scholarly journals A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2986 ◽  
Author(s):  
Gang Lei ◽  
Nai Cao ◽  
Di Liu ◽  
Huijie Wang
Keyword(s):  
Porous Media ◽  
Flow Velocity ◽  
Flow Behavior ◽  
Quantitative Model ◽  
Hertzian Contact ◽  
Flow In Porous Media ◽  
Conformable Derivative ◽  
Linear Flow ◽  
Proposed Model ◽  
Non Linear

Prediction of the non-linear flow in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on non-linear flow in porous media are not yet definitive. The principal aim of this paper is to develop a meaningful and reasonable quantitative model that manifests the most important fundamental controls on low velocity non-linear flow. By coupling a new derivative with fractional order, referred to conformable derivative, Swartzendruber equation and modified Hertzian contact theory as well as fractal geometry theory, a flow velocity model for porous media is proposed to improve the modeling of Non-linear flow in porous media. Predictions using the proposed model agree well with available experimental data. Salient results presented here include (1) the flow velocity decreases as effective stress increases; (2) rock types of “softer” mechanical properties may exhibit lower flow velocity; (3) flow velocity increases with the rougher pore surfaces and rock elastic modulus. In general, the proposed model illustrates mechanisms that affect non-linear flow behavior in porous media.

scholarly journals Multi-Scale Insights on the Threshold Pressure Gradient in Low-Permeability Porous Media

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 364 ◽  
Author(s):  
Huimin Wang ◽  
Jianguo Wang ◽  
Xiaolin Wang ◽  
Andrew Chan
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Water Saturation ◽  
Flow Behavior ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Linear Flow ◽  
Multi Scale ◽  
Non Linear

Low-permeability porous medium usually has asymmetric distributions of pore sizes and pore-throat tortuosity, thus has a non-linear flow behavior with an initial pressure gradient observed in experiments. A threshold pressure gradient (TPG) has been proposed as a crucial parameter to describe this non-linear flow behavior. However, the determination of this TPG is still unclear. This study provides multi-scale insights on the TPG in low-permeability porous media. First, a semi-empirical formula of TPG was proposed based on a macroscopic relationship with permeability, water saturation, and pore pressure, and verified by three sets of experimental data. Second, a fractal model of capillary tubes was developed to link this TPG formula with structural parameters of porous media (pore-size distribution fractal dimension and tortuosity fractal dimension), residual water saturation, and capillary pressure. The effect of pore structure complexity on the TPG is explicitly derived. It is found that the effects of water saturation and pore pressure on the TPG follow an exponential function and the TPG is a linear function of yield stress. These effects are also spatially asymmetric. Complex pore structures significantly affect the TPG only in the range of low porosity, but water saturation and yield stress have effects on a wider range of porosity. These results are meaningful to the understanding of non-linear flow mechanism in low-permeability reservoirs.

scholarly journals Effect of Non-Newtonian Flow on Polymer Flooding in Heavy Oil Reservoirs

Polymers ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1225 ◽  
Author(s):  
Xiankang Xin ◽  
Gaoming Yu ◽  
Zhangxin Chen ◽  
Keliu Wu ◽  
Xiaohu Dong ◽  
...  
Keyword(s):  
Porous Media ◽  
Polymer Solution ◽  
Oil Recovery ◽  
Heavy Oil ◽  
Flow Behavior ◽  
Polymer Flooding ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Newtonian Flow ◽  
Heavy Oil Reservoirs

The flow of polymer solution and heavy oil in porous media is critical for polymer flooding in heavy oil reservoirs because it significantly determines the polymer enhanced oil recovery (EOR) and polymer flooding efficiency in heavy oil reservoirs. In this paper, physical experiments and numerical simulations were both applied to investigate the flow of partially hydrolyzed polyacrylamide (HPAM) solution and heavy oil, and their effects on polymer flooding in heavy oil reservoirs. First, physical experiments determined the rheology of the polymer solution and heavy oil and their flow in porous media. Then, a new mathematical model was proposed, and an in-house three-dimensional (3D) two-phase polymer flooding simulator was designed considering the non-Newtonian flow. The designed simulator was validated by comparing its results with those obtained from commercial software and typical polymer flooding experiments. The developed simulator was further applied to investigate the non-Newtonian flow in polymer flooding. The experimental results demonstrated that the flow behavior index of the polymer solution is 0.3655, showing a shear thinning; and heavy oil is a type of Bingham fluid that overcomes a threshold pressure gradient (TPG) to flow in porous media. Furthermore, the validation of the designed simulator was confirmed to possess high accuracy and reliability. According to its simulation results, the decreases of 1.66% and 2.49% in oil recovery are caused by the difference between 0.18 and 1 in the polymer solution flow behavior indexes of the pure polymer flooding (PPF) and typical polymer flooding (TPF), respectively. Moreover, for heavy oil, considering a TPG of 20 times greater than its original value, the oil recoveries of PPF and TPF are reduced by 0.01% and 5.77%, respectively. Furthermore, the combined effect of shear thinning and a threshold pressure gradient results in a greater decrease in oil recovery, with 1.74% and 8.35% for PPF and TPF, respectively. Thus, the non-Newtonian flow has a hugely adverse impact on the performance of polymer flooding in heavy oil reservoirs.

scholarly journals Numerical Simulation of Two-Phase Flows in Heterogeneous Porous Media

2020 ◽  
Vol 21 (2) ◽  
pp. 339
Author(s):  
I. Carneiro ◽  
M. Borges ◽  
S. Malta
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Water Injection ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
High Porosity ◽  
Two Phase ◽  
Recovery Method ◽  
Porosity And Permeability

In this work,we present three-dimensional numerical simulations of water-oil flow in porous media in order to analyze the influence of the heterogeneities in the porosity and permeability fields and, mainly, their relationships upon the phenomenon known in the literature as viscous fingering. For this, typical scenarios of heterogeneous reservoirs submitted to water injection (secondary recovery method) are considered. The results show that the porosity heterogeneities have a markable influence in the flow behavior when the permeability is closely related with porosity, for example, by the Kozeny-Carman (KC) relation.This kind of positive relation leads to a larger oil recovery, as the areas of high permeability(higher flow velocities) are associated with areas of high porosity (higher volume of pores), causing a delay in the breakthrough time. On the other hand, when both fields (porosity and permeability) are heterogeneous but independent of each other the influence of the porosity heterogeneities is smaller and may be negligible.

Modeling Unstable Flow Dynamics in Porous Media Associated With CO2 Sequestration

2008 ◽  
Author(s):  
Amir Riaz ◽  
Yildiray Cinar ◽  
Hamdi Tchelepi
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Co2 Sequestration ◽  
Flow Behavior ◽  
Flow In Porous Media ◽  
Unstable Flow ◽  
Fundamental Physics ◽  
Macroscopic Models ◽  
Wide Range ◽  
Vertical Glass

Multiphase flow in porous media is fundamentally a microscopic process that governs the behavior of geologic scale processes. The application of existing (standard) macroscopic models to problems of geologic scale multiphase flow has proved to be unsatisfactory within a wide range of governing parameters. Our objective is to develop the missing link between the fundamental physics of multiphase flow at the pore-scale and the phenomenological representation of dynamic behaviors across a hierarchy of geologic scales. An essential prerequisite to such an analysis is a qualitative understanding of the flow behavior in terms of flow structures that exist for various parameter combination within the regime of CO2 sequestration. An experimental study addressing these objectives is presented. Experiments are carried out at the laboratory scale in a vertical glass-bead pack, in the parameter range of sequestration flows. Experimental results are interpreted with the help of invasion percolation models.

A Robust Asymptotically Based Modeling Approach for Two-Phase Flow in Porous Media

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
M. M. Awad ◽  
S. D. Butt
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Single Phase ◽  
Present Model ◽  
Flow In Porous Media ◽  
Pressure Gradients ◽  
Two Phase ◽  
New Model ◽  
Proposed Model ◽  
Phase Liquid

A simple semitheoretical method for calculating the two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x≅0 is nearly identical to the single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x≅1 is nearly identical to the single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (ϕl2) or a two-phase frictional multiplier for gas flowing alone (ϕg2) as a function of the Lockhart–Martinelli parameter X. The advantage of the new model is that it has only one fitting parameter (p), while the other existing correlations, such as the correlation of Larkins et al., Sato et al., and Goto and Gaspillo, have three constants. Therefore, calibration of the new model to the experimental data is greatly simplified. The new model is able to model the existing multiparameter correlations by fitting the single parameter p. Specifically, p=1/3.25 for the correlation of Midoux et al., p=1/3.25 for the correlation of Rao et al., p=1/3.5 for the Tosun correlation, p=1/3.25 for the correlation of Larkins et al., p=1/3.75 for the correlation of Sato et al., and p=1/3.5 for the Goto and Gaspillo correlation.

Particulate transport in a porous media under non-linear flow conditions

1991 ◽  
Vol 29 (3) ◽  
pp. 373-385 ◽  
Author(s):  
D. M. Joy ◽  
W. C. Lennox ◽  
N. Kouwen
Keyword(s):  
Porous Media ◽  
Flow Conditions ◽  
Linear Flow ◽  
Particulate Transport ◽  
Non Linear

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks

2015 ◽  
Vol 29 (19) ◽  
pp. 1550135 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Xiao-Ping Li ◽  
Jian-Yi Liu ◽  
Lie-Hui Zhang ◽  
Jianchao Cai
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
Inversion Method ◽  
Type Curves ◽  
Fractal Properties ◽  
Proposed Model ◽  
The Laplace Transform ◽  
Fractal Characteristics

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks was presented based on the fractal properties of tree-shaped capillaries and generalized Darcy's law. The dimensionless expression of flowing pressure was developed using the Laplace transform and Stehfest numerical inversion method. The bilogarithmic type curves were illustrated and the influences of different fractal factors on dimensionless flowing pressure were also discussed. The presented study indicated that the fractal characteristics for the tree-shaped fractal networks should be considered in analysis of transient flow in the heterogeneous porous media. The proposed model may be conducible to a better understanding of the mechanism for transient flow in the multi-porosity porous media.

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