scholarly journals Linear estimation of flux sensitivity to uncertainty in porous media

2015 ◽  
Vol 768 ◽  
pp. 600-622
Author(s):  
A. J. Evans ◽  
C. P. Caulfield ◽  
Andrew W. Woods
Keyword(s):  
Porous Medium ◽  
Layered Structure ◽  
Single Phase ◽  
Pressure Field ◽  
Porous System ◽  
Integral Expression ◽  
Permeability Model ◽  
Fully Nonlinear ◽  
Phase Fluid ◽  
Good Agreement

We derive an integral expression for the flux of a single-phase fluid through a porous medium with prescribed boundary conditions. Taking variations with respect to the parameters of a given permeability model yields an integral expression for the sensitivity of the flux. We then extend the method to consider linear changes in permeability. This yields a linearised flux expression which is independent of changes in the pressure field that result from the changes in the permeability. For demonstration purposes, we first consider an idealised layered porous medium with a point source and point sink. We show how the effects of changes in permeability are affected by the position of the source and sink relative to the layered structure as well as the layer height and orientation of the layered structure. The results demonstrate that, even in a simple porous system, flux estimates are sensitive to the way in which the permeability is represented. We derive relationships between the statistical moments of the flux and of the permeability parameters which are modelled as random variables. This allows us to estimate the number of permeability parameters that should be varied in a fully nonlinear calculation to determine the variance of the flux. We demonstrate application of the methods to permeability fields generated through fast Fourier transform and kriging methods. We show that the linear estimates for the variability in flux show good agreement with fully nonlinear calculations for sufficiently small standard deviations in the underlying permeability.

scholarly journals Décomposition de domaine pour un milieu poreux fracturé : un modèle en 3D avec fractures

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Laila Amir ◽  
Michel Kern ◽  
Jean E. Roberts ◽  
Vincent MARTIN
Keyword(s):  
Porous Medium ◽  
Domain Decomposition ◽  
Single Phase ◽  
Decomposition Methods ◽  
Interface Problem ◽  
Domain Decomposition Methods ◽  
Standard Interface ◽  
International Audience ◽  
Milieu Poreux ◽  
Phase Fluid

International audience In this paper, we are interested in modeling the flow of a single phase fluid in a porous medium with fractures, using domain decomposition methods. In the proposed approach, the fracture is regarded as an active interface, the transmission conditions and the exchanges between the rock and the fracture taking into account the flow in the fracture. The problem to be solved is then a non standard interface problem which takes into account the flow in the fractures.

scholarly journals Pushing Droplet Through a Porous Medium

2021 ◽  
Author(s):  
Maciej Matyka
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Mechanical Model ◽  
Single Phase ◽  
Soft Body ◽  
Mass System ◽  
Porous Domain ◽  
Phase Fluid

AbstractI use a mechanical model of a soft body to study the dynamics of an individual fluid droplet in a random, non-wettable porous medium. The model of droplet relies on the spring–mass system with pressure. I run hundreds of independent simulations. I average droplets trajectories and calculate the averaged tortuosity of the porous domain. Results show that porous media tortuosity increases with decreasing porosity, similar to single-phase fluid study, but the form of this relationship is different.

Homogenization of a stochastic model of a single phase flow in partially fissured media

2021 ◽  
pp. 1-38
Author(s):  
Chigoziem Emereuwa ◽  
Mogtaba Mohammed
Keyword(s):  
Stochastic Model ◽  
Stochastic Partial Differential Equations ◽  
Single Phase ◽  
Double Porosity ◽  
Perforated Domain ◽  
Probability Measures ◽  
Porous System ◽  
Single Phase Flow ◽  
Phase Fluid ◽  
Porosity Model

In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.

scholarly journals Experimental Study on Water Sensitivity Difference Based on Oiliness of Porous Medium Rock

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Jie Li ◽  
Wei Li ◽  
Li Li
Keyword(s):  
Experimental Study ◽  
Nuclear Magnetic Resonance ◽  
Porous Medium ◽  
Single Phase ◽  
Sensitivity Experiment ◽  
Water Sensitivity ◽  
Influence Mechanism ◽  
Multiphase Fluid ◽  
The Impact ◽  
Phase Fluid

This study presents the differences of water sensitivity experiment of porous medium rock between conventional dry core samples and oil-bearing core. The comparison was made to analyze the impact of single-phase fluid and multiphase fluid on the actual sensitivity of rock. The nuclear magnetic resonance (NMR) test was carried out to reveal the distribution of oil in porous medium and the microscopic influence mechanism of oil phase. The study shows that the initial oil in place could isolate the clay from water, and then the expansion and the migration of the clay were prevented to reduce the decrease of degree of damage.

scholarly journals Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid

2019 ◽  
Vol 7 ◽  
Author(s):  
Olav Galteland ◽  
Dick Bedeaux ◽  
Bjørn Hafskjold ◽  
Signe Kjelstrup
Keyword(s):  
Porous Medium ◽  
Single Phase ◽  
Phase Fluid

LATTICE BOLTZMANN SIMULATION OF THE FLOW OF NON-NEWTONIAN FLUIDS IN POROUS MEDIA

2003 ◽  
Vol 17 (01n02) ◽  
pp. 99-102 ◽  
Author(s):  
EDO S. BOEK ◽  
JONATHAN CHIN ◽  
PETER V. COVENEY
Keyword(s):  
Porous Medium ◽  
Lattice Boltzmann ◽  
Effective Viscosity ◽  
Single Phase ◽  
Newtonian Fluids ◽  
Lattice Boltzmann Simulation ◽  
Local Shear ◽  
Simulation Results ◽  
Flow Experiments ◽  
Good Agreement

We present a LB study of the flow of single-phase non-Newtonian fluids, using a power law relationship between the effective viscosity and the local shear rate. Channel flow experiments were carried out to measure the velocity profiles. The simulation results are found to be in good agreement with theory. We also report simulations of the flow of non-Newtonian fluids in a 2-D porous medium.

scholarly journals Modelling fluid flow and heat transfer in a saturated porous medium

2000 ◽  
Vol 4 (2) ◽  
pp. 165-173 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Viscous Dissipation ◽  
Single Phase ◽  
Saturated Porous Medium ◽  
Inertial Effects ◽  
Flow And Heat Transfer ◽  
Phase Fluid

Since the days of Darcy, many refinements have been made to the equations used to model single-phase fluid flow and heat transfer in a saturated porous medium, to allow for such basic things as inertial effects, boundary friction and viscous dissipation, and also additional effects such as those due to rotation or a magnetic field. These developments are reviewed.

COMPUTER MODELING OF CHEMICAL EQUILIBRIUMS IN WO3–H2O SYSTEM

2017 ◽  
pp. 35-48 ◽  
Author(s):  
V.P. Bondarenko ◽  
O.O. Matviichuk
Keyword(s):  
Transition Temperature ◽  
Gas Phase ◽  
Single Phase ◽  
Reference Data ◽  
Maximum Amount ◽  
Reaction Products ◽  
Influence Of Temperature ◽  
Equilibrium Chemical ◽  
Program Data ◽  
Good Agreement

Detail investigation of equilibrium chemical reactions in WO3–H2O system using computer program FacktSage with the aim to establish influence of temperature and quantity of water on formation of compounds of H2WO4 and WO2(OH)2 as well as concomitant them compounds, evaporation products, decomposition and dissociation, that are contained in the program data base were carried out. Calculations in the temperature range from 100 to 3000 °С were carried out. The amount moles of water added to 1 mole of WO3 was varied from 0 to 27. It is found that the obtained data by the melting and evaporation temperatures of single-phase WO3 are in good agreement with the reference data and provide additionally detailed information on the composition of the gas phase. It was shown that under heating of 1 mole single-phase WO3 up to 3000 °С the predominant oxide that exist in gaseous phase is (WO3)2. Reactions of it formation from other oxides ((WO3)3 and (WO3)4) were proposed. It was established that compound H2WO4 is stable and it is decomposed on WO3 and H2O under 121 °C. Tungsten Oxide Hydrate WO2(OH)2 first appears under 400 °С and exists up to 3000 °С. Increasing quantity of Н2О in system leads to decreasing transition temperature of WO3 into both liquid and gaseous phases. It was established that adding to 1 mole WO3 26 mole H2O maximum amount (0,9044–0,9171 mole) WO2(OH)2 under temperatures 1400–1600 °С can be obtained, wherein the melting stage of WO3 is omitted. Obtained data also allowed to state that that from 121 till 400 °С WO3–Н2O the section in the О–W–H ternary system is partially quasi-binary because under these temperatures in the system only WO3 and Н2O are present. Under higher temperatures WO3–Н2O section becomes not quasi-binary since in the reaction products WO3 with Н2O except WO3 and Н2O, there are significant amounts of WO2(OH)2, (WO3)2, (WO3)3, (WO3)4 and a small amount of atoms and other compounds. Bibl. 12, Fig. 6, Tab. 5.

The Productivity of Horizontal Wells in an In-Line Development System in Fields with Oil Rims

2021 ◽  
Author(s):  
Dmitriy Alekseevich Samolovov ◽  
Artem Igorevich Varavva ◽  
Vitalij Olegovich Polyakov ◽  
Ekaterina Evgenevna Sandalova
Keyword(s):  
Numerical Experiments ◽  
Single Phase ◽  
Analytical Formula ◽  
Horizontal Wells ◽  
Flow Equation ◽  
Development Pattern ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Limited Applicability ◽  
Good Agreement

Abstract The study proposes an analytical method for calculating the productivity of horizontal wells in a line-drive development pattern in fields with oil rims. The paper presents an analysis of existing techniques and compares them with the results of detailed numerical experiments. It also shows the limited applicability of existing techniques. On the basis of the obtained solution of a single-phase flow equation for a line-drive pattern of horizontal wells, an analytical formula was obtained which more accurately describes the productivity of wells beyond the limits of applicability of existing methods. The resulting formula is in good agreement with the results of a detailed numerical experiment.

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