Modeling and Simplicity: Occam’s Razor in the 21st Century

EORI IOR/EOR Conference

September 2012

Larry W. Lake

Department of Petroleum and

Geosystems Engineering

The University of Texas at Austin

The University of Texas at Austin

• Founded in 1883

• 51,000 students enrolled from more than 100

countries (12,000+ in grad school)

• Annual operating budget: $2.3B

• Research funding: $640M

• 3,000 faculty, 18,000 staff

• 4 museums, 14 libraries

• 450,000 alumni

• PGE: 600 UG; 185 Grad

Outline

• A nod to history

• Enter the gorilla

• Simple models

• Summary

A nod to history.. William of Occam

1288-1348 CE

Occam’s Razor:

Entities should not be multiplied

endlessly

A way to shave away irrelevant explanations

Aka…the law of

Parsimony

Succinctness

Economy

The simplest explanation is the best

But…There is always a well-known solution

to every human problem…neat, plausible,

and wrong

H.L. Mecklen

And…All principles, rules and methods

increasing lack universality and absolute

truth the moment they become a positive

doctrine

C. von Clausewitz

Early Models-Tanks

1964

Early Models-Displacement

1950

1963

Lest We Forget…

1956

Modeling Timeline

Schilthius

(1935)

Buckley and

Leverett (1941)

Welge (1948)

1930 1940 1950 1960 1970 1980 1990

Muskat / Stiles / van

Everdingen and Hurst (1949)

Dietz / Dykstra

and Parsons (1950)

Hubbert / Blair

and Peaceman (1953)

Arps / Higgens and

Leighton (1956)

Koval / Havelina

and Odeh (1963)

Hearn (1972)

Pope and

Nelson (1978)

Hewett and

Behrens (1989)

Reservoir Engineering Practice

• Develop a model

– Usually done by someone else

– An equation or a simulator

• Accumulate and analyze data

• Fit model to data

– History match

– Mostly done by hand…still

– Model is calibrated

• Extrapolate to desired answer

– Project life

– Ultimate recovery

– Net present value

Outline

• A nod to history

• Enter the gorilla

• Simple models

• Summary

Basic Equations...

• Conservation of

– Mass

– Energy

• Empirical laws

– Darcy

– Capillary

pressure

– Phase behavior

– Fick

– Reaction rates

Basic Equations...

Simulation Schematic...

Conservation law...

• {Rate In} - {Rate Out} = {Accumulation}

• For each component (oil, gas, water, energy)

• For each cell

In

Out

y

In

Out

z

In Out x

Grid block

or cell

System

Input Output

Division

Separation

Output

Recombine

? =

Predict

Reductionist View…

106 pieces

106 pieces

Input

Output

Study

Combine

Req

uir

ed

106

106

106

106

106

106

How Measured

L = Logs (103)

C = Core (102)

S = Seismic (105)

WT = Well Test (101)

Measu

red

105

102

101

103

103

101

L, C,

S, WT

Measu

red

Dir

ectl

y

102

102

101

103

102

101

C,

WT A

t C

orr

ect

Scale

105

101

0

103

103

0

L,

WT

In S

itu

105

101

101

103

103

0 L, S,

WT

All

0

0

0

0

0

0

--

Porosity

Horizontal Permeability, kh

Vertical Permeability, kz

Pressure

Saturation

Relative Permeability

Measurement Density for

Numerical Simulation

"Requiem for Large-Scale Models"

• By Douglass B. Lee, American

Institute of Planning, May 1973, pp.

163-178

• The paper that set urban planning

back 25 years

Seven Sins of Large-Scale

Models (Lee, 1973)

• Hypercomprehensiveness

• Grossness

• Hungriness

• Wrongheadedness

• Complicatedness

• Mechanicalness

• Expensiveness

Outline

• A nod to history

• Enter the gorilla

• Simple models

• Summary

Tank Models Revisited

(Walsh and Lake, Chap. 9)

Tank Models…

Cumulative

production definition

Microscopic

Macroscopic

9 parameters

Tank Models…

Depletion

flow

Rate

Np

Constant rate

EL

Recoverable Oil

North Sea Production...

0,0

0,1

0,1

0,2

0,2

0,3

0,3

0,4

0,4

0,5

0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0

Akkumulert olje (mill Sm3)

Oljera

te -

olj

e p

er

mån

ed

(m

ill

Sm

3)

GYDA

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0,0 100,0 200,0 300,0 400,0 500,0 600,0

Akkumulert olje (mill Sm3)

Olje

rate

- o

lje

pe

r må

ne

d (

mill S

m3

)

STATFJORD

Conclusions from Validation

• Model can easily match data

• Provides a physical basis for ideal behavior

• A standard for deviations from ideal behavior

• Larger fields (more wells) behave ideally

• Precursor for numerical simulation

Capacitance Resistance Models

(Fei Cao)

Capacitance-Resistance Model (CRMP)

f2j

f6j

f4j

f3j

f5j

f1j

f11 f12

f13

I6

I1

I2

I3

I4 I5

qj(t)

( ) ik

n

i

ij

tt

kjjk Ifeeqqi

jj å=

D-D-

- ÷ø

öçè

æ-+=

1

1 1tt

j

pt

jJ

Vc

÷÷ø

öççè

æ=t

11

£å=

pn

j

ijf

Time constant

Inter-well connectivity or gain

Drainage volume

around a producer

Cranfield Field

Reservoir located at 10,000 ft (3,000 m) depth

Gas cap, oil ring, downdip water leg existed before development

Discovered in 1943 and produced oil and gas (1944 – 1965)

Due to strong water drive, reservoir pressure returned to near initial pressure

Cranfield

Field

faultfault

faultfault

Study Area

Geology: A fault that is sealing , except in

the north part of the field, divides that

productive formation into 2 reservoirs

Cranfield Field

Producer j

I1 I2

I3 I4

f2

j

f1

j f3

j

f4

j

2

1 1

min ( )pt

nnobs

jk jk

k j

z q q

, 0ij jf

1

1pn

ij

j

f

( 1)

1

(1 )i

j j

nt t

jk j k ij ik

i

q q e e f I

Algorithm-Review of the original CRM

2

_ 1

min ( )pn

obs

jk jk

k well testing j

z q q

( 1)

1

(1 )i

j j

nt t

jk j k ij ik

i

q q e e f I

, 0ij jf

1

1pn

ij

j

f

obs

jk k

j

q q

Algorithm-Well testing case

Producer j

I1 I2

I3 I4

f2

j

f1

j f3

j

f4

j

Cranfield Gain Map

Conclusions from Validation

• Always good total fluid matches

• Oil production matches ok, but less good

• Several instances of connection at a

distance

• Validated against…

– Numerical simulation

– Tracers

– Seismic

– Structure

• May help produce additional oil

Displacement Models

(Alireza Molleai)

Final Bank Initial

Flow

c a&b

c

c b

a

Time

Rate

SoF SoB SoI

vS voB

Fractional Flow Solution (Two Fronts)

97% oil recovery

0.009 final oil saturation

Pore Volumes

Fra

cti

on

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Cumulative Residual

Oil Recovery

Oil Fraction

Pope, et al., 2007

Flow

c b c

b

a

Time

Rate

a

Final

Initial

EL SoF SoB SoI

Field Oil Bank Formation

Final Bank Initial

Flow

c a&b

c

c b

a

Time

Rate

SoF SoB SoI

vS voB

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5

Oil

Cu

t, f

o

Injected PV, tD

Lost Soldier Field

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Oil

Cu

t, f

o

Injected PV, tD

Rangely Field

CO2 Project Results

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Oil

Cu

t, f

o

Injected PV, tD

Slaughter Pilot

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5

Oil

Cu

t, f

o

Injected PV, tD

Twofreds Field

SACROC 4 Field

SACROC 17 Field

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5 2.0

Oil

Cu

t, f

o

Injected PV, tD

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Oil

Cu

t, f

o

Injected PV, tD

CO2 Project Results

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Oil

Cu

t, f

o

Injected PV, tD

Wertz Field

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.0 0.5 1.0 1.5

Oil

Cu

t, f

o

Injected PV, tD

West Sussex Pilot

Conclusions from Validation

• Model matches field behavior

• Generic ranges of values for input variables

• No strong correlations among any input

variables

• ...and with field values

• Pilots perform slightly better than field scale

• Pore volume problem - (So)Field << (So)Lab

Multistage Models

(Cristina Para-Sanchez)

Cash Flow Components: Inflow

= theoretical ultimate

recovery efficiency

where

= recovery efficiency

at time zero

= time constant

for production

The recovery efficiency is taken to be:

E∞

E0

R

R

Data Fit

1 = 16 years

2 = 7.9 years

3 = 5 years

4 = 6.7 years

From Brokmeyer et al., 1996

Primary

Peripherical Waterflood

Pattern Waterflood

CO2 Tertiary

Actual data

Calculated Data

Maximize NPV per Recovery Phase

Myopic Optmization

Optimize Global NPV

Assumptions and Summary

• E∞R is constant

is constant

• i = 10%

• $oil = $55 per bbl

• $opex-1ry = $3 per bbl

• $opex-1ry = $5 per bbl

• $opex-1ry = $6 per bbl

Case1:MaxNPVper

phaseCase2:NPVData Case3:OptimizeNPV

NPV(billion) $0.97 $1.08 $1.90

tLife(years) 88 61 26

OOIPrecovered(%) 51.3 52.7 50.0

Conclusions from Study

• Matches history very well

• Life cycle optimization always increases NPV

• Decreases ultimate recovery

• Ratio of contribution to NPV:

– Primary: 1

– Secondary: ½

– Tertiary: 1/10

Outline

• A nod to history

• Enter the gorilla

• Simple models

• Summary

Numerical Simulation (Multicell)

• The industry standard

• Requires millions of inputs

– Hugely over parameterized

– None are exactly correct (history matching

required)

– Spawned entire technologies

• Can always history match (with an effort)

• No great history of prediction

• Complexity..

– Discourages application

– Allows investigation of interacting effects

• Provides a calibration for simple models

• Any application that requires 1000s of runs

– Multiple reservoirs (screening)

– Sensitivity studies

– Decision/risk analysis

– Alternative scenarios

– Concept selection

– Value of information

• Easy to history match

• We are not trying to draw an elephant

Simple Models?

Other Views on Modeling…

• Bratvold and Bickel…two types

– Verisimilitude- the appearance of reality

– Cogent- enables decisions

• Haldorsen….the progress of ideas

– Youth= simple, naïve

– Adolescence=complex, naïve

– Middle age=complex, sophisticated

– Maturity= simple, sophisticated

• “All models are wrong. Some are useful." G.E.P. Box