1PE 212 ERock Properties

Mustafa Onur

Fall 2011

General Instructor: Prof. Dr. Mustafa Onur Teaching Assistant: Melek Deniz Office: C-218 Office Hours:

Whenever my door is open, but try not to come to myoffice in the hour before my classes.

Phone: 285-6269 E-mail: onur@itu.edu.tr Course notes, homework and solutions will be

available at http://ninova.itu.edu.tr/tr/

ReferencesThere is no text for the course, but the following

references will be mainly used: Recommended Petroleum Reservoir

Engineering: Physical Properties by J. W. Amyx, D. M. Bass, Jr. and R. L. Whiting, McGraw-Hill (1960) New York.

Properties of Reservoir Rocks: Core Analysis by R. P. Monicard, Institute Francais du Petrole Publications (1980) Gulf Publishing Company, Houston.

2Grading Policy

Exam 1: Friday, November 18 20% Exam 2: Friday, December 23 20% Final Exam: 40% Unannounced quizzes 10% HWs 10%

Notes on Grading

Quiz problems will be similar to homework problems.

On each exam, you will be responsible for all material covered to that point in the course. The date of the final is fixed. It is possible, but unlikely that the times of the other exams will be changed.

Notes on Grading There will be no makeup of exams or quizzes. If you

miss an exam, you will receive a zero on the exam, unless (i) you notify me prior to the exam that you will miss it and (ii) have a medical excuse that is supported by a letter from a medical doctor. If you miss an exam and satisfy the two conditions listed above, the exam missed will be replaced by the average of your grades on the other exams. You are free to miss 2 quizzes for any reason, medical or otherwise.

You cannot pass this course without taking the final exam.

Note that %70 attendance is required and quizzes are given during class time.

The University policy on cheating will be enforced.

3Basic Rock Properties

Porosity Absolute permeability Effective and Relative permeability Capillary pressure Rock compressibility

Topics

Porosity Definition factors governing its magnitude

(distribution of grain size, cementation/consolidation, compaction)

rock compressibility estimation of oil and gas initially in place measurement of porosity

Topics Absolute Permeability

factors governing its magnitude (distribution, shape and size of grains, cementation/consolidation, fracturing, dissolution)

Darcys experiment and Darcys Law Poiseuilles Law anisotropy and heterogeneity (beds in parallel

and beds in series for radial and linear flow)

4Topics Absolute Permeability (contd)

Hawkins equation for the skin factor and its effect on radial steady-state inflow performance

Klinkenberg effect measurement Gas flow, steady-state flow form of Darcys

Law in terms of pressure squared, brief comments on non-Darcy flow.

Topics Capillary pressure and relative permeability

interfacial tension and wettability relation to pore radii imbibition versus drainage (hysteresis) reservoir vertical saturation profile based on

gravity capillary equilibrium Darcys Law measurement Effect of relative permeabilities on producing

water-oil ratio and gas-oil ratio

Introduction

Imagine you were looking at a sandy beach from a distance Beach appears to be solid and continuous Close inspection shows that the beach is

made up of millions of sand grains Grains do not fit perfectly together

Spaces between grains

5Introduction

A cup filled with dry sand can still hold water

Water fills spaces between sand grains Porosity

Punch a hole in the bottom of the cup Water poured into the cup flows through the

sand and exits the cup through the hole in the bottom Permeability

Introduction

Rocks that make up hydrocarbon reservoirs are both porous and permeable. Porosity is a measure of storage capacity of the rock;

i.e., it determines the quantity of hydrocarbon stored between the rock grains

Permeability is a measure of a rocks ability to transmit hydrocarbons (or fluids in general); i.e., it determines how easily the hydrocarbons will flow through the rock.

Requirements for a Hydrocarbon Reservoir

A source: material from which hydrocarbon is formed: carbon and hydrogen, the remains of land and sea life that was buried in the mud and silt of ancient seas or bodies of water.

Porous and permeable beds in which hydrocarbons may migrate and accumulate after being formed.

A trap: subsurface condition restricting further movement of hydrocarbons such that it may accumulate in commercial quantities.

6Formation of Source Rock

Over time organic rich silts are compacted and grains are cemented to form siltstone Very porous high water and organic matter

content Very low permeability

Heat, pressure, bacteria, and perhaps other natural forces transform organic materials to hydrocarbons, and rock to shale (though the complete process of this transformation is not known).

Formation of Reservoir Rock

Sand grains on beaches are buried and cemented together to form sandstone. Porous, permeable with high water content.

Over geological time, areas change from swamps to beaches and vice versa. Layers of shales and sandstones in contact with

each other. Migration of hydrocarbons from source rock to

reservoir rock.

Formation of Reservoir Rock

Over time stresses in the earths crust compacted the sediments and bent, twisted and broke the beds that were originally horizontal

Loose sediments were cemented into rock

7Hydrocarbon Reservoirs

Over time petroleum migrated from source rock into adjacent sands and limestones

Eventually petroleum was lost at the surface or became trapped in underground structures

Reasons for Migration

Compaction of sediments as depth of burial increases

Diastrophism: crustal movements causing pressure differentials and consequent subsurface fluid movements.

Capillary forces causing hydrocarbons to be expelled from fine pores by the preferential entry of water.

Gravity which promotes fluid segregation according to density differences.

Hydrocarbon Reservoirs

Oil/and or gas migrates upward from source rock until it trapped in porous belts at a higher structural position.

Trap- a combination of rock and structural properties which terminate migration. Hydrocarbons accumulate at the peak, displacing water downward.

8Hydrocarbon Reservoirs

However, it seems that the salt water seldom was completely displaced by oil or gas from the pore spaces even within the trap.

Often the pore spaces contain from about 10 to over 50% salt water even in the midst of hydrocarbon accumulation.

It appears that the remaining water (calledconnate water) fills the smaller pores and also exists as a coating or film covering the rock surfaces of larger pore spaces.

Traps Dome or Anticline

Trap - Faulting

9Trap - UnconformityIMPERVIOUS CAP ROCK

Piercement Salt Dome

Sand Lenses

NON-POROUSROCK

10

Porous Zones in Limestone

Limestone formations often have areas of high porosity that form traps like shown above

Relative Permeability

Since the reservoir pores are occupied by water as well as hydrocarbons, the separate phases (oil, water and gas) compete for channel space during flow.

If only one phase exists, flow is governed by absolute permeability; multiple phase flow is governed by effective permeability which equals absolute permeability times relative permeability.

Reservoir Engineering

Hydrocarbon reserves are determined in part by the porosity of the reservoir rock.

Reservoir performance is strongly affected by absolute permeability and relative permeability to each flowing phase.

11

Porosity Consider a rock sample

of any shape. Vt or Vb denotes the

total or bulk volume of sample, (L3).

Vp denotes volume of hollow space (pore volume) between the solid grains of rock, (L3).

Vg denotes the total volume of the solid rock grains, (L3).

Porosity

Note:

Porosity is defined as the ratio of the pore volume to the total volume, i.e.,

Note is dimensionless and 0 1. Porosity is expressed as a decimal or a percent.

gpb VVV +=

b

p

b

gb

VV

VVV ==

Notes on Porosity

Porosity is a measure of the storage capacity of the reservoir rock. Only interconnected pore space is of interest. If pore space is isolated, i.e., there is no network of pores that channel fluids to wells, fluid can not be produced.

12

Classification of Porosity

Effective porosity is the ratio of interconnectedpore space to the total bulk volume (i.e., porosity due to voids which are interconnected).

Residual porosity is the ratio of the volume of isolated pore spaces divided by total bulk volume. (Effective porosity is what we care about and what we

actually mean if we simply say porosity.) Total (or absolute) porosity is the sum of

residual and effective porosity.

Porosity

Geologic Classification of Porosity

Primary porosity (intergranular): is the porosity formed at the time the sediment was deposited. The voids contributing to this type are the spaces between individual grains of the sediment.

Secondary porosity: is the void spaces formed after the sediment was deposited. The magnitude, shape, size, and interconnection of the voids bear no relation to the form of the original sedimentary particles.

13

Geologic Classification Secondary porosity has been subdivided into three

classes based on the mechanism of formation: Solution porosity: voids formed by the solution of the more

soluble parts of the rock due to percolation of surface and subsurface waters containing carbonic and other organic acids. This is also called vugular porosity and the individual holes are called vugs.

Fractures, fissures, and joints: are formed by structural failure of the rock under loads caused by folding and faulting. It is very difficult to evaluate quantitatively.

Porosity due dolomitization: is formed due the dolomitization process by which limestone is transformed into dolomite.

Secondary Porosity

Porosity Important factors which affect porosity

include the following: Sorting or uniformity of grain size (well

sorted means grains are all of roughly uniform size)

Compaction Contribution of secondary porosity i.e.,

vugs or fractures Type of packing and cementation.

14

Types of Grain Packings

Porosity

Simple Model Spherical grains Uniform Size What is the porosity of

this system?

Construct a cube by joining adjacent sphere centers.

Cube contains 1 sphere + pore space.

Porosity Simple Model

Length of a side of the cube = 2r.

Bulk volume of cube = 8r3

Grain Volume = Volume of 1 sphere = (4r3)/3

Pore Volume = Bulk Volume Grain Volume = (24 - 4) r3 /3

Porosity =

r

476.024

424 =

15

Rhombohedral Packing

Consider the model shown where uniform spherical grains are packed in a rhombohedralarrangement.

Here, porosity is 0.2595

Packing

Parameters that affect Porosity

If grains are spherical and of uniform size, porosity is only affected by the packing and not by the actual size of the spherical grains.

In real reservoirs, grains are not uniform in size and shape and may or not be well sorted.

Actual size of the grains does not directly affect porosity, but the degree of sorting, non-uniformity and cementation does.

16

Packing non-uniform grains

Sorting A rock is well sorted if all

the rock grains in a sample are of essentially the same size.

For the figure shown, only coarse grains lie above the dashed line, while fine grains lie below Excellent Sorting.

Poor Sorting

Figures show examples of poorly sorted rocks

Non-uniformity in size permits smaller particles to fill pores between larger particles and tends to decrease porosity.

17

Cementation The filling of void space between rock grains

by minerals (calcium carbonate, silica, etc,) carried by interstitial water. (Interstitial water is water that is in the rock pores

at any time.) Increasing the degree of cementation tends

to decrease the porosity. Unconsolidated rocks refer to those have

low degree of cementation Have higher porosity than those that are highly

consolidated.

Compaction

As materials builds up pressure increases and particles may be squeezed closer together.

If pressure is sufficient to crush grains and eliminate bridging and arching across void space, there may be an appreciable decrease in porosity.

Compaction

No absolute rule about effect of Compaction If particles start out assembled in a way to

yield close to minimum porosity for any possible natural packing, then compaction may have virtually no effect on porosity.

For sandstones and limestones, deeper formations can have higher porosity than more shallow formations.

18

Compaction versus Cementation

In general, cementation has a far greater effect on post-depositional decreases in porosity than does compaction.

Notes on Shale Pure clay is composed of aluminum silicate. Shale is a fine grained rock formed from clay by

compaction. Freshly deposited clay is typically well sorted, loosely

packed and exhibits significant bridging. With compaction porosity may decrease significantly. Shales may have significant porosity but have very

low permeability. Shale layers in sandstone reservoirs are

practically impermeable. Retards vertical flow.

Hydrocarbon Reservoirs

Oil and gas reservoirs represent rock structures where the pore space is filled with oil and gas.

Virtually all hydrocarbon reservoirs contain water and are often associated with an aquifer. An aquifer is a porous rock structure that contains

water that is in pressure communication with a hydrocarbon reservoir

19

Water Influx If the pressure in the oil (or gas) reservoir is

reduced below the pressure in the aquifer, water will flow from the aquifer into the oil reservoir.

If producing wells are drilled and completed in the oil-bearing zone, the pressure in the oil reservoir decreases as oil is produced.

Water influx displaces oil to the producing wells and helps to maintain the reservoir pressure. Natural Water Drive

Saturation

Given a sample of rock where the pore volume contains a combination of oil, gas, and water, the saturation of phase m is defined as the fraction of the pore volume occupied by phase m, i.e.,

Volume Pore"" phase of Volume mSm =

Notes on Saturation

Saturation is dimensionless. Sum of saturations must be equal to unity,

i.e.,

Oil in place depends on oil saturation. Effective and relative permeabilities depend

on phase saturations.

1=++ gwo SSS

20

Pore and Hydrocarbon Volumes

If the average aerial extent of the reservoir is A ft2, average thickness is hft, average porosity is and average oil saturation is So, then the pore volume is Vp = Ah

The oil volume is Vo = AhSo

Note

How much oil in place is of interest, but the most important thing to us is how much of the oil can be economically produced. Porosity and oil saturation govern how much oil is originally in place (denoted by N or OOIP), usually converted to stock-tank or standardconditions.

Types of Reservoir Rock

21

Sandstone

Sandstone consists primarily of quartz (SiO2).

Porosity typically ranges from about 10percent in a highly cemented rock to perhaps 35 percent in very highly unconsolidated formations.

Carbonates Formed from animals (shellfish, corals)

and plants. The principle carbonates are limestone

and dolomite. Limestone

Consists primarily of calcium carbonate (CaCO3) which is slightly soluble in water.

Carbonates

Limestone If water circulating through pores contains

carbon dioxide CO2, then carbonic acid (H2CO3) is formed which reacts with calcium carbonate to form calcium bicarbonate Ca(HCO3)2 which is easily dissolved in water.

The dissolution of rock results in cavities (vugs) which increase porosity locally.

22

Carbonates

Dolomites If water circulating through limestone contains

magnesium, it reacts with calcium carbonate to produce dolomite, CaMg(CO3)2. This process is referred to as dolomitization.

Rocks that contain large amounts of CaMg(CO3)2 as well as large amounts of calcium carbonate are referred to as dolomites.

The ionic volume of magnesium is smaller than that of calcium which it replaces, so the process of dolomitization increases porosity.

Carbonates

Carbonates are more brittle than sandstone and may break during faulting opening fractures through which oil can easily be transported.

Typical porosities range from 5 to 25 percent for carbonates, but local porosity can be higher if significant leaching by water produces large vugs.

Measurement of Porosity

23

Introduction

A measurement of porosity (or permeability) pertains to some specific rock volume.

Assuming you have a large piece of rock, and the factors (e.g., degree of cementation, packing etc.) that influence porosity are uniform on this sample, we could consider any smaller rock sample cut from this large piece of rock and obtain the same measurement of porosity.

Introduction

If samples cut from this rock become too small, the porosity measured may vary significantly from sample to sample. Some very small samples may consist primarily of

rock grains (little pore space) and have very low porosity

Others may contain a non-representative amount of pore space and have a large porosity

Representative Elementary Volume, REV

The smallest sample volume that will yield a reliable representative measurement of the property For larger volumes, measurements will

yield the same value. As sample volume decreases below the

REV, measurements become variable and unreliable.

24

Significance of Scale

10-10 10-7 10-6

m

10-5 10-4 10-3

Size of H2O molecules

1010

Earth to sun

107

Earth diameter

10-2 10-1 100 101102 103

mm cm m

deepest sediment

Block size In flow simulators

wellbore diameter

pore sizes

vugs

core sample

Visible light

Microscopic scale(Navier stokes and PoiseuilleEquation)

Macroscopic scale(Darcys equation and continuum approach)

Porosity Measurement

In the lab measurement of porosity it is necessary to determine only two of the three basic parameters; bulk volume (Vb), pore volume (Vp) and grain volume (Vg)

b

p

b

gb

VV

VVV ==

Porosity Measurement

Method 1

25

Boyles Law PorosimeterGauge 1 Gauge 2

Valve 2

Valve 1

Bleed Valve

Cell 2Cell 1

NitrogenPressure

Bottle

Boyles Law - Review

For a fixed mass of gas at constant temperature

Pressure is in absolute units, psia

2211 VPVP =

Schematic of ExperimentGauge 1 Gauge 2

Valve 2

Valve 1

Bleed Valve

Cell 2Cell 1

NitrogenPressure

Bottle

Vi V2

Vt = Vi + V2

26

Nomenclature

We let Vi denote the volume of cell 1 plus the volume of the piping system in communication with cell 1 with valves 1 and 2 both closed.

Let the volume Vt denote the volume of cell 1 plus cell 2 plus the volume of the piping system in communication with the two cells with valve 1 closed, valve 2 open and the bleed valve closed.

Calibration

Begin with all valves open (except the valve on the nitrogen bottle) so that the system is at zero gauge pressure.

Place a non-porous solid cylinder of volume Vc,1 into cell 2 and close all valves.

Open the valve on the nitrogen bottle until nitrogen pressure regulator reads about 150 psig.

CalibrationGauge 1 Gauge 2

Valve 2

Valve 1

Bleed Valve

CoreCell 1

NitrogenPressure

Bottle

Vi V2

V = Vi + V2 - Vc,1

Vc,1

27

Calibration

Open valve 1 and keep open until gauge 1 reads approximately 140 psig and then close valve 1, Pi,1, psia At this point gauge 2 still reads 0 psig (14.7

psia). Now open valve 2 so the nitrogen flows

across valve 2 and occupies both cells plus the all of the piping system between valve 1 and the bleed valve.

Calibration

Gauge 1 and Gauge 2 pressure should now be identical and we denote the corresponding pressure in psia by Pf,1and the volume occupied by gas as V

By Boyles Law

( )1,1,1,1, ctffii VVPVPVP ==1,

1,1,

f

iitc P

PVVV =

Calibration

Repeat the experiment with different non-porous cores.

Plot Vc versus Pi/Pf Intercept: Vt Slope: Vi

Cor

e Vo

lum

e

Initial Pressure/Final Pressure

Slope = Vi

Intercept = Vt

28

Measurement

Repeat the experiment with a porous core of measured bulk volume Vb

In this case the total volume is

Boyles Law( )pbtpbt VVVVVVV =+=

( ) ( )gtfpbtfii VVPVVVPVP == )(

Calculation

Solve for pore volume or grain volume, grain volume can also be read from graph used in calibration step.

Compute porosityf

iitg P

PVVV =

b

gb

b

p

VVV

VV ==

Porosity Measurement

Method 2

29

Comparing Dry and Saturated Cores

Start with clean dry core and weigh it. The density of air is negligible for the

purpose of this experiment. Fully saturate the core with water which

has density 62.4 lb-mass/ft3 (equal to one gram per cubic centimeter). It may take some time to fully saturate the

core.

Measurement

The weight (mass) of the water is equal to the weight of the saturated core minus the weight of the dry core

pwwaterdrysat VmWW ==

w

drysatp

WWV

=

Measurement of Bulk Volume

Although the bulk volume may be computed from the measurements of the dimensions of a uniformly shaped sample, the usual procedure utilizes the observation of the volume of fluid displaced by the sample. This can be accomplished by coating the rock with paraffin or a similar substance by saturating the rock with the fluid into which it is to be

immersed by using mercury, which does not tend to enter the

pore spaces of most intergranular materials.

30

Water-Saturated Sample Immersed in Water

Fully (100%) saturate the core with water which has density 62.4 lb-mass/ft3 (equal to one gram per cubic centimeter) and weigh it in the air. (Wsat )

Then immerse the saturated core in water and weigh it in the water (Wsatw)

satwsatdw WWW =

wdwb WV /=