Porosity is a measure of the void spaces in a rock that can contain fluids. It is calculated as the ratio of pore volume to bulk volume. Effective porosity refers only to interconnected pores that can produce fluids from a well. Total porosity includes all pores, but some may be isolated. Primary porosity forms during deposition, while secondary porosity forms through geological processes after deposition. Porosity depends on factors like grain size, shape, packing, and cementation. Permeability measures a rock's ability to transmit fluids and depends on pore connectivity and size. Darcy's law describes fluid flow through porous media and permeability can be measured experimentally under steady-state conditions.

1. Rock Properties
Chandran Udumbasseri
Technical Consultant
Reservoir

2. Porosity
• Porosity is a measure of the storage capacity
of a reservoir. It is defined as the ratio of pore
volume to bulk volume, and it may be
expressed as either a percent or a fraction.
• In equation form, Porosity, φ, is given as
•

3. Porosity
• Total porosity and effective porosity
• Total porosity is the ratio of all pore spaces to the bulk volume of rock
• Effective porosity is the ratio of interconnected void spaces to the bulk volume
of the rock
• Only effective porosity contains fluids that can be produced from a well
• For granular rocks like sand stone the effective porosity approaches total
porosity
• For some limestone and cemented rocks there is large variation from effective
to total porosity
• There two types of porosity classified based on origination, the primary and
secondary.
• Primary porosity is caused during the original deposition of sediment.
Secondary porosity is cause by geological process like ground stresses, water
movement, other geological activities.
• For uniform grains the porosity in independent of their size. For cubic packing
the porosity is 47.6%, for rhombohedral packing it is 26%
• Porosity is depending on grain size distribution, grain arrangement, cementing
material quantity.

4. Rock packing

5. Rock porosity…..
• Petroleum explorenists sedimentary rock’s stratigraphy and
sedimentology to conclude the possibility for the existence of
petroleum system
• Then a decision is taken on drilling and well completion
• Significant part is to estimate the possible quantity of crude oil
• Reservoir characteristic is determined through a study of rock
properties
• Sedimentary rocks are made up of sandstone (quartz sand),
carbonate mud or dolomite. Dolomite reservoirs are good one
compared limestone as porosity is better in the former type.
• Sandstone rocks are composed of silica grains with minimal
fragmented particles.
• Carbonate rocks are made up of fossils of non even size.

6. Porosity ….
• Porosity gives the information on the capacity of
reservoirs to contain fluids
• The primary porosity (formed during original
sedimentation) has two types, inter and intra particle.
Inter particle porosity is lost through cementing. Intra
particle porosity is created by carbonate interiors
• Secondary porosity which was formed by geographical
processes can lead to dissolution porosity due to
carbonate dissolution and leaching. Another type of
secondary porosity is from fracture of rock leading to
less volume

7. Dissolution and fracture porosity

8. Porosity and permeability
• Morphological porosity
– Caternary in which the pore open to more than one throat
passage
– Cul-de-sac in which the pore open to only one throat
passage
– Closed pore in which there is no connection with other
pores.
• Permeability is one ability for fluids to communicate
through porous medium
• Rock can be porous without being permeable
• Rock with permeability is suitable for fluid
accumulation

9. Pores-geographical processes
• The pores created during the initial sedimentation can under go changes
in the subsequent processes due to weight and dissolution.
• The weight from added top sediment can press the pores which may get
closed or some may get isolated
• This secondary process alter pore space and fuid flow through pores. The
fluid that was trapped in the closed pores cannot be produced.
• The brine that flow through the rock can plug the pores by cementing
grain to grain contact area.
• Sometimes the cation exchange can take place. The calcium ion from lime
may get replaced by Mg. this usually results in the space reduction thus
increasing available pores.

10. Calcite sediment to dolomite

11. Pore volume –contributory factors
• Factors effecting pore volume:
– Grain size and packing pattern
– Shape of the grains: spherical grains makes good
packing thus reduce pore volume.
– Size of gains: uniformity in size causes uniformity
in pore volume
– Compaction causes reduction in volume.
Sandstone is less compressive compared to clay

12. Measurement-porosity
• Sample collection: core sample may be collected during drilling from
known depths
• Small samples called core plugs are cut from the core sample
• Samples are then cleaned using solvents to remove oil and water present
in the sample
• Bulk volume is the sum of grain volume and pore volume
• Bulk volume, Vb = Vg +Vp where Vg is grain volume and Vp is pore volume
• Absolute Porosity, φ, = Vp / Vb

13. Porosity-bulk volume measurement
• Cylindrical core sample is cut out with cross sectional area, Ac and length, L
• Volume is Ac*L
• For irregular sample use a water displacement method
• The sample is weighed initially and coated with wax and again weighed. Note
down both weights
• Take certain volume of solvent in a graduated glass cylinder. The volume of solvent
should be enough to submerge the sample. Note the volume . Now hang the
sample in the glass cylinder as shown in (a) so that the sample submerge in the
solvent without any adhered air bubbles. Note down the volume on the cylinder.
The difference in volume from the initial one gives the physical volume of the
sample.
• The wax coating volume should be subtracted from above noted volume to get the
bulk volume ( wax coating volume = coating weight /wax density)

14. Bulk volume and grain volume

15. Porosity calculation
• If the rock is made of uniform grain like quartz
then grain volume is
• Vg = mass of core sample/density of the mineral (core sample)
• For core with unknown mineral, an uncoated core sample in immersed in
suitable solvent as before for sufficient time so that all the pores are filled
with solvent. Now note down the volume on the cylinder. The difference
from initial volume gives the grain volume (Vg)
• Knowing both bulk volume and grain volume, then porosity may be
calculated

16. Pore measurement
• Measuring pore directly gives more accurate porosity value
• The cleaned and dried core sample is weighed and placed in a vacuum
flask as shown for a few hours
• Now introduce water slowly until the sample is completely submerged in
water.
• Now take out sample and shake the sample to remove outside water and
weigh quickly.
• Increase in mass is the weight of water taken up by pores. The water
weight may be converted to volume of water which is the pore volume
• Porosity, φ = pore volume/bulk volume

17. Pore volume measurement

18. Porosity -indirect method
• Porosity can be measured indirectly using well logs. Sonic (acoustic) log is
one such method.
• The instrument sonde generates sound waves which travel in the vicinity
of well bore and their return time is noted
• Travel time (generation time and return detection time) is recorded with
depth of reservoir.
• Travel time is related to porosity by the equation:

19. Formation density log
• Another logging sonde that emits gamma rays
is used to compute bulk density of the
reservoir.
• This bulk density value is related to porosity:

20. Compressibility
• It is the shrinkage of a unit volume of substance per unit
increase in pressure
•Minus sign is added to give a positive compressibility value
• compressibility slightly vary with temperature
•All minerals found in sedimentary rocks are elastic in nature

21. Compressibility
• Reservoir rocks are subjected to overburden pressure from all rocks strata
above it
• Also the fluids in the pore exert pressure on the grains. This pore pressure
in independent of the overburden pressure. The pore pressure is the
atmospheric pressure allowing air to move within cavities.
• An increase in overburden pressure causes compaction in pore volume.
• The porosity measured in lab is independent of this overburden pressure.
So a correction is introduced to lab value while considering for reservoir:
• Porosity Correction: Δφ = - cp φlab ΔP o b, net
• ΔP o b, net is the net overburden pressure; φlab is the porosity result from
lab test; cp is the pore volume compressibility

22. Compressibility measurement
• Pore volume compressibility is measured in the lab by measuring variation
in pore volume at different conditions of overburden pressure (Pob) and
pore pressure (Pp)
• Pore volume is measured first at atmospheric pressure and reservoir
temperature
• The saturated sample is loaded to a core holder which is a device where
different combinations of Pob and Pp can be applied.
• The liquid that is squeezed out at each combination these two pressure
values are collected and measured the volume. Use these values to
compute current porosity values.
• Now plot φ against each Pob
• The graph is given below

23. Instrument for compressibility

24. Plot of porosity vs overburden pressure

25. Application of rock compressibility
• Rock compressibility is used to correct the lab measured porosity
• Production rate of a well suddenly changes with pressure over a period of
time. The results are interpreted using compressibility values
• Total reserves in a well is calculated using pore pressure and production
data. The pore volume of the reservoir changes as Pp decreases with
production, and cp is needed to correct the pore volume from its initial
value.

26. Fluid saturation
• The pores of the reservoir rock is partially
filled with water and hydrocarbon which can
be in the gas, liquid and solid state
• The saturation level of the fluid is given by:

27. Variation in fluid saturation
• Saturation level of the fluid in the rock helps the explorers to estimate
available oil in the reservoir.
• The saturation level never remains constant. When the oil is pumped out
the space left is taken up by water. When pressure drops the dissolved gas
get released and occupy the space. If gas is injected to the reservoir then
gas saturation occurs. So it is necessary to measure the level of all fluids
periodically.
• Measurement of fluid:
• The fluid in a core rock sample is extracted and individual volume
determined.
• The weighed core sample is placed in the thimble of the extraction unit
and heated. The solvent evaporates carries along with it the fluid in the
core sample and get condensed in the receiver flask.

28. Fluid extraction
•The mass of oil is computed using the
equation:

29. Resistivity
• Resistance of a material to the flow of electric
current is the resistivity of the material

30. Resistivity -measurement
• Rock materials are having high resistivity, also crude oil and natural gas
• Water which present along with crude oil is saline and having low
resistivity
• This difference is used to study the presence of crude oil in the rock
• In the above resistivity measuring sample holder fill with saline water the
resistivity will come down
• If some water is replaced with crude oil, the resistivity will go up.
• By varying water and crude oil quantity in the sample holder a series of
resistivity value are determined. Plot the values against percentage of
crude oil in the mixture and construct a graph. This graph is applicable to
that particular sample only.

31. Resistivity-porosity relation
• Let Rw (Ωm) is the resistivity of reservoir water, Ro (Ωm) is the resistivity of
reservoir rock saturated with reservoir water and Rt (Ωm) the resistivity of
reservoir rock saturated with oil and water
• Defining the formation factor as F= Ro/ R w
• F is related to porosity by the expression:
• For sand stone the value for C= 0.62 and m=2.15
• Now oil saturation expression is given by Sw
n = C φ –m R w / R t
• This expression is used for the calculation of oil saturation in the reservoir
rocks

32. Resistivity-porosity relation
• When resistivity sonde is sent into a reservoir to measure the resistivity
with depth of reservoir a typical graph as shown is obtained. High oil zones
show large resistivity while water zones show low resistivity.

33. Resistivity-porosity relation
• Mathematical calculation: for the above reservoir the water resistivity is
1.2Ωm, saturation exponent m=2.2, estimating the oil saturation at the
depth 4226ft where porosity is 24%
• Sw
n = C φ –m Rw / Rt
• Sw
2.2 = 0.62 (0.24) –2.15 x 1.2 / 400 = 0.04
• S w = 0.232 = 23.2%
• So = 100-23.2 = 76.8%
• At the depth 4226ft the oil saturation is 76.8%

34. Rock permeability
• Permeability is defined as the ability of a porous medium, e.g.,
sedimentary rock, to conduct fluids. The larger the permeability, the more
fluid flow can be achieved through the medium for a given set of
conditions. Darcy relationship:
• K is the coefficient of permeability (called simply as Permeability),
regardless of dimensions

35. • Permeability is given a dimension with the following definition
• If 1 atmosphere of pressure drop is required to flow a liquid of 1 cp
viscosity through a porous medium of 1 cm length and 1 cm2 cross-
sectional area at a rate of 1 cm3 per second, then the medium has a
permeability of 1 darcy.
• 1 darcy = 9.869 x 10-9 cm2.
• A more common unit of reservoir rock permeability is the millidarcy (md),
which is one thousandth of a darcy. Since the petroleum industry still uses
the system of field units, a conversion factor is introduced in Darcy’s law as
follows
• where q, k, A, ΔP, μ and L are in bbl/day, darcy, ft2, psi, cp and ft,
respectively.

36. Rock permeability and Darcy law
• The generalized differential form of Darcy’s
law is given below:
• ρ : density of the fluid, g/cm3
– g : gravitational acceleration (980 cm/s2)
– d : depth measured from a reference horizon, cm

37. Permeability measurement
• Laboratory measurement is performed under steady-state conditions
using a permeameter.
• The clean and dry core sample is mounted in the core holder and then
placed under a suitable confining pressure to simulate reservoir
overburden conditions.
• The sample is then placed under vacuum for a sufficient period of time to
remove all air from the sample.
• The fluid – usually brine, oil or air – is then flowed through the sample
until steady-state flow is established.
• The flow rate and the inlet pressure are then recorded
• the test is usually repeated at different sets of flow rate and inlet pressure
and the data is plotted
• The slope of the straight line is the core sample’s permeability multiplied
by A/ μL.

38. Permeability measurement

39. Permeability computation from graph

40. Permeability calculation
• Compute the permeability of the core sample whose flow data is shown in
above graph if the sample is 5 cm in diameter and 10 cm long. The fluid
used in the experiment is an oil with a viscosity of 1.6 cp.
• The cross-sectional area of the sample is , A = [π(5)2]/4= 19.63 cm2
• The slope of the best-fit line, m, is 6.25 cm3/min/atm, or 0.1 cm3/s/atm.
The core permeability is: k = m μ L / A = 0.1 x 1.6 x 10 / 19.63 = 0.0815 d
• = 81.5 md
This method of measurement needs some precautions
• If the sample is sandstone which contains some clay particles, distilled
water should not be used
• The flow rate should be low as the law does not work for excessive flow
• Inlet pressure should not be closed to confining pressure otherwise the
flow can bypass the sample
• If gas is used mean pressure (average of inlet and outlet) should be used
for plotting

41. Permeability and porosity
• For clean sandstone the permeability is related to porosity, k = a φ b
• If some clay particles are present in sandstone then a correction factor is
added
• k = a φ b (1-Vsh)c
• For carbonate rocks (calcite, dolomite, gypsum) such correlation not found
• Mineral deposits have minor effect on permeability
• Minute fractures improve permeability but no effect on porosity

42. Linear flow from Darcy law
• For incompressible fluid (no change in density with pressure) assume flow
direction along the x direction Darcy equation changes to:
• Rearranging the pressure at any location in the x direction is given by: