By Liz Thompson

HOUSTON–Three-dimensional models are becoming part of the standard workflow for

assessing and exploiting hydrocarbon reserves. A key element of the workflow is constructing

3-D grids that accurately represent reservoir geometry, followed by property modeling,

where the grid is populated with reservoir properties such as porosity and permeability.

This modeling usually is based on the detailed analysis of subsurface data carried out

as part of a reservoir characterization study, and employs tools that have been tried and

tested through years of demanding use. These software tools generally are regarded as

robust and reliable, but they cannot get away from the limitations of the data. Models

generally are built from dense, low-resolution seismic data and sparse, very high-resolution

well data. Inherently, such models have a degree of irreducible uncertainty, since the

correlation between the detailed well data and the low-resolution seismic data is an inter-

pretation and may be partially wrong or inaccurate.

In addition, the stochastic modeling techniques used in property modeling give one

possible representation of the reservoir based on the input data and model parameters.

Although this is not a true and complete representation of the reservoir (even with multiple

realizations of the model), it provides a good approximation for calculating in-place

volumes and simulating dynamic behavior. For some time, this has been the most reliable

basis for business decisions.

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Given that the user’s knowledge of properties between thewells is unavoidably uncertain, the use of stochastic techniquesis a pragmatic and effective solution. After all, if the interpreterknows that the data interpretation has a margin of error, then amultiple realization approach can embody and visualize that.But is it possible to do better than simply visualizing it? Statistical analysis by spreadsheet has become common, but

using a spreadsheet to quantify reserves uncertainty has its lim-itations. One can assess the impact of ranges of variable values,but a spreadsheet is a poor tool for working with spatially-variable data, since the spatial element is usually lost.

Quantifying Uncertainty

Using 3-D models as the basis for reservoir uncertaintyquantification is now feasible thanks to advances in hardwareand the development of software that supports the automatedgeneration of multiple 3-D models. Instead of average values,distributions of input parameters such as porosity, permeability,velocity, etc., can be used to define a set of equally valid 3-Dstructural models and 3-D grid property distributions.As a result, it is now possible to base all internal rock and

fluid modeling, reservoir flow simulation and volumetric analysison models that include not only the best in reservoir characteri-zation and modeling, but also the best in uncertainty assessment.By combining these two, more reliable decisions can be madethan by using either the 3-D model or the spreadsheets alone.Three-D uncertainty modeling workflows require the definition

of input distributions for key parameters for all the significantmodeling stages–from velocity modeling and depth conversionthrough to facies modeling, saturation modeling and flow sim-ulation. Distributions for parameters such as velocity, surface

location, porosity and permeability can be repeatedly sampledto generate multiple equally valid models.When building full 3-D property models, it is not viable to

generate thousands of 3-D grid models similar to the way inwhich thousands of spreadsheet simulations are produced. In onereservoir modeling solution, for example, Latin hypercube sampling(LHS) from distributions has been implemented to reduce thenumber of realizations needed while still achieving a representativecoverage of the input parameters. As applied to analysis, LHStechnology essentially generates distributions of plausible collectionsof parameter values from a multidimensional distribution.The key point is that 3-D models are three dimensional; they

are built so that the interpreter can use spatial data in theircorrect relation to the data around them for visualization andfor calculations, whereas statistical spreadsheet simulationsdeal with averaged input values and spatially detached data.The 3-D workflow is far more appropriate for evaluatingsignificant contingent resources and for reliably quantifyingcommercial reserves. It is also suitable for providing input todevelopment plans and concept design choices, as well as formanaging fields in early phases of production.Figure 1 is a schematic of a 3-D uncertainty modeling workflow,

showing the most common inputs, stages in the 3-D modelingprocess and corresponding outputs. Multiple 3-D models are gen-erated by stochastic sampling of the input distributions, and allvolumetric calculations are based on the 3-D models.

Simulating Variability

Many vendors are integrating tools for simulating variabilityas a result of uncertainty. Uncertain data are not randomlyvariable. Both limits and patterns can be set on the ways datacan vary, and it is possible to examine the effects of usingdifferent values sampled, for example, from a normal distribution.Reservoir modeling software is designed to turn geological un-derstanding derived from the characterization of the reservoirinto a reliable model of the subsurface. Within reservoir models, key sources of uncertainty are the

structure of the reservoir, porosity (a direct result of the faciesmodel), water saturation, defining the column height, and the lo-cation of hydrocarbon contacts. Connectivity within the reservoir,a source of uncertainty in simulation modeling, is also largelycontrolled by the distributions used in the facies modeling.Fracture modeling, an area with very significant degrees of un-certainty, also can be integrated into the modeling workflow.With the right software, it is possible to make assessments ofmost of the major sources of uncertainty in geometric reservoirmodeling.The structural model is a very significant source of uncertainty,

with seismic quality and the fault interpretation contributing ir-reducible unknowns.Some reservoir modeling solutions can assess the impact of

variable correctness in the seismic and depth conversion areas,and although structural modeling still generally requires manualgeneration of scenarios, new developments now automate theprocess to a far greater degree, making generating multipleversions of the model a practical goal. Of course, the stochasticrealization structure of facies and petrophysical modeling, whichgenerates tens or even hundreds of realizations of the modelfrom the same control input, lends itself naturally to uncertaintyassessment.

FIGURE 13-D Uncertainty Modeling Workflow

INPUT 3-D MODELS OUTPUT

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The most important benefit of working in 3-D is that intrinsicsubsurface dependencies are treated in a realistic manner. Thisproduces more correct estimations of uncertainty and providesa better foundation for informed asset management. The 3-Dmodeling workflow also produces a variety of additionalproducts, such as probability maps and cubes that are useful forquantifying and understanding the spatial variability of uncer-tainty.

Key Application Areas

So how can uncertainty analysis be applied? One key appli-cation area is assessing the volume of reserves. Using statisticalspreadsheet analysis and the standard volumetric equation isnow common in screening and assessing the value of hydrocarbonassets. Uncertainty in static volumes and recoverable reservesare quantified by Monte Carlo sampling of probability distributionsfor the controlling parameters in the volumetric equation.Although these approaches are very fast, it is often difficult

to estimate the intrinsic dependencies between input parameters,such as hydrocarbon contacts and spill points, for example.They also provide no quantification or visualization of thespatial location and variability of the uncertainty.An alternative is to use a 3-D model as the basis for

volumetric calculations. This allows the dependencies betweenthe various input parameters, such as the shape of the reservoirand hydrocarbon contact location, to be treated in a realisticmanner and provides information on the spatial variability ofthe uncertainty.Another application area is assessing the effect of uncertainty

on facies variation. Three-D facies architecture models usuallyare generated using stochastic modeling algorithms. These al-gorithms create multiple realizations of facies architecture bychanging the random seed numbers used in the stochastic sim-ulation. However, it is not enough to vary random seeds aloneto quantify realistic uncertainties. From well data and generalpaleogeographic knowledge, it is not possible to precisely knowthe “true” channel facies volume fraction, average channel sandbody width, or average azimuth.If the random seed numbers are varied and the geometric pa-

rameters are kept constant, the simulated channel geometriesare locally different, but the overall connectivity and architectureare quite similar. When the input parameters are varied in acontrolled manner using input distributions, the result is a muchricher variation in geometries that more closely reflects true un-certainty in the sand channel architecture and connectivity.Figure 2 shows realizations of a sand channel architecture

generated using a stochastic modeling algorithm. The “seedvariation” realizations were generated using identical geometricinput parameters, while the “parameter variation” realizationswere generated with variable sand fraction, channel dimensionsand azimuth.

Full Range Of Values

The benefit of being able to sample a full range of possiblevalues rather than collapsing the range of possibilities to asingle value is important in all forms of property modeling,whether porosity, permeability, saturation level, etc. Using adistribution greatly increases the accuracy of predictions in sit-uations where there is an identifiable trend to the variation inproperty value.Again, where this is a spatially controlled variation, the true

impact of the variability can only be assessed by using a spatial(or 3-D) model populated using the range of values and theguiding trend.An important source of porosity uncertainty that needs to be

taken into consideration when defining input distributions isrelated to sampling the wells. Porosity is seldom constant withina structure. With only a few wells, it is difficult to know whetherthe “average porosity” calculated at the well locations is repre-sentative of the field. This uncertainty is particularly significantif there are strong lateral trends or depth-dependent trends.The impact of internal trends depends on the relationships of

the trends to the structure and contacts, and again, these de-pendencies need to be modeled in 3-D to be properly understoodand quantified. This is illustrated by a simple example of agentle anticline structure with a single discovery well locatednear the crest (Figure 3). Note the vertical trend in the porosityvalues. The discovery well penetrated 79 feet of fully saturatedsand with an average porosity of 17 percent. The reservoir sandis characterized by a fining-upward depositional trend. Porosityvalues near the base are about 22 percent and decrease to 12percent near the top of the sand.This trend can be incorporated into a 3-D uncertainty model.

For example, for the base case structure and a contact 10 metersunder the lowest known hydrocarbon, incorporating the fining-upward trend leads to an 8 percent reduction in the pore volumesestimated from the model when compared with the estimatesderived using no trend and an average value from the welllocation. This is because the high-porosity base of the sandstonedips under the fluid contact and there are larger volumes of thelow-porosity upper part of the reservoir in the hydrocarbon col-umn.By using uncertainty analysis to map variations in porosity

distribution and structural geometry, multiple models can becreated and their pore volumes measured. These estimates canbe used to define the range of pore volumes to be consideredwhen making reserves estimates.

Simulated Porosity Distribution in Cross Section

FIGURE 2Channel Modeling (Seed and Parameter Variation)

Seed Variation Parameter Variation

FIGURE 3

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

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3-D Modeling Products

In addition to defining histograms and probability distributionsfor in-place volumes and reserves, 3-D uncertainty modelingprovides 3-D grids and a wide array of additional products thatare useful for asset management and field development decisions.Maps can be generated to describe lateral variations in un-

certainties. These maps are useful for general quality controlpurposes and for communicating the spatial distribution of un-certainty. For instance, a gross pay uncertainty map can provideuseful input for targeting appraisal wells.At the other end of the spectrum, uncertainty quantification

cannot be divorced from history matching of production datawhen dealing with mature fields. Uncertainty modeling andhistory match optimization need to be done together. As an ex-ample, one software package has been developed to optimizehistory matching and quantify uncertainty in future productionprofiles. The main controlling parameters are related to the pro-duction data and history match. However, the software can belinked with the geologic models to provide a “big loop” historymatch and uncertainty modeling workflow.Reservoir characterization is a highly skilled part of the hy-

drocarbon production process, generating an essential under-standing of the reservoir. The models that embody that under-standing are created by a well established and sophisticatedarea of geologic modeling, but even now there is only so far itcan go. However, the limits of the data do not have to represent

the limits of usefulness for the models.Uncertainty analysis can enhance the models by allowing an

assessment of where any given model is likely to be mostaccurate and where it may be unreliable. Using this informationto focus further data collection, locate wells and make justifiableestimates of reserves can greatly improve the utility of themodel and allow the underlying reservoir characterization workto contribute even more to the success of an asset. r

LIZTHOMPSON

Liz Thompson is technical information manager at Roxar,responsible for ensuring that all technical information isgathered and made available to the marketing and productgroups. Thompson was formerly product manager for Roxar’sfracture modeling software and technical product managerfor Roxar’s structural geologic tools.

SpecialReport: Reservoir Characterization & Exploitation