achieved promising results in modeling extremely complicated phenomena in the industry. In the complete paper, the authors generate a model by using an artificial-neural-network (ANN) technique to predict both capillary pressure and relative permeability from resistivity. Capillary Pressure and Resistivity Capillary pressure and resistivity are two of the most significant parameters governing fluid flow in oil and gas reservoirs. Capillary pressure, the pressure difference over the interface of two different immiscible fluids, traditionally is measured in the laboratory. The difficulty of its calculation is related to the challenges of maintaining reservoir conditions and the complexity of dealing with low-permeability and strong heterogeneous samples. Moreover, unless the core materials are both available and representative, a restricted number of core plugs will lead to inadequate reservoir description. On the other hand, resistivity can be obtained by either lab-oratory analysis or through typical and routine well-logging tools in real time. Both parameters have similar attributes, given their dependence on wetting-phase saturation. Despite many studies in the literature that are reviewed in the complete paper, improvement of capillary pressure and resistivity modeling remains an open research area. Artificial Intelligence in Petroleum Engineering In addition to labor and expense concerns, conventional methods to measure resistivity, capillary pressure, and relative permeability depend primarily, with the exception of resistivity from well logs, on the availability of core samples of the desired reservoir. The literature provides several attempts to model these parameters in order to avoid many of the requirements of measurement. However, the performance of many of these models is restricted by assumptions and constraints that require further processing. For example, the accuracy of prediction of capillary pressure from resistivity is highly dependent on the tested core permeability, which requires measuring it as well to achieve the full potentiality of the model.

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