Abstract— The operation of drilling rigs is highly expensive.
It is therefore important to be able to identify and analyse
factors affecting rig operations. We investigate the use of two
Genetic Algorithms, K2GA and ChainGA, to induce a Bayesian
Network model for the real world problem of Rig Operations
Management. We sample from a unique dataset derived from
the commercial market intelligence databases assembled by
ODS-Petrodata Ltd. We observe a trade-off between K2GA,
which finds significantly better scoring networks on our
dataset, and ChainGA, which uses only one quarter of the
computation time. We analyse the best structures produced
from an industry standpoint and conclude by outlining a few
potential applications of the models to support rig operations.
I. INTRODUCTION
HE oil and gas sector is an active industry constantly
seeking to research and apply new technologies.
However, the competitiveness of the sector often leads to
high levels of secrecy concerning technology, operations,
production and support methods and data. Drilling rigs are
operated by contractors who hire out their services to oil
companies for both exploration and exploitation. The
operation of drilling rigs is highly expensive. Typically a rig
operating offshore in the Gulf of Mexico can cost from
$400K to $600K per day.[1] With rig operations lasting
weeks or even months at a time, variations in the efficiency
with which rigs are operated can affect profitability by
millions of dollars. It is therefore important to be able to
identify and analyse factors affecting efficiency.
There are many ways of defining efficiency. Drilling Rig
efficiency is usually assessed by industry experts on the
basis of practical experience [2] but there is currently no
industry-standard approach for the objective measurement
and prediction of efficiency. Efficiency on its own cannot be
directly compared between rigs without considering many
influencing factors such as, weather, the specific nature of
the geological layers being drilled through, and other
environmental or managerial factors. The selection of which
factors are relevant and how they are related is largely left to
the judgment of managers and other experts in the field.
Their approach is mainly based on empirical observations
and experience. In some cases, the rig selected for a job will
be over-specified or under-specified leading either to

Manuscript received May 02, 2010. This work was supported by ODS-
Petrodata Ltd. (www.ods-petrodata.com) and the Technology Strategy
Board under the KTP scheme (Award: KTP006922).
F.A. Fournier, J. McCall and A. Petrovski are with the IDEAS Research
Institute at Robert Gordon University, Aberdeen, Scotland. (email:
{f.a.j.fournier,j.mccall,a.petrovski}@rgu.ac.uk)
F.A. Fournier and P.J. Barclay are with ODS-Petrodata Ltd., Aberdeen,
Scotland. (e-mail: ffournier@ods-petrodata.com).
unnecessary expense or poor outcomes such as significant
delay. It is this uncertainty surrounding the rig selection
process which motivates rig operations management as an
application area for data modelling.
In this paper, we are interested in the use of evolutionary
algorithms to evolve Bayesian Networks relating a range of
factors selected from an extensive oil and gas industry
dataset. We aim to explore the utility of the models
produced. Also we provide a comparison of two published
algorithms on a new real world problem.
In the next section, we provide a more detailed account of
drilling rig operations and the rig tendering process. We also
describe the dataset used and our approach to factor
selection. In section 3, we summarise the Bayesian Network
modelling approach and describe the two search and score
evolutionary algorithms used to build these networks from
the data. In Section 4, we describe our experiments with Rig
and Wells data. The experimental results are analysed in
Section 5 and a discussion of possible applications appears
in section 6. The final section contains conclusions and a
brief outline of planned future work.
II. RIG OPERATIONS AND THE GULF OF MEXICO
A. Offshore Drilling
The offshore drilling process is mainly split into two main
steps: exploration and exploitation. Various offshore drilling
platform types exist within those two categories. Table 1,
derived from Nergaard [3] summarises the different types of
offshore drilling platforms available.

Table 1: Offshore Drilling platform types
Exploration Floaters Semi-Submersible
Ships
Bottom Support Jack-ups
Production /
Exploitation
Surface
platforms
Permanent
Tenders
Subsea Semi-Submersible
Ships
Jack-ups

Rig owners contract rigs to drilling companies for specific
pre-established needs in both exploration and production.
The offshore drilling market is dynamic, highly competitive,
and regionally-specific. Key differences across regions are
legislative and geological variations, however, cultural
differences and practices across regions and across
companies often also impact on rig results.
Evolved Bayesian Network Models of Rig Operations in the
Gulf of Mexico
François A. Fournier, John McCall, Andrei Petrovski, Peter J. Barclay
T

Freudenrich [4] explains a simplified path to oil and gas
production. Oil is located using various survey methods and
tools including geological analysis, gravity meters,
magnetometers and seismology technologies. Once a site is
selected, it is surveyed to find its boundaries. Then a drilling
rig is brought on site and starts drilling. As drilling
progresses, mud circulates through the pipe and out of the
drill bit to float the rock cuttings out of the hole. When a
pre-set depth is reached, the drill bits are removed from the
hole and a steel-and-cement casing is installed. When
reaching the final depth, various logs and tests are performed
and samples are taken for analysis. The well is then secured
and installed in order to let the oil flow in a controlled
manner. Once the oil is flowing, the oil rig is removed from
the site and production equipment is set up to extract the oil
from the well. [4]
Regarding performance, Harris, in a 1989 publication [2]
explains that no two wells perform the same but that
consistently good results are a good indication of a rigs
capability. He highlights three main criteria, currently used
to select rigs: technical suitability, price, and availability.
Osmundsen et al. [5], in a more recent publication, highlight
more evaluation criteria for selection. In no particular order,
he states that typical evaluation criteria can be: expertise,
financial strength, day rates, ability to complete on time,
compliance with regulations, operational efficiency and
achievements, Health and Safety Executive system and
culture, high pressure, high temperature (HPHT) expertise
and experience. [5]
B. The Rig Tendering Process
Rig tendering is the process by which a company
contracts a rig for a given operation. According to Harris [2],
a successful operation depends on many factors which are
difficult to measure. The tendering process for selecting a rig
has remained largely unchanged since his publication in
1989.
When selecting a rig for a drilling programme an operator
typically has three main criteria: technical suitability, price,
and availability. Some technical parameters are absolute and
determine the type of rig and equipment. Examples are water
depth, pressure and temperature ratings, etc. However,
alternatives can sometimes be suitable: semi-submersibles
have been seen to operate in jack-up water depth [2]. Many
of the other technical requirements included in an invitation
to tender are often preferences rather than necessities. It is
commonly recognised that, if the well is drilled efficiently, a
higher priced bid can lead to a lower overall cost. Also, a
low priced bid can become expensive if accidents extend the
drilling time. [2] Considering availability, requirements will
tend to be stricter in a low-demand rig market compared to
when rigs are in short supply. However, the market
maintains a system of “extension options” which is one of
the main sources of uncertainty on rig availability [2].
Another potential measure is the safety ratings as there is a
correlation between a good operation and a good safety
record.
The usual process starts by a company in search of a
contractor sending out an invitation to tender. The contractor
will then respond to the invitation, presenting various
options available, depending on the nature of a potential
non-compliance. Within all the responses will appear some
variation in potential and decisional tradeoffs open to
judgement.[2] In recent years, a move toward the search of
quality has been made and bidders in Europe are often asked
to provide percentage downtime and indicators of drilling
efficiency for the past six wells including water depth,
mooring time, loss of time, repair time. [5] However this is
not often available information in most regions across the
globe.
C. The Gulf of Mexico Rigs and Wells Dataset
This dataset is covering Rigs and Wells data sourced by
ODS-Petrodata Ltd [6] within its market intelligence
commercial databases. ODS-Petrodata's RigPoint[1]
database covers worldwide offshore drilling rig contract and
activity. Currently, it covers over 25 years of historical rig
activity. One recent addition to their databases coverage is
Wells data. This extension covers both historical and current
drilling activities within the offshore industry. We selected
data representing Rigs operations and Wells data in Gulf of
Mexico. Historical and current data are collected in several
tables of ODS-Petrodata’s RigPoint [6] and Wells databases.
We compiled those data in a single flat table of related data
fields. There are potentially between 700 and 1000 data-
fields (or factors) per record in this table ranging from
operational data (water depth, footage drilled, operation
dates and durations, etc) to technical data (cantilever
capacity, water depth rating, age, etc). Not all fields have
been included in the experiment because of availability,
completeness and accuracy of the data. Overall we identified
37 available factors of particular interest and then reduced it
to 17 key factors to reduce the computation load, by
removing the fields with insufficient data coverage and the
ones with a large number of distinct values. When available,
the fields selected covered the information considered in [5]
as necessary to estimate rig efficiency. To give an idea of the
scope, one of the variables has 72 distinct nominal values
while another one had 350. Factors are either taken directly
from particular data fields or derived from them when not
usable in a meaningful way directly (for example, start and
end dates are transformed into durations). All the numerical
fields (for example water depth or footage drilled) are
discretised in industry-meaningful categories, established
using industry expertise, such as rig operating categories or
usual operating ranges of particular equipment. The other
fields have been left unprocessed and directly copied over to
our dataset. The outcome is a dataset consisting of 6670
rows containing related values of 17 factors.
Table 2 shows the variables selected and the number of
values they can take.

Table 2: Selected Fields, index and variable count
III. BAYESIAN NETWORKS
Various attempts to use Bayesian Networks applied to the
Oil and Gas industry have been made over the years. Some
examples are petrophysical decision support [7] [8], safety
instrumentation and risk reduction [9].
A. Bayesian Network theories
Bayesian Networks are probabilistic models based on
Bayesian Inference [10]. They are useful for representing
knowledge under uncertainty. They can be represented using
a Directed Acyclic Graph associated with a joint probability
distribution [11]. Each node of the graph represents a
random variable Xi related to a problem domain. Conditional
dependencies between variables are represented by edges in
the graph and the joint probability distribution can be
factorised according to these conditional dependencies.
Formally, the joint probability distribution P(X) over the set
of random variables X1,…,Xn, given Pa(Xi) as the set of
parent nodes for node Xi, is represented by
∏
=
=
n
i
iin XPaXPXXXP
1
21 ))(|(),...,,( (1)
To make use of the power of Bayesian Networks in
knowledge representation and inference, the network has to
be constructed for the given problem. The underlying
Directed Acyclic Graph structure representing the network
has to be learned and then the conditional probabilities
calculated. Learning the underlying structure is a hard
problem [12] because the number of possible structures
grows super-exponentially with the number of variables
[13]. One widely used approach to this problem is search
and score. A metaheuristic is used to search a space
representing possible networks. Each solution is scored
according to how well it represents the observed distribution
of the data. Various authors have presented a variety of
metaheuristic approaches to this task including Genetic
Programming [14] and Genetic Algorithms [15][16][17][18].
Other approaches include hill-climbing methods [19] and
Simulated Annealing [20].
B. The K2 algorithm
The K2 algorithm was proposed by Cooper and
Herskovitz [21]. K2 assumes that a priori all structures are
equally likely and that cases in the data occur independently
and are complete. Moreover, it assumes the presence of a
node ordering and imposes a maximum number of parents
for each node (inbound edges). When these conditions are
satisfied, K2 starts with an empty ancestor set for each node
and incrementally adds links that maximize the score of the
resulting structure. The algorithm stops when no more
ancestor node additions improve the score. As in [11], we
observe that although simple to implement and widely used,
K2 is prone to local optima and may not find the globally
best structure. Moreover, it relies on prior knowledge of the
node ordering and so may return non-equivalent structures
given different orderings.
C. K2GA and ChainGA
One popular search and score approach is to search the
smaller space of variable node orderings using a
metaheuristic and use a greedy algorithm to build solutions
from each ordering. These solutions are then scored and the
result passed back to the metaheuristic. This is more
efficient than searching through the space of Bayesian
Network structures and it has the additional advantage of
eliminating all cyclic structures and structures incompatible
with the given ordering. It remains to say however that an
exhaustive search through all orderings for large problems
remains intractable (( ( )!nO for a problem of size n). [11]
In [16], Larrañaga et al. propose a genetic algorithm to
search the space of node orderings rather than the full space
of structures. The initial individuals in the population are
randomly created node orderings which are then evolved
until a good ordering is found. In each generation, a pair of
individuals is selected for crossover and mutation given the
rank of their fitness values in the population. Only one
individual offspring is created at a time and, if better, it
replaces the worst individual in the current population. The
fitness of each ordering is calculated by running the greedy
search algorithm K2 on that ordering and returning the score
of the network structure found. For the purpose of this paper,
we denote Larrañaga’s algorithm by K2GA. Figure 1a
provides a schematic representation of its operation.
Kabli et al. [11] propose an alternative way of reducing
the computational cost related to this by using chain
structures to evaluate orderings, replacing the K2 expensive
evaluation in K2GA.
ChainGA follows a similar approach to K2GA: it searches
the space of node orderings and assigns a value to each
ordering based on the K2-CH score [21]. However rather
than using K2 to construct a network on each ordering,
ChainGA evaluates a fixed chain structure. This low
resolution evaluation phase terminates in a set of orderings
Field Name Number
of values
Well Phase 6
Well Deviated 4
Well Type 6
Well Status 7
Well Result 17
Days On Location Discretised 11
Number of days to total Depth Discretised 10
Total Vertical Depth Discretised 18
Total Footage Drilled Discretised 18
Average Feet drilled Per Day Discretised 16
Shore Base 54
Region 59
Water Depth Discretised 10
Rig Type 6
Harsh Environment Capability 2
Rig Owner 72
Rig Contractor 70

that have the highest evaluated K2-CH scores found with
this structure. The K2-CH score captures the probability of a
candidate network structure Bs given a set of data D.
Formally the discrete probability P(Bs,D) is given by:
∏∏ ∏
== =
−+
−
=
ri
k
ijk
n
i
qi
j iij
i
ss NrN
r
BPDBP
11 1
!
)!1(
)!1(
)(),( (2)
Here qi denotes the number of possible different instances
the parent of variable Xi can take. ri is the number of values
Xi has, Nijk denotes the number of cases in the dataset D in
which Xi takes value k of its xi instance when its parent Pai
has its jth value. Nij is the sum of all Nijk for all values xi can
take. For the Gulf of Mexico dataset, several variables have
large value sets, leading to significant computational cost
using this approach. ChainGA then enters a second phase
where K2 is run on a percentage of the best orderings found
to search for a good structure. Overall, ChainGA results in a
reduced computation time since the number of links to
evaluate is fixed and in general much smaller than that
required by K2GA. In [11], Kabli et al. compared K2GA
and ChainGA on a set of benchmark problems with known
networks and trade-offs were observed between computation
cost and the quality of the structure found. In the following
section we describe experiments with these algorithms run
on our rig operations dataset. Figure 1b illustrates
schematically its operation.
IV. DATA PREPARATION AND EXPERIMENTS
Various standard data sets are available for experimenting
on Bayesian Networks from such domains as medical
diagnosis [11], car diagnosis [12], intensive care patient
alarm monitoring [11], interplanetary probe raw data
interpretation [22], search heuristic for problem solving [22],
virtual office assistants [22] or automatic context detection
[22]. Some of these datasets have been used in previous
work on K2GA and ChainGA by Kabli et al. [12].
A. Oil and Gas Market Intelligence Data Set
In our work, we obtained a new and unique dataset,
exposing a brand new problem to this research field. This
dataset covers Rigs and Wells data sourced by ODS-
Petrodata Ltd. It is an extensive dataset offering a promising
and challenging problem for our Bayesian Network learning
algorithms In addition to the number of factors, two other
elements have a direct influence on the run length: the
number of values in each variable and the size of the dataset.
For this experiment, we used a subset of 2500 cases
randomly selected from the dataset. One reason is that more
cases were making this experiment impossible to compute in
our available time, given the processing facilities available
to us. Table 4 illustrates run times for 2500 cases. For 100
and 2500 cases, using K2GA, the run times were about 20
minutes and up to about 42 hours respectively, while for
ChainGA, run times were about 3 minutes and up to about
13 hours respectively. No preliminary run could be
completed at present using all the 6670 cases available in the
dataset.
B. Experiment setting
Following the steps of the K2GA and ChainGA
algorithms described above, we built our Bayesian network
model that represents the data we have selected
The K2GA and ChainGA algorithm implementations
were run 45 times each with 200 generations with a
population size of 30 node orderings. Displacement
Mutation and Cycle Crossover rates were 0.05 and 0.9
respectively. The selection used was a tournament selection
of size 4. Those values were optimised empirically using test
runs with 100 cases randomly selected from our dataset. The
best scored resulting network was then chosen as the optimal
model for the problem at hand. We ran each algorithm 45
times over the Rig-Well dataset and compared the results
using a 2-tailed T-test in SPSS [23] to validate their
significance.
V. EXPERIMENTAL RESULTS
A. K2GA vs ChainGA on the Wells-Rigs dataset
Figure 2 illustrates the resulting Bayesian network models
as displayed by BNJ [24]. In this figure, we can clearly see
some intuitive relationships formed in the models created by
both K2GA (Figure 2a) and ChainGA (Figure 2b). These
relationships are analysed in more detail below.
As illustrated by the t-test statistical results in Table 3,
K2GA is producing significantly better scoring structures
than ChainGA on our dataset. The best-ever individual for
K2GA scored -55534 compared to -60203 for ChainGA.
This is consistent with observations made on the car
diagnosis dataset in [11]. The results from the Car Diagnosis
Problem also showed the score of ChainGA is significantly
poorer. The Car Diagnosis Problem and the Rig-Wells
Problem have a similar number of cases in their dataset. It is
to be noted from [11] that ChainGA produces significantly
better scoring structure on using the ALARM dataset which
contains 37 nodes and 46 edges. The performance of
ChainGA relating to K2GA appears therefore to be highly
problem-dependent. The influence of problem-specific
features however will require further research.

Table 3: 2-tailed t-test of Best Individuals K2 Score
across all runs
N Mean Score Standard
Deviation
P
K2GA 45 -56197.44 205.2 < 0.0005
ChainGA 45 -66434.34 1237.7 < 0.0005

Table 4, shows that the ChainGA runtime is about a
quarter of the K2GA runtime required to determine the
network structure, leading to a tradeoff situation. K2GA
took an average of 42 hours and 28 minutes to complete a
single run whereas ChainGA only tool about 11 hours. The
overall long computation times required on this problem are
in a large part due to the number of distinct values taken by
many of the variables. Considering the vast amount of data

available to us, K2GA might not be feasible in some cases
for building larger models whereas ChainGA will allow us
to build a model.
Table 4: Time Statistics per run over all runs
Average Standard Deviation
K2GA 42h 28min 5h 9min
ChainGA 11h 1min 1h 11min
B. Expert evaluation of the Model
The networks produced by both K2GA and ChainGA have
been presented to Rig and Wells data experts. Both
algorithms discovered interactions between Rig Capabilities,
Rig Types and Water Depth nodes. Experts highlighted that
those are linked because specific rig types typically operate
at a specific range of water depth. Those rig types have
specific capabilities for operating at those depths. Another
group of interactions is identifiable between Well Result,
Well Status and Well Type. In turn the Total Footage Drilled
node also interacts with the node representing the Drilling
Phase and the one representing the Footage Drilled per Day.
Ignoring directions, we can see edges common to both
networks. This includes an interaction between the Water
Depth and the Rig Type. Those will be logically related
because of the technical abilities of specific rigs to allow
them to work at specified depth. The relationships between
the Rig Type, the Rig Owner and the Rig Contractor are
justified by the propensity of rig owner and contractors to
work together repetitively and to be specialized in specific
type of rigs built on the same plans. Our networks also
identify a relationship between the Shore Base and the
region where the drilling rig is operating. This is another
logical geographical association showing the abilities of both
networks to learn valid information from data.
The partial separation between Well-related and Rig-
related variables (With the exception of geographical and
water depth variables) suggests a potential difficulty in using
the model as a prediction across domains, but adding some
additional key variables might solve that problem. Water
depth, originating from the well database has emerged as a
key variable that correlates with the rig capabilities and
hence is likely to be significant to the choice of rig. In the
Gulf of Mexico, which typically has a uniform geological
profile, this may be a reasonable assumption. Alternatively
there may be other factors in Wells and Rigs, not selected
for this experiment, that do correlate more closely. Also we
would expect geological and other factors to be relevant in
more heterogeneous regions. Given the computation times
on the 17 factors chosen there are significant technical
challenges to be overcome in selecting useful subsets of
factors for modelling.
VI. APPLICATION AND USES OF THE BAYESIAN NETWORK
MODEL
Discussions with our collaborators within the oil and gas
industry have highlighted a range of potential applications
for validated models of rig operations data.
A. Drilling Rig Selection
The model can constitute the basis for a robust and
flexible tool for assisting businesses in finding the best rig
for a particular job. Consulting the model for optimal match,
it enables the identification of rigs suitable for a specific
operational demand. Going further, it would be possible to
build a recommender system around this model. A
recommender system is a system performing information
filtering to bring information items to a user; this
information is filtered in a way that it is likely to interest the
user [25] Adding variables related to the intended drilling
task and user preferences in the model allows filtering
relevant rig recommendations, using the Bayesian Network-
based Model to provide an expectation of performance on
the given task..
B. Rig Performance Forecasting
Rig Performance Forecasting is a particularly interesting
application of such a model. This would support businesses
in their decision to hire a specific rig for a specific job by
using performance expectation. Our discovered structures
have shown that rig type is conditionally related to features
from the Wells dataset. This supports our intuition that
combining Wells and Rigs data will inform the rig selection
process.
C. Rig Scheduling
To assist a user or software in scheduling rigs, the
application would need to estimate a range of expected
completion times for a coordinated set of rig operations
parameters. Using the Bayesian Network to provide the
expectations of the various task times would enable such an
application.
VII. CONCLUSION AND FUTURE WORK
In this paper we explored methods for the discovery of
Bayesian Network from oil and gas data. We have built a
Bayesian network model to represent Rigs and Wells data
generated from ODS-Petrodata’s databses. With this, we
explored the use of both K2GA and ChainGA, Genetic
Algorithms based on node orderings. Both algorithms found
credible network structures as evaluated by industry experts.
Although most of the relationships discovered are obvious at
this stage, quantification of the conditional dependencies
may be of commercial interest. K2GA found significantly
better structures than ChainGA on this dataset; however, the
computational effort required for ChainGA is about a
quarter, on average. Due to the size and complexity of the
datasets being considered, irrespectively of which approach
is used, further work will be required to improve the
computation time and to meet the challenge of factor
selection. One possible improvement would be to use
different scoring metrics such as Minimum Description
Length (MDL) [26] [14] [18] [14] as suggested by Kabli et
al. [12]
This research is a step toward a model that could be used

Figure 2: Network Representations for K2GA and ChainGA


Population
Selection
Crossover
Mutation
One offspring
If fitter than
worst individual,
Insert in
population
Breed
K2 Search
Find Structure and Score
Return Score as ordering fitness
Evaluate
a) K2GA
Figure 1: K2GA and ChainGA