porosity and permeability

Suez University

Faculty of Petroleum & Mining Engineering

Porosity and Permeability

Student

Belal Farouk El-saied Ibrahim

Class / III

Section / Engineering Geology and Geophysics

Presented to Prof. Dr. / Ali Abbas

Porosity and Permeability

Both are important properties that are related to fluids in sediment and sedimentary rocks.

Fluids can include: water, hydrocarbons, spilled contaminants.

Most aquifers are in sediment or sedimentary rocks.

Virtually all hydrocarbons are contained in sedimentary rocks.

Porosity: the volume of void space (available to contain fluid or air) in a sediment or sedimentary rock.

Permeability: related to how easily a fluid will pass through any granular material.

I. Porosity (P)

V Where VP is the total volume of pore space

and VT is the total volume of rock or sediment.

The proportion of any material that is void space, expressed as a percentage of the total volume of material.

In practice, porosity is commonly based on measurement of the total grain volume of a granular material:

100T G

Where VG is the total volume of grains within the total volume of rock or sediment.

P T GV V V

Porosity varies from 0% to 70% in natural sediments but exceeds 70% for freshly deposited mud.

Several factors control porosity.

a) Packing Density

Packing density: the arrangement of the particles in the deposit.

The more densely packed the particles the lower the porosity.

e.g., perfect spheres of uniform size.

Porosity can vary from 48% to 26%.

Shape has an important effect on packing.

Tabular rectangular particles can vary from 0% to just under 50%:

Natural particles such as shells can have very high porosity:

In general, the greater the angularity of the particles the more open the framework (more open fabric) and the greater the possible porosity.

b) Grain Size

On its own, grain size has no influence on porosity!

Consider a cube of sediment of perfect spheres with cubic packing.

100T G

d = sphere diameter; n = number of grains along a side (5 in this example).

100T G

Total number of grains: n n n = n3

Volume of a single grain: 3

Total volume of grains (VG):

3 3 3 3

6 6GV n d n d

Length of a side of the cube = d n = dn

Volume of the cube (VT):

3 3TV dn dn dn d n

100T G

6GV n d

3 3TV d nWhere: and

3 3 3 3

3 36 100

d n n dP

Therefore:

100d n

Rearranging:

Therefore: 1 100 48%6

d (grain size) does not affect the porosity so that porosity is independent of grains size.

No matter how large or small the spherical grains in cubic packing have a porosity is 48%.

There are some indirect relationships between size and porosity.

i) Large grains have higher settling velocities than small grains.

When grains settle through a fluid the large grains will impact the substrate with larger momentum, possibly jostling the grains into tighter packing (therefore with lower porosity).

Unconsolidated sands tend to decrease in porosity with increasing grain size.

Consolidated sands tend to increase in porosity with increasing grain size.

ii) A shape effect.

Generally, unconsolidated sands undergo little burial and less compaction than consolidated sands.

Fine sand has slightly higher porosity.

Fine sand tends to be more angular than coarse sand.

Therefore fine sand will support a more open framework (higher porosity) than better rounded, more spherical, coarse sand.

Consolidated sand (deep burial, well compacted) has undergone exposure to the pressure of burial (experiences the weight of overlying sediment).

Fine sand is angular, with sharp edges, and the edges will break under the load pressure and become more compacted (more tightly packed with lower porosity).

Coarse sand is better rounded and less prone to breakage under load; therefore the porosity is higher than that of fine sand.

c) Sorting

In general, the better sorted the sediment the greater the porosity.

In well sorted sands fine grains are not available to fill the pore spaces.

This figure shows the relationship between sorting and porosity for clay-free sands.

Overall porosity decreases with increasing sorting coefficient (poorer sorting).

For clay-free sands the reduction in porosity with increasing sorting coefficient is greater for coarse sand than for fine sand.

The difference is unlikely if clay was also available to fill the pores.

For clay-free sands the silt and fine sand particles are available to fill the pore space between large grains and reduce porosity.

Because clay is absent less relatively fine material is not available to fill the pores of fine sand.Therefore the pores of fine sand will be less well-filled (and have porosity higher).

d) Post burial changes in porosity.

Includes processes that reduce and increase porosity.

Porosity that develops after deposition is termed secondary porosity.

Overall, with increasing burial depth the porosity of sediment decreases.

50% reduction in porosity with burial to 6 km depth due to a variety of processes.

Porosity that develops at the time of deposition is termed primary porosity.

i) Compaction

Particles are forced into closer packing by the weight of overlying deposits, reducing porosity.

May include breakage of grains.

Most effective if clay minerals are present (e.g., shale).

http://www.engr.usask.ca/~mjr347/prog/geoe118/geoe118.022.html

Freshly deposited mud may have 70% porosity but burial under a kilometre of sediment reduces porosity to 5 or 10%.

ii) Cementation

Precipitation of new minerals from pore waters causes cementation of the grains and acts to fill the pore spaces, reducing porosity.

Most common cements are calcite and quartz.

Here’s a movie of cementation at Paul Heller’s web site.

iii) Clay formation

Clays may form by the chemical alteration of pre-existing minerals after burial.

Feldspars are particularly common clay-forming minerals.

Clay minerals are very fine-grained and may accumulate in the pore spaces, reducing porosity.

Eocene WhitemudFormation, Saskatchewan

v) Pressure solution

Quartz is relatively soluble when pore waters have a low Ph.

Solution of grains reduces VG, increasing porosity.

Solution is the most effective means of creating secondary porosity.

The solubility of mineral grains increases under an applied stress (such as burial load) and the process of solution under stress is termed Pressure Solution.

The solution takes place at the grain contacts where the applied stress is greatest.

iv) Solution

If pore waters are undersaturated with respect to the minerals making up a sediment then some volume of mineral material is lost to solution.

Calcite, that makes up limestone, is relatively soluble and void spaces that are produced by solution range from the size of individual grains to caverns.

Pressure solution results in a reduction in porosity in two different ways:

1. It shortens the pore spaces as the grains are dissolved.

2. Insoluble material within the grains accumulates in the pore spaces as the grains are dissolve.

v) Fracturing

Fracturing of existing rocks creates a small increase in porosity.

Fracturing is particularly important in producing porosity in rocks with low primary porosity.

POROSITY DETERMINATIONFROM LOGS

Most slides in this section are modified primarily from NExT PERF Short Course Notes, 1999.However, many of the NExT slides appears to have been obtained from other primarysources that are not cited. Some slides have a notes section.

Well LogSP Resistivity

OPENHOLE LOG EVALUATION

Oil sand

Gammaray

Resisitivity Porosity

Increasingradioactivity

Increasingresistivity

Increasingporosity

POROSITY DETERMINATION BY LOGGING

POROSITY LOG TYPES

3 Main Log Types

• Bulk density

• Sonic (acoustic)

• Compensated neutron

These logs do not measures porosity directly. To accurately calculate porosity, the analyst must know:•Formation lithology • Fluid in pores of sampled reservoir volume

DENSITY LOGS• Uses radioactive source to generate gamma

• Gamma ray collides with electrons in formation, losing energy

• Detector measures intensity of back-scattered gamma rays, which is related to electron density of the formation

• Electron density is a measure of bulk density

DENSITY LOGS

• Bulk density, b, is dependent upon:

– Lithology

– Porosity

– Density and saturation of fluids in pores

• Saturation is fraction of pore volume occupied by a particular fluid (intensive)

GRAPI0 200

CALIXIN6 16

CALIYIN6 16

RHOBG/C32 3

DRHOG/C3-0.25 0.25

DENSITY LOG

Caliper

Density correction

Gamma ray Density

Formation (b)

Long spacing detector

Short spacing detector

Mud cake(mc + hmc)

Source

BULK DENSITY

fmab 1

Matrix Fluids influshed zone

•Measures electron density of a formation

•Strong function of formation bulk density

•Matrix bulk density varies with lithology

–Sandstone 2.65 g/cc

–Limestone 2.71 g/cc

–Dolomite 2.87 g/cc

POROSITY FROM DENSITY LOG

Porosity equation

xohxomff S1S

Fluid density equation

We usually assume the fluid density (f) is between 1.0 and 1.1. If gas is present, the actual f will be < 1.0 and the calculated porosity will be too high.

mf is the mud filtrate density, g/cc

h is the hydrocarbon density, g/cc

Sxo is the saturation of the flush/zone, decimal

DENSITY LOGS

Working equation (hydrocarbon zone)

mashshsh

hcxomfxob

b = Recorded parameter (bulk volume)

Sxo mf = Mud filtrate component

(1 - Sxo) hc = Hydrocarbon component

Vsh sh = Shale component

1 - - Vsh = Matrix component

DENSITY LOGS• If minimal shale, Vsh 0

• If hc mf f, then

b = f - (1 - ) ma

d = Porosity from density log, fraction

ma = Density of formation matrix, g/cm3

b = Bulk density from log measurement, g/cm3

f = Density of fluid in rock pores, g/cm3

hc = Density of hydrocarbons in rock pores, g/cm3

mf = Density of mud filtrate, g/cm3

sh = Density of shale, g/cm3

Vsh = Volume of shale, fraction

Sxo = Mud filtrate saturation in zone invaded by mud filtrate, fraction

GRC0 150

SPCMV-160 40ACAL

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/f150 50

001) BONANZA 1

BULK DENSITY LOG

Bulk DensityLog

1.95 2.95

NEUTRON LOG

• Logging tool emits high energy neutrons into formation

• Neutrons collide with nuclei of formation’s atoms

• Neutrons lose energy (velocity) with each collision

NEUTRON LOG

• The most energy is lost when colliding with a hydrogen atom nucleus

• Neutrons are slowed sufficiently to be captured by nuclei

• Capturing nuclei become excited and emit gamma rays

NEUTRON LOG• Depending on type of logging tool either gamma rays

or non-captured neutrons are recorded

• Log records porosity based on neutrons captured by formation

• If hydrogen is in pore space, porosity is related to the ratio of neutrons emitted to those counted as captured

• Neutron log reports porosity, calibrated assuming calcite matrix and fresh water in pores, if these assumptions are invalid we must correct the neutron porosity value

NEUTRON LOG

Theoretical equation

Nmashshsh

NhcxoNmfxoN

N = Recorded parameter

Sxo Nmf = Mud filtrate portion

(1 - Sxo) Nhc = Hydrocarbon portion

Vsh Nsh = Shale portion

(1 - - Vsh) Nhc = Matrix portion where = True porosity of rock

N = Porosity from neutron log measurement, fraction

Nma = Porosity of matrix fraction

Nhc = Porosity of formation saturated with

hydrocarbon fluid, fraction

Nmf = Porosity saturated with mud filtrate, fraction

Vsh = Volume of shale, fraction

Sxo = Mud filtrate saturation in zone invadedby mud filtrate, fraction

GRC0 150

SPCMV-160 40ACAL

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/f150 50

001) BONANZA 1

POROSITY FROM NEUTRON LOG

NeutronLog

0.45 -0.15

Upper transmitter

Lower transmitter

ACOUSTIC (SONIC) LOG

• Tool usually consists of one sound transmitter (above) and two receivers (below)

• Sound is generated, travels through formation

• Elapsed time between sound wave at receiver 1 vs receiver 2 is dependent upon density of medium through which the sound traveled

Mud wavesRayleigh

wavesCompressional

Lithology Typical Matrix TravelTime, tma, sec/ft

Sandstone 55.5Limestone 47.5Dolomite 43.5Anydridte 50.0Salt 66.7

COMMON LITHOLOGY MATRIXTRAVEL TIMES USED

Working equation

mashshsh

hcxomfxoL

tS1tSt

tL = Recorded parameter, travel time read from log

Sxo tmf = Mud filtrate portion

(1 - Sxo) thc = Hydrocarbon portion

Vsh tsh = Shale portion

(1 - - Vsh) tma = Matrix portion

• If Vsh = 0 and if hydrocarbon is liquid (i.e. tmf tf), then

tL = tf + (1 - ) tma

maLs tt

s = Porosity calculated from sonic log reading, fraction

tL = Travel time reading from log, microseconds/ft

tma = Travel time in matrix, microseconds/ft

tf = Travel time in fluid, microseconds/ ft

USFT140 40

%30 10

API0 200

IN6 16

Sonic travel time

Sonic porosity

Caliper

Gamma Ray

SONIC LOG

The response can be written as follows:

fmalog t1tt

tlog = log reading, sec/ft

tma = the matrix travel time, sec/ft

tf = the fluid travel time, sec/ft

= porosity

GRC0 150

SPCMV-160 40ACAL

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/f150 50

001) BONANZA 1

SONIC LOG

SonicLog

150 50us/f

EXAMPLE

Calculating Rock Porosity Using an Acoustic Log

Calculate the porosity for the following intervals. The measured travel times from the log are summarized in the following table.

At depth of 10,820’, accoustic log reads travel time of 65 s/ft.

Calculate porosity. Does this value agree with density and neutron logs?

Assume a matrix travel time, tm = 51.6 sec/ft. In addition, assume the formation is saturated with water having a tf = 189.0 sec/ft.

GRC0 150

SPCMV-160 40ACAL

ILDC0.2 200

SNC0.2 200

MLLCF0.2 200

RHOC1.95 2.95

CNLLC0.45 -0.15

DTus/f150 50

001) BONANZA 1

SPHIss45 -15

EXAMPLE SOLUTION SONIC LOG

FACTORS AFFECTING SONIC LOG RESPONSE

• Unconsolidated formations

• Naturally fractured formations

• Hydrocarbons (especially gas)

• Rugose salt sections

RESPONSES OF POROSITY LOGS

The three porosity logs:– Respond differently to different matrix

compositions– Respond differently to presence of gas or

light oils

Combinations of logs can: – Imply composition of matrix– Indicate the type of hydrocarbon in pores

GAS EFFECT

• Density - is too high

• Neutron - is too low

• Sonic - is not significantly affected by gas

ESTIMATING POROSITY FROM WELL LOGS

Openhole logging tools are the most common method of determining porosity:

• Less expensive than coring and may be less risk of sticking the tool in the hole

• Coring may not be practical in unconsolidated formations or in formations with high secondary porosity such as vugs or natural fractures.

If porosity measurements are very important, both coring and logging programs may be conducted so the log-based porosity calculations can be used to

calibrated to the core-based porosity measurements.

Influence Of Clay-Mineral DistributionOn Effective Porosity

Dispersed Clay• Pore-filling• Pore-lining• Pore-bridging

Clay Lamination

Structural Clay(Rock Fragments,

Rip-Up Clasts,Clay-Replaced Grains)

ClayMinerals

Detrital QuartzGrains

FlowUnits

Gamma RayLog

PetrophysicalData

PoreTypes

LithofaciesCore

CorePlugs

CapillaryPressure

GEOLOGICAL AND PETROPHYSICAL DATA USED TO DEFINE FLOW UNITS

Schematic Reservoir Layering Profilein a Carbonate Reservoir

Baffles/barriers

SA -97A SA -251 SA -356 SA -71 SA -344 SA -371

SA -348 SA -346 SA -37

Flow unit

From Bastian and others

Why is porosity important?

Especially because it allows us to make estimations of the amount of fluid that can be contained in a rock (water, oil, spilled contaminants, etc.).

Example from oil and gas exploration:

How much oil is contained in the discovered unit?

In this case, assume that the pore spaces of the sediment in the oil-bearing unit are full of oil.

Therefore, the total volume of oil is the total volume of pore space (VP) in the oil-bearing unit.

V Total volume of oil = VP, therefore solve for VP.

3800 200 1 160,000TV m m m m

Therefore:

10 160,000

316,000m of oil

II. Permeability (Hydraulic Conductivity; k)

Stated qualitatively: permeability is a measure of how easily a fluid will flow through any granular material.

More precisely, permeability (k) is an empirically-derived parameter in D’Arcy’s Law, a Law that predicts the discharge of fluid through a granular material.

Those are all properties that are independent of the granular material.

There are also controls on permeability that are exerted by the granular material and are accounted for in the term (k) for permeability:

k is proportional to all sediment properties that influence the flow of fluid through any granular material (note that the dimensions of k are cm2).

Two major factors:

1. The diameter of the pathways through which the fluid moves.

2. The tortuosity of the pathways (how complex they are).

1. The diameter of the pathways.

Along the walls of the pathway the velocity is zero (a no slip boundary) and increases away from the boundaries, reaching a maximum towards the middle to the pathway.

Narrow pathway: the region where the velocity is low is a relatively large proportion of the total cross-sectional area and average velocity is low.

Large pathway: the region where the velocity is low is proportionally small and the average velocity is greater.

It’s easier to push fluid through a largePathway than a small one.

2. The tortuosity of the pathways.

Tortuosity is a measure of how much a pathway deviates from a straight line.

2. The tortuosity of the pathways.

Tortuosity is a measure of how much a pathway deviates from a straight line.

The path that fluid takes through a granular material is governed by how individual pore spaces are connected.

The greater the tortuosity the lower the permeability because viscous resistance is cumulative along the length of the pathway.

Pathway diameter and tortuosity are controlled by the properties of the sediment and determine the sediment’s permeability.

The units of permeability are Darcies (d):

1 darcy is the permeability that allows a fluid with 1 centipoise viscosity to flow at a rate of 1 cm/s under a pressure gradient of 1 atm/cm.

Permeability is often very small and expressed in millidarcies ( )1

a) Sediment controls on permeability

i) Packing density

Smaller pathways reduce porosity and the size of the pathways so the more tightly packed the sediment the lower the permeability.

Tightly packed sediment has smaller pathways than loosely packed sediment (all other factors being equal).

ii) Porosity

In general, permeability increases with primary porosity.

The larger and more abundant the pore spaces the greater the permeability.

Pore spaces must be well connected to enhance permeability.

Shale, chalk and vuggy rocks (rocks with large solution holes) may have very high porosity but the pores are not well linked.

The discontinuous pathways result in low permeability.

Fractures can greatly enhance permeability but do not increase porosity significantly.

A 0.25 mm fracture will pass fluid at the rate that would be passed by13.5 metres of rock with 100 md permeability.

iii) Grain Size

Unlike porosity, permeability increases with grain size.

The larger the grain size the larger the pore area.

For spherical grains in cubic packing:

Pore area = 0.74d2

A ten-fold increase in grain size yields a hundred-fold increase in permeability.

iv) Sorting

The better sorted a sediment is the greater its permeability.

In very well sorted sands the pore spaces are open.

In poorly sorted sands fine grains occupy the pore spaces between coarser grains.

v) Post-burial processes

Like porosity, permeability is changed following burial of a sediment.

In this example permeability is reduced by two orders of magnitude with 3 km of burial.

CementationClay formationCompactionPressure solution

All act to reduce permeability

b) Directional permeability

Permeability is not necessarily isotropic (equal in all directions)

Fractures are commonly aligned in the same direction, greatly enhancing permeability in the direction that is parallel to the fractures.

Variation in grain size and geological structure can create directional permeability.

E.g., Graded bedding: grain size becomes finer upwards in a bed.

Fluid that is introduced at the surface will follow a path that is towards the direction of dip of the beds.

Fabric (preferred orientation of the grains in a sediment) can cause directional permeability.

E.g., A sandstone unit of prolate particles.

The direction along the long axes of grains will have larger pathways and therefore greater permeability than the direction that is parallel to the long axes.

porosity and permeability

porosity p

porosity higher

lower porosity

overall porosity

possible porosity

primary porosity

high porosity

secondary porosity

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