scholarly journals Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Lihua Zuo ◽  
Ruud Weijermars
Keyword(s):  
Porous Media ◽  
Fluid Transport ◽  
Initial Conditions ◽  
Time Of Flight ◽  
Flight Path ◽  
Flow In Porous Media ◽  
Transport Mechanisms ◽  
Local Porosity ◽  
Fluid Properties ◽  
Porosity And Permeability

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule  1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule  2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

scholarly journals Rules for Flight Paths and Time of Flight for Flows in Porous Media with Heterogeneous Permeability and Porosity

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Lihua Zuo ◽  
Ruud Weijermars
Keyword(s):  
Porous Media ◽  
Fluid Transport ◽  
Initial Conditions ◽  
Time Of Flight ◽  
Flight Path ◽  
Flow In Porous Media ◽  
Transport Mechanisms ◽  
Local Porosity ◽  
Fluid Properties ◽  
Porosity And Permeability

Porous media like hydrocarbon reservoirs may be composed of a wide variety of rocks with different porosity and permeability. Our study shows in algorithms and in synthetic numerical simulations that the flow pattern of any particular porous medium, assuming constant fluid properties and standardized boundary and initial conditions, is not affected by any spatial porosity changes but will vary only according to spatial permeability changes. In contrast, the time of flight along the streamline will be affected by both the permeability and porosity, albeit in opposite directions. A theoretical framework is presented with evidence from flow visualizations. A series of strategically chosen streamline simulations, including systematic spatial variations of porosity and permeability, visualizes the respective effects on the flight path and time of flight. Two practical rules are formulated. Rule  1 states that an increase in permeability decreases the time of flight, whereas an increase in porosity increases the time of flight. Rule  2 states that the permeability uniquely controls the flight path of fluid flow in porous media; local porosity variations do not affect the streamline path. The two rules are essential for understanding fluid transport mechanisms, and their rigorous validation therefore is merited.

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.

scholarly journals Numerical modeling of porosity waves as a mechanism for rapid fluid transport in elastic porous media

2015 ◽  
Author(s):  
◽  
Ajit Joshi
Keyword(s):  
Porous Media ◽  
Fluid Transport ◽  
Fluid Pressure ◽  
Source Rocks ◽  
Lithostatic Pressure ◽  
Accretionary Wedge ◽  
The World ◽  
Porosity And Permeability ◽  
High Fluid ◽  
High Fluid Pressure

The rapid ascent of fluids through kilometer-scale thicknesses of low permeability sediments at rates much faster than predicted Darcy fluxes has been observed in numerous locations around the world. A consistently observed condition associated with this anomalously rapid fluid flow is high fluid pressure approaching lithostatic pressure. This high fluid pressure can be produced by a number of geologic processes, including the production of hydrocarbon fluids by maturation of organic matter, the production of water through dehydration reactions of hydrous minerals, compaction disequilibrium during the deposition and burial of sediments, and earthquakes. As fluid pressure increases in a deformable porous medium, the pore spaces in the medium expand, increasing porosity and permeability. This zone of increased fluid pressure, porosity, and permeability, termed a porosity wave, may travel much faster than fluids flowing at Darcy fluxes in the surroundings, provided that permeability is a sensitive function of fluid pressure or effective stress. In addition, because porosity waves have higher porosity than their surroundings, they can serve as a mechanism for enhance fluid transport. The main goal of the present study was to evaluate the formation and fluid transport capabilities of porosity waves in elastic rocks. The study was performed using a numerical solution to a mass conservation equation for fluids in porous media and Darcy's law. Results of the study show that rates of fluid pressure generation by sediment compaction disequilibrium and hydrocarbon formation in porous media saturated with dense and viscous fluids like oil or water can generally only form porosity waves at depths below ~4 km, and are unable to form porosity waves in porous media saturated with low density and viscosity fluids like methane. In order to form porosity waves in methane-saturated porous media, geologically instantaneous rates of fluid pressure generation are needed, which may be possible from earthquakes. Once formed, methane-saturated porosity waves may travel at speeds of ~10's of m per year for distances of 1-2 km under geological conditions similar to those of the Eugene Island hydrocarbon field in the Gulf of Mexico basin, one of the focus areas of the present study. However, porosity waves are unlikely to have played a major role in transporting methane to shallow reservoirs at Eugene Island. This is in part because Eugene Island appears to have been seismically quiescent throughout its geological history and because most of the reservoirs are separated by more than two kilometers from the hydrocarbon source rocks. In the Nankai accretionary wedge, another focus area of the present study, results show that porosity waves formed at a depth of ~2 km can ascend along the decollement at the minimum 1's of km per day velocities needed to cause aseismic slip, provided that fluid pressures in porosity source region either exceed lithostatic pressure or are slightly below lithostatic pressure but other hydrogeologic parameters are near the limits of their geologically reasonable ranges. Though the present study was focused on two specific field sites, the results have implications for rapid fluid transport in other geologically similar environments in other locations around the world.

Control-Volume Model for Simulation of Water Injection in Fractured Media: Incorporating Matrix Heterogeneity and Reservoir Wettability Effects

SPE Journal ◽  
2007 ◽  
Vol 12 (03) ◽  
pp. 355-366 ◽  
Author(s):  
Jorge E.P. Monteagudo ◽  
Abbas Firoozabadi
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Control Volume ◽  
Water Injection ◽  
Fractured Media ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Fluid Properties ◽  
Delaunay Triangles

Summary The control-volume discrete-fracture (CVDF) model is extended to incorporate heterogeneity in rock and in rock-fluid properties. A novel algorithm is proposed to model strong water-wetting with zero capillary pressure in the fractures. The extended method is used to simulate:oil production in a layered faulted reservoir,laboratory displacement tests in a stack of matrix blocks with a large contrast in fracture and matrix capillary pressure functions, andwater injection in 2D and 3D fractured media with mixed-wettability state. Our results show that the algorithm is suitable for the simulation of water injection in heterogeneous porous media both in water-wet and mixed-wettability states. The novel approach with zero fracture capillary and nonzero matrix capillary pressure allows the proper prediction of sharp fronts in the fractures. Introduction This work is focused on the numerical treatment of two main physical aspects of multiphase flow in fractured porous media: heterogeneity in rock-fluid properties and reservoir wettability. In a previous work (Monteagudo and Firoozabadi 2004), a CVDF method was used to discretize the system of equations governing water injection in fractured media with strong-water-wettability state and homogeneous matrix and rock-fluid properties. The method was restricted to a finite contrast in matrix-fracture capillary pressure. In this work, we extend the CVDF model for simulation of water injection in fractured media comprised of heterogeneous rocks and wettability conditions from strong-water-wetting to mixed-wetting conditions. We also present a formulation for infinite contrast in capillary pressures of matrix and fractures (zero capillary pressure in the fracture and finite capillary pressure in the matrix). The control volume (CV) method, first proposed by Baliga and Patankar (1980), is a finite-volume formulation over dual cells (CVs) of a Delaunay mesh. It is locally conservative and suited for unstructured grids. It has been widely employed for the simulation of multiphase flow in porous media (Monteagudo and Firoozabadi 2004; Verma 1996; Helmig 1997; Helmig and Huber 1998; Bastian et al. 2000; Geiger et al. 2003) and the convergence of the method for two-phase immiscible flow in porous medium has already been proved (Michel 2003). Numerical treatment of heterogeneity in the framework of the CV method has been extensively studied in the past (Edwards 2002; Edwards and Rogers 1998; Prevost 2000; Aavatsmark et al. 1998a, b). Nevertheless, those works have focused on absolute permeability heterogeneity and anisotropy in single-phase flow. The main concern in those works is the use of full tensor permeability and the accurate generation of streamlines (required by the streamline numerical method). It is well known that the standard CV method produces inaccurate velocity fields around the interfaces of heterogeneous media as the contrast in permeability is increased (Durlofsky 1994). In the standard CV method, Delaunay triangles are locally homogeneous and the polygonal CV cell may be heterogeneous (see Fig. 1a). For accurate streamlines, several authors (Verma 1996; Edwards 2002; Edwards and Rogers 1998; Prevost 2000; Aavatsmark et al. 1998a) have proposed that the polygonal CV cell must be locally homogeneous, implying heterogeneous Delaunay triangles (see Fig. 1b). The latter configuration, however, generates additional problems in the simulation of multiphase flow in porous media. Basically, from mesh generation standpoint, it may not be possible to generate an unstructured mesh where the boundaries of the CV median-dual cell conform to heterogeneous interfaces in the domain. Conforming mesh is important for the discrete-fracture approach. Therefore, it would be necessary to first generate a standard CV cell mesh, and later a homogenization procedure would be required to obtain CV cells with constant permeability. The homogenization or upscaling of permeability is somehow possible, but the same is not true for rock-fluid properties; most challenging is capillary pressure with different endpoints. Therefore, the approach with the homogeneous CV cell may be suitable for single-phase simulation where rock-fluid interactions are not part of the problem. However, rock-fluid interactions have to be taken into account for simulation of multiphase flow in fractured porous medium. Frequently, capillary pressure is disregarded in two-phase flow simulations; however, capillary pressure is of importance for simulation of multiphase flow in fractured porous media (Monteagudo and Firoozabadi 2004; Karimi-Fard and Firoozabadi 2003). Predictions of flow pattern and oil recovery may be severely affected if capillary pressure effect is neglected.

Conservation of Energy

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Porous Media ◽  
Thermal Energy ◽  
Mechanical Energy ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Conservation Of Energy ◽  
Euler’S Equations ◽  
Buoyancy Driven Flows ◽  
Fluid Properties ◽  
Euler's Equations

We briefly considered in Chapter 6 a geologically important class of flows—buoyancy driven flows—in which thermal effects hold an essential part in creating the forces that induce flow. We also should recall that fluid properties such as viscosity can vary with temperature. As fluids are heat-conducting media, taking into account the thermal energy conditions and heat flow within a fluid therefore is often an essential part of describing a flow field. Thermal energy, however, is not transported merely by conduction; in a moving fluid, thermal energy also is advected from position to position. In addition, recall that the thermal energy of a fluid, according to the first law of thermodynamics, is inextricably coupled with energy in the form of work performed between a fluid element and its surroundings. It is therefore important to consider the mechanical energy of a fluid when describing its thermal conditions. To this end, the developments below concern conservation of energy in both thermal and mechanical forms. Analogous to our treatment of conservation of mass, we will derive equations that describe a condition—conservation of energy—which must be satisfied at each coordinate position in a fluid. An important outcome of our development of expressions for conservation of energy is a set of dynamical equations for the special case of an ideal fluid. In component form, these are referred to as Euler’s equations, and arise from conservation of purely mechanical energy, neglecting thermal forms. (We will derive Euler’s equations again in Chapter 10 using an explicit treatment of the forces involved in fluid motion.) Conservation of energy also applies to flow in porous media; the relevant expressions are similar to those for purely fluid flow, but with several important differences that arise from the two-phase character (solid and fluid) of flow in porous media. In relation to this topic, we also will develop the idea of Hubbert’s potential, and the relation of this potential to piezometric head. This is a cornerstone of the theory of flow in porous media. Our objective is to illustrate how Hubbert’s potential, and head, are obtained from applying the idea of conservation of mechanical energy to a fluid.

Simulations of Single-Fluid Flow in Porous Media

1998 ◽  
Vol 09 (08) ◽  
pp. 1505-1521 ◽  
Author(s):  
A. Koponen ◽  
M. Kataja ◽  
J. Timonen ◽  
D. Kandhai
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Lattice Gas ◽  
Effective Porosity ◽  
Flow In Porous Media ◽  
Lattice Boltzmann Simulations ◽  
Porosity And Permeability ◽  
Flow Through ◽  
2D And 3D ◽  
Good Agreement

Several results of lattice-gas and lattice-Boltzmann simulations of single-fluid flow in 2D and 3D porous media are discussed. Simulation results for the tortuosity, effective porosity and permeability of a 2D random porous medium are reported. A modified Kozeny–Carman law is suggested, which includes the concept of effective porosity. This law is found to fit well the simulated 2D permeabilities. The results for fluid flow through large 3D random fibre webs are also presented. The simulated permeabilities of these webs are found to be in good agreement with experimental data. The simulations also confirm that, for this kind of materials, permeability depends exponentially on porosity over a large porosity range.

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