An Interactive 5-Day Training Course
Petroleum Geostatistics
Quantifying Uncertainty in Static Reservoir Models
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Duration
5 Days
Price
$ 3,500
Starting From
06 Dec 2027
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Petroleum Geostatistics
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Petroleum Geostatistics - GG-GSTAT-PEA27
| Code | Date | Time | Duration | Location | Currency | Early Bird Fee Per Person |
|---|---|---|---|---|---|---|
| GG-GSTAT-PEA27 | 06 - 10 Dec 2027 | 10 AM CST | 4 Hours Per Day |
Online |
USD |
3500 |
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Petroleum Geostatistics
This training covers geostatistics as applied in petroleum reservoir modelling. It works through spatial statistics and the variogram, kriging and its variants, stochastic simulation methods, indicator and Gaussian approaches, multi-point statistics, co-simulation with secondary data, uncertainty quantification, realisation selection and ranking, and the practical diagnosis of geostatistical results that look wrong.
Description
Geostatistics underlies every property and facies model built in the industry, and most practitioners use it through software without understanding what the algorithms do. That is workable until something goes wrong: a model with unrealistic continuity, a kriged map that smooths away the variability, realisations that are all effectively identical, or a simulation that honours the wells but produces geology nobody recognises. Diagnosing these requires understanding the methods, which is what this training provides.
The course develops the subject from first principles with reservoir application throughout. Spatial statistics are established first, covering stationarity, the spatial correlation concept and the assumptions that underlie everything that follows. The variogram is then developed in detail, covering its calculation, the effect of lag and direction choices, model fitting, anisotropy, nugget interpretation and the problems of calculating variograms from sparse well data. Kriging follows, covering simple, ordinary and universal kriging, the kriging system, the smoothing effect and the circumstances where kriging is and is not appropriate. Stochastic simulation is then developed as the alternative, covering sequential Gaussian and sequential indicator simulation, the algorithms and their behaviour. Multi-point statistics follow. Co-simulation with secondary data is then addressed, covering collocated cokriging and related methods for conditioning to seismic. Uncertainty quantification, realisation ranking and selection follow. The training closes with the practical diagnosis of results that look wrong.
Kriging smooths and simulation does not, and the choice between them follows from the use. Kriging produces the best local estimate at each point, which means it reproduces the mean well and underestimates the variability, giving a smooth map that looks reasonable and has the wrong distribution of extreme values. Simulation produces realisations that reproduce the correct histogram and variogram but are locally less accurate. For a map of expected porosity, kriging is right; for a model whose flow behaviour depends on the extremes and their connectivity, simulation is right.
The variogram is usually the weakest input and is rarely acknowledged as such. Calculating a horizontal variogram requires well pairs at a range of separations, and a field with twenty wells provides very few pairs at short separations, which is exactly where the information matters. The resulting experimental variogram is noisy and the fitted range is largely a choice. Deriving ranges from outcrop analogues, from seismic where it resolves the relevant scale, or from the depositional model, and labelling them as such, is more honest than fitting a curve to six points.
Realisations that are all the same indicate a problem. If multiple stochastic realisations produce nearly identical volumes and connectivity, either the wells are so dense that little freedom remains, or the conditioning is over-constraining, or the variogram range is so long that the model is effectively deterministic. Multiple realisations are generated to span the uncertainty, and if they do not span anything the uncertainty is being understated, which defeats the purpose of running them.
Finally, the geology has to be recognisable. A statistically correct model that produces channel bodies with the wrong width to thickness ratio, facies that occur in impossible juxtapositions, or permeability fields with no spatial organisation is not fit for purpose regardless of how well it reproduces the input statistics. Visual inspection against the geological concept is a legitimate and necessary quality control step, and a model that a sedimentologist does not recognise should not be used.
By the end of this training, participants will be able to:
- Apply spatial statistics concepts including stationarity and its assumptions
- Calculate, interpret and fit variograms including anisotropy and nugget
- Recognise the limitations of variograms calculated from sparse well data
- Apply kriging variants and understand the smoothing effect
- Select between estimation and simulation for a given purpose
- Apply sequential Gaussian and sequential indicator simulation
- Apply multi-point statistics and select training images
- Condition models to secondary data including seismic
- Quantify uncertainty and rank and select realisations
- Diagnose geostatistical results that are statistically valid but geologically wrong
The training combines method exercises with reservoir modelling practice. Participants calculate variograms from well data and from densely sampled reference data to see how much the sparse calculation misses. Kriged and simulated models are built from the same data and compared for distribution, extremes and flow behaviour. Realisation sets are examined for whether they span meaningful uncertainty. Models with statistically correct but geologically implausible results are diagnosed.
Organisations sending participants to this training will:
- Select appropriate methods rather than software defaults
- Derive variogram parameters from defensible sources
- Generate realisation sets that span real uncertainty
- Diagnose and correct geostatistically flawed models
- Condition models to seismic appropriately
- Improve the technical defensibility of reservoir models
Participants will:
- Understand what the modelling algorithms actually do
- Calculate and fit variograms competently
- Choose between estimation and simulation correctly
- Diagnose models that look wrong
- Quantify and present model uncertainty
- Use modelling software knowing its limitations
- Reservoir modellers and geomodellers
- Reservoir geologists supplying model inputs
- Petrophysicists working on property distribution
- Reservoir engineers using geostatistical models
- Geostatisticians new to petroleum application
- Technical staff reviewing reservoir models
- Geoscientists requiring method understanding
Module 1 - Spatial Statistics Foundations
- Regionalised variables and spatial correlation
- Stationarity and its assumptions
- Intrinsic and second order stationarity
- Trends and their removal
- Histograms and declustering
- Declustering methods and weights
- Normal score transformation
- Back transformation and its issues
- Support and the scale of measurement
- Exploratory data analysis before modelling
- Data quality and its statistical effects
Module 2 - The Variogram
- Variogram definition and calculation
- Experimental variogram construction
- Lag distance and tolerance selection
- Directional variograms and anisotropy
- Variogram models: spherical, exponential, Gaussian
- Range, sill and nugget
- Nugget interpretation and causes
- Nested structures
- Vertical against horizontal variograms
- Sparse data and unreliable experimental variograms
- Deriving ranges from analogue and seismic
- Documenting variogram basis
Module 3 - Kriging
- Kriging principle and objective
- Simple kriging
- Ordinary kriging
- Universal kriging and trends
- The kriging system and weights
- Kriging variance and its meaning
- Smoothing effect and its consequences
- Search neighbourhood selection
- Kriging with anisotropy
- When kriging is appropriate
- When kriging misleads
- Kriged maps and their use
Module 4 - Stochastic Simulation
- Simulation against estimation
- Reproducing the histogram and variogram
- Sequential Gaussian simulation algorithm
- Sequential indicator simulation
- Indicator thresholds and their selection
- Truncated Gaussian simulation
- Conditioning to well data
- Random seeds and realisation generation
- Number of realisations required
- Simulation quality control
- Comparing simulated and input statistics
- Choosing simulation method by application
Module 5 - Object and Multi-Point Methods
- Object based modelling principles
- Object geometry and dimension inputs
- Conditioning objects to wells
- Object based convergence problems
- Multi-point statistics concept
- Training image selection and construction
- Training image stationarity requirements
- Pattern based simulation algorithms
- Conditioning in multi-point simulation
- Comparing variogram, object and multi-point results
- Method selection by depositional system
- Practical limitations of each
Module 6 - Secondary Data and Co-Simulation
- Secondary data types in reservoir modelling
- Seismic attributes as secondary data
- Correlation between primary and secondary
- Cokriging and its requirements
- Collocated cokriging
- Correlation coefficient selection
- Cloud transform methods
- Bayesian updating approaches
- Trend modelling from secondary data
- Over-conditioning and its symptoms
- Validating secondary data conditioning
- When secondary data should not be used
Module 7 - Uncertainty and Realisations
- Sources of uncertainty in modelling
- Parameter against scenario uncertainty
- Generating uncertainty across realisations
- Varying structural, facies and property inputs
- Realisation sets that span the uncertainty
- Diagnosing realisations that are too similar
- Volume distributions from realisations
- Connectivity distributions
- Realisation ranking methods
- Selecting representative realisations
- Low, mid and high case selection
- Carrying uncertainty into simulation
Module 8 - Diagnosis and Practice
- Models that are statistically valid and geologically wrong
- Unrealistic continuity and its causes
- Implausible facies juxtapositions
- Property fields with no organisation
- Artefacts from grid and search settings
- Diagnosing smoothing problems
- Diagnosing over-conditioning
- Visual quality control against geological concept
- Statistical quality control checks
- Common software default problems
- Documenting geostatistical choices
- Reviewing a model's geostatistical basis
Upon successful completion of this training course, delegates will be awarded an official Certificate of Completion issued by the Petroleum Engineers Association (PEA), an ISO 9001:2015 certified training organization. The certificate carries 10 Credits and formally records the total learning hours completed.
Each certificate is signed by the Course Facilitator and the CEO of the Petroleum Engineers Association, and serves as verifiable proof of professional training that delegates can present to employers and professional bodies worldwide.
Frequently Asked Questions
All course bookings made through PEA are strictly non-refundable. By registering for a course, you acknowledge and accept that all fees are payable in full and are not subject to refund under any circumstances, including changes in personal or professional commitments or partial attendance.
PEA reserves the right to make reasonable adjustments to course content, trainers, or schedules where necessary, without entitling delegates to a refund. Comprehensive details of each course — including objectives, target audience, and content — are clearly outlined before enrolment, and it is the responsibility of the delegate to ensure the course's suitability prior to booking.
For any inquiries related to cancellations or bookings, please contact our support team, who will be happy to assist you.
