ENGINEERINGUPES DEHRADUN

LECTURE-04 13.09.10

RESERVOIR

POROSITY

ROCK

Porosity

• Porosity is defined as percentage or fraction of void to the bulk volume of the rock.

• The void space in reservoir rocks is the inter-granular spaces between the sedimentary particles

Let us consider a rock sample. Its apparent volume, or total volume VT, consists of a solid volume VS and a pore volume Vp. The porosity Φ is:

Φ = expressed in %

= = = 1 -

V pore--------V total

VP-------- VT

--------

VSVT

VT

- --------

VSVT

Porosity relations

Intera Porosity relations• The porosity of interest to reservoir specialist is

that which allows the fluids in the pores to circulate, is the effective porosity Φu which corresponds to the pores connected to each other and to formation.

• Also defined is the total porosity Φt, corresponding to all the pores whether interconnected or not, and to residual porosity Φr, which only takes account of isolated pores.

• Φt, = Φu + Φr

Φt, = Φu + Φr

(Φr) (Φu)

Utility limits of porosity• The effective porosity of rocks varies

between less than 1% to 40%.• It is often stated that the porosity is:

(a) Low if Φ < 5%(b) Mediocre if 5% < Φ < 10 %(c) Average if 10%< Φ < 20 %(d) Good if 20%< Φ < 30 %(e) Excellent Φ > 30%

Remarks

A distinction is made between inter -granular porosity, dissolution porosity (as in lime stones for example) and fracture porosity.The fracture porosity related to rock volume is often much less than 1%As a rule, porosity decreases with increasing depth.

Effective porosity is basically usedfor reserve calculation.In moderate to high porosity rocks,there is little difference in total and effective porosity, but low porosityvalue there has appreciable andsignificant difference.

Remarks

Types on the basis of origin:• Original porosity (primary)• Induced porosity (secondary) Rocks having original porosity are more

uniform in their characteristics than rocks with an induced porosity

Porosity- related information

Primary porosity • Is the space between grains that were not

compacted together completely• This is related to pores/voids between

sand grains or solid particles, as well as space between sub layers and voids created after decaying of organisms.

• It is characterised by more or less uniform distribution in the rock.

• Found in sand and sand stones , clays , conglomerates.

Porosity- related information

Secondary porosity • Is the porosity created through alteration of rock,

commonly by processes such as dolomitization, dissolution and fracturing

• Developed as a result of diagenesis.• Connects the altered void spaces with fractures

resulting from tectonic disturbances.• Characterised with non uniform distribution and

it is not possible to establish any trend through out the reservoir.

On the basis of connectivity

• Absolute and effective porosity are distinguished by their access capabilities to reservoir fluids

Art-micrograph of sandstone with oil

Void spacescontributesto absoluteporosity

Permeable spacescontributesto effectiveporosity

Factors effecting the porosity

• Relative arrangement of grains• Shape and size of grains,• Grain size distribution• Presence and type of cementing materials• Solution and precipitation of salts■ Porosity decreases with reduction in grain size.■ It also decreases with large variation in grain

size as smaller grains occupy the pore spaces between larger grains.

Packing Models

An attempt to determine the approx. Limits of

porosity values, Slichter and, later, Graton & Fraser computed porosities for various packing arrangements and given as :-

Parallel cylindrical pores Irregular-packed spheres with different radii

Regular orthorhombic-packed spheres

Regular cubic-packed spheresRegular rhombohedral-packed spheres

Estimation of porosity accounting to this model:

“Regular Cubic-Packed Spheres”

Estimation of porosity accounting to this model:

“Regular Orthorhombic-Packed Spheres”

• Estimation of porosity accounting to this model:

“Regular Rhombohedral-Packed Spheres”

Estimation of porosity accounting to this model:

“Parallel Cylindrical Pores”

Porosity Range

ROCK TYPE POROSITY RANGE,%

Argillaceous shale 0.54 - 1.40

Clays 6.00 - 50

Sands 6.00 - 52

Sand stones 3.50 - 29

Carbonates 0.65 - 33

• Measurement of Porosity

Well Logs Core Analysis

In situ Surface

Informatics on porosity measurements

• Essential property for intelligent estimate of hydrocarbon reserves and the economic aspect of oil and gas production.

• The results of porosity measurement-by what ever method are ,cannot exactly correspond to in situ conditions due to:

A) Possible relaxation of pores upon release of over burden and fluid pressure

B) The hydraulic and mechanical actions of the coring process.

In situ techniques

• Several logging tools like - Electrical, Nuclear, Density, or Sonic methods are used to estimare porosity.

• Resolution is effective around the well bore.• Measurements need to be confirmed / calibrated

against porosities measured at surface conditions,

• The relationship developed apply only to those surface conditions.

Core Analysis► Following equation is used:

► On a sample of generally simple geometric form, two of the three values Vp , Vs and VT are therefore determined.

►The standard sample (plug) is cylindrical, Its cross section measures about 4 to 12 cm2 and its length is varies between 2 to 5 cm.

►The plugs are first washed and dried.►The measuring instruments are coupled to

microcomputers to process the results rapidly.

Φ

A. Measurement of VT(a) Measurement of the buoyancy exerted by

mercury on the sample immersed in it (IFP)

APPARATUSThe apparatus has a frame C connected by a rod to a float F immersed in a beaker containing mercury.A reference index R is Fixed to the rod. A plate B is suspended from the plate.(a) First measurement: the sample is placed on plate B with a weight P1 to bring R in,in contact with the mercury. (b) Second measurement: the sample is placed under the hooks of float F, and theweight P2 is placed on plate B to bring R in to contact with the mercury. If ρHg is the density of at measurement temperature. Then:VT

VT

V

Method: Without a sample using the piston,mercury is pushed to mark, indicated on the reference valve (V).The vernier of the pump is set at zero.With the sample in place, the mercury is again pushed to samemark. The vernier of the pump is read and the volume VT isobtained. The measurement is only valid if mercury does notpenetrate into the pores. The accuracy is ± 0.01 cm3.

(b) Use of positive displacement pump

VT

(c) Measurement:The foregoing methods are unsuitable if the rock contains fissures or macro pores, because mercury will penetrate into them.Here a piece of cylindrical core’s diameter “d” and height “h” can be measured using sliding caliper:

B. Measurement of VT

Measurement of VSMeasurement of the buoyancy exerted on the sampleby a solvent with which it is saturated.

VS by immersion method

The method is most accurate but difficultand time consuming to achieve completesaturation. The operations are normallystandardized.The difference between the weights of sample in air (P air)

and the solvent in which it is immersed (P immersed) gives VS as :

Regardless of specific apparatus used i.e. singe cell or doublechamber, the sample is subjected to known initial pressure bygas, which was originally at atmospheric pressure.The pressure is then changed by varying the volume of gas inchamber.The variation in volume and pressure are measured by usingBoyle’s law.

P1 V1 = P2 V2 The equipments using single cell and double are shown innext slide.

Measurement of VSUse of compression chamber and Boyle’ law

1 is chamber for core2 is constant volume chamber3 is core 4 & 5 is pressure manometers6 is source of gas

1 is chamber for core2 is core3 is volume plunger4 is pressure guage

Measurement of VSUse of compression chamber and Boyle’ law

Use of single cell Use of double cell

1

2

3

4,5

62

4

3

1

C. Determination of VPThe pore volume can be measured directly, by measuring the volume of air in the pores, by weighing a liquid filling the pores, or by mercury injection

The mercury positive displacement pump is used for this purpose. After measuring VT ,the value of the sample core holder is closed and the air in the interconnected pores is expanded. The variation in volume and pressure are neasured using Boyle’s law.

a. Measurement of air in the pores :

b. Measurement by weighing a liquid filling the effective pores

This liquid is often brine

c. Measurement by mercury injection

In this case the mercury should never the interconnected pores. The value obtainedcan be effectively used .

Special Method :Fluid Summation• The method involves the analysis of a FRESH

sample containing water, oil and gas.• The distribution of these fluids is not the same

as in the reservoir. because the core has been invaded by the mud filtrate and decomposed when pulled out.

• Still/but the sum of the volumes of these three fluids, for a unit volume of rock, gives the effective porosity of the sample.

• The total volume is determined by mercury displacement pump.

(1) VP = Vw + VO + VG

(1) Sw + SO + SG = 100%

Special Method :Relation of Fluid Summation and porosity

Sw = Vw/ VP SO = Vo/ VP SG = VG/ VP

What is new• NMR SPECROSCOY

By measuring the proton signal strength at time zero compared to proton signal of known standard.In addition to bulk measurements of core porosity , it is also useful to produce porosity images in order to map out details fluids like kind, location, porosity changes/ variationtions, drilling mud invasion, formation anomaly etc.

* The technique is not applicable to shaly sand stone due to resolution problems.

Example analysis is presented / compared:

NMR SPECROSCOY

Rock Weight Porosity

NMRPorosity

% Error

Sand stone1Lime stone1Dolomite1Dolomite2

Sand stone2Sand stone3

22.713.616.112.920.418.7

22.413.016.013.219.617.8

-1.3-4.4-0.6+2.33.94.8

CT Scan Analysis

Sample Radius(mm)Capillary

pressure Avg Radius Avg cap pr.

I-5-32 1.3 1,107.69 1.66 868.97

2.9 496.55

1.5 960.00 0.0126 psi

1.1 1,309.09

1.4 1,028.57

1.2 1,200.00

2.2 654.55

total 11.6

Sf T(dyne/cm^2) 72

Computer Assisted Petrographic Analysis (CAP)

Allows petrographer to make quantitative measurements of textural and mineralogic properties

Grain size distribution, grain shape (angularity), grain contact statistics, grain perimeter/porosity perimeter measurements

Porosity type/size/and distribution; framework grain and authigenic phase mineralogy and distribution

500

500

Brazos, Mustang Island, Matagorda Island

Controlling FactorsControlling Factors::•Sand texture, composition Sand texture, composition •Compaction - VES historyCompaction - VES history•Burial history - temperature, Burial history - temperature, timetime•Cementation - fluid flow historyCementation - fluid flow history•Secondary porositySecondary porosity

250

Porosity-Depth Trends -Porosity-Depth Trends -

Allie 1984; Taylor 1987, 1998

Reservoir Quality Prediction Reservoir Quality Prediction for Sandstonesfor Sandstones

Tc+Mt

Tc-Mt

10,136 ft

10,139 ft

Mt slumped

Tc ( to SMD?

Mt > Tc

Mt slumped

CORE 1, SAND 571

3

2

10,133 ft

10,136 ft

Tc

Mt

Tc-Tb

Mt

Tc? Slumped

3

2

3

Tc-Td >> Tb & Mt

3

10,139 ft

10,142 ft

Tb

Tc - Tb

Mt

Mt

MSD (2a.)

Tc

Mt

1 b

2

3

2

13,673.00 ft

13,676.00 ft

Ta-S?

S-Ta?

13,667.00 ft

13,670.00 ft

MT?

Ta

13,670.00 ft

13,673.00 ft

Ta

MT?

more abundant mud intraclast content …Ta

CORE 6, SAND 767

ISE, 2002

1000

1000

Tc

S

ConclusionsФ (porosity) is a measure of the storage capacity given as that is capable of holding fluids, Mathematically ,it may be given as

Absolute porosity Ratio of the total pore space in the rock to that of the bulk volume

Effective porosityIs the percentage of interconnected pore space with respect to the bulk volume

original porosity is that developed in the deposition of the material,induced porosity is that developed by some geologic process subsequent to deposition of the rock

The grain volume of rock sample of 1.5” dia and 5.6 cm length was found to be 56.24 cc and bulk volume of the sample using mercury displacement method was measured 73.80 cc. If dry weight of the sample is149.88 gms, find the grain density.Calculate the pore volume and porosity of the sample.

Example 1

Application of Effective porosityDetermining the original hydrocarbon volume in placeFor a reservoir with an areal extent of A acres and an average thickness of h feet

Bulk volume = 43,560 Ah, ft3 OR 7,758 Ah, bbl

effective porosity is the value that is used in all reservoir engineering calculations

important application of the effective porosity is its use in determiningthe original hydrocarbon volume in place

The reservoir pore volume PV in cubic feet gives: PV = 43,560 AhФ, ft3

The reservoir pore volume PV in cubic feet gives: PV = 7,758 AhФ, bblExample – 2 An oil reservoir exists at its bubble-point pressure of 3000 psia and temperature of 160°F. The oil has an API gravity of 42° and gas-oil ratio of 600 scf/STB. The specific gravity of the solution gas is 0.65. The following additional data are also available• Reservoir area = 640 acres• Average thickness = 10 ft• Connate water saturation = 0.25• Effective porosity = 15%Calculate the initial oil in place in STB.

Example 1*Pore volume = Bulk volume-Grain volume

=73.80 – 56.24=17,56 cc*Porosity,% =(Pore volume/Grain volume) x 100

=(17.56/73.80)X100 = 23.79%*Grain density=Dry weight of sample/Grain volume

= 149.88/56.24 = 2.665 gms/cc

Example – 2 Step 1. Determine the specific gravity of the stock-tank oil as 0.8156Step 2. Calculate the initial oil formation volume factor as 1.306 bbl /STB

Step 3. Calculate the pore = 7758 (640) (10) (0.15) = 7,447,680 bbl

Step 4. Calculate the initial oil in place. Initial oil in place = 12,412,800 (1 - 0.25)/1.306 = 4,276,998 STB

Solution

Average reservoir porosityBedding planes show large variations in porosity vertically and arithmetic average porosity or the thickness - weighted average porosity is used to describe the average reservoir porosity. If porosity in one portion of the reservoir to be greatly different from that in another area due to sedimentation conditions, the areal weighted averageor the volume-weighted average porosity is used to characterize the average rock porosity.averaging techniques are expressed mathematically in the following forms: Arithmetic average Thickness-weighted average Areal-weighted average Volumetric-weighted averageExample Calculate the arithmetic average and thickness-weighted average from the following measurements

Porosity = void volume ÷ soil volumePorosity = 0.3 cubic meters ÷ 1.0 cubic meters

Porosity = 0.3

POROSITY ?