*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 IN SUBSURFACE UNKNOWNS*

Laurent Alessio, Leap Energy Partners Sdn Bhd, Arnout Everts, Leap Energy Partners Sdn Bhd, and Faeez Rahmat, 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, 18–20 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 been reviewed 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, its officers, 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, delivers valuable 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 comprehensive upfront 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 couldn’t 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-logging and 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, and finally assessing how ranges should evolve with time.

The first step through the Uncertainty Assessment workflow is Identification. We’re 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

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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 modelling history 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’: this equates 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 often leads 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 of uncertainties, 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 important responsibility 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 that we will be focusing in this paper.

IDENTIFICATION OF UNCERTAINTIES

Ensuring all critical information and data is considered Let’s 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 couldn’t 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 X’s 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 whilst seismic 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.

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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 80’s, confirmed that nearly 80% of the wells suffered some losses in this interval, and about 50% experienced very severe 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 could finally 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 couldn’t 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 of geological 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 the petrophysical 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 dataset consider 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 trapping component. 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

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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 ¼ of the seismic wavelength). This information was then used to consistency check and complement 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 the field, 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 A FUNCTION 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. We’re 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: a given 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 does neither 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 this point 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

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fractured system. However, the approach can be used for any statistical distribution, as we’re using a discretisation of the curves to conduct our analysis. The Figure 7 shows an example distribution (this is an illustration only and not associated with a specific field or asset)

Developing the concept of confidence curves from a practical observationThe idea of Confidence Curves emerged from a practical observation of a resource play, where the variability of production metrics such as peak production rates (gas, water) was assessed. Because of the very large variability of key subsurface parameters such as permeability usually present in fractured resource plays, estimating field or area performance with the knowledge of only a few wells’ actual performance can be highly misguided, and lead to erroneous conclusions on the attractiveness of an acreage.

In essence, this large variability, where peak rates or permeability can vary well over a log cycle or more, creates an intrinsic sampling bias when only a few samples (wells) are available. This sampling bias must be recognised, understood, and accounted for in the assessment of expected field averages.

The problem at hand is as follows: having drilled a number ‘p’ of wells in an area where it is planned to drill a total number ‘n’ of wells, and having established key subsurface parameters for each of these wells, what level of confidence can we have in the averages computed from these wells to be representative of the final ‘n’ wells average.

In trying to answer this question, the subsurface team selected as an observation set a large enough area, that could be considered fully drilled and developed by some 100 wells. Using some assumptions, productivity of each well was calculated, and converted to an average well permeability. It was therefore possible to create a distribution of average well permeability over this area. The workflow presented in this section was devised on a real field case, but for the purpose of this paper, an illustrative case with generic and non-case specific numbers are used. The methodology is re-constructed around this illustrative case. The parameter input PDF (well permeability) that are used in the following sections is shown on Figure 7 – note this is illustrative variability distribution curve was selected to have a variance that is not uncommon of permeability in fractured reservoir plays (P10/P90 > 10)

Now, assuming the size of the area is significant enough, i.e. 100 wells are a sufficiently large dataset, this distribution can be taken as representative of the variability of the field. This assumption only holds provided that this area is itself representative of the rest of the field, and we are not again suffering from a sampling bias, at a larger scale! Next, the following mathematical operations were applied

For a range of p values (p number of wells), within the universe of n=100 values:

Compute a statistically significant number of average values resulting from combinations of p samples within n=100. Note that it is not easy to compute all the possible ones: C100

10 ~ 1.7e13, so a practical approach is called for. In our case, to keep within spreadsheet limitations, a maximum of 30,000 simulations was used.

Plot the averages of ‘p’ wells combinations against the number of wells drilled ‘p’. The X-axis can also be normalised to a normalised area by using ‘p/n’. This plot will be called ’Parameter Uncertainty Curves’

An example plot of the resulting Parameter Uncertainty curve is shown on Figure 5 Such curves can be read as follows; note that as a parameter we are going to use ‘productivity’: In a given area, where eventually a number ‘n’

(100 for our example) of wells may be drilled, we are looking at the possible values of averages of ‘p’ wells, chosen randomly.

We are essentially simulating the possible outcomes of sampling randomly this resource play and observing the range of hypothetical trajectories of a computed average (Mean).

These curves provide a visual and quantitative assessment of the possible trajectories of how averages of populations of wells could evolve with the number of wells drilled. The example shown on Figure 6, shows how a reservoir engineer reviewing the results of early wells and computing a average well curve (or type well curve), could initially post a very high average, his assessment falling victim of having sampled a few ‘high’ outliers. Then, with more drilling, the variability PDF curve is sampled, and for the sake of this example, lets assume now that the ‘low’ end of the PDF is sampled predominantly. In this case, the red trace would show the assessment of a representative ‘Mean’ based on the population of wells available at give times.

This example is evidently selected to illustrate the point that under large variability, as it is common with fractured plays, there is a real possibility for extreme sampling biases to occur and cloud a ‘type’ curve assessment. This has a particularly important implication for appraisal of highly variable resource play: If the play is expected to be very variable, then the

uncertainty at an early drilling phase is very significant. In the example presented, the true uncertainty when less than 5% of drilling has occurred is ca. 3 fold. That means the final field average may be within a factor 3 of the current computed average (CCA).

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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 (<5% drilling of the play), can be very misleading. Realistic uncertainty bands may be up to within a 3-5 fold range of the mean of wells drilled to date.

3. The uncertainty band decreased rapidly with the first 10% of the wells and hit a pleateau with 20% of the wells drilled (Figure 6). This suggests the possible optimum early drilling well count of up to20% of the total wells drilled in a target area as increased well count wil not significantly reduce the uncertainty.

Introducing the concept of Confidence Curves We are introducing here a particularly effective manner to construct quantitatively, versus available data or time, a representative range for field-wide uncertainty metrics such as P90, P10. We’re also able to answer more generally the following question: For a given level of confidence (for instance 85%),

what is the level of uncertainty in the final field average parameter (for instance permeability), measured as a fold or multiplier of the current measured average from the available data?

As a function of the available data collected to date. In our approach, we are using as a measure the percentage (%) of data available. For resource plays, a percentage (%) of wells drilled can be used, if one wants to assess the uncertainty in field overall well rates or average field permeability.

Given our understanding of the variability: importantly, a model of the statistics of the variability needs to be known, or assumed. This can be achieved either through a direct measure, or by analogy.

The resulting assessment can be plotted as shown on Figure 7 where the confidence curves, expressed as a fold

of the current Mean can be represented vs. the percentage of data available.

Applications of the confidence curves methodologyConfidence curves were initially devised for resource plays, where large variability is present and uncertainty is known to remain high after appraisal and only progressively reduce through the development phase. They provide a structured way to conduct three main assessments: Uncertainty levels as a function of available data, and

therefore determining a realistic field uncertainty range from an understanding of variability.

Determine the value of information for new data; VoI can be expressed in terms of field uncertainty reduction potential. VoI's can actually be statistically assessed (this will be developed in a future publication).

Determine if areas within the resource play can be justifiably high-graded or down-graded – statistical representativeness can again be determined from the use of confidence curves.

Future areas of study The technical contribution of this paper’s section on confidence curves is limited to understanding their basic construction and simply highlighting their possible applications. Future work will be focus on developing further the key applications areas of these curves.

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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 how sampling 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 for subsurface 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.

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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

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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, 18–20 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.

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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

Unc

erta

inty

Man

agem

ent

Wor

kflo

w (U

MW

)

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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

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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 of “amplitude supported” domain

Amplitude value = 2.14.9 – 7.7 m pay (P90-P10)

Limit of visible pay= 1/8 seismic wavelength= 3.5 – 5.5 m pay

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

Maximum constructive interference= 1/4 seismic wavelength= 7 – 11 m pay

Bright Very Bright(Brightest 5%)

Cu

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lative %

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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), Normalised to 1

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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

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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 drilled early, and later wells are sampled in the low end of the variability curve

(Final) Mean for the total population (100wells), Normalised to 1

0%

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1.00 10.00 100.00 1000.00

Cum

Pro

babi

lity

Well parameter - permeability (mD)

illustrative well parameter PDFwell permeability distribution curve (generic and non-specific

case)

Example PDF – well K (mD)This example assumes a P10/P90 range of 10 fold, which is not uncommon in fractured resource playsThis is the VARIABILITY curve

SPE-133518-PP 13

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

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

% C

onfid

ence

in F

ield

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% Data available

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

1.10

1.25

2.00

3.00

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9.00

10.00

88% confidence in a fold of 2.00At 10% data available (% well drilled)

40% confidence in a fold of 1,25At 10% data available (% well drilled)