04 - Permeability

Question 1

Definition

Permeability

Answer 1

it is the ease at which water can move through rock or soil

ability of rock to transmit fluid

controlled by connected passages of pore space

independent of fluid type

Question 2

Permeability

methods to determine it (4)

Answer 2

1. direct measurements at samples (core,plug)
2. direct test (well and drillstem tests, wireline formation testers, pump tests)
3. indirect using grain size (unconsolidated sediments)
4. indirect using wireline logs (NMR)

Question 3

Definition

Absolute Permeability

Answer 3

laminar flow of a single non-reactive fluid

Question 4

Definition

Effective Permeability

Answer 4

Flow of one fluid in presence of another fluid (immiscible)

Question 5

Definition

Relative permeability

Answer 5

Ratio of effective and absolute Permeability

Question 6

Permeability measurement

Hassler cell

(cell construction slide 4)

Answer 6

using darcy’s law:

k = eta * u * l / ( A * (p1-p2))

k=permeability in A*m²
u=fluid flow V/(A*t)
A= area
eta = dynamic viscosity
L = length of hassler cell
p1-p2= pressure gradient

Question 7

Bernoulli’s Principle

Answer 7

states that speed of moving fluid increases

when pressure within fluid decreases

Question 8

Laminar vs. turbulent flow

Answer 8

graph slide 4:

Q/A vs. (p1-p2)/L
with Q=flow velocity

–> first linear increase = viscous flow

–> flattens reach constant Q/A = turbulent flow

Question 9

Klinkenberg effect

Answer 9

independent of fluid type

prewuisite: non-reactive liquid

permeability not constant at core sample when using gas/fluid

k_gas = k_liquid * ( 1 + (b/p))

Question 10

Correlation between permeability and porosity

Answer 10

with increasing porosity
the permeability also increase

double logarithmic -> power law relationship!

Question 11

permeability in clastic sediments

Answer 11

increases with increasing grain size

-> function of pore space structure

Question 12

permeability in carbonates and magmatic rocks

Answer 12

increases in preferred flow paths:

• connected fractures
• karstification

Question 13

permeability controlled by ..

Answer 13

• pore space structure
  
  • -> grain size
  • -> grain size distribution
  • -> grain orientation
  • -> packing
  • -> bedding
  • -> sorting
  • -> cementation
  • -> clay content
• mineral alteration
  
  • -> dolomitization
• fractures

Question 14

Hydrolic conductivity k_f

Permeability Description in Hydrogeology

Answer 14

k_f = (uL) / (A(h1-h2))

u        = fluid flow
h1-h2 = height difference
L        = length

Clay to gravel -> k_f increase

Question 15

Correlation between permeability and shale content

Answer 15

decreases with increasing shale content

Question 16

Correlation between permeability and overburden pressure

Answer 16

decreases with increasing overburden pressure

• > effective pressure compresses pore space
• > closes pore throats and fractures

Question 17

Capillary Tube Model

Answer 17

Grain-scale model

models permeability as function of the corss sectional diameter of pore throats

Question 18

CT-scan

Answer 18

visualize the distribution of pore space

Question 19

different between

water-saturated sediment and liquefaction

Answer 19

water-saturated sediment:

• water fill pore space
• friction holds sediment grains

liquefaction:

• water surrounds grains
• no grain-grain contact anymore
• Sediment flows like fluid

Question 20

measurement during well logging

Answer 20

Fluid filled pores:

1. via Stoneley wave analysis
2. NMR logging

Question 21

Stoneley wave analysis

Answer 21

boundary wave (or interface wave)

propagates along a solid-solid interface of the fluid-
filled borehole

low-frequency component from seismic source

sensitive to fractures

Question 22

Correlation permeability and Stoneley wave velocity

Answer 22

increases if velocity decreases (incl. dispersion)

Question 23

NMR logging

Answer 23

Nuclear Magnetic Resonance

measures induced magnet moment of hydrogen protons

• > present hydrogen protons in pore fluids
• > volume, composition, viscosity

Question 24

NMR principle

Answer 24

based on response of atomic nuclei to
external magnetic fields

nuclei have a net magnetic moment and
spin (e.g. H2O).

in presence of an external
magnetic field, the atomic nucleus interacts with the magnetic field.

results in a precession motion around the direction of the external field

hydrogen nuclei = tiny bar magnets aligned with the spin axes of
the nuclei

by absence of an external magnetic field, the nuclear-
magnetic axes are randomly aligned

Question 25

NMR measurement

Answer 25

B_0 = external static field
–> aligns nuclei

M = magnetic moment

B_1 = electromagnetic frequency pulses and perpendiculat to B_0
–> analysis of relaxation & delayed magnetization

Question 26

NMR - results

rockmatrix
Water
gas
oil

Answer 26

rockmatrix:
invisible

Water:
clay - few milliseconds
capillary - tens of milliseconds
moveable - tens-hundreds of milliseconds

oil:
hundrets-thousands of milliseconds

gas different for transverse (10-100) & longitudinal (100-1000) relaxation time

Question 27

what dominates for water in a water-wet rock?

Answer 27

surface relaxation

fast

Question 28

Permeability with NMR logging

Answer 28

bounded water relaxes fast
–> low permeability

movable water relaxes slow
–> high permeability