1. Flow and Transport Through Porous Media
Instructor
Dr. Renu V
Dept. Civil Engineering
IIT (ISM) Dhanbad

2. Flow and Transport Through Porous Media
Course Code: CEO401 (3-0-0)
Course Credit : 9
Course Objective: This course is designed to provide students a fundamental understanding of flow and transport processes occurring within the porous systems.
Learning Outcome: Upon successful completion of this course, students will:
Understand theoretical principles for characterizing and predicting single phase flow processes in porous systems.
Have an in-depth knowledge of multiphase flow processes in porous systems.
Have a basic understanding on flow and transport processes in fractured rock systems.
Understand various transport mechanisms influencing the fate and transport of solutes in porous systems.

3. Course Syllabus Unit no:1 Topics to be covered Lectures
Learning Outcome 1
Introduction to Flow through Porous Media: Types of Porous Media. Application of study- Groundwater engineering, Oil Exploration, Mining, Waste Disposal, Geothermal Energy Extraction
Single Phase Fluid Flow: Introduction to single phase and multiphase fluid systems. Concept of Porosity, Permeability, Factors affecting Porosity and Permeability, Correlations between porosity and permeability, Fluid movement below and above the water table, Reynolds number in Porous Media Flow, Darcy’s Law and range of validity, Experimental determination of permeablity- Constant and variable head Permeameters, Mass, Momentum and Energy Conservation Equations for Fluid movement in Porous media, Steady state flow concepts- Laminar and Turbulent flow, Derivation of Diffusivity
Equation for Single phase fluid flow.
[16L]
Understand theoretical principles for characterizing and predicting single phase flow processes in porous systems. 2
Multiphase fluid flow: Multiphase flow through porous systems, Concept of Relative Permeability, Saturation, Wettability and
Capillary Pressure, Capillary pressure-Saturation relationship,
Darcy’s Law for Multiphase flow, Immiscible displacement, BuckleyLeverett theory, Multiphase mass continuity equation.
Fractured rock-system: Flow and Transport mechanism through fractured rock systems, Comparison between flow and transport processes through classical porous media and fractured rock systems.
[14L]
Have an in-depth knowledge of
multiphase flow processes in porous systems.
Have a basic understanding on flow and transport processes in fractured rock
systems. 3
Transport Mechanisms: Advection, Diffusion, Fick’s Law, Hydrodynamic Dispersion, Concept of Tortuosity, Advection-Dispersion Equation, Sorption- Physisorption and Chemisorption, Equilibrium and Kinetic Sorption, Dissolution, Biodegradation, Radio-active decay, Concept of Single- component and Multi-component solute transport.
[9L]
Understand various transport mechanisms influencing the fate and transport of solutes in
porous systems.

4. Reference Books Text Books:
Amit, P. (2014), Introduction to Fluid Flow through Porous Media, Lambert Academic Publishing.
Civan, F.(2011), Porous media transport phenomena, John Wiley & Sons, Inc.
Reference Books:
Sahimi, M. (2011),Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches, 2nd Edition, Wiley VCH Verlag GmbH & Co. KGaA.
Bear, J.(1972),Dynamics of fluids in porous media,Environmental science series, New York.
Rastogi, A.K. (2007), Numerical Groundwater Hydrology, 1st Edition, Penram International Publishing.

5. Lecture Plan Topic No: Lectures
1. Introduction to Flow and Transport through Porous Media 1
2. Single Phase Fluid Flow: Introduction to single phase and multiphase fluid systems. Concept of Porosity, Permeability, Factors affecting Porosity and Permeability, Correlations between porosity and permeability 5
3. Fluid movement below and above the water table, Reynolds number in Porous Media Flow, Darcy’s Law and range of validity, Experimental determination of permeablity- Constant and variable head Permeameters 6
4. Mass, Momentum and Energy Conservation Equations for Fluid movement in Porous media, Steady state flow concepts- Laminar and Turbulent flow, Derivation of Diffusivity Equation for Single phase fluid flow.
5. Multiphase fluid flow: Multiphase flow through porous systems, Concept of Relative Permeability, Saturation, Wettability and Capillary Pressure, Capillary pressure-Saturation relationship, Darcy’s Law for Multiphase flow, Immiscible displacement, BuckleyLeverett theory, Multiphase mass continuity equation. 8
6. Fractured rock-system: Flow and Transport mechanism through fractured rock systems, Comparison between flow and transport processes through classical porous media and fractured rock systems.
7. Transport Mechanisms: Advection, Diffusion, Fick’s Law, Hydrodynamic Dispersion, Concept of Tortuosity, Advection-Dispersion Equation 4
Sorption- Physisorption and Chemisorption, Equilibrium and Kinetic Sorption, Dissolution, Biodegradation, Radio-active decay, Concept of Single- component and Multi-component solute transport.

6. Evaluation Pattern Component Marks Quiz 10 Mid semester 32 Term paper
End semester 48
Total
100

7. Introduction

8. Definition of Porous Media
What constitutes a porous media
When we call a media to be a porous media
What are the essential parameters that describe a porous media
What are the applications that come under this subject of flow through porous media.

9. What is Porous Media ??
A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame".
The pores are typically filled with a fluid (liquid or gas). The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media.

10. What is Porous Media ?? (Contd..)
All solids and semi-solids contain interstitial space. When this space is sufficiently large, a flow can be established and then it becomes “porous”.
Except metals, some dense rocks, and some plastic materials, all solid and semi-solid materials are porous
Majority of porous media comprises of interconnected 3-D network of capillary channels of uniform sizes and shapes (referred as pore or void).

11. What is Porous Media ?? (Contd..)
A material or structure must have these two properties in order to qualify as a porous medium:
It must contain spaces, so-called voids or pores, free of solids, imbedded in the solid or semi-solid matrix. The pores usually contain some fluid, such as air, water, oil or a mixture of different fluids.
It must be permeable to a variety of fluids, i.e., fluids should be able to penetrate through one face of a sample of material and emerge on the other side.

12. DIFFERENT TYPES OF POROUS MEDIA

13. What is Porous Media ?? (Contd..)
Everything around us is porous
Human body is porous
Earth is porous.
So, this porous media or how a transport process takes place inside a porous media, how a fluid flows through a porous media is extremely important,

14. Application of Flow and Transport Through Porous Media
Essentially the flow through the pores is what we are concerned with in varied applications
for example for obtaining some resources from earth
to understand, or exploring how a medicine will travel through human body.
absorption column or membranes or the reverse osmosis unit that we use for separating dissolved solids from water.

15. Applications- Hydrology
Source:

16. Applications- Enhanced Oil Recovery
Source:

17. Application- Geothermal Energy Extraction
Source:

18. Contaminant Transport Studies

19. Application – Aquifer Remediation

20. Application- Groundwater Control

21. Application-Subsurface Sequestration

22. Application – Engineered Porous Media
Filter Adsorbent Electrode Catalyst

23. Application – Biomaterials
Drug Delivery
Tissue Engineering
Skin/bone/tissue grafts
Implants

24. Fluid Flow Problems Single Phase Flow Problems
Multi-Phase Flow Problems
the flow of a single homogeneous phase, e.g.,, water, air.
Multiphase flow refers to the simultaneous flow of more than one fluid phase through a porous media. 

25. Multiphase Fluid Flow
When two fluids are completely mixed into each other without identifiable interface, they are termed as miscible fluids. Eg. Sea water and fresh water
If two fluids are non-mixing with identifiable interphase, they are called immiscible fluids. Eg. Oil and water

26. Characteristics of Porous Media
How the porous media looks like,
We see here various grains and there are some void spaces within.
So, I can see here, these light brown colored spheres; these are basically grains
we can see some empty spaces within, which we call interstitial space or void space.

27. Characteristics of Porous Media
The first term that, we define for a porous media is called porosity.
Porosity is essentially the volume of the void space divided by the total volume; that means, porosity is void volume divided by total volume.
What that means is that if the total volume of a porous material 100 milliliter, and out of that, if 20 milliliter is the void volume and the rest i.e., 80 milliliter is the volume of intact solid, then, we can say that, the porosity would 20 divided by 100, which is equal to 0.2.

28. Porosity Porosity is a measure of the void space in rock,
hence, measures how much HC in rock
Porosity φ = Vp/Vb = (Vb-Vm)/Vb; Vb = Vp + Vm

29. Characteristics of Porous Media

30. Homogenization of Porous Media
When we define we are assuming that this porous medium is completely homogeneous. So, when can we define this porosity this way? See, it depends on what kind of sampling volume we have in mind.
For example we can see here, that we can pick up a sample volume, the sample over which we measured the porosity; the sample over which we can measure the porosity; we can take the sample volume of size of this much or we can take some other sample size.
I have a sample volume here and you have a much larger sample volume here, over which we measured the porosity.

31. Homogenization of Porous Media
Therefore, we can choose a sampling volume which is large or we can choose the sampling volume which is small.
What you would see in these case is, when the sampling volume is large we will consistently see a porosity, which is let us say, you said 0.2 right 100 milliliter out of that 20 milliliter is void volume and 80 millimeter is the solid volume. So, you will find that, it would be consistently averaging out to 0.2
However, if the sampling volume is much smaller then, it could be that the major part of the sampling volume is void, and there would be a small part in the solid.
Or at some other location you will find it is mostly solid and very small amount would be the void; in that case you will find that, below a threshold value of the sampling volume you will get random values of porosity.

32. Representative Elementary Volume for porous media
Representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield a value representative of the whole porous media

33. Classification of Porosity
Porosity can be classified into;
Original porosity
Induced porosity
Original porosity (primary) is formed during the deposition of rock materials, e.g. porosity between granular in sandstone, porosity among crystal and oolitic in limestone
Induced porosity (secondary) is developed by some geological process on the deposited rock material.
E.g; Fractures, or vugs cavity usual occur in limestone
(chemical reaction b/w CaCO3 and MgCl2)

34. Classification of Porosity
Sand grain
Cement material
Effective / connected
porosity (25%)
Ineffective Porosity (5%)
Total Porosity (30%)

35. Classification of Porosity
3 kinds porosity includes:
Effective porosity
Ineffective/ Isolated porosity
Total porosity
Effective porosity is the measure of the void space that is filled by recoverable oil and gas / water; or the amount of pore space that is sufficiently interconnected to yield its oil & gas for recovery.
φ =( Vol. of interconnected pores + Vol. of deadend) /Total or bulk vol. of reservoir rock

36. Classification of Porosity
Total porosity, t =
Total Pore Volume
Bulk Volume
Effective porosity, e =
Interconnected Pore Space
Bulk Volume
Effective porosity – of great importance;
contains the mobile fluid

37. Porosity (Contd…)
It should be noted that the porosity does not give any information concerning pore sizes, their distribution, and their degree of connectivity.
Thus, rocks of the same porosity can have widely different physical properties. An example of this might be a carbonate rock and a sandstone.
Each could have a porosity of 0.2, but carbonate pores are often very unconnected resulting in its permeability being much lower than that of the sandstone.

38. Type of Porosity used in Hydrocarbon industry

39. FACTORS THAT AFFECT POROSITY
PRIMARY
Particle sphericity and angularity
Packing
Sorting (variable grain sizes)

40. SECONDARY (DIAGENETIC)
Mechanical Processes
Overburden stress (compaction)
Geochemical Reactions

41. Porosity
Measure of pore space in porous media

42. Packing

43. Sorting Porous media contain a distribution of grain sizes
First imagine a rock with two grain sizes, one of which has 1/100th the diameter of the other. The first mechanism applies when there are sufficient of the larger grains to make up the broad skeleton of the rock matrix. Here, the addition of the smaller particles reduces the porosity of the rock because they can fit into the interstices between the larger particles.
The second mechanism is valid when the broad skeleton of the rock matrix is composed of the smaller grains. There small grains will have a pore space between them. Clearly, if some volume of these grains are removed and replaced with a single solid larger grain, the porosity will be reduced because both the small grains and their associated porosity have been replaced with solid material.

44. Grain Shape
Several studies have been carried out on random packings of non-spherical grains, and in all cases the resulting porosities are larger than those for spheres.

45. Grain Size
The equilibrium porosity of a porous material composed of a random packing of spherical grains is dependent upon the stability given to the rock by frictional and cohesive forces operating between individual grains.
These forces are proportional to the exposed surface area of the grains.
The specific surface area (exposed grain surface area per unit solid volume) is inversely proportional to grain size.
This indicates that, when all other factors are equal, a given weight of coarse grains will be stabilised at a lower porosity than the same weight of finer grains.

46. Porosity Measurements
From definition of porosity, porosity of rock sample can be determined by measuring any two of these quantities:
bulk volume
pore volume
grain volume
in-porous-media/chapter-2-the-porous- medium/porosity/laboratory-porosity-measurement/

47. Laboratory Determinations
Direct Measurement
Here the two volumes V and Vs are determined directly.
This method measures the total porosity, but is rarely used on rocks because Vs can only be measured if the rock is totally disaggregated, and cannot, therefore, be used in any further petrophysical studies.

48. Mercury Injection The rock is evacuated, and then immersed in mercury.
At laboratory pressures mercury will not enter the pores of most rocks. The displacement of the mercury can therefore be used to calculate the bulk volume of the rock.
The pressure on the mercury is then raised in a stepwise fashion, forcing the mercury into the pores of the rock). If the pressure is sufficiently high, the mercury will invade all the pores. A measurement of the amount of mercury lost into the rock provides the pore volume directly.
The porosity can then be calculated from the bulk volume and the pore volume. Clearly this method also measures the connected porosity.
In practice there is always a small pore volume that is not accessed by the mercury even at the highest pressures. This is pore volume that is in the form of the minutest pores. So the mercury injection method will give a lower porosity compared to other methods.
This is a moderately accurate method that has the advantage that it can be done on small irregular samples of rock, and the disadvantage that the sample must be disposed of safely after the test.

49. Gas Expansion
This method relies on the ideal gas law, or rather Boyle’s law. The rock is sealed in a container of known volume V1 at atmospheric pressure P1.
This container is attached by a valve to another container of known volume, V2, containing gas at a known pressure, P2. When the valve that connects the two volumes is opened slowly so that the system remains isothermal, the gas pressure in the two volume equalises to P3.
The value of the equilibrium pressure can be used to calculate the volume of grains in the rock Vs.. Boyle’s Law states that the pressure times the volume for a system is constant. Thus we ca write the PV for the system before the valve is opened (left hand side) and set it equal to the PV for the equilibrated system (right hand side):

50. Gas Expansion