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Course Notes for Petroleum Engineering 311 Reservoir Petrophysics Authors: 1980 — Von Gonten, W.D. 1986 — McCain, W.D., Jr. 1990 — Wu, C.H. PETROLEUM ENGINEERING 311 RESERVOIR PETROPHYSICS CLASS NOTES (1992) Instructor/Author: Ching H. Wu DEPARTMENT OF PETROLEUM ENGINEERING TEXAS A&M UNIVERSITY ...

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Course Notes for

Petroleum Engineering 311 Reservoir Petrophysics Authors: 1980 — Von Gonten, W.D. 1986 — McCain, W.D., Jr. 1990 — Wu, C.H.

PETROLEUM ENGINEERING 311 RESERVOIR PETROPHYSICS CLASS NOTES (1992)

Instructor/Author: Ching H. Wu

DEPARTMENT OF PETROLEUM ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TEXAS

TABLE OF CONTENTS I.

ROCK POROSITY I) II) III) VI) V) VI) VII)

II.

I-1

Definition Classification Range of values of porosity Factors affecting porosity Measurement of porosity Subsurface measurement of porosity Compressibility of porous rocks

I-1 I-1 I-2 I-3 I-5 I-13 I-25

SINGLE PHASE FLOW IN POROUS ROCK

II-1

I) Darcy's equation II) Reservoir systems

II-11 II-15

III. BOUNDARY TENSION AND CAPILLARY PRESSURE I) II) III) IV) V) VI) VII) VIII) IX) X) XI)

Boundary tension Wettability Capillary pressure Relationship between capillary pressure and saturation Relationship between capillary pressure and saturation history Capillary pressure in reservoir rock Laboratory measurement of capillary pressure Converting laboratory data to reservoir conditions Determining water saturation in reservoir from capillary pressure data Capillary pressure variation Averaging capillary pressure data

IV. FLUID SATURATIONS

III-1 III-3 III-5 III-13 III-14 III-17 III-19 III-25 III-27 III-29 III-31 IV-1

I) Basic concepts of hydrocarbon accumulation II) Methods for determining fluid saturations V.

III-11

IV-1 IV-1

ELECTRICAL PROPERTIES OF ROCK-FLUID SYSTEMS

V-1

I) Electrical conductivity of fluid saturated rock II) Use of electrical Formation Resistivity Factor, Cementation Factor, and Saturation Exponent III) Laboratory measurement of electrical properties of rock IV) Effect of clay on resistivity

V-1

VI. MULTIPHASE FLOW IN POROUS ROCK I) II) III) IV) V) VI)

Effective permeability Relative permeability Typical relative permeability curves Permeability ratio (relative permeability ratio) Measurement of relative permeability Uses of relative permeability data

ii

V-8 V-9 V-18 VI-1 VI-1 VI-2 VI-2 VI-14 VI-14 VI-33

VII. STATISTICAL MEASURES I) II) III) IV) V) VI) VII) VIII) IX) X)

VII-1

Introduction Frequency Distributions Histogram Cumulative Frequency Distributions Normal Distribution Log Normal Distribution Measures of Central Tendency Measures of Variability (dispersion) Normal Distribution Log Normal Distribution

VII-1 VII-2 VII-3 VII-6 VII-8 VII-9 VII-10 VII-11 VII-12 VII-16

iii

I. ROCK POROSITY I)

Definition A measure of the pore space available for the storage of fluids in rock

In general form: Porosity = φ =

Vp Vb - Vm = Vb Vb

where: φ is expressed in fraction Vb = Vp + Vm Vb = bulk volume of reservoir rock, (L3) Vp = pore volume, (L3) Vm= matrix volume, (L3)

II)

Classification A.

Primary (original) Porosity Developed at time of deposition

B.

Secondary Porosity Developed as a result of geologic process occurring after deposition

C.

Total Porosity φt =

D.

total pore space Vb - Vm = Vb Vb

Effective Porosity φe = 1. 2.

interconnected pore space Vb Clean sandstones: φe = φt Carbonate, cemented sandstones: φe < φt

I-1

VI)

Factors affecting porosity A.

Factors: 1. Particle shape 2. Particle arrangement 3. Particle size distribution 4. Cementation 5. Vugs and fractures

B.

Particle shape Porosity increases as particle uniformity decreases.

C.

Packing Arrangement Porosity decreases as compaction increases

EFFECT OF NATURAL COMPACTION ON POROSITY (FROM KRUMBEIN AND SLOSS.) 50

40 SANDSTONES

POROSITY, %

30

20

SHALES 10

0 0

1000

2000

3000

4000

DEPTH OF BURIAL, ft

I-3

5000

6000

D.

Particle Size Distribution Porosity decreases as the range of particle size increases

SAND

SILT

CLAY

100

CLEAN SAND FRAMEWORK FRACTION

WEIGHT %

SHALY SAND

INTERSTITIAL MATERIALS AND MUD FRAGMENTS 0 1.0

0.1

0.01

0.001

GRAIN SIZE DIAMETER, MM

E.

F.

Interstitial and Cementing Material 1.

Porosity decreases as the amount of interstitial material increases

2.

Porosity decreases as the amount of cementing material increases

3.

Clean sand - little interstitial material Shaly sand - has more interstitial material

Vugs, Fractures 1.

Contribute substantially to the volume of pore spaces

2.

Highly variable in size and distribution

3.

There could be two or more systems of pore openings - extremely complex

I-4

V)

Measurement of porosity φ=

Vb - Vm Vp = Vb Vb

Table of matrix densities Lithology ρ m (g/cm3) ___________ ___________

A.

Quartz

2.65

Limestone

2.71

Dolomite

2.87

Laboratory measurement 1.

Conventional core analysis a.

measure any two 1) 2) 3)

b.

bulk volume, Vb matrix volume, Vm pore volume, Vp

bulk volume 1) 2)

calculate from dimensions displacement method a)

volumetric (measure volume) (1)

drop into liquid and observe volume charge of liquid

(2)

must prevent test liquid from entering pores space of sample (a) (b) (c)

b)

coat with paraffin presaturate sample with test liquid use mercury as test liquid

gravimetric (measure mass) (1)

Change in weight of immersed sampleprevent test liquid from entering pore space

(2)

Change in weight of container and test fluid when sample is introduced

I-5

c.

matrix volume 1)

assume grain density dry weight Vm = matrix density

2)

displacement method Reduce sample to particle size, then

3)

a)

volumetric

b)

gravimetric

Boyle's Law: P1V1 = P 2V2 a) P(1)

V (1)

V A LV E CLO SED b)

Put core in second chamber, evacuate

c)

Open valve

P(2)

CO RE

V A LV E O PEN

4)

Vm

V2

=

Volumetric of first chamber & volume of second chamber-matrix volume or core ( calculated)

VT

=

Volume of first chamber + volume second chamber (known)

=V T - V2

I-6

d.

pore volume 1)

gravimetric Vp =

2)

saturated weight - dry weight density of saturated fluid

Boyle's Law: P1V1 = P 2V2 a) P(1)

V (1)

CO RE

V A LV E CLO SED

b)

Put core in Hassler sleeve, evacuate

c)

Open valve

P(2)

V (1)

CO RE

V A LV E O PEN

3)

V2

=

Vp

= V2 - V1

I-7

Volume of first chamber + pore volume of core (calculated)

2.

Application to reservoir rocks a.

b.

intergranular porosity (sandstone, some carbonates) 1)

use representative plugs from whole core in laboratory measurements

2)

don't use sidewall cores

secondary porosity (most carbonates) 1)

use whole core in laboratory measurements

2)

calculate bulk volume from measurements

3)

determine matrix or pore volume from Boyle's Law procedure

I-8

Example I-1 A core sample coated with paraffin was immersed in a Russell tube. The dry sample weighed 20.0 gm. The dry sample coated with paraffin weighed 20.9 gm. The paraffin coated sample displaced 10.9 cc of liquid. Assume the density of solid paraffin is 0.9 gm/cc. What is the bulk volume of the sample?

Solution: Weight of paraffin coating = 20.9 gm - 20.0 gm = 0.9 gm Volume of paraffin coating = 0.9 gm / (0.9 gm/cc) = 1.0 cc Bulk volume of sample = 10.9 cc - 1.0 cc = 9.9 cc

Example I-2 The core sample of problem I-1 was stripped of the paraffin coat, crushed to grain size, and immersed in a Russell tube. The volume of the grains was 7.7 cc. What was the porosity of the sample? Is this effective or total porosity.

Solution: Bulk Volume

=

9.9 cc

Matrix Volume

=

7.7 cc

V - Vm 9.9 cc- 7.7 cc φ= b = = 0.22 Vb 9.9 cc

It is total porosity.

I-9

Example I-3 Calculate the porosity of a core sample when the following information is available: Dry weight of sample = 427.3 gm Weight of sample when saturated with water = 448.6 gm Density of water = 1.0 gm/cm3 Weight of water saturated sample immersed in water = 269.6 gm

Solution: Vp

=

sat. core wt. in air - dry core wt. density of water

Vp

=

448.6 gm - 427.3 gm 1 gm/cm3

Vp

=

21.3 cm3

Vb

=

sat. core wt. in air - sat. core wt. in water density of water

Vb

=

448.6 gm - 269.6 gm 1 gm/cm3

Vb

=

179.0 cm3

φ

=

Vp = 21.3 cm3 = .119 Vb 179.0 cm3

φ

=

11.9%

I - 10

What is the lithology of the sample? Vm

=

Vb - Vp

Vm

=

179.0 cm3 - 21.3 cm3 = 157.7 cm 3

ρm

=

wt. of dry sample matrix vol.

= 2.71 gm/(cm3) 157.7 cm3

= 427.3 gm

The lithology is limestone. Is the porosity effective or total? Why? Effective, because fluid was forced into the pore space.

I - 11

Example I-4 A carbonate whole core (3 inches by 6 inches, 695 cc) is placed in cell two of a Boyles Law device. Each of the cells has a volume of 1,000 cc. Cell one is pressured to 50.0 psig. Cell two is evacuated. The cells are connected and the resulting pressure is 28.1 psig. Calculate the porosity of the core.

Solution: P V 1 1

=

P V 2 2

V 1

=

1,000 cc

P

=

50 psig + 14.7 psia = 64.7 psia

=

28.1 psig + 14.7 = 42.8 psia

V 2

=

(64.7 psia) (1,000 cc) / (42.8 psia)

V 2

=

1,512 cc

V m

=

VT - V2

V m

=

2,000 cc - 1,512 cc - 488 cc

φ

=

VT - Vm 695 cc - 488 cc = = .298 = 29.8% VT 695 cc

P

1 2

I - 12

VI)

Subsurface measurement of porosity A.

Types of logs from which porosity can be derived 1.

Density log: ρ -ρ φd = m L ρm - ρf

2.

Sonic log: φs =

3.

∆tL - ∆tm ∆tf - ∆tm

Neutron log: e- kφ = CNf

Table of Matrix Properties (Schlumberger, Log Interpretation Principles, Volume I) Lithology

∆tm µsec/ft

ρ m gm/cc

Sandstone

55.6

2.65

Limestone

47.5

2.71

Dolomite

43.5

2.87

Anhydrite

50.0

2.96

Salt

67.0

2.17

189.0

1.00

Water

I - 13

B.

Density Log 1.

Measures bulk density of formation

M UD CA KE

FO RM A TIO N

GA M M A RA Y SO URCE

SHO RT SPA CE DETECTO R

LO NG SPA CE DETECTO R

2.

Gamma rays are stopped by electrons - the denser the rock the fewer gamma rays reach the detector

3.

Equation ρL =

ρm 1 - φ + ρf φ

ρ -ρ φd = m L ρm - ρf

I - 14

FORMATION DENSITY LOG

ρ, gm/cc

depth, ft

G R, A PI

4100

4120

4140

4160

4180

4200

4220

4240 0

40

80

120

160

200

2.0

I - 15

2.2

2.4

2.6

2.8

3.0

Example I-5 Use the density log to calculate the porosity for the following intervals assuming ρ matrix = 2.68 gm/cc and ρ fluid = 1.0 gm/cc. Interval, ft

ρ

__________

L, gm/cc _________

4143-4157 4170-4178 4178-4185 4185-4190 4197-4205 4210-4217

2.375 2.350 2.430 2.400 2.680 2.450

φd ,% ______ 18 20 15 17 0 14

Example: Interval 4,143 ft -4,157 ft : ρ = 2.375 gm/cc L ρ -ρ 2.68 gm/cc - 2.375 gm/cc φd = m L = = 0.18 ρm - ρf 2.68 gm/cc - 1.0 gm/cc

I - 16

C.

Sonic Log 1.

Measures time required for compressional sound waves to travel through one foot of formation

T

A

B C

R1 D

E R2

2.

Sound travels more slowly in fluids than in solids. Pore space is filled with fluids. Travel time increases as porosity increases.

3.

Equation ∆tL = ∆tm 1 - φ + ∆tf φ

I - 17

(Wylie Time Average Equation)

SONIC LOG

GR, API

∆T, µ seconds/ft

depth, ft 4100

4120

4140

4160

4180

4200

4220

4240 0

100

200

140

I - 18

120

100

80

60

40

Example I-6 Use the Sonic log and assume sandstone lithology to calculate the porosity for the following intervals.

∆tL µ second/ft

Interval (ft)

φs ,%

4,144-4,150

86.5

25

4,150-4,157

84.0

24

4,171-4,177

84.5

24

4,177-4,187

81.0

21

4,199-4,204

53.5

1

4,208-4,213

75.0

17

Example: Interval 4144 ft - 4150 ft : ∆tL φs =

= 86.5 µ-sec/ft ∆tL - ∆tm 86.5 µ sec/ft- 51.6 µ sec/ft = = 0.25 ∆tf - ∆tm 189.0 µ sec/ft- 51.6 µ sec/ft

I - 19

D.

Neutron Log 1.

Measures the amount of hydrogen in the formation (hydrogen index)

Maximum Energy Loss/ Collision, %

Average Number Collisions

Element Calcium Chlorine Silicone Oxygen Carbon Hydrogen

371 316 261 150 115 18

Atomic Collision

8 10 12 21 28 100

40.1 35.5 28.1 16.0 12.0 1.0

20 17 14 8 6 1

CLEA N SA N D PO RO SITY = 15%

10 3 O

10 2 Si 10

H

SLO W IN G D O W N PO W ER

RELA TIV E PRO BA BILITY FO R CO LLISIO N

CLEA N SA N D PO RO SITY = 15%

Atomic Number

1

10-1 H

O

10-2

Si

10-3

1

.1

1

10

10 2 10 3 10 4 105

10 6 107

.1

NEUTRO N ENERGY IN ELECTRO N V O LTS

1

10

10 2 10 3 10 4 10 5

10 6 107

NEUTRO N ENERGY IN ELECTRO N V O LTS

2.

In clean, liquid filled formations, hydrogen index is directly proportional to porosity. Neutron log gives porosity directly.

3.

If the log is not calibrated, it is not very reliable for determining porosity. Run density log to evaluate porosity, lithology, and gas content.

I - 20

NEUTRON DENSITY LOG

φ (CD L)

depth, ft

G R, A PI

4100

4120

4140

4160

4180

4200

4220

4240 0

200

I - 21

30

-1 0

Example I-7 Use the neutron log to determine porosity for the following intervals.

Solution:

Interval (ft)

φ

n (%)

.

4,143-4,149

23

4,149-4,160

20

4,170-4,184

21

4,198-4,204

9

4,208-4,214

19

I - 22

Example I-8 Calculate the porosity and lithology of the Polar No. 1 drilled in Lake Maracaibo. The depth of interest is 13,743 feet. A density log and a sonic log were run in the well in addition to the standard Induction Electric Survey (IES) survey. The readings at 13,743 feet are: bulk density travel time

= 2.522 gm/cc = 62.73 µ-sec/ft

Solution: Assume fresh water in pores. Assume sandstone: ρ m = 2.65 gm/cc ∆tm = 55.5 µ-sec/ft ρ -ρ 2.65 gm/cc - 2.522 gm/cc φd = m L = = 7.76% ρm - ρf 2.65 gm/cc - 1.0 gm/cc

φs =

∆tL - ∆tm 62.73 µ sec/ft- 55.5 µ sec/ft = = 5.42% ∆tf - ∆tm 189.0 µ sec/ft - 55.5 µ sec/ft

Assume limestone: ρm

= 2.71 gm/cc

∆tm

= 47.5 µ-sec/ft

ρ -ρ 2.71 gm/cc - 2.522 gm/cc φd = m L = = 10.99% ρm - ρf 2.71 gm/cc - 1.0 gm/cc φs =

∆tL - ∆tm 62.73 µ sec/ft - 47.5 µ sec/ft = = 10.76% ∆tf - ∆tm 189.0 µ sec/ft - 47.5 µ sec/ft

I - 23

Assume dolomite: ρm

= 2.87 gm/cc

∆tm

= 43.5 µ-sec/ft

φd

ρ -ρ 2.87 gm/cc - 2.522 gm/cc = m L= = 18.619% ρm - ρf 2.87 gm/cc - 1.0 gm/cc

φs

=

φlimestone

∆tL - ∆tm 62.73 µ sec/ft - 43.5 µ sec/ft = = 13.22% ∆tf - ∆tm 189.0 µ sec/ft - 43.5 µ sec/ft = 11%

Since both logs "read" nearly the same porosity when a limestone lithology was assumed then the hypothesis that the lithology is limestone is accepted. Are the tools measuring total or effective porosity? Why? The density log measures total compressibility because is "sees" the entire rock volume,including all pores. The sonic log tends to measure the velocity of compressional waves that travel through interconnected pore structures as well as the rock matrix. The general consensus is that the sonic log measures effective porosity when we use the Wyllie "time-average" equation. It is expected that the effective porosity is always less than ,or equal t...