paper geospatial

8/10/2019 Paper Geospatial

1/13

*Previously presented at the IPA Annual Convention, Jakarta 2010

SPE Paper Number SPE-133518-PP

UNCERTAINTY MANAGEMENT: A STRUCTURED APPROACH TOWARDS

RECOGNIZING, QUANTIFYING AND MANAGING SAMPLING BIASES INSUBSURFACE UNKNOWNS*

Laurent Alessio, Leap Energy Partners Sdn Bhd, Arnout Everts, Leap Energy Partners Sdn Bhd, and FaeezRahmat, Leap Energy Partners Sdn Bhd

Copyright 2010, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Asia Pacific Oil & Gas Conference and Exhibition held in Brisbane, Queensland, Australia, 1820 October 2010.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to

reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

ABSTRACT

This paper illustrates, through field studies examples, why

and how a structured approach towards managing

uncertainties, and especially sampling biases, deliversvaluable insights through the successive early asset life

stages - exploration, appraisal and field development

phases. In doing so, we respond to three fundamental

questions.

Firstly, What are the key uncertainties those that

matter? Field studies should begin with a comprehensiveupfront assessment of uncertainties impact on historical

and future well and field performance. However, often

major factors are overlooked, leading to under-prediction

of true outcome ranges and the inability to reconcile

historical production. Our illustration is a large producing

carbonate field, where after 15 years of production, large

scale Karstification was finally evidenced to be the

explanation for the field performance that couldnt be

history matched with the measured matrix porosity and

permeability ranges.

Secondly What are realistic ranges for these

uncertainties? Known Industry best practices include

intensive expert-assist, integration of drilling, mud-loggingand other traditional sources of data from the field,

resorting to analogue benchmarking. Despite these, we

often fail to understand and correct for sampling bias,

which we show often leads to over-optimism. The paper

will highlight why such biases are present and propose

simple and practical methods to remove them. The case

study is the volumetric assessment of a gas discoveries

portfolio, where geophysical techniques were instrumental

in exploration and appraisal drilling.

Finally How these uncertainties will evolve with time?

This is an important question for assessing value of

Information: the impact that additional data may have on

the uncertainty range of uncertainties and the base case.

Unconventional fractured plays, often characterized by

data abundance but extreme variability, provide surprising

insights on how uncertainties ranges evolve. This paper

presents methods to develop confidence curves for

important parameters.

INTRODUCTION

This paper illustrates, through field studies examples, why

and how a structured approach towards managing

sampling biases in reservoir evaluation delivers valuable

insights through the successive early asset life stages -

exploration, appraisal and field development phases.

Whilst the purpose of the paper is not to provide a

comprehensive review of uncertainty management best

practices, a workflow and fundamental steps are discussed

herein, to provide some contextual framework. We then

focus our illustration around identification of key

uncertainties, defining realistic ranges for these, andfinally assessing how ranges should evolve with time.

The first step through the Uncertainty Assessment

workflow is Identification. Were essentially responding to

the question What are the key uncertainties those that

matter. Most subsurface professionals would agree on the

need for a comprehensive assessment of uncertainties

conducted upfront, and developing an understanding of

their impact on historical and future well and field


2/13

2 SPE-133518-PP

performance. However, often major factors are

overlooked, leading to under-prediction of true outcome

ranges and when applicable, the inability to reconcile

historical production. A field case of a very large

producing carbonate field, where after over 15 years of

production history, the main uncertainty impacting field

performance was found to an intense Karstification; a

factor that had been essentially overlooked until, as part of

a major field review, a comprehensive reservoir modellinghistory match-ing exercise highlighted the impossibility to

obtain a match with the measured carbonate matrix

porosity and permeability ranges.

The second step in the workflow is Assess Ranges: thisequates to asking the following question what are realistic

ranges for these uncertainties? This is a very typical issue

for green field developments. Known and well

documented Industry best practices include intensive

expert-assist, integration of drilling, mud-logging, and

other traditional sources of data from the field, resorting to

analogue benchmarking. What remains generally an issue

is our ability to understand and correct for sampling bias

unfortunately at the early stage of the asset life, bias oftenleads to over-optimism. The paper will highlight why such

biases are present and propose simple and practical

methods to remove them. The illustrating case is a

portfolio of clastics gas discoveries. Geophysical

techniques are often instrumental in exploration and

appraisal drilling, and as a consequence, assessing

sampling bias and correlations are a very important step in

the volumetric assessment.

The third and final question is how some of these

uncertainties will evolve with time. This is an important

question to answer for an adequate assessment of Value of

Information (VoI) but also to understand how much

impact should additional data have onto the range ofuncertainties, and of course, the base case. Fractured

resource plays, with their abundance of data but extreme

variability, provide surprising insights on how

uncertainties ranges evolve. This paper will present a

practical method to develop confidence curves for

important parameters.

UNCERTAINTY MANAGEMENT BEST

PRACTICES AND CONTEXT

Because of the inherent difficulty in understanding what

cannot be clearly seen and measured the subsurface, it is

recognized widely that managing uncertainties is critical to

E&P ventures, and therefore a very importantresponsibility of the Subsurface and Front End teams. It is

by nature an inter-disciplinary capability that operators

must develop and apply across their assets.

As a consequence, fairly well established practices do

exist, and have been published in the past (Alessio et. al.,

2005); (Charles et. al., 2001); (Corre et. al., 2000), so it is

not the objective of this paper to provide a thorough

account of the best practices of uncertainty management,

but rather to focus on the particular aspect of sampling

bias and its impact on the uncertainty management

workflows.

Uncertainty management can be broken up into two main

phases: Assessment and Mitigation. Each of these can be

articulated around a number of steps: an account of those

is proposed in Figure 1. Sampling bias problems do occur

mostly in the Assessment phase, and so this is the part thatwe will be focusing in this paper.

IDENTIFICATION OF UNCERTAINTIES

Ensuring all critical information and data is consideredLets introduce the first problem: why despite elaborate

and rigorous workflows, using probabilistic and

geostatistical techniques (Charles et. al., 2001); (Corre et.

al., 2000), it still sometimes happens that field

performance expectations fall outside the P90/P10 range.

The first example provides an interesting case whereby a

producing field (which we will call Field X through this

paper) consistently out-performed expectations, and

couldnt initially be history matched conventionally,despite the availability of a fairly extensive core dataset,

and post-drilling transient testing data on the early

production wells. Field X is a large, multi-Tscf, carbonate

gas field, located in a prolific carbonate province, in Asia.

Field Xs production started in 1987 from a total of 11

deviated wells placed in the central part of the field, drilled

on a dataset of multi-vintage, good quality 2D seismic.

Little was known about the detailed reservoir architecture

away from well penetrations. Following 15 years of

production and half of the expected reserves produced, a

3D survey was acquired in mid 2002 to support an infill

drilling campaign and a potential field re-development. At

the same time, the field review initiative started and whilstseismic processing and inversion was carried out and

iterated, a first pass material balance and static-dynamic

modelling exercise was initiated.

These early static-dynamic modelling iterations rapidly led

to the conclusions that a combination of enhanced

permeabilities in the lower producing intervals and

possibly higher volumes were required to match (and slow

down) the combination of rise of contact and pressure data

in the field. This was in part consistent with the fact that

horizontal permeabilities derived from core data were

consistently lower than the well-test derived ones. In

addition, it was found that lower gas residual saturations in

these zones also improved the quality of the history match,and so could greater gas volumes in that zone. This

indicated the possible role of a non-matrix element to

flow, either fractures or Karsts. In the earlier dynamic

models (pre-2002), permeability multipliers were applied

to layers to match the well test results, but neither the

mechanism nor the spatial distribution of the property

enhancements were properly understood.


3/13

SPE-133518-PP 3

As these observations were consistently reported from the

reservoir engineer back into the subsurface team, a new

hypothesis emerged: presence of an extensive Karsts

network in the lower part of the reservoir could explain the

required enhancement of properties of this zone

(permeability, storability and residual gas). A close

examination of the drilling history, back in the late 80s,

confirmed that nearly 80% of the wells suffered some

losses in this interval, and about 50% experienced verysevere losses. Following this lead, seismic multi-attribute

extractions revealed an extensive dendritic Karsts network

(Bourdon et. al., 2004); (L. Bourdon, 2004) covering the

vast majority of the Lower reservoir. Because of their

shear size and density, this imaged Karsts system couldfinally explain the matrix property enhancement, in terms

of volumes, effective permeability, and petrophysical

property alterations.

The process of introducing a new facies (Karsts) provided

the team with a defendable, plausible, explanation for the

performance of the field, without reverting to arbitrary

transforms of the reservoir properties.

It is here interesting to acknowledge the sampling bias

issue with this case study: despite very early significant

observations that non-matrix properties had to be

responsible for the massive and consistent drilling induced

losses, this fact was not eventually carried through, as

knowledge, into the later phases of reservoir management.

Up until it was recognised that the field performance

couldnt be reconciled using the sampled ranges of

petrophysical parameters (porosity, permeability, residual

gas saturation), the uncertainty assessment work

essentially ignored a fundamental parameter. This is an

extreme case of sampling bias: the omiting of a critical

parameter!The lessons learned from this case study are:

Ensure all possible sources of information are

considered in the first step of the Uncertainty

Assessment stage (Figure 1).

Field reviews must be a fully multi-disciplinary

exercise

Ensure a learning system is in place within the

organisation to ensure critical information is retained

DEFINING REALISTIC RANGES FOR

UNCERTAINTIES

What are realistic ranges for uncertainties?In this part, the technical contribution of this paper is to

provide some practical insights, through another case

study, towards sampling bias presence in volumetric

assessment.

This case study depicts a fairly common situation where

exploration is conducted using seismic attribute high-

grading techniques, such as AVO, inversion etc. Direct

hydrocarbon indicators (DHI) have become a very popular

de-risking exploration application that has helped increase

dramatically the (Pg) probability of geological success

(Roden et. al.).

An indirect consequence of this improvement ofgeological success is the introduction of a sampling bias,

within the fields that are being discovered. Not

dissimilarly to the basin creaming curve effect well known

to explorationists, guided exploration and appraisal

drilling has a tendency to produce a skew in thepetrophysical and geological sums and averages, for a

combination of the following reasons:

Early exploration wells are drilled on amplitude

highs which are hoped to and often do hold higher net

hydrocarbon volumes

Early exploration wells are drilled on structural highs,

to maximise the chance of encountering a charged

hydrocarbon column, hence encountering non-representative elevated saturations

Delineation wells may be drilled down-dip to test

minimum economic columns, and therefore may find

low saturations

None of these remarks should come at a surprise to the

seasoned subsurface professionals. Accounting for such

biases is however not always straight-forward, will

involve elaborate data analysis and integration and may

actually emphasise remaining uncertainty in the field.

Case study: portfolio of gas discoveries, drilled through

DHI (Direct Hydrocarbon Indicators)

At an early appraisal stage, we are often confronted to a

dataset of wells that were predominantly targeted at

amplitude sweet spots. Removal of sampling bias will

typically start with obtaining statistics of the area covered

by sweet spots versus the total field area. This would

then be combined with either geologically and/or

geophysically driven estimates of the expected reduction

in net pay and/or reservoir properties in the seismically

dimmer areas compared to the sweet spots.

To illustrate the issue of dealing with a biased well datasetconsider the case study of Field Z, consisting of fluvial

and marginal marine sandstones in a three-way dip closure

with a bounding fault and possibly a stratigraphic trappingcomponent. An amplitude map of the main reservoir level

in Field Z is shown in Figure 3. Two wells were drilled to

appraise the structure and from the amplitude map, it is

obvious that both wells were specifically targeted at

reservoir sweet spots. The problem presented to the

asset team was to arrive at a realistic range in net pay for

the field despite the obvious bias in the well data. The

workflow followed by the team on this particular example


4/13

4 SPE-133518-PP

is one of the many possible methodologies. First,

geophysical analysis and seismic modelling studies

established that for the main reservoir in Field Z, the

thickness cut-off for seismically visible pay is around

3.5 to 5.5 m (about 1/8th

of the seismic wavelength) whilst

the maximum constructive interference (i.e., brightest

amplitudes) are expected for a pay thickness of around 7

to 11 meter (around of the seismic wavelength). This

information was then used to consistency check andcomplement the well data in establishing the relationship

between pay and seismic amplitude (Figure 4). Histograms

of amplitude distribution in the field were then used to

determine area weighed average amplitude for the

amplitude and non-amplitude supported domains in thefield, as well as ranges of pay expected in these two

domains. As expected, the range in pay for the amplitude

supported area of the field as estimated with this method

(Figure 4) is substantially less than the average of the two

wells.

Sampling bias and 3D geostatistical modelling

workflow

The issue of sampling bias is again at play when it comes

to more sophisticated resource assessment techniques

involving 3D reservoir modelling. Reason being,

commonly used techniques to stochastically simulate

reservoir and/or property distribution in 2D or 3D domain

such as Gaussian simulation, are designed to replicate the

statistics of the input data. If the input data consists of a

biased set of wells like in the example of Field Z, the risk

is this bias will be extrapolated to field scale. Whilst it is

true that modern mapping and 3D modelling tools do

provide ample mitigation options against this risk such as

use of areal trends, such sophistication is not always

applied especially not in fast track assessments (which,

not surprisingly, tend to lead to over optimism).

Moreover, without considering the possibility of the actual

statistics of pay and/or property distribution in the field

being different from what is seen in the wells, repeated

stochastic simulation in nested workflows - a popular

technique in modern field assessment - will simply

reproduce the well data - albeit with different areal

distribution - resulting in unrealistically narrow

uncertainty ranges for the field. In other words, to cover

the full range of outcomes for a field, it is important to

consider the possibility of a bias in the well data especially

if the data is scarce.

EVOLUTION OF UNCERTAINTY RANGES AS AFUNCTION OF AVAILABLE DATA

A quantitative approach using Confidence Curves

Objective and problemIn this part, we are focusing specifically on highly

heterogeneous systems, such as highly fractured

carbonates, chalks, or unconventional reservoirs such as

tight sands, shales and coalbed methane. Were trying to

establish a systematic method to quantify, as a function of

the amount of data available, the uncertainty in a field

average metric, such as an average permeability, or peak

rate per well.

Variability and uncertainties

With highly heterogeneous systems, where large

differences are found from one observation (ex: agiven well) to another observation (a neighbouring well),

it is important to recognise the distinction between

variability and uncertainty, as these are two often confused

for one another, and thereby leading to significant

misrepresentations of field uncertainty ranges.

Variability is defined as a short to medium scale (up

to inter-well scale) variations of a given parameter,

such as permeability, porosity, gas content (for CBM

reservoirs), hydrocarbon saturation etc. These

variations can be often extreme, with several orders of

magnitude differences in permeability commonly

observed in fractured reservoirs. Variability is

intrinsic and non-temporal, which means it that doesneither change with time nor with the number of data

points, and it is a characteristic of the reservoir (for a

given sampling scale*). Ultimate understanding of

variability often remains spatially poorly predictive,

so the authors recommend a statistical approach is

always conducted in parallel.

Uncertainty is defined at the field scale, or at least, a

sector or segment of the field (field unit), where

multiple wells will be ultimately drilled. It represents,

at a given time, how well a field unit is understood.

Generally, uncertainty reduces with time and

information becoming available, provided the right

framing and uncertainty assessment was conducted(ref previous section). Arguably, the uncertainty in

subsurface givens, such as field porosity average, or

in place volumes is strictly a consequence of our lack

of knowledge. Development related metrics, such as

field recoverable volumes or production performance,

at a given time, are a consequence of our level (or

lack of) of understanding of the subsurface and the

concept development choices we have made and will

be making.

*Note: variability is indeed intimately linked to sampling

scale; for the purpose of this paper, we are assuming that

all measures are taken at the same scale (ex: vertical wells

through a reservoir section), and we will not discuss thispoint further.

A statistical representation of variability

Variability of a particular parameter can always be

represented by a PDF (Probability Density Function). In

our approach, we are using lognormal curves as those

describe well a number of naturally occurring phenomena

and parameters in the subsurface, such as permeability of a


5/13


6/13

6 SPE-133518-PP

The uncertainty decline rapidly with a few early

wells, since the process of drilling these wells

reduces swiftly the chances of sampling

consistently outliers in the same part of the curve

(either Hi or Lo). For the curves presented in this

example, this occurs in the first 5% of the drilling.

It may be possible to more rigorously generalise

this result, for various parameter variability input

PDFs.

The important findings at this stage are that, for highly

variable resource plays, where intensive drilling does

occur:

1. Assuming known the variability of an important

parameter (ex: well permeability), it is possible to

predict conceptually the uncertainty bands of a field

average vs. the amount of data and knowledge

available.

2. With highly variable plays, early information from

a few wells (


7/13

SPE-133518-PP 7

CONCLUSIONS

We have presented, through examples, how critical are the

Uncertainty Identification and Range Assessment phases

in the Uncertainty Management Workflow (UMW), and

provided a number of tools and approaches to improve the

recognition, assessment and management of subsurface

unknowns.

Firstly, we have shown how key subsurface features may

be omitted if not all data and information sources are

considered; the necessity of a multi-disciplinary approach

is highly recommended, in order to reduce this risk.

Secondly, we are providing clear examples of howsampling bias creeps into the subsurface assessment work,

and provided practical illustration on how this

phenomenon can be accounted for and removed. Thirdly

and finally, we have proposed a method to quantify

uncertainty based on an understanding of variability vs.

available date, using Confidence Curves.

The methodologies and practical solutions to the problem

of sampling bias in quantifying uncertainty ranges forsubsurface assets have been illustrated through case

studies inspired from actual field reviews, field

development planning projects and other subsurface

assessments; note that for the purpose of this paper, all

confidential information has been duly removed by the

authors, data, maps, well results have all been suitably

altered so that no sensitive information is made public.


8/13

8 SPE-133518-PP

ACKNOWLEDGMENTS

Special thanks to Peter Friedinger and Artur Ryba for

providing valuable insights and support for the production

of this paper.

Special thanks to Indonesian Petroleum Association (IPA)

for granting permission to publish this paper.

REFERENCES

L.Alessio, S. Coca, L.Bourdon, 2005, Experimental

Design as a Framework for Multiple Realisation History

Matching: F6 Further Development Studies. SPE 93164presented at the SPE Asia Pacific Oil and Gas Conference

and Exhibition held in Jakarta, Indonesia, 5 7 April

2005.

L.Alessio, S. Coca, L.Bourdon, 2004, "3D-All-The-Way"

In F6 Field Further Development. SPE 87014 presented at

the SPE Asia Pacific Conference on Integrated Modelling

for Asset Management held in Kuala Lumpur, Malaysia,

29-30 March 2004.

L. Bourdon, L. Alessio, S. Coca, 2004, Karsts

Identification and Impact on Development Plan. SPE

88520, presented at the SPE Asia Pacific Oil and Gas

Conference and Exhibition held in Perth, Australia, 1820

October 2004.

L. Bourdon, 2004, Unravelling the reservoir architecture

from 3D seismic using multi-attribute Volume

interpretation: Central Luconia Karsts Modelling.

RGC2004, internal Shell event.

Bratvold, R., Begg, S.H., Campbell, J.C., 2002, Would

you know a good decision if you saw one?", SPE 77509.

Cheong, Y.P and R. Gupta, 2004, Experimental Design

and Analysis Methods in Multiple Deterministic

Modelling for Quantifying Hydrocarbon In-Place

Probability Distribution Curve, SPE 87002, presented at

the SPE Asia Pacific Conference on Integrated Modelling

for Asset Management held in Kuala Lumpur, Malaysia,

29-30 March 2004.

Cheong Y.P, R. Gupta, 2003, Experimental Design in

Deterministic Modelling: Assessing Significant

Uncertainties. SPE 80537.

Robert G. Loucks, 1999, Paleocave Carbonate Reservoirs:

Origins, Burial-Depth Modifications, Spatial Complexity,

and Reservoir Implications. AAPG Bulletin, V. 83, No.

11, P. 1795-1834.

Cheong Y.P, R. Gupta, Smith G. et al, Experimental

Design Methodology for Quantifying UR Distribution

Curve - Lessons learnt and still to be learnt, SPE 88585

White C, Royer S., 2003, Experimental Design as a

Framework for Reservoir Studies. SPE 79676.

Charles T., Guemene J.M., Corre B., Vincent G., Dubrule

O., 2001, Experience with the Quantification ofSubsurface Uncertainties paper, SPE 68703.

Corre B., Thore P, V.de Feraudy, Vincent G., 2000,

Integrated Uncertainty assessment for project evaluation

and risk analysis. SPE 65205.

Van Elk J.F, Guerrera L., Vijayan K and Gupta R., 2000,

Improved Uncertainty management in field development

studies through the application of the experimental designmethod to the multi-realisation approach. SPE 64462.

Charles T, Guemene J.M, Corre B, Vincent G, Dubrule O.,

2001, Experience with the quantification of subsurface

uncertainties. SPE 68703.

M. Feraille, F. Roggero,E. Manceau, L.Y. Hu, I. Zabalza-

Mezghani, L. Costa Reis, Application of Advanced

History Matching Techniques to an Integrated Field Case

Study. SPE 84463

Eide, L. Holden, E. Reiso, S. Aanonsen, 1994, Automatic

History Matching by use of Response Surfaces and

Experimental design, ECMOR 7-10 June 1994

T. Egeland, E. Hatlebakk, L. Holden, E.A Larsen,

Designing Better Decisions, 1992, SPE 24275.

Saxena Umesh, Vjekoslav Panelic, Factorial Designs as an

Effective Tool in Mining and Petroleum

Engineering,1971, SPE 3333.

Sawyer et al, Factorial Design of Wet combustion drive,

1974, SPE 4140

R. Roden, M. Forrest, Roger Holeywell. DOI- 19983, DHI

Threshold Effect in Prospect Risking


9/13

SPE-133518-PP 9

Figure 1: Uncertainty Management Worflow (UMW) : Uncertainty Assessment and Mitigation workflows

Figure 2 : Addition of Karstification as a significant parameter allows a match to be obtained

Identify

Uncertainties

Quantify

ranges

Assess

impact Rank

Select

representative

uncertainties

Construct

models

Test

concept

scenarios

Develop

mitigation

plans

Uncertainty assessment workflow

Uncertainty mitigation workflow

UncertaintyManage

ment

Workflow(UMW

)


10/13

10 SPE-133518-PP

Figure 3 : Amplitude map of field Z. The two appraisal wells drilled to date both used the seismic to target reservoir sweet spots.The result is a clear example of a biased well dataset. Map and well locations have been altered from actual case study to ensur

Well 2

Well 1

Amplitude map Field ZMap has been altered from actual case


11/13

SPE-133518-PP 11

Figure 4 : Histogram of amplitude values in field Z derived from the map shown in Figure 3 Indicated are the pay seen in the wells,

the estimated pay cutoff for seismically visible pay and the optimum tuning thickness range. All of these were used by the asset

Figure 5 : Parameter Uncertainty Curves: plotted below is the relative parameter value vs. the sample size (ranging from 1 to 100)

Relatively bright

= Amplitude supported

Relatively dim

= Non-Amplitude supported

Well-2(12.8 m pay)

Amp Range

Well-1 (6 m pay)

Amp Range

Area weighed average ofamplitude supported domain

Amplitude value = 2.1

4.9 7.7 m pay (P90-P10)

Limit of visible pay= 1/8 seismicwavelength= 3.5 5.5 m pay

Lower amplitude areaLower pay 1-5 m range (P90-P10)

Maximumconstructiveinterference= 1/4 seismicwavelength= 7 11 m pay

Bright Very Bright(Bright est 5%)

Cumulative%

100

0

0.0

0.1

1.0

10.0

0 10 20 30 40 50 60 70 80 90 100

CALCULATION OF AVERAGES

No Samples 50

No Samples 1

No Samples 2

No Samples 4

No Samples 6

No Samples 8

No Samples 10

No Samples 15

No Samples 20

No Samples 25

No Samples 30

No Samples 35

No Samples 40

No Samples 45

No samples 100

Parameter Uncertainty CurvesRelative parameter value vs. Sample size (1 to 100)

Envelop of maximum deviation to the

final mean (for 100 wells)

Mean for the total population

(100wells), Normalisedto 1


12/13

12 SPE-133518-PP

Figure 6 : Possible trajectory of averages vs. Parameter Uncertainty Curves: showing in red a possible, although not very likely,trajectory of population well averages

Figure 7 : Variability PDF curve for well parameter (permeability, mD): this is a possible illustration only of a well variability,

which was used for the computation of the Uncertainty and Confidence curves

0.0

0.1

1.0

10.0

0 10 20 30 40 50 60 70 80 90 100

CALCULATION OF AVERAGES

No Samples 50

No Samples 1

No Samples 2

No Samples 4

No Samples 6

No Samples 8

No Samples 10

No Samples 15

No Samples 20

No Samples 25

No Samples 30

No Samples 35

No Samples 40

No Samples 45

No samples 100

Parameter Uncertainty CurvesRelative parameter value vs. Sample size (1 to 100)

A possible trajectory of computed

averages from drilled wellsThis example assumes that (Hi) outliers are drilledearly, and later wel ls are sampled in the low end of

the variability curve

(Final) Mean for the total population

(100wells), Normalised to 1

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.00 10.00 100.00 1000.00

CumProbability

Well parameter - permeability (mD)

illustrative well parameter PDF

well permeability distribution curve (generic and non-specific

case)

Example PDF well K (mD)This example assumes a P10/P90range of 10 fold, which is not

uncommon in fractured resource playsThis is theVARIABILITY curve


13/13

SPE-133518-PP 13

Figure 8 : Confidence Curves: charting confidence folds (as a % certainty) vs. % data available

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60%

%

ConfidenceinFieldM

ean

% Data available

Plot 1: Evolution of Confidence Curves (varying folds) vs. % data available

1.10

1.25

2.00

3.00

5.00

7.00

9.00

10.00

88% confidence in a f old of 2.00

At 10% data available (% well drilled)

40% confidence in a f old of 1,25

At 10% data available (% well drilled)

paper geospatial

Documents