07 - Valuation Techniques

7/27/2019 07 - Valuation Techniques

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Introduction

Probability, Distributions and Correlation

Estimating Under Uncertainty

Tight Clastics / Carbonate Assessment

Shale Assessment

Reservoir Flow

Valuation Techniques

Risk, Uncertainty & Economic Analysis

for Resource Assessment and Production

Forecasting in Shale and Tight Reservoirs

Decline Curve Analysis Approaches• Arps with best fit b

• Modified Hyperbolic Approach

• Hyperbolic followed by exponential

• Hyperbolic ‘b’ exceeds 1, then by hyperbolic ‘b’ less than 1

• Variable ‘b’ with time methods

• Stretched Exponential Production Decline (SEPD)

• Power Law Loss-Ratio

• Duong method – Assume all flow is linear

• The 5 Year rule for Modified Hyperbolic

• Reservoir Modeling

• Great progress but simulators require SRV input

© Rose & Associates, LLP 1 Ch 7 - Valuation Techniques AAPG Cartagena 2D course, Sept. 2013



Arps Equation:

(1+bDit)1/b

Exponential decline b = 0

Harmonic decline b = 1

Hyperbolic decline b is between 0 and 1

This is a good approximation technique when we have steady

state flow conditions, with an unchanging drainage area.

Unfortunately in Resource Plays this is not the case!

q(t) = qi * eDit

q(t) = qi / (1+ Dit )

qi

Reserve Determination From Production Data

q(t) =

Arps Decline Equation

q(t) = Production rate at time t

qi = Initial Production rate

Di = The initial decline rate, in percent per year

t = Cumulative time in days, since the start of production

b = Arps’ decline constant

Arps Equation:

(1+bDit)1/b

qiq(t) =




Arps’ Decline Models

John Lee, SPE Short Course

Critique of Arps’ Model

Requires: – Constant bottom-hole pressure

– Unchanging drainage area

– A fixed skin factor

– Stabilized (boundary dominated) flow for validity

Recent Observations – Best-fit ‘b’ values almost always >1 for recent gas wells

– Extrapolation to economic limit with high ‘b’ value leads to

unrealistically large reserves estimates – Linear flow likely for most of the economic life

of the well in ultra-low permeability reservoirs

Reserves → ∞ as rate → 0 (time → ∞) for b ≥ 1

After John Lee (2011)

q i

(1+bDit)1/bq(t) =




10 YearsNo Boundary

SPE 138987 Brent Hale, W. Cobb & Associates

Barnett Vertical Wells

Linear Flow Plots

• Straight line on a 1/q vs sqrt of t plot

• ½ slope on a log rate vs log time plot

Performance of Very Low Perm Fractured Wells

Hough and McClurg (2011)




0.1

1

10

0.00 5.00 10.00 15.00 20.00 25.00

R a t e M M S C F D

Time in Years

Exponential

Decline used

b = 0

Assumed

Dmin

Hyperbolic

decline used

b > 1

Common approach (i.e. PhD Win, Aries, PEEP):‘exponential tail-off’ after a hyperbolic decline:

Hyperbolic decline used until annual decline rate reaches

a pre-defined min, called Dmin., which in turn is based on

analogs or the experience of the engineer.

Typically Dmin of 4-10% is being used

An unconstrained extrapolation with best-fit b > 1 is unrealistic

Decline Curves Approaches: Modified Hyperbolic

Advantages

• Widely used for 20+ years

• Uses Industry standard Arps empirical model – Hyperbolic based on history matching followed by Exponential once

a predefined minimum decline rate is reached (terminal decline rate)

• Keeps reserves estimates conservative but within reason

• The two errors in this approach compensate each other – The imperfect ‘b’ value (exceeds 1) causes an over prediction of

reserves

– Applying a exponential terminal decline results in a negative error,

which causes a conservative estimate

Disadvantage

• Appropriate Analog data is required to estimate theminimum terminal decline rate

Decline Curves Approaches: Modified Hyperbolic

John Lee, SPE Short Course




Terminal Decline & ‘b’ Value Variation

-Bakken Elm Coulee Field

SPE 149273, B. Kurtoglu, C.A. Cox, H. Kazemi

10 20 30 40 50

Years

10

100

1,000

Oil Rate, B / D

Dmin, (%/yr): 10 8 6 5 4

Forecasting EUR: Vertical Devonian Shale, KY

D(20 YRS) = 2.25%Field Average

169 Wells > 30

yrs prod history

D(20 YRS) = 2.37%

CUM = 704MMCF

EUR = 807MMCF

D(20 YRS) = 2.88%

CUM = 296MMCF

EUR = 715MMCF

D(20 YRS) = 3.2%

CUM = 199MMCF

EUR = 638MMCF

5 YEARS PROD

FED GAS OIL & COAL CO

(808685)

15 YEARS PROD


(808685)

50 YEARS PROD


(808685)

b = 2.0

Di = 23%

b = 1.94

Di = 31%

b = 1.6

Di = 29%

b = 1.4

Di = 34%




Production Type Curves

The type curve approach is ideal when we have:d

• Random per-well recovery, not related, in a predictablemanner, to geological or operating parameters.

• Observed frequently:Shale in general

Cordilleran tight gas trends, Wamsutter, Jonah, Pinedale,

Canadian Deep basin

Neuquen Basin, Argentina

Spraberry Field , Canyon Sand– W Texas

But why not use reservoir models?

Kuuskraa (2007)

Estimates of well drainage

can be developed from

type-curve matching of

early production data once

reservoir properties are

established

in low perm sands

Type curve matching determines drainage area




Steps to Generate Production ‘Type Curves’

1. Normalize rate time data to a common date.

2. Develop Type well curves for each distinct geological trend

with the same lithology.

3. Develop Type Curves which reflect your anticipated well

spacing.

4. Technology levers cause shifts in rate. Generate plots by

Time periods (30+ data before you subdivide), by Operator

and by Completion technology.

5. Determine the Correlation between the Initial and Average

30, 60 and 90 day Rate and the projected EUR for each

well.

Design of Production Type Curves


• Do not eliminate any wells unless it can be clearly demonstrated thatyou will never realize that outcome again. For example a failed newfrac fluid or early days when only 3 of 15 planned stages areexecuted.

• Extrapolate all wells using a best fit of the data. If in linear flow usethe 5 year rule for shale and 3 year rule for tight gas and tight oil

sands.

• Do NOT look for a typical P90 or P10 well and then use itsperformance to deliver the P90-P50-P10 Type curves. Wells aredynamic in their delivery. P10 wells become P90 wells etc as different

frac stages fluctuate in their delivery.

• Type curves should be based on well capability against planned backpressures. You will then need to account for operational downtimeas a separate line item. A good discipline in production optimization.

• Use monthly data. Using Excel statistics functions is good for largewell counts. Remember, Excel uses the data not the fitted curve.





Why Not Use The Nearest Offset?

SWN Energy July 2012 Investor Presentation

PetroHawk Investor Presentation May 2011

Honour All Wells in Developing Your Type Curves

- Extrapolate limited life wells and then normalize









spacing.






well.


Meek and Levine (2005)

TPA 1: mod

to low; low rank

coal area

TPA 2:

TPA 3:

TPA 4: mod

to high; meteoric

rechargeColorado

v. lowoily coal

v. high

TPA = Type Producing Area

New Mexico

Fruitland

Coal

Outcrop

Fruitland Coals

Type Curves for Each Sub-trend

10 miles




No flow boundary, as

coals begin to pinch out

and lose perm

Moderately

productive area w

abundant recharge

Structural

hingeline

Type Curves for Each Sub-trend

Lithology, setting and recharge impact production

Fruitland

Coal

Outcrop

10 miles

1,000

2,000

3,000

4,000

40 80 1200

0

M C F G / D

Months

TPA 3

n = 52

TPA4, n = 58

1, n = 65

2, n = 74

Peak water production

Fruitland Coals

Here the sweet spot of the trend is obvious, but

we will return for the need to compare geology to rate

Type Curves for Each Geologic Sub-trend

Meek and Levine (2005)









spacing.






well.


Slick-Water Fracs

Time in Days

100

1 0 0 10

100500 150 200

SPE 107435, Russell K. Hall

Fayetteville Shale

D

a i l y G a s P r o d u c t i o n ,

M M C F D

1

0.1

Nitrogen Enhanced Fracs

Technology Levers Cause Shift in Rates




Barnett StimulatedRock Volume for

Cross-linked Gel vs

Slick Water.

Increased SRV

validated by

doubling of the gas

production rates

Cipolla et al SPE 125532


Southwestern Energy August 2010 Investor Presentation





Southwestern Energy July 2011 Investor Presentation


Southwestern Energy July 2012 Investor Presentation










spacing.






well.


The term ‘Wolfberry’ was coined by Van Temple of Henry Resources

Shale Oil Exercise: WolfberryVariation in the Mean of the ERU based on Early Rate Data




Assignment: Your Management has made a few simple requests:

1. What is the your estimate of the 80% confidence range in the average well

EUR for the upcoming 40 wells given the 7 wells drilled to date and the

analog selected?

2. You have two new wells with 30 day production rates of 160 BOE/D and

300 BOE/D respectively. You are asked to provide a best technical

estimate of the EUR. Using only the initial 7 well data set provide a range

for the EUR of these new wells.

3. Your budget calls for 10 wells based on a P50 rate of 150 BOE/D or more.

How large of a drilling program is required to realize an 90% confidence

that the program will average 150 BOE/D (the minimum to meet our hurdlerates)?


SPEE (2011) Monograph 3

a n a l o g s

North American Unconventional Resource Plays P10/P90

of

Peak

Production

Month




Assignment: Your Management has made a few simple requests:

a) Determine your assumed P10 / P90 ratio when more data are available.

Hint: Let’s agree to use 4. As you will see this is a good start.

b) Plot the data in Table 1 using the Mid-Point Approach

c) Use your P10 / P90 from step (a) to determine a range of EUR outcomes

with increased sampling. For simplicity assume the Mean will be found at

the same percentile and determine the range in Means based on your revised P10 / P90 ratio.

1. What is the your estimate of the 80% confidence range in the average well

EUR for the upcoming 40 wells given the 7 wells drilled to date and the

analog selected?


EUR / Peak Rate: Rank them largest to smallest

Using the mid-point approach, build a Rate or EUR

Type Curve on linear and log vs probability paper:

1. Arrange all data by size, largest first and assign Rank

3. Tabulate data sizes with %tiles

4. Plot the data pairs

Percent ile = 100/n * (Rank – 0.5)

2. Determine the Percentile ValuesData %tile

1

2

3

4

etc

Rank

Largest

…

…

…

Smallest

100/n * (1 – 0.5)

100/n * (2 – 0.5)

100/n * (3 – 0.5)

100/n * (4 – 0.5)





TABLE 1Source: Drilling Info

Well #

Oil IP

(BO/D)

Gas IP

(MCF/D)

Oil Equiv

IP

(BOE/D)

Max

Month

Oil Rate

BO/D

Max

Month

Gas

Rate

MCF/D

Max

Month

Rate

BOE/D

Cum Oil

(BO)

Cum

Gas

(MCF)

Cum Oil

Equiv

(BOE)

EUR

(MBOE)

G2 80 108 98 86 110 104 11,820 13,258 14,030 92

H1 229 75 242 269 658 379 40,787 83,481 54,701 235

H2 186 114 205 202 298 252 41,486 71,468 53,397 152

H3 124 123 144 122 122 142 10,653 11,524 12,574 177

H4 210 273 256 115 223 152 63,752 167,800 91,719 309

H6 60 89 75 77 147 102 9,662 20,300 13,045 149

S1 64 56 73 145 165 173 43,336 60,681 53,450 137

Wolfberry Eastern Shelf Data




Rank Order the EUR & Determine the

309 1 7.1

235 2 21.4

177 3 35.7

152 4 50.0

149 5 64.3

137 6 78.6

92 7 92.9

EUR

MBOE Rank

(100/n) *

(Rank - 0.5)

Force fit the Data to Lognormal

with a P10/P90 ratio of 4

Using the P10/P90 ratio of 4 line,

build an envelope where:

The Left side boundary passes

through the point furthest away

from the best fit line.

The right side boundary passesthrough the data point furthest to

the right of the best fit line.

© Rose & Associates, LLP 19






P10 / P90 of various aggregateper well EUR distributions

P10 / P90

P m e a n ,

%

t i l e







0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 10 20 30 40 50 60 70

A d j u s t m e n t f r o

m M e a n t o P r o t f o l i o P 9 0

Log-N

Log-N

Log-N

Log-N

Log-N

Log-N

Aggregated Well Count

P e r c e n t a g e o f t h e M e a n V a l u e t o B o o k a s P r

o v e d

Trumpet Chart Approximation Method

For The Determination of The EUR

80% Confidence Interval

The P90 is approximately % of t

with a sample size of 7 wells and a

=

Assuming near symmetry from the

The P10 is approximately % of

a sample size of 7 wells and a P10=







Assignment: Your Management has made a few simple re

2. You have two new wells with 30 day production rates of

300 BOE/D respectively. You are asked to provide a be

estimate of the EUR. Using only the initial 7 well data s

for the EUR of these new wells.

STEPS:

a) Cross-plot initial production rate versus EUR

b) Determine which Percentile 160 BOE/D and 300 BOE/D

c) Read off the EUR at the same Percentile.

d) Based on the Correlation Coefficient determine the rang

estimate.

Shale Oil Exercise: WolfberryVariation in the Mean of the ERU based on Early Rate D







R² = 0.6622

0

50

100

150

200

250

300

0 100 200 300

IP vs EUR

EUR ‐ MBOE

I P ‐

B O E / D

30 Day Rate vs EUR

R =







Rank Order the Rate & Determine the

256 1 7.1

242 2 21.4

205 3 35.7

144 4 50.0

98 5 64.3

75 6 78.6

73 7 92.9

IP

BOE/D Rank

(100/n) *

(Rank - 0.5)

Force Fit to Lognormal with a P10/P90 =







Track Actuals vs. The Forecasted Aggregate Type CurveWhat Would You Recommend in This Scenario?

Actuals

• Information costs money.How can it add value?

• We can evaluate how this expenditure can addvalue with a decision tree

– One branch includes the expenditure

– One branch does not

• Information adds value if the expected value of the branch with the expenditure is greater than

the expected value of the branch that does not

Let’s look at an example

What is The Value of Information?




After Both Coins Have Been Tossed,for a Small Fee You Can PEEK atOne Coin. If It Is a HEAD, You PLAY the Game FOR $5.

If the first coin Is a TAIL, You Cannot Win,So You Avoid the $5 LOSS.

How Much Would You Be Willing to Pay for a Peek at the FirstCoin Before You Decide to Play?

How about $1

Two Coin FlipBoth Heads, You Win $25

Any Tails, You Win 0

Expected Value & VOI

$0.00



(0.25)($25 - $6) = +$4.75

(0.25)(-$6) = -$1.50

(0.25)(-$1) = -$0.25

WIN

(0.25)(-$1) = -$0.25Cost of

peek= $1

(0.25)($25-$5) = +$5.00

(0.25)(-$5) = -$1.25

WIN

(0.25)(-$5) = -$1.25

(0.25)(-$5) = -$1.25

HH

HT

TH

TT

HH

HT

TH

TT





$0.00

WIN

Cost of peek= $1

WINHH

HT

TH

TT

HH

HT

TH

TT



Solve

Value of peek:$2.75 – $1.25= $1.50

(0.25)($25 - $6) = +$4.75

(0.25)(-$6) = -$1.50

(0.25)(-$1) = -$0.25

(0.25)(-$1) = -$0.25

(0.25)($25-$5) = +$5.00

(0.25)(-$5) = -$1.25

(0.25)(-$5) = -$1.25

(0.25)(-$5) = -$1.25




Value of the Peek:

A) Increased EV of VentureB) Lowered Exposure on Half the OutcomesC) Increased odds of Final Investment From 1:4 to 1:2

Value of Peek relative to Prize?$1 / $19 = or about 6 Percent

Now, who wil l play this game???I will play until I loose my $25





Two Coin FlipPost Appraisal

What is the EV if you plannedto spend the $1 for the peek and $5for the second coin regardless of the firstcoin’s outcome?

EV = 0.25($25 -$6) + 0.75 (-$6) = 0.25

Without the ‘back-away’ option, this Is notan attractive alternative, relative to fl ippingboth coins

WORTHLESS


Two Coin FlipPost AppraisalSummary:

Prize: $25.00 - ($5.00+Peek)Pc = 0.25

Peek Cost % of Prize EV of Venture$1.00 6 $2.75

$2.50 14 $1.25 (same as EV w/o peek)

For This Venture, Your Spending Limit For New Data is 14% of the Value of the Prize





Prevalent Assumptions:

• Only 1 Well Site Considered• Seismic Data will identif y, with certainty if Closure is high or low• A successful wel l has a PV of $1.0 MM• A dry hole has a PV of - $(0.8) MM• Seismic costs $100 K

The New Seismic Data Will Not:-- Illustrate Other Leads-- Change the Size (and Hence Value) of the Prospect-- Modify the Reservoir Chance

Chance Factors:

Source = 1.00Timing = 1.00Reservoir = 0.80Trap/Closure = 0.75Seal/Containm ent = 1.00 _____________________________

Pg = 0.60

Value of Informationa Ex VOI - 1

Scenario 1

Scenario 2

ProposedSeismic Line

ProposedSeismic Line

Chance Factors:

Source = 1.00Timing = 1.00

Reservoir = 0.80Closure = 0.75

Containment = 1.00

Pg = 0.60

Only 1 Well Site ConsideredSeismic Data Will Identify, with Certainty if Closure is High or Low.

E d g e of 3 D

E d g e of 3 D

owc

owcTop of Structure

Value of Information Ex VOI - 1







Build tree in chronological order … with a place to

Drill (no seismic)

Shoot seismic

Value of Information












Pitfalls in The VOI Approa

• Failing to realize that new information wresolve some of your uncertainties.

• When dealing with imperfect informatioassessing values in the wrong order on

decision tree often yields biased results

• Allowing the new information to alter thrange.

• Using intuition to estimate the value of information.







Types of Informatio

• Perfect – Once you have the information, all d

removed

• Imperfect – Although the information has been

some questions, sometimes all of thquestions, still remain

– We will need to address this issue, have tools to do that







2nd Stage Pilot CoCD

With encouraging information from analysis of past wells in an area, ybelieves that Pc for developing this UCR trend is 0.60; i.e. Pc = 0.60

(Option 1, time to commercial declaration = 2 years)

Upon additional assessment, your team believes that:1. An ini tial pi lot (IP = 4 wells), if successful will increase the Pc = 0

(Option 2, delaying commercial declaration by 3 years)2. If the IP is successful, you could conduct a 2nd stage pilot (16 we

further increasing the Pc = 0.9.(Option 3, delaying commercial production by 4 years)

3. PV of commercial success = $200 MM (not including any pilot cos4. PV of commercial failure

1. Option 1 PV (f) = $ -150 MM2. Option 2 PV (f) = $ -100 MM3. Option 3 PV (f) = $ - 25 MM

5. PV (IP) = $ - 7 MM6. PV (2nd) = $ -19 MM if a failure7. PV (2nd) = $ - 5 MM if a success8. Each pilot stage will defer commercial dev by 1 year.

The PV(success) will decrease by $15 MM for each year of dela

Initial PilotIP 2SP

Exercise – UCR Pilot Evaluatio







P(CD) now = 0.60P(CD) given IP succeeds = PP(CD) given IP and 2nd stage

P(IP)

0.9

0.75

0.1

P(

P(

P(

0

0

P(

P(

proceed to CD (commercial dev)

initialpilot

proceed to commercial dev

proceedto CD

P(2SP)

P(2SP)~

P(IP)~

2nd Stage Pilot CoCDInitial PilotIP 2SP

Option 2 with Init Pilot

P(Ch wt value for Option1 = $60 MM

IP



















P(CD) now = 0.60P(CD) given IP succeeds = PP(CD) given IP and 2nd stage

0.80

0.9

0.75

0.1

CDIP 2SP

P(

P(

0.9

0.


initialpilot


proceedto CD

0.17

0.20

0.83


Determine value at endnodes to determine mostvaluable option

200 (CD) - 7 (IP) - 5(2SP) - 30 (2 Y

- 7 (IP) - 5(2SP) - 25 (

- 7 (IP) - 19 (2

0.

0.

200 (CD) - 7 (IP) - 15 (1 Y

- 7 (IP) - 100 (







0.80

0.75

CDIP 2SP

P(

P(


initialpilot


proceedto CD

0.17

0.20

0.83


Observations:Prob at each CD = 0.60

0.

0.

0.

0.

Option 1: $60.0 MM

Option 2: $85.4 MM

Option 3: $87.5 MM







developexplore demonstrate

proceed

to CD

delineate

P10

P90

P50

Fail, exit

Fail, exit

proceed directly to Commercial Dev

Regardless of which stage the project is in, Economics are to be run on a point forward basis.

Assume 40 ac spacing

over 10,000 ac

Cum well count = 293

@ $4MM / well > $1B Let’s recap: where is the portrayal of risk?

Fail, exit

e.g.

Drill 3 wells

check

min suiteand rates

e.g. comm demo

Drill 20 + wells

Uniformity/comm

Optimize frac

e.g.Drill 7 wells

Proof of concept


proceedto CD

delineate

P10

P90

P50




over 10,000 ac

Let’s recap: where is the chance?

Fail, exit

Fail, exit

Fail, exit





proceed

to CD

delineate

P10

P90

P50




over 10,000 ac

Let’s recap: where is the uncertainty?

Fail, exit

Fail, exit

Fail, exit

Let’s recap: uncertainty in the type curve

months

RateFrom Modified Arps

Arps Eq (hyperbolic)

Modified Arps

Stretched Exponential

Power Law Loss

Duong Equation

Russell et al hybrid 5 yr

Transient Hyperbolic Exp

Methods described




Let’s recap: portrayal of avg production

and costs

Play resources

from drilling programNote the symmetry that

comes from

addition

EUR / wellfrom type curve

GIP per wellNote the asymmetry

that comes from

mult.

Let’s recap: Resources involved

EUR / wellfrom analog




Pg = 100%

Pe = 52%

PV

$296 M

Let’s recap: Distribution vs Decision Tree

Conclusions (1- 7 of 13)

1) Charging creates the pressure anomalies

2) When sample size is limited, rely on first principles

for distribution (population) shape and analogs for

population variability.

3) Reservoirs (except CBM) tend to be low perm.

4) Porosity cut-off considerations lowered with

improved completion techniques

5) In organic rich, thermally mature shales, different

mineral suites can become productive, as long as

clay content is minimal

6) Consider compositing multiple criteria to spatially

high-grade segments

7) Different segments (different geologic ingredients)

likely deserve different type curves.




8) Consider completion techniques and spacing when

forecasting uncertainty in type curves.9) Type curves are critical for valuation, link play

chance assessments to minimal IP rates

modeled

10) A high play chance can lead to a very low Pe for a

drilling program; integrate engineering work with

geoscience early

11) Staged investments require staged plans.

Assessments should separate geologic chance

from commercial risk

12) From the reference decision point, the product of

all success case probabilities must be the same

for all options that reach that success state.

13) Confidence (chance) of achieving is related to

sample size

Conclusions (8-13 of 13)

Risk, Uncertainty & Economic Analysis

for Resource Assessment and ProductionForecasting in Shale and Tight Reservoirs

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07 - Valuation Techniques

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