A Visual Analytics Framework for Exploring Uncertainties in Reservoir

Models

Zahra Sahaf

, Hamidreza Hamdi

1,2

, Roberta Cabral Ramos Mota

, Mario Costa Sousa

and Frank Maurer

Department of Computer Science, University of Calgary, Calgary, Canada

Department of Geoscience, University of Calgary, Calgary, Canada

Keywords:

Visual Analytics, Mutual Information, Clustering, Uncertainty Analysis, Volumetric Ensembles.

Abstract:

Geological uncertainty is an essential element that affects the prediction of hydrocarbon production. The

standard approach to address the geological uncertainty is to generate a large number of random 3D geological

models and then perform ﬂow simulations for each of them. Such a brute-force approach is not efﬁcient as

the ﬂow simulations are computationally costly and as a result, domain experts cannot afford running a large

number of simulations. Therefore, it is critically important to be able to address the uncertainty using a few

geological models, which can reasonably represent the overall uncertainty of the ensemble. Our goal is to

design and develop a visual analytics framework to ﬁlter the geological models and to only select models

that can potentially cover the uncertain space. This framework is based on the mutual information for the

calculation of the distance between the models and clustering for the grouping of similar models. Interactive

visualization tasks have also been designed to make the whole process more understandable. Finally, we

evaluated our results by comparing with the existent brute force approach.

1 INTRODUCTION

Uncertainty is related to poor knowledge of a phe-

nomenon. In petroleum engineering applications, for

instance, we have lots of uncertainties in all aspects

of petroleum production phases. This is essentially

due to a large number of unknows that exist at any

particular stage of exploration, development, and pro-

duction workﬂow. In the exploration phase, which

is the focus of this paper, the lack of knowledge in

representing the measured data (e.g., due to noise),

expressing the depositional settings, spatial conﬁgu-

rations of the rock types, or mathematical uncertainty

in representing the geology, are the key elements that

largely impact the decision making process based on

modeling (Caers, 2011).

Reservoir models are essential to portray the im-

pact of uncertainty. A reservoir model is a 3D grid-

based digital representation model of the subsurface

composed of a large number of cells/voxels. Each

cell has a location in space and a set of attributes de-

scribing geological properties (such as porosity and

permeability).

Geostatistical methods are used to estimate at-

tribute values of the cells where no information is

available. The inherent uncertainties of these geosta-

tistical models imply that the attribute values of a cell

can be assigned to different values and still be consis-

tent with known facts. Geologists capture the inher-

ent uncertainty by creating a large number of models.

Flow simulations then take the models as an input and

determine the expected outcome on variables of inter-

est (like overall oil production volume) over time. The

large number of cells in the digital reservoir model

and the computational cost of processing ﬂow simu-

lations (i.e., usually requiring several hours) prohibit

a brute-force approach for conducting the numerical

ﬂow simulation for all possible models. Therefore,

it is substantially favorable to carefully select a few

models with great diversity that can reasonably repre-

sent the overall uncertainty (Idrobo et al., 2000).

Another critical requirement for domain experts is

an efﬁcient way to compare the 3D models in a large

ensemble without running the costly ﬂow simulations.

This aspect can help identify how models are different

or similar to each other spatially and visually. Using

that, the users can ﬁnd out which spatial areas have

more contribution toward quantifying the uncertainty

and thereby the oil production.

To address all these requirements, we have de-

Sahaf, Z., Hamdi, H., Mota, R., Sousa, M. and Maurer, F.

A Visual Analytics Framework for Exploring Uncertainties in Reser voir Models.

DOI: 10.5220/0006608500740084

In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 3: IVAPP, pages 74-84

ISBN: 978-989-758-289-9

signed and developed a visual analytics framework

to identify the models that can potentially cover the

uncertain space (that is referred to as ”representative

models”). The proposed process can resolve exist-

ing issues of previous studies. Current techniques

like ranking (Ballin et al., 1992), random selection, or

probability-based techniques (Rahim and Li, 2015),

are all costly regarding computation. They are auto-

matic processes preventing the domain experts from

guiding the selection process. Moreover, they are not

modular and target only some speciﬁc types of reser-

voirs (Yazdi and Jensen, 2014).

The ﬁrst step in the proposed process is to es-

tablish a representative metric for calculating the

(dis)similarity between a pair of 3D geological mod-

els. As such, a new distance measure has been de-

signed based on the mutual information (MI) concept

(Lin, 1998) (Goshtasby, 2012). Distances are then

employed within a clustering algorithm to create sets

of similar models (i.e., models where simulation re-

sults are likely to be similar). In this state, cluster cen-

ters are identiﬁed as the default representative mod-

els, and the users can only run the simulation for this

limited set of selected models. We show the accu-

racy of our selection method by comparing the actual

ﬂow simulation results of the selected models with the

brute-force approach. A particular selection is accu-

rate when the simulation results of all models in one

cluster are very similar to each other. In addition, the

representative models should cover a similar cumula-

tive hydrocarbon production uncertainty range as the

brute force approach. In summary, the main contribu-

tions of this paper are:

• Novel dis(similarity) metric for calculating pair-

wise distances between the 3D geological models

(section 5).

• Analytical framework for uncertainty assessment

of dynamic properties (e.g. oil production) that

utilizes our proposed similarity metric (section 4

and 6).

• A visual analytics tool that supports the proposed

framework and provides visual and interactive

tasks for steering the uncertainty assessment pro-

cess (section 8).

2 RELATED WORK

2.1 Current Approaches for Selecting of

Geological Models

Various methods are available for selecting geologi-

cal realizations which can be broadly classiﬁed as ran-

dom selection, ranking, probability distance-based re-

alization reduction method, and clustering technique.

While randomly selecting a subset of realizations

is a straightforward method for implementation, it

may result in a wrong measure of geological uncer-

tainty especially when the number of selected real-

izations is small. Ranking (Ballin et al., 1992) is the

most common method for selecting geological real-

izations. This method arranges the geostatistical mod-

els based on an easily computable measure in an as-

cending/descending order and then selects the ones

that have low, medium, and high values of that mea-

surement. One of the major limitation of the existing

ranking methods is that they rely signiﬁcantly on the

measure used. If the measure has a weak correlation

with the production of the reservoir, then the selected

models will not adequately represent the full set of

realizations (Li et al., 2012).

Probability distance-based realization reduc-

tion/selection methods have also been recently

investigated by some researchers (Rahim and Li,

2015). In this approach, an optimization problem

is solved to ﬁnd an optimal subset that has similar

statistical distribution characteristics to the superset

of models. The main issue with these optimization

problems is that they could be very complicated and

time-consuming for a broad set of models, and in

the presence of the outlier models, the optimization

process might not converge. Clustering methods

have also been proposed recently in the domain. For

instance, (Scheidt and Caers, 2010) used simpliﬁed

simulation results to compute the distance between

the models to form a distance matrix. Then these

distances were used to perform the clustering. The

need of petroleum industry to address the geological

uncertainty using a limited number of geological

realizations necessitates designing an analytical

framework that is computationally less expensive,

dependent on the static properties of geological

models rather than ﬂow simulation results, visual and

interactive, and capable of showing differences and

similarities between the models.

2.2 Visual Analytics Techniques for

Multirun Data

The most similar dataset in computer science domain

to the geological models in petroleum engineering is

multirun models. In areas such as climate research

and engineering, multirun data is often generated to

study the variability of models and to understand

the model sensitivity to speciﬁc control parameters

(Kehrer and Hauser, 2013). In general, multirun data

stem from a type of process (like geostatistical algo-

A Visual Analytics Framework for Exploring Uncertainties in Reservoir Models

rithms in our case) that is repeated multiple times with

varied parameter settings, leading to a large number

of collocated data volumes (Wilson and Potter, 2009).

Since multirun data consists of a superset of volumet-

ric models, their representation and analysis are chal-

lenging.

The representation of multirun data is somewhat

new to the visualization community. It is a challeng-

ing task since the data is often high dimensional, mul-

tivariate, and large at the same time. Accordingly, one

of the common ways is to aggregate the distributions

of multirun data, by computing statistical summaries

(Love et al., 2005). Subsequently, the resulting data is

visualized using mainly box plots (Kao et al., 2002),

line charts (Demir et al., 2014), glyphs (Kehrer et al.,

2011), or InfoVis techniques such as parallel coordi-

nates or scatterplot matrices combined with statistics

(Nocke et al., 2007).

On the analytics side of multirun data, statisti-

cal methods are among the ﬁrst candidates to be

used for reducing the data dimensionality. For ex-

ample, (Kehrer et al., 2010) proposes a method to

integrate statistical moments (mean, variance, skew-

ness, and kurtosis) into the visual analysis of multi-

run data. Alternatively, mathematical and procedural

operators are also used to transform the multirun data

into some compact forms (e.g., streamlines, isosur-

faces, or pseudocoloring) where existing visualization

techniques are applicable (Love et al., 2005) (Fofonov

et al., 2016).

Data mining techniques are also among the recent

methods being used to explore the multirun data (Cor-

rea et al., 2009). (Bordoloi et al., 2004) applied hi-

erarchal clustering techniques to multirun data. In

a recent work, Bruckner and Moller (Bruckner and

Moller, 2010) presented a result driven exploration

approach for physically-based multirun simulations.

Each volumetric time sequence is ﬁrst split into sim-

ilar segments over time and then is grouped across

different runs using a density-based clustering algo-

rithm. This approach supports the user in identifying

similar behavior across different simulation runs.

Our analytics approach ﬁts into the data min-

ing category since the similarity between ensembles

needs to be discovered both effectively and visually.

However, most of the proposed clustering approaches

are based on the 2D ensembles such as images. Even

though the 3D ensembles are available, their aggrega-

tions are used for the clustering task. In this work, we

want to perform the clustering on the 3D ensembles

directly without using their aggregation, and that re-

quires an accurate deﬁnition of distance between ge-

ological 3D ensembles.

3 REQUIREMENT ANALYSIS

Through extensive discussions with the reservoir en-

gineers from our industry partners, we gathered the

following required elements as engineering require-

ments needed for designing a useful analytics frame-

work:

R1. Limited selection of reservoir models. How

can we select few representative models from a super

set of models?

R2. Low computational cost. How can we have

a fast selection process? The reason is that reservoir

engineers usually want to save time in the engineering

tasks (running costly simulations) as much as possi-

ble.

R3. Flexibility on the reservoir properties used

in the selection process. Depending on the type of

reservoir, different reservoir properties are provided.

R4. Flexibility on the area of interest. How can

we perform the selection process based on an area of

interest in the reservoir model? Usually, only speciﬁc

areas of reservoir model (e.g., areas around wells) are

considered signiﬁcant. Therefore, there is a need to

perform the selection process based on a region of in-

terest that the user selects.

R5. Illustration of reservoirs (dis)similarity dis-

tance. For instance, which area of models contribute

more in the (dis)similarity value or how to spatially

and visually observe the comparison between a set of

3D reservoir models.

4 ANALYTICAL FRAMEWORK

FOR DESCRIPTIVE

UNCERTAINTY ASSESSMENT:

OVERVIEW

An overview of our proposed process is represented

in Figure 1. Initially, we have a set of 3D geologi-

cal models (a). Our proposed block-based similarity

metric is calculated for all pairs of models (b). The

similarity values are then utilized to project models

into a 2D space using multidimensional scaling tech-

niques (c). Each point in 2D space corresponds to

a 3D model. The distance between points in the pro-

jected space represents the similarity between models,

the closer the points, the more similar the 3D mod-

els. The ﬁnal step is to cluster the points and pick

a representative model from each cluster (d). The is

an iterative and interactive process, which depends on

the size of the similarity block, clustering property,

the number of clusters, etc. Each of these stages is

explained in more detail in the subsequent sections.

IVAPP 2018 - International Conference on Information Visualization Theory and Applications

Figure 1: Overview of proposed ﬁltering Process.

5 CALCULATION OF

(DIS)SIMILARITY METRIC

A majority of reservoir simulation studies are per-

formed on a single geological model. Therefore, ’dis-

tance’ between reservoir models is somewhat new

concept in that domain (Fenwick and Batycky, 2011).

Therefore it is essential to deﬁne a distance that re-

ﬂects the requirement of the engineering tasks. Two

models are called similar when they have a sim-

ilar dynamic result (reservoir performance). The

(dis)similarity distance can be calculated in a manner

that should leverage two primary requirements. First,

it has to be well correlated to the dynamic behav-

ior of reservoir or ﬂow response(s) interest (Scheidt

et al., 2009). Second, its calculation should not be

very costly. According to our discussions with the

domain experts and domain literature evaluation stud-

ies (Rahim and Li, 2015), static measures meet the

two mentioned requirements and much preferred than

dynamic measures. The reason is that static mea-

sures are simpliﬁed metrics designed to achieve a

good correlation with the reservoir production perfor-

mance variable of interest. For instance, Original oil-

in-place(OOIP) is one of the critical terms calculated

in reservoir simulation. It is calculated by the sum-

mation of the product of the following static proper-

ties volume (V), porosity (φ) and oil saturation of cell

c (OOIP =

∑

(1 − S

))). Therefore, it shows

how static properties are highly correlated with the

dynamic (ﬂow) terms. In addition to that, static mea-

sures are computationally much easier for evaluation

when compared to reservoir ﬂow simulation. It can

be easily calculated for a broad set of realization (R2).

In the next sections, we explain how these static mea-

sures use with our proposed similarity metric.

Reservoir models have 3D geometries with corre-

lated spatial properties. Additionally, they can have

some favorable 3D sub-structures (e.g., geological

channels). Hence, any appropriate similarity mea-

surement should be able to acknowledge these lat-

eral geological heterogeneities (Figure 2). Therefore,

we use a moving 3D template (block) approach to

calculate (dis)similarity distance between a pair of

models. The idea is to divide each 3D model into

a set of smaller 3D blocks (Figure 2) where each

block consists of a speciﬁc number of grid cells. The

(dis)similarity measure is computed between corre-

sponding blocks (templates) initially. Next, we take

an average of the(dis)similarity values between all

corresponding blocks. During this process, to reduce

the bias of the ﬁxed spatial position of blocks, we

move the blocks in speciﬁc directions (x, y, z and di-

agonal) and distances (>1 and <block size). The ﬁ-

nal distance will be the average of (dis)similarity val-

ues in all the possible movements. For simplicity, a

2D representation of movement is shown in Figure 3.

The yellow highlighted cells represent a prominent

geological feature. Equation 2 shows how the ﬁnal

(dis)similarity is calculated between the two sample

models with one movement and two states.

Figure 2: (a) A sample important 3D structure in the geo-

logical models. (b) A sample 3D block.

Figure 3: Representation of a sample favorable structure

(highlighted in yellow), and movement of templates (dark

blue frames).

MI = MutualIn f ormation, Sim = Similarity, B = Block, M = Model (1)

(state 1)Sim(M1, M2) = mean(MI(M1 B1, M2 B1), MI(M1 B2, M2 B2),

MI(M1 B3, M2 B3), MI(M1 B4, M 2 B4))

(state 2)Sim(M1, M2) = mean(MI(M1 B1, M2 B1), MI(M1 B2, M2 B2),

MI(M1 B3, M2 B3), MI(M1 B4, M 2 B4),

MI(M1 B5, M2 B5), MI(M1 B6, M 2 B6))

TotalSim = mean(Sim(M1, M2) state 1, Sim(M1, M2) state 2)

Clearly, the similarity metric deﬁned above can be

used for any geological property (R3). This can be

A Visual Analytics Framework for Exploring Uncertainties in Reservoir Models

speciﬁed interactively from the application interface

based on domain expert knowledge. There are also

scenarios that users need to consider multiple proper-

ties. In this scenario, (dis)similarity values are calcu-

lated separately for each property (using the proposed

approach) initially. After then, all those values are av-

eraged to determine the ﬁnal (dis)similarity between

two models.

5.1 Distance Speciﬁcation

The next step in the similarity calculation process is

to determine the distance between a pair of corre-

sponding 3D blocks. Similarity-based approaches are

widely used in different problems of science and en-

gineering. A number of distance-based formulations

have been proposed (Goshtasby, 2012), where Haus-

dorff and Euclidean distances are the most commonly

used in the reservoir engineering domain. The lat-

ter one is being found effective more for images and

2D surfaces such as time lapse seismic maps (Hut-

tenlocher et al., 1993), and Euclidean distance mostly

takes care of linear correlations. Therefore, we pro-

pose to use Mutual Information (MI) as a relatively

multi-purpose measure. MI is a popular information-

theoretic measure of similarity which has been ap-

plied in many areas of visualization and graphics do-

main like image registration, multi-modality fusion

and viewpoint selection (Bruckner and M

oller, 2010)

(Haidacher et al., 2008). The major beneﬁts of MI for

our case are:

1) Applicability. It is applicable as long as the do-

main has a probabilistic model. This aspect allows the

measure to be used in the domains where no similarity

measure has previously been proposed (e.g., reservoir

engineering domain).

2) Non-linear dependency detection. MI considers

all types of dependencies (i.e., linear and non-linear)

between two objects (Cover and Thomas, 2012). The

relationship between the property values in a pair of

geological models could be non-linear, and MI con-

siders all these types of dependencies.

3) Noise detection. Many studies show that MI is

robust to alleviate the impact of noise than the other

distances (Cole-Rhodes et al., 2003). Reservoir mod-

eling procedures can create outliers in the simulated

spatial structures. Therefore, it is critical not to be

sensitive to the noise data.

To further observe the effectiveness of MI over

other common distances in the domain, we create a

simpliﬁed dataset as represented in Figure 4. This

dataset can mimic some simpliﬁed channelized reser-

voir models. The ﬁrst column (Figures 1, 4, 7) shows

the original models, some noise is added to the mod-

els in the second column (Figures 2, 5, 8), and the

models in the third column (Figures 3, 6, 9) are 90

degrees rotated. A reasonable distance should be less

sensitive to noise, in a way that the distance between

an original model and its noisy version should be min-

imal. On the other hand, the distance between an orig-

inal model and its rotated version should be consid-

erable, because they are indeed two different models.

Figure 5 shows the distance calculation for three met-

rics: MI, Euclidean, and Hausdorff distances. The re-

sults show that Euclidean distance is not sensitive to

rotation, and the Euclidean distance between a model

(1) and its rotated version (3) is zero, and they are

collocated in Figure 5. The similar pattern can be

seen for the other pair of models ((4,6) and (7,9)).

Although rotation is detected by Hausdorff distance

and the rotated models are located far from the origi-

nal models (see (1,4,7) vs (3,6,9) in Figure 5), noise

is not detected by this distance and noisy models are

considered as very different models and located far

from the original models ((see (1,4,7) vs (2,5,8) in

Figure 5). Finally, it can be seen how MI distance

detects movements like rotation and also ignores the

noise. For instance, models with their noisy version

are located close to each other such as (4,5), (1,2),

(7,8) in Figure 5. Moreover, on the other hand, move-

ments like rotation are also captured perfectly (see

how (6,3,9) in Figure 5 are located very far from the

original models). These beneﬁts of MI can highlight

its effectiveness for many reservoir simulation stud-

ies. This is because, on one hand, even tiny move-

ments can translate to a signiﬁcant effect on the sim-

ulation result, and on the other hand, modeling errors

can lead to creating some noisy structures in the geo-

logical models.

5.2 Block Size Speciﬁcation

In this research, we advocate a block wise approach

for calculating the distance between the models. Such

a block-wise strategy is widely used in image and

video processing to exploit spatial and/or temporal

locality and coherence. A critical aspect of this ap-

proach is to select a proper block size. As sug-

gested by many researchers (Wang et al., 2008), block

size should not be too small to sacriﬁce performance.

Moreover, it should not be too large to ignore the lo-

cality and coherence feature of blocks. We use the

concept of entropy, as suggested in (Honarkhah and

Caers, 2010), to base the optimal block size. This op-

timal value is provided as a suggestion to the users in

our designed application; however, users can change

it based on their knowledge such as the use of corre-

lation length as it is used in generating some geolog-

IVAPP 2018 - International Conference on Information Visualization Theory and Applications

Figure 4: Dataset generated for evaluation of similarity dis-

tances.

Figure 5: Comparison of different distance calculation

methods including Euclidean, Hausdorff and Mutual Infor-

mation.

ical patterns. Entropy measures the information con-

tained in a message as opposed to the portion of the

message that is determined. This concept, when ap-

plied to blocks in reservoir models, can determine the

minimum information required to represent the whole

model reliably. Hence, our method for optimal block

selection is to scan a reservoir model with different

block sizes using our proposed moving block method.

For each block size, we calculate the average (mean)

entropy values of all blocks. Then, the entropy values

are plotted for each block size. We did some numeri-

cal experiments for this algorithm including using dif-

ferent reservoir models, blocks with different sizes in

each dimension, and blocks with equal sizes in all di-

mensions. Our empirical studies show the following

essential trends in the speciﬁcation of block size:

• In the ﬁrst stages of increasing block size, the en-

tropy sharply increases since the average number

of information bits needed to encode the underly-

ing patterns in the model is increasing.

• At a later stage where the block size has increased

above the optimal block size, entropy increases at

a much slower pace.

• In the stages that block size is close to the size of

the original model, entropy stops increasing. The

reason is that block contains repeated patterns and

hence, the amount of carried information ceases to

increase.

Therefore, according to these trends, the optimal size

of the block is in the stage that entropy slowly in-

creases as highlighted in Figure 6.

Figure 6: Mean entropy plot for different block sizes, with

highlighted maximum entropy.

Figure 6 shows the entropy plot for increasing the

block size (the scanning template) in the x direction.

The size of the original model in the x dimension is

140, and from Figure 6, it can be seen that a block size

with an x dimension around 25 to 30 (the highlighted

area) is an optimal value. This is where the average

entropy curve reaches its maximum for the ﬁrst time.

We can perform a similar procedure for the y and z

dimensions, and get the optimal values for the other

dimensions as well. In our case, for a model with size

140 ×69 ×9, a block with size 23× 12 × 2 was found

to be the optimal size.

6 PROJECTION WITH

CLUSTERING

The calculated distances are utilized within a cluster-

ing algorithm to group similar models. Each clus-

ter center is a default representative member of the

containing cluster, which leads to our main require-

ment: to reduce the number of models needed for

simulation (R1). The K-Means clustering (KMC)

algorithm (Correa et al., 2009) is employed in this

step because of its computational efﬁciency on large

datasets. However, KMC suffers from a noticeable

A Visual Analytics Framework for Exploring Uncertainties in Reservoir Models

drawback. In the case where the data embeds a com-

plex structure (e.g., data are non-linearly separable),

a direct application of KMC is not suitable because

of its tendency to split data into globe-shaped clusters

(MacKay, 2003). To solve this problem, as suggested

in (Shawe-Taylor and Cristianini, 2004), data will be

mapped by a kernel transformation (Sch

olkopf et al.,

1998) to a new space where samples become linearly

separable. Although there are many available kernel

functions in this study, we use radial basis function

(RBF). To make the RBF kernel more general - that

is not to be only the function of the Euclidean dis-

tance but also any other distances - the kernel is com-

bined with multidimensional scaling (MDS) (France

and Carroll, 2011) (Scheidt and Caers, 2010). MDS is

a classical approach that projects the original high di-

mensional space to a lower dimensional space, which

can preserve the original distances. In the projected

space, the spatial position is not critical; the crucial

aspect is the distance between projected points. The

closer points are to each other, the more similar they

are based on the initially deﬁned distance. The pro-

jection algorithm is summarized as follows:

1. Use MI to calculate the block-based distance d(x

, x

) between each pair of models.

2. Use MDS to plot these locations in a low dimen-

sion, call these locations x

d,i

and x

d, j

with d the

dimension in the MDS plot.

3. Calculate the Euclidean distance between x

d,i

and

d, j

4. Calculate the kernel function with given σ .

i j

= K(x

, x

) = exp(

d,i

− x

d, j

)

d,i

− x

d, j

)

2σ

) (2)

Other than having better and simpler visualiza-

tion of projected models using kernel transformation,

it has also a great beneﬁt for clustering algorithm

(Scholkopf and Smola, 2001). K-means clustering

works well for cases such as Figure 7.b, but goes

wrong in complex cases such as Figure 7.a, where the

variation of objects/points in the 2D plot is nonlinear.

Therefore, it is frequently helpful to ﬁrst transform

the points using a kernel transformation, as shown

in Figure 7.b, and then perform k-means clustering.

This technique is called kernel k-means in the litera-

ture (Williams, 2002) (Dhillon et al., 2004).

The efﬁciency of kernel KMC in clustering the ge-

ological models is shown in Figure 8. It shows how

the representation of data and clustering is different

in two scenarios: projection with and without kernel

transformation. It can be seen that the representation

of data looks better and more importantly clustering

Figure 7: (a) represents projection with MDS, (b) repre-

sents projection with MDS using kernel methods. (Zhang

et al., 2010).

results are more representative when a kernel transfor-

mation has been applied. Without kernel transforma-

tion, projected points are very close to each other, and

that makes separation of clusters complicated. How-

ever, with kernel transformation, a well organized and

linear structure can be seen in the results, and clusters

are better represented and separated.

Figure 8: Difference between multidimensional scaling

with (right) and without (left) kernel transformation on the

case study dataset.

7 EVALUATION

For evaluation of our proposed analytical framework,

we compared our results with the current alternative

process in the industry (i.e., to run ﬂow simulation for

all models individually). We run the complete ﬂow

simulation for all the models using the CMG reser-

voir simulator package, and plot the simulation re-

sults for the ’oil recovery factor’ dynamic property

(Figure 10). The plotted results show a range of un-

certainty on the oil production and we expect that our

cluster centers cover this range adequately. Regard-

ing the datasets, our industry partner generated differ-

ent datasets for us using different geostatistical algo-

rithms and scenarios. The idea was to cover almost

all different types of datasets in the domain. To evalu-

ate the performance of our proposed analytical frame-

work, they provided a various dataset with a different

number of Cartesian models (15 to 100 models) and

sizes (1000 to 100,000 cells). Therefore, we evalu-

ated our process in all different scenarios. In the ﬁrst

simple scenario, 15 models were created in 5 groups,

and they only changed ’facies’ property in each group

(Figure 9). Facies is an important geological property

that reﬂects the rock type depositions. When we run

IVAPP 2018 - International Conference on Information Visualization Theory and Applications

the ﬂow simulation for all the 15 models, and plot a

dynamic property (like oil recovery factor vs time), a

range of uncertainty can be seen in the plotted curves

(high, medium and low recovery factor). To capture

this range of uncertainty with fewer of models, our

proposed ﬁltering framework is used to cluster mod-

els into three clusters. Cluster centers are shown with

a star in Figure 11. The results show how cluster

centers can represent the range of uncertainty. High-

lighted curves in Figure 10 shows the cluster centers.

In addition to that, our approach is much faster than

the traditional brute-force approach. Depending on

the complexity and size of the reservoir model, the ex-

ecution time of a ﬂow simulation could be different.

In this case study, running a complete ﬂow simulation

takes around 5 minutes per model, that resulting in 75

minutes (an hour and a half) for all the models in total.

However, our approach takes around only 3 minutes

to calculate the distance between the models and gen-

erates the clustering result. Therefore, it can be seen

that our approach is very time efﬁcient in comparison

to the existent techniques.

Figure 9: Different types of facies property that used for

the creation of geological models.

Figure 10: Simulation results of 15 geological models for

Oil Recovery Factor property.

In another scenario, domain experts changed the

value of all the properties (porosity, permeability, sat-

uration, etc) and they created 100 models. The idea

is to see how our proposed analytical framework per-

forms for such scenarios. Figure 12 shows the ﬂow

simulation curves for all the 100 models. The range

of uncertainty is much broader than the previous sce-

nario. Our clustering result shows how this range

of uncertainty can be represented by only six models

(see the cluster center stars in Figure 13 and their cor-

responding curves in Figure 12). Similar to the pre-

vious case study, our approach had a very signiﬁcant

Figure 11: Clustering result for 15 geological models.

performance in comparison to the current brute force

approach. The reason is that the ﬂow simulations for

all the 100 models took around 7 hours, while our ap-

proach generates the clustering results in only 45 min-

utes.

Figure 12: Simulation results of 100 geological models for

Oil Recovery Factor.

Figure 13: Clustering result for 100 geological models.

8 VISUAL ANALYTICS

APPLICATION

This selection process has been designed and devel-

oped in a visual analytics framework (Figure 14). It

helps the users perform the selection process with a

set of user-deﬁned parameters and compare the mod-

els at different levels of details and views. The users

A Visual Analytics Framework for Exploring Uncertainties in Reservoir Models

Figure 14: Projection and clustering of loaded models.

can import any number of the models into the applica-

tion. Each model can be visualized in 3D. The color

scale shows the value of a selected property. Warm

colors show the higher value of the selected property

and in reverse for the cool colors. There are two main

visual analytical processes in this prototype: selection

process and comparison analysis.

8.1 Selection Process

The selection process consists of two main steps:

calculation of (dis)similarity and clustering. Two

main parameters are speciﬁed by the users: block

size and reservoir property(ies). The default optimal

block size is calculated in the background (using the

entropy-based approach mention in section 5.2) and

is provided in the interface as a suggestion. However,

users can also change that according to their knowl-

edge of the reservoir. Block size is speciﬁed by three

values for each 3D dimension: x, y, and z. Each of

them can be changed by the users interactively. The

other parameter that should be speciﬁed is the static

reservoir property(ies) that are used for the distance

calculation. Users can specify one or more number of

properties (R3).

After that, the number of clusters should be spec-

iﬁed by the user, that is determined based on user’s

budget and time for running ﬂow simulation. The

clustering outcome is presented on a diagram in the

2D view. Each point in the diagram corresponds to a

projected geological model. The color legend on the

2D diagram shows the clustering results (Figure 14).

In result, the median member of each cluster is se-

lected as the representative member of that cluster

(R1). Since the calculated distances are mapped to

the 2D view, it also helps the users to have an overall

representation of models.

According to our discussions with domain ex-

perts, they need to perform selection process based

on a speciﬁc region of a model. This is because

they are sometimes dealing with very large reservoirs,

and not the whole reservoir geometry is important to

them. For instance, in a substantially large reservoir

model, the engineers are usually interested in the ar-

eas around wells. To leverage this requirement, the

users can freely sketch an arbitrary 3D area on the

model. And then the selection process constrains the

calculation of (dis)similarity only to that speciﬁc re-

gion (R4). (Figure 15)

Figure 15: Filtering process for an arbitrary area of interest.

8.2 Comparison Analysis

In addition to the calculated distance values, the users

also frequently need to get more detailed spatial in-

formation about the differences between models. For

instance, the engineers might need to get some in-

IVAPP 2018 - International Conference on Information Visualization Theory and Applications

sights into the regions that the models show a signif-

icant difference. To provide this feature, users can

select any number of models from the 2D view. A

3D similarity map is calculated and visualized for the

speciﬁc selected models (R5). In the similarity map,

the users can observe the local similarity between the

models - i.e., which parts of the model contribute

additional weights in the similarity and dissimilarity

calculations. For instance, Figure 16 is a similarity

map for four selected models. The color scale shows

the amount of mutual information between all these

four models. The results show that these models are

very similar in the red and dark blue areas, and they

are very different light green areas. This feature not

only helps identify the important regions of models

but also utilizes a useful feature of mutual informa-

tion that can be calculated between multiple objects

at the same time with multivariate mutual information

techniques (Batina et al., 2011).

Figure 16: Similarity map for the selected models.

9 CONCLUSION AND FUTURE

WORKS

In this paper, we introduced a new visual analytical

framework for selecting a few representative models

from an ensemble of geostatistical models that repre-

sents the overall production uncertainty. To achieve

this purpose, a new block wise (dis)similarity metric

was deﬁned based on mutual information. This met-

ric is projected to a lower dimension using the MDS

technique, and then the new projected distance is used

in a kernel KMC algorithm to group models based on

their distances. The proposed workﬂow was evalu-

ated using some datasets generated from various geo-

statistical algorithms. The results of the case stud-

ies show that our technique is accurate and efﬁcient

in comparison to the existent techniques. In the fu-

ture, with the help of domain experts, we need to ﬁnd

more adequate parameters for uncertainty assessment

of geological models. Moreover, regarding the appli-

cation, we need to support comparing of clustering

results, and in continuing that, provide more infor-

mation to the users such as what is the best number

of clusters, or what are the effective parameters. We

will also further evaluate our application using a for-

mal user study, that helps identify additional weak-

ness and strengths of the current application and pro-

cess.

ACKNOWLEDGMENT

We wish to thank the anonymous reviewers for their

constructive comments, CMG (Computer Modelling

Group Ltd.) for providing the reservoir data sets and

Masoud Zehtabioskuie for his valuable help and feed-

back on the implementation of the application. This

research was supported in part by NSERC.

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