P663 14B Mod 01b RESENG (Petrophysics) … · Formation Evaluation and the Analysis of Reservoir...

Formation Evaluation and the Analysis of Reservoir Performance Tom BLASINGAME | [email protected] | Texas A&M U.

T.A. Blasingame, Texas A&M U.Department of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 — [email protected]

Formation Evaluation and the Analysis of Reservoir Performance

Reservoir PetrophysicsIntroduction to Geology

Slide — 1


Geology: Basic Porosity Types

Fabric Selective:● Porosity (and permeabil-

ity are functions of de-position and digenesis.

Not Fabric Selective:● Fractures, etc.● Porosity and

permeability may (or may not) be a function of deposition and diagenesis.

Slide — 2


Geology: Basic Porosity Types — Sandstones

Features:● Note intergranular porosity ("conventional reservoir concept).● Clays can cause significant degradation of porosity.

Slide — 3


From: Reservoir Sandstones — Berg (1986).

a. Various sandstone depositional sequences — note the "transport" system evolves basinward.

b. These schematics illustrate similarity in depositional processes and also give insight into heterogeneity.

Sandstone Reservoirs:● Depositional sequences are well-established/accepted.● Turbidite reservoirs are probably of most current interest.

Geology: Sandstone Depositional Systems

Slide — 4


Carbonate Reservoirs: Permeability/Porosity Character●Porosity and permeability often weakly correlated in carbonates.●Permeability in carbonates most often dependent on diagenetic processes.

From

:Car

bona

te R

eser

voir

Cha

ract

eriz

atio

n—

Luci

a (1

999)

.

a. Crossplot of permeability versus porosity (logarithmic scales). Includes particle size as a variable.

b. Permeability-porosity profiles for various carbonate depositional sequences.

Geology: Carbonate Depositional Systems — and k

Slide — 5


Weber Example Core: Laminated Aeolian sandstone. Thin beds (<1 cm) are common. Some laminations have zero permeability

(influence on vertical flow?). General Considerations:

Core-scale heterogeneities may or may not affect overall reservoir performance (depends on continuity).

Attempts to correlate small-scale heterogeneities are likely to fail, except for isolated samples.

Issues: How do such features affect:

— Pressure transient behavior (well test time scale events)?

— Pseudosteady-state behavior(production time scale events)?

Solutions for increasing reservoir exposure? (hydraulic fracturing?)

Petrophysics: Effect of Small-Scale Heterogeneities

From: Weber, KJ.: "How Heterogeneity Affects Oil Recovery — from Reservoir Characterization, Academic Press, Inc.-Harcourt Bruce Jovanovich, Publishers, New York (1986) (Edited by: Lake, L.W. and Carroll, H.B., Jr.).

Slide — 6


Permeability Comparison: Santa Barbara Field (Venezuela)●Major conclusion is that these data due not appear to be correlated.●High permeability values probably "overweigh" klog mean estimate.● kPTA values higher than kWPA, but we have only 3 (three) kPTA values.

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

Prob

abili

ty (F

requ

ency

/n)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Logarithm of permeability, log(md)

Well TM-1E/Permeability Histogram (Upper Naricual)

Well TM-1E(Upper Naricual -- n = 354)

Statistics for kMedian log(k) = 1.0483Mean log(k) = 13204Standard deviation = 1.1686Mean k = 20.9 md

16300

16200

16100

16000

15900

15800

15700

15600

15500

15400

Dep

th, f

t

0.300.250.200.150.100.050.00Porosity, fraction

Well TM-1E/Porosity Distribution with Depth(Upper Naricual)

16300

16200

16100

16000

15900

15800

15700

15600

15500

15400

Dep

th, f

t

10-1 100 101 102 103 104

Permeability, k, md

Well TM-1E/Permeability Distribution with Depth(Upper Naricual)

Petrophysics: Example — kWPA, kPTA with klog mean

From

:Med

ina,

T.:

Cha

ract

eriz

atio

n of

Gas

Con

dens

ate

Res

ervo

irs

Usi

ng P

ress

ure

Tran

sien

t and

Pro

duct

ion

Dat

a-Sa

nta

Bar

bara

Fi

eld,

Mon

agas

, Ven

ezue

la, M

.S. T

hesi

s Te

xas

A&

M U

nive

rsity

(M

ay 2

003)

.

Slide — 7


Reservoir Scaling Issues

b. (Halderson) Volume of investigation of a pres-sure build-up test and cross section indicating large-scale internal heterogeneities.

a. (Haldorsen) Four conceptual scales associated with porous media averages.

NANO or ATTO?

Reservoir Scale Issues: Halderson Schematics

From

:Sim

ulat

or P

aram

eter

Ass

ignm

ent a

nd th

e Pr

oble

m o

f Sc

alin

g in

Res

ervo

ir En

gine

erin

g—

Hal

ders

on (1

986)

.

Slide — 8


Geology/Petrophysics: Questions to ConsiderQ1. Validity of correlations of petrophysical data?A1. These will always be "local" correlations, difficult to extend or

extrapolate across depositional systems.

Q2. Role of geology in PTA?A2. Must consider geology in general, but particularly for cases where

the following reservoir models are employed:● Linear sealing or leaky faults. (any geologic evidence?)● Bounded reservoir system. (geologic or petrophysical evidence?)● Naturally fractured/dual porosity reservoir. (any geologic evidence?)●Multilayered reservoirs. (geologic or petrophysical evidence?)

Q3. Correlation of kcore with kPTA?A3. Always a comparison of "apples and oranges" due to:

● Sample size. (core data are extremely localized)● Saturation/mobility issues. (kcore evaluated using gas at low pressures)

Q4. Effect of reservoir heterogeneity on PTA?A4. Interesting question — volume-averaging appears to dominate the

estimate of permeability obtained from PTA. Attempts to estimate permeability "distributions" will be non-unique and/or overly sim-plified.

Slide — 9





Reservoir PetrophysicsFlow in Porous Media

Slide — 10



Flow Concepts: Concepts for Fluid Flow in Porous Media

Concept:● "Tortuous paths"● Darcy flow.

Concept:● Perfect paths.● Poiseuille flow.● How to reconcile?

Slide — 11


Flow Concepts: Klinkenberg Effect

Liquid Flow:●Governed by "viscous flow."● Analog = Poiseuille flow.● "Zero-slip" at wall concept.

Gas Flow:●Molecules "slip" at wall.●Gradient is lower than expected.● Computed permeability higher.● Results MUST be corrected.

Slide — 12


Flow Concepts: High-Velocity Flow in Porous Media

Slide — 13


Flow Concepts: Klinkenberg Effect — H2, Air, and CO2

Issues:● Smaller molecules =

more severe Klinken-berg effect.

● The Klinkenberg effect can be derived and is a subset of "Knudsen Flow."

Slide — 14


Nelson, P.H. "Pore-throat Sizes in Sandstones, Tight Sandstones, and Shales,AAPG Bulletin, V. 93, no. 3 (March 2009), pp. 329-340.

Petrophysics: Low/Ultra-Low Permeability Issues (Nelson)

Simply Put:●Molecules of fluid are

on the same order of size as pores.

● Very different flow behavior than traditional "Darcy's Law."

● Also affects phase behavior (i.e., com-position, density, temperature, and pressure relations).

● Definition of "uncon-ventional" reservoirs.

Slide — 15


Permeability Characterization/Correlation:●Permeability = f(, composition, texture, grain size, sorting, etc.).●Simplified correlations for permeability will only be of "local" use.

From

:The

Fun

dam

enta

ls o

f Cor

e A

naly

sis

—K

eela

n (1

972)

.

a. "Cartoon" of kair versus — illustrates k=aexp(b).

b. "Cartoon" of kair versus Swi — illustrates the influence of pore throat structure.

From

:API

Dril

ling

and

Prod

. Pra

c.—

Bru

ce a

nd W

elge

(194

7).

Petrophysics: Permeability Characterizations/Correlations

Slide — 16


Sketched Trends:● Increase in porosity → increase

in permeability (obvious).● k = a exp[b ]???● This does not seem intuitive

(statistics)?●What about:

k = A B

●What about other variables?

Petrophysics: k = a exp[b ] (Schematic Trends)

Slide — 17


1000

Porosity (Percent)

Perm

eabi

lity

(md)

● Sketched Trends:●Similar to previous

schematic plot.● This is the "original"

presentation by Archie (to the best of our knowledge, this is the first plot of log(k) versus ).

● There are many other variables:

— Grain sizes— Sorting— Texture— Angularity— …

● These variables can not be directly quantified.

Petrophysics: k = a exp[b ] (Archie Trends)

Slide — 18


Archie Results:●Porosity:

F = a/m

● This result "makes sense" (i.e., volume of the room is proportional to the volume of the electrolyte).

●Permeability:F = A/kB

● This result DOES NOT"make sense" (i.e., the size of the door is proportional to the volume of the room???).

Petrophysics: Archie k--F Relations

Slide — 19


a. Crossplot of formation (resistivity) factor versus permeability (F = a/m).

Porosity Model: Permeability Model:

m

w

o aRR F

Bw

okA

RR F

Equating the Models: Solving for k:

Bm kAa

/1

B

maAk

This exercise suggests that permeability and porosity are related by a power law relation — this observation is only true for

uniform pore systems.

b. Crossplot of formation (resistivity) factor versus permeability (F = A/kB).

Petrophysics: Archie k--F Relations

Slide — 20


Legend: Thin Sections (photomicrographs)A. Upper shoreface ( = 0.207, k = 46.5 md) Vinton Cty, OH. B. Lower shoreface ( = 0.085, k = 3.43 md) Hocking Cty, OH.C. Tidal channel ( = 0.066, k = 0.0178 md) Carroll Cty, OH.D. Tidal flat ( = 0.053, k = 0.0011 md) Portage Cty, OH.E. Fluvial ( = 0.087, k = 15.3 md) Kanawha Cty, WV.F. Estuarine ( = 0.068, k = 0.0048 md) Preston Cty, WV.

b. Appalachian samples — permeability is approximated as a power law function of porosity.

a. Thin sections of Lower Silurian Sandstones, Appalachian Basin (US).

c. Attempt to correlate Morrow samples by deposition —similar to Appalachian samples.

From: Castle, J.W. and Byrnes, A.P.: "Petrophysics of Lower Silurian Sandstones and Integration with The Tectonic-Stratigraphic Framework, Appalachian Basin, United States," Bull., AAPG (2005) 89, 41-60.

Petrophysics: Porosity-Permeability — Power Law Relation

Slide — 21


a. Pape concept model plot — based on a fractal pore distribution. Some concern regarding the additive structure of the model (this seems to be a simplistic reduction of the fractal concept).

b. Legend for the Pape concept model plot. Note that there are several quite different data sets shown, yet the "structure" of the correlation appears consistent.

From: Pape, H., Clauser, C., Iffland, J.: "Permeability Prediction Based on Fractal Pore-Space Geometry," Geophysics (1999) Vol. 64, (September-October 1999), 1447–1460.

103

221 aaak

Pape et al Fractal Model for Permeability:

Petrophysics: Fractal Model for Permeability (Pape)

Slide — 22


a. Data from Beard and Weyl, and Morrow et al. These are unconsolidated sand samples.

b. Log-log plot of k/d2 versus — extraordinary agreement given data quality (note slope ≈ 8).

From: Beard, D.C. and Weyl, P.K.: "Influence of Texture on Porosity and Permeability of Unconsolidated Sand," Bull., AAPG (1973) 57, 349-369. Morrow, N.M, Huppler, J.D., and Simmons III, A.B: "Porosity and Permeability of Unconsolidated, Upper Miocene Sands From Grain-Size Analysis," J. Sed. Pet. (1969) Vol. 39, No. 1, 312-321.

Beard and Weyl Data:

Morrow Data: (selected)

Petrophysics: Influence on and k (Unconsolidated Sand)

Slide — 23


East Texas Tight Gas Sand

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-

04

1.E-

03

1.E-

02

1.E-

01

1.E+

00Measured Permeability (md)

Cal

cula

ted

Perm

eabi

lity

(md)

Correlation Linek_EOS Model

]exp[

8)( )( 32

1maxc

wc

b

Sccc

bcak

From:Siddiqui, A. Towards a Characteristic Equation for Permeability, M.S. Theses, Texas A&M University (May 2008).

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E-

02

1.E-

01

1.E+

00

Porosity (fraction)

Perm

eabi

lity

(md)

Permeability Correlation13140

13160

13180

13200

13220

13240

1.E-

04

1.E-

03

1.E-

02

1.E-

01

Permeability (md)

Dep

th (f

t)

a. Correlation plot of calculated versus measured permeability. — East Texas (US) tight gas example.

b. Log-log correlation plot of kversus . The correlation function yields an envelope.

c. Correlation plot of depth versus log(k). Correlation appears to be excellent.

Correlation relation for this case.k=f(,Sw)

Petrophysics: and k (Power Law Relation)

Slide — 24


Fanc

her,

G.H

., Le

wis

, J.A

., an

d B

arne

s, K

.B.:

"Som

e Ph

ysic

al C

hara

cter

istic

sof

Oil

Sand

s,"

Pa. S

tate

Col

lege

, Min

. Ind

. Exp

. Sta

. Bul

l. 12

(193

3), 6

5-17

1.

Orientation:●Possibly one of the most important

sequences of experimental results in Petroleum Engineering.

Observations:●Do you see "Darcy's Law?"● Is it a good idea to formulate

pressure drop as a "friction factor" for flow in porous media?

●What would you do?Comment:●Note that this approach is not perfect,

ALL trends should overlay if the friction factor and Reynolds number are properly defined.

●Reformulate?

Petrophysics: Early Concepts for Flow in Porous Media

Slide — 25


Formulation:●Cornell and Katz appear to

have chosen appropriate definitions for Reynolds number and friction factor.

●Are all of these variables "measurable?"

Observations:●Excellent conformance for

all cases?● The curved and flat portions

are for "Forchheimer" flow (pressure gradient is proportional to velocity squared).

Comment:●Non-linear, requires

numerical solutions.

Petrophysics: Cornell-Katz Relation for High-Velocity Flow

Slide — 26





Reservoir Petrophysics(End of Lecture)

Slide — 27


P663 14B Mod 01b RESENG (Petrophysics) … · Formation Evaluation and the Analysis of Reservoir...

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