Diffusion Equations for Fluid Flow in Porous Rocks

2017 ◽  
Vol 9 (01) ◽  
pp. 05-13
Author(s):  
Pramod Kumar Pant
Keyword(s):  
Fluid Flow ◽  
Diffusion Equation ◽  
Flow Rate ◽  
Oil Recovery ◽  
Darcy’S Law ◽  
Volume Flow Rate ◽  
Petroleum Industry ◽  
Darcy's Law ◽  
Flow In Porous Media ◽  
Porous Rocks

The multiphase flow in porous media is a subject of great complexities with a long rich history in the field of fluid mechanics. This is a subject with important technical applications, most notably in oil recovery from petroleum reservoirs and so on. The single-phase fluid flow through a porous medium is well characterized by Darcy’s law. In the petroleum industry and in other technical applications, transport is modeled by postulating a multiphase generalization of the Darcy’s law. In this connection, distinct pressures are defined for each constituent phase with the difference known as capillary pressure, determined by the interfacial tension, micro pore geometry and surface chemistry of the solid medium. For flow rates, relative permeability is defined that relates the volume flow rate of each fluid to its pressure gradient. In the present paper, there is a derivation and analysis about the diffusion equation for the fluid flow in porous rocks and some important results have been founded. The permeability is a function of rock type that varies with stress, temperature etc., and does not depend on the fluid. The effect of the fluid on the flow rate is accounted for by the term of viscosity. The numerical value of permeability for a given rock depends on the size of the pores in the rock as well as on the degree of interconnectivity of the void space. The pressure pulses obey the diffusion equation not the wave equation. Then they travel at a speed which continually decreases with time rather than travelling at a constant speed. The results shown in this paper are much useful in earth sciences and petroleum industry.

Modelling of fluid flow in porous media and filtering water process: Langevin dynamics and Darcy’s law based approach

2020 ◽  
Vol 30 ◽  
pp. 870-875
Author(s):  
Yassine Hariti ◽  
Younes Hajji ◽  
Ahmed Hader ◽  
Hamza Faraji ◽  
Yahia Boughaleb ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Darcy’S Law ◽  
Langevin Dynamics ◽  
Darcy's Law ◽  
Flow In Porous Media

scholarly journals Penerapan Dinamika Fluida dalam Perhitungan Kecepatan Aliran dan Perolehan Minyak di Reservoir

2014 ◽  
Vol 5 (2) ◽  
pp. 707
Author(s):  
Dwi Listriana Kusumastuti
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Flow Velocity ◽  
Oil Recovery ◽  
Control Volume ◽  
Petroleum Industry ◽  
Reservoir Rock ◽  
Curved Pipe ◽  
Fluid Flow Velocity ◽  
Control Volumes

Water, oil and gas inside the earth are stored in the pores of the reservoir rock. In the world of petroleum industry, calculation of volume of the oil that can be recovered from the reservoir is something important to do. This calculation involves the calculation of the velocity of fluid flow by utilizing the principles and formulas provided by the Fluid Dynamics. The formula is usually applied to the fluid flow passing through a well defined control volume, for example: cylinder, curved pipe, straight pipes with different diameters at the input and output, and so forth. However, because of reservoir rock, as the fluid flow medium, has a wide variety of possible forms of the control volumes, hence, calculation of the velocity of the fluid flow is becoming difficult as it would involve calculations of fluid flow velocity for each control volume. This difficulties is mainly caused by the fact that these control volumes, that existed in the rock, cannot be well defined. This paper will describe a method for calculating this fluid flow velocity of the control volume, which consists of a combination of laboratory measurements and the use of some theories in the Fluid Dynamics. This method has been proofed can be used for calculating fluid flow velocity as well as oil recovery in reservoir rocks, with fairly good accuration.

scholarly journals Experimental Investigation of Chemical Flooding Using Nanoparticles and Polymer on Displacement of Crude Oil for Enhanced Oil Recovery

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imran Akbar ◽  
Hongtao Zhou ◽  
Wei Liu ◽  
Muhammad Usman Tahir ◽  
Asadullah Memon ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Petroleum Industry ◽  
Chemical Flooding ◽  
Polymer Gel ◽  
Core Flooding ◽  
High Concentration ◽  
Remaining Oil ◽  
Water Cut

In the petroleum industry, the researchers have developed a new technique called enhanced oil recovery to recover the remaining oil in reservoirs. Some reservoirs are very complex and require advanced enhanced oil recovery (EOR) techniques containing new materials and additives in order to produce maximum oil in economic and environmental friendly manners. In this work, the effects of nanosuspensions (KY-200) and polymer gel HPAM (854) on oil recovery and water cut were studied in the view of EOR techniques and their results were compared. The mechanism of nanosuspensions transportation through the sand pack was also discussed. The adopted methodology involved the preparation of gel, viscosity test, and core flooding experiments. The optimum concentration of nanosuspensions after viscosity tests was used for displacement experiments and 3 wt % concentration of nanosuspensions amplified the oil recovery. In addition, high concentration leads to more agglomeration; thus, high core plugging takes place and diverts the fluid flow towards unswept zones to push more oil to produce and decrease the water cut. Experimental results indicate that nanosuspensions have the ability to plug the thief zones of water channeling and can divert the fluid flow towards unswept zones to recover the remaining oil from the reservoir excessively rather than the normal polymer gel flooding. The injection pressure was observed higher during nanosuspension injection than polymer gel injection. The oil recovery was achieved by about 41.04% from nanosuspensions, that is, 14.09% higher than polymer gel. Further investigations are required in the field of nanoparticles applications in enhanced oil recovery to meet the world's energy demands.

An Approximate Method for Non -Darcy Radial Gas Flow

1964 ◽  
Vol 4 (02) ◽  
pp. 96-114 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Linear Equation ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Gas Flow ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Non Linear Equation ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Flow Law

Abstract Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is shown to be very good. Some observations on the interpretation of gas well tests are made. Introduction The flow of gases in porous media is a problem that has been the subject of much study in recent years, and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law (1) leads to a non-linear equation of the form (2) in a homogeneous medium, assuming an equation of state(3) It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form (4) This form of equation was first suggested by Forchheimer and, later, Katz and Cornell, and Irmay, developed a similar equation. Houpeurt derived this form of equation using the concept of an idealized pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type, for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al., and Aronofsky and Jenkins, but the latter solutions, apart from the simple linearization of equation [2] to yield a diffusion equation in p2, are not so well-known. SPEJ P. 96ˆ

Transport Modelling of Multi-Phase Fluid Flow in Porous Media for Enhanced Oil Recovery

2020 ◽  
Vol 400 ◽  
pp. 38-44
Author(s):  
Hassan Soleimani ◽  
Hassan Ali ◽  
Noorhana Yahya ◽  
Beh Hoe Guan ◽  
Maziyar Sabet ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Constitutive Relations ◽  
Mobility Control ◽  
Flow In Porous Media ◽  
Wettability Alteration ◽  
Adsorption Effect ◽  
Phase Fluid

This article studies the combined effect of spatial heterogeneity and capillary pressure on the saturation of two fluids during the injection of immiscible nanoparticles. Various literature review exhibited that the nanoparticles are helpful in enhancing the oil recovery by varying several mechanisms, like wettability alteration, interfacial tension, disjoining pressure and mobility control. Multiphase modelling of fluids in porous media comprise balance equation formulation, and constitutive relations for both interphase mass transfer and pressure saturation curves. A classical equation of advection-dispersion is normally used to simulate the fluid flow in porous media, but this equation is unable to simulate nanoparticles flow due to the adsorption effect which happens. Several modifications on computational fluid dynamics (CFD) have been made to increase the number of unknown variables. The simulation results indicated the successful transportation of nanoparticles in two phase fluid flow in porous medium which helps in decreasing the wettability of rocks and hence increasing the oil recovery. The saturation, permeability and capillary pressure curves show that the wettability of the rocks increases with the increasing saturation of wetting phase (brine).

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