Application of Real-Time Field

Data to Optimize Drilling

Hydraulics Using Neural
Network Approach
Yanfang Wang
University of Louisiana at Lafayette, Real-time drilling optimization improves drilling performance by providing early warn-
Lafayette, LA 70504 ings in operation Mud hydraulics is a key aspect of drilling that can be optimized by
e-mail: wyfhope@hotmail.com access to real-time data. Different from the investigated references, reliable prediction of
pump pressure provides an early warning of circulation problems, washout, lost circula-
Saeed Salehi tion, underground blowout, and kicks. This will help the driller to make necessary correc-
Assistant Professor tions to mitigate potential problems. In this study, an artificial neural network (ANN)
University of Louisiana at Lafayette, model to predict hydraulics was implemented through the fitting tool of MATLAB. Following
Lafayette, LA 70504 the determination of the optimum model, the sensitivity analysis of input parameters on
e-mail: sxs9435@louisiana.edu the created model was investigated by using forward regression method. Next, the
remaining data from the selected well samples was applied for simulation to verify the
quality of the developed model. The novelty is this paper is validation of computer models
with actual field data collected from an operator in LA. The simulation result was promis-
ing as compared with collected field data. This model can accurately predict pump pres-
sure versus depth in analogous formations. The result of this work shows the potential of
the approach developed in this work based on NN models for predicting real-time drilling
hydraulics. [DOI: 10.1115/1.4030847]

Keywords: drilling optimization, hydraulics, MATLAB, artificial neural networks, forward

regression

1 Introduction propagation by stress analysis near wellbore region have been of

great concerns in recent years [5]. Nowadays, computer modeling
Drilling optimization has helped in cutting cumulative
supported by drilling fluid’s laboratory testing is the most com-
nonproductive time (NPT) and often has also increased produc-
mon approach to development and verification of hydraulic
tion. Drilling optimization dates back to 1950s, which is called
designs. Efficient velocity profiles deliver hydraulic energy to the
scientific period to start expansion of drilling research and optimi-
points that are in need of it most at the time, even in cases for
zation of drilling. In 1952, Smith Bits was the first to introduce jet
which drilling flow rates are compromised.
type roller cone bits. Idea of using a regression analysis of offset
However, the challenge in drilling hydraulics prediction still
drilling data to evaluate constants was proposed by Graham and
exists due to the restricted conditions like fluid rheology in down-
Muench [1], which was considered as the first drilling optimiza-
hole conditions, pipe roughness, and fast lithological changes.
tion. In 1963, Galle and Woods [2] investigated the best selection
The set-it-and-forget-it approach and inherent inefficiencies of the
of drilling parameters such as weight on bit (WOB) and rotary
automatic driller are inadequate for keeping bit parameters
speed (RPM). They provided graphs for the best selection of the
matched to lithology and wellbore conditions. Therefore, the
drilling parameters combination resulting in the cost reduction.
industry requires a new methodology to help rig-site personnel
Several bit models were developed and validated in drilling opera-
make informed drilling parameter decisions based on real-time
tions [3,4]. In 1994, Hareland and Rampersad presented a new
offset data analysis that increases operating efficiency to reduce
model to predict the rate of penetration (ROP) of polycrystalline
drilling costs [6]. Traditionally using available data from existing
diamond compact bits that take into account the interaction
wells to plan new wells is a standard practice; however, learning
between the cutter and rock, lithology, and bit wear.
efficiently from these previous experiences and using it has been a
Starting from 1970s, drilling optimization techniques have been
challenge. The planned parameters are applied during the bit
prosperously used through the last decades. Real-time operation,
run without taking into consideration the real-time downhole
real-time data monitoring, and real-time drilling optimization
conditions causing the data quality to compromise and the scope
were partially implemented in the rig-sites. Multiple regressions
of the data to be incomplete.
were the normal method to model ROP calculation using field
data.
The goal in an efficient drilling optimization is to increase 2 Literature of Drilling Optimization Techniques
ROP. Predicting and optimizing wellbore hydraulics can further
NPT reduction in drilling is still a major concern due to the fact
help in better hole cleaning and mitigating stuck pipe and well-
that drilling of a well is often the most expensive process.
bore stability issues. Wellbore stability and fracture initiation and
Throughout oil and gas industries, simulation is capable of
increased learning and reducing the actual cost. Rostami and
Khaksar [7] conducted a simulation study on predicting stuck pipe
Contributed by the Petroleum Division of ASME for publication in the JOURNAL
OFENERGY RESOURCES TECHNOLOGY. Manuscript received December 5, 2014; final
problems while drilling by NN analysis. Salehi et al. [8] devel-
manuscript received May 26, 2015; published online July 7, 2015. Editor: Hameed oped an ANN approach based on the parameters affecting casing
Metghalchi. collapse to estimate the potential collapse for the wells to be

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 drilled and the current wells producing in the field. The output of Simulation experiments concluded that ELM gave the best results
the model predicted collapsed depth and casing collapse risk in in terms of accuracy and processing time. Jahanbakhshi and
the next 5 years. Samuel [9] provided and validated a modified Keshavarzi [15] developed an ANN model to investigate and pre-
model to predict severe damaging vibration, analysis techniques, dict the ROP in one of Southern Iranian oilfields. Formation types,
and guidelines to avoid the vibration damage bottom hole assem- rock mechanical properties, hydraulics, bit type and its properties,
bly (BHAs) and their associated downhole tools in the riser-less WOB, and the RPM were considered as the input parameters to
highly deviated wells. Based on this study, severe vibrations caus- predict the ROP. The results proved the efficiency of ANN in the
ing potentially damaging operating conditions were avoided. field and could be used in drilling planning and real-time opera-
Dubinsky and Baecker [10] introduced a drilling dynamics simula- tion of any oil and gas wells in the related field. Monazami et al.
tor of the drill-string based on the closed loop drilling concept. [16] developed a new model based on the ANN using NN fitting
Although this approach represented a significant step forward in pre- tool of the MATLAB programming software. The influence of the
dictive drilling dynamics modeling, it achieved only limited success input parameters was considered when developing ANN models.
as it was appropriate only for the identification of linear systems. At In order to predict and optimize ROP, Jacinto et al. [17] proposed
the same time, it was stated that since the system of understanding a Bayesian inference approach for targeting the elicitation process
the dynamic behavior of drill-string has some quite complicated and subsequent combination of models and a dynamic evolving
nonlinearity, black box models such as ANNs could be a better neural-fuzzy inference system. Basarir et al. [18] developed sev-
solution. Dashevskiy et al. [11] further developed the drilling eral models to predict penetration rate of diamond drilling. The
dynamics simulator using the power of NNs. This system still had methods included multiple linear and nonlinear regression
some limitations yet to overcome. There was a limited amount of methods and an adaptive neurofuzzy inference system as a soft
data for training the model, and data points were much localized. computing approach to model. The results revealed that the
The effect of inputs on the NNs model was yet to investigate. adaptive neurofuzzy inference model exhibited better perform-
As of today, there is no exact mathematical relationship ance to predict penetration rate than the prediction performance of
between drilling rate and different drilling variables. This is due multiple regression models.
to uncertainty of most the drilling parameters and existence of a
nonlinear and complex relationship between them. This is often
more challenging when drilling exploratory wells in the new field. 2.2 Drill Bit Selection and Drill Bit Wear. Optimum bit
It is a common practice to collect and analyze offset drilling data selection is one of the important issues in daily drilling operation.
and use for optimization of the next well drilled in the field. Usually, optimum bit selection is determined by the lowest cost
The drilling parameters can be generally classified into two per foot and is a function of bit cost and performance as well as
types: rig/bit related parameters and formation parameters. The penetration rate.
rig/bit parameters can often controllable by the operator; however, Bilgesu et al. [19] presented a new methodology of ANN to
the formation parameters cannot be controlled. The parameters select rotary drilling bits. This model was used to determine the
recorded for drilling optimization are critically important to be complex relationship between formation and bit properties
representative of data due to the fact that they are meant to reflect. together with operating parameters. For different data sets used in
Table 1 gives a brief classification of some important drilling the study, the correlation coefficients for the predicted and field
parameters. used bit types ranged between 0.857 and 0.975. Yilmaz et al. [20]
conducted a study to use the power of ANN and fractal geostatis-
2.1 ROP Prediction. Bahari et al. [12] applied genetic algo- tics to solve the optimum bit selection problem. In order to
rithm to determine constant coefficients of Bourgoyne and achieve this goal, a back-propagation ANN model was developed
Young’s ROP model. This method solved the problem where by training the model using real rock bit data for several wells in a
Bourgoyne and Young’s multiple regression method had proven carbonate field. The model was tested using various drilling sce-
to be physically, meaningless in some situations and the simula- narios in different lithological units. It was officially confirmed
tion results had proven to be proficient to determine constant coef- that the model provided satisfactory results. Bataee et al. [21] pre-
ficients of Bourgoyne and Young model. Bataee and Mohseni sented two techniques to optimum drill bit selection. ANNs were
[13] developed an ANN to recognize complex connections to recognize complex connection between variables. Jamshidi and
between drilling variables. They developed a model to predict Mostafavi [22] created and compared two models using artificial
ROP, optimize the drilling parameters, estimate the drilling time intelligence. The first model provided appropriate drilling bit
of wells, and finally reduce the drilling cost for future wells. Amar selection based on desired ROP to be obtained by applying spe-
and Ibrahim [14] compared the conventional multiple regression cific drilling parameters. The second model used proper drilling
model with two artificial intelligence techniques: extreme learning parameters obtained from optimizing procedure to select drilling
machines (ELMs) and radial basis function networks. These two bit which provided maximum achievable ROP. The correlation
techniques were implemented using MATLAB function codes. coefficients for predicted bit types and optimum drilling parame-
ters in testing the obtained networks are 0.95 and 0.90,
respectively.
Table 1 Drilling parameters classification Arehart [23] constructed an ANN to determine the grade (state
of wear) for a drill bit while drilling. The system was trained with
Rig and bit related parameters Formation parameters
(controllable) (uncontrollable) laboratory data collected using bits of known grades drilling
through known lithologies. This network was then tested on syn-
WOB Local stresses thetic formations of various bed thicknesses constructed from the
Torque test data. Bilgesu et al. [19] designed a three-layer ANN and
RPM Mineralogy trained with measured data to predict three-cone bit-tooth and
Flow rates bearing wear. The result of this model showed that it was success-
Density of drilling fluid (MW) Formation fluids ful in predicting the condition of the bit. Gidh et al. [24] devel-
Pump stroke speed (SPM) oped an ANN drilling parameter optimization system to provide
Pump pressure Depth
rig-site personnel real-time information. Using the ANN software
Hook load
Inclination-azimuth Unconfined Rock Strength (UCS system, operating parameters can be selected based on the docu-
ROP mented physical rock characteristics (offset log data) of forma-
Differential pressure Mechanical specific energy (MSE) tions being penetrated and then fine-tuned for the bits specific
Type of the bit cutting structure and wear-rate. Yi et al. [25] proposed a method
to compute values of rock strength and bit-tooth wear by using the

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 “shuffled frog leaping algorithm.” This method was verified to
arrive the optimum drilling parameters efficiently and quickly.

3 Summary of the Literature

Many detailed and effective research studies had been per-
formed in the area of drilling optimization most of them aiming to
reduce the cost. There are various parameters that have impact on
the drilling efficiency and finally the drilling cost. The relationship
between them is complex and nonlinear. From the literature
review, it is observed that using the power of NNs to develop opti-
mization tools can still provide a better solution. Development of
this approach is still under investigation.
Recent studies are observed to do drilling optimization in real-
time; however among the investigated references, there is few
practice working with drilling hydraulics by predicting pump
pressure considering various drilling parameters. A recent
research conducted by Fruhwirth et al. [26] proved the feasibility Fig. 1 Artificial neuron or processing neuron
of NNs to predict pressure losses in wellbores. Deviated well con-
dition was included for consideration. For this modeling, they
used two different wells drilled in similar geological areas. In range for drilling engineers to identify and mitigate problems. For
Sec. 4, a summary of NNs and hydraulic prediction with NN example, too low pump pressures can be caused by washed out
approach is presented. pipes, bit nozzles, loose joints, broken drill-strings, worn pump
packing liners, or lost returns due to creation of formation frac-
ture. On the other hand, too high pump pressures could indicate a
4 ANNs plugged drill bit or an increase in mud density or viscosity. There-
ANNs are essential tools used in modeling complex systems fore, the result of this work shows the potential of a NN approach
that seek to simulate human brain behavior by processing data to model the hydraulic behavior in a well.
during a trial-and-error basis. For example, ANN has been well
known as a tool to recognize and to optimize complicated nonlin- 4.1.1 Data Normalization. Before the input is applied to the
ear relationships between parameters. network, the input will be processed by normalization functions.
A multilayer NN usually consists of an input layer, one or more Different processing functions can normalize data set to different
hidden layers, and one output layer. The number of input neurons ranges. For example, the mapminmax processing function normal-
corresponds to the number of parameters that are presented to the izes the data so that all inputs fall in the range [1, 1].
network as inputs. The same is true for output layer. Neurons Normalization of data required to train NNs allows translating
within hidden layers are responsible primarily for feature extrac- all variables into a similar scale for a more efficient learning pro-
tion. The number of hidden layers and hidden neurons is ambigu- cess. One commonly used method is known as min–max normal-
ous and can continue to keep going forth. They provide increased ization [30] which linearly scales the data to values between 0 and
dimensionality and assist these factors as classification and deter- 1, using the following equation:
mine the type of pattern occurring. However, an optimal network X  Xmin
size is necessary to achieve efficiency, accuracy, and excellent Xmin  max ¼ (1)
results in finite time. Xmax  Xmin
Back-propagation algorithm is used to train the ANN in only
one direction. The learning process is actually the adjustment of where X is the value of the parameter to be normalized and Xmin
weight between links after the comparison of the actual output and Xmax , minimum and maximum values, respectively, the
and expected output. The learning process will not stop until the parameter is then normalized from the analyzed sample. Using
problems between the ANN predicted output and the anticipated this method, the network output will always fall into a normalized
output diminishes to a reasonable value. There is an activation range. After training the ANNs, the network output can then
function inside each neuron of the ANN to process information. reverse back into the units of the original target data when the net-
After processing, each output data comes out and attaches with work is put to use within the field.
the corresponding weight and this new value becomes input data 4.1.2 Train and Analyze NNs. Each back-propagation training
into the following processing neuron of the next layer until it session commonly starts with different initial weights, biases, and
arrives at the last output neuron. Figure 1 depicts the processing in different divisions of data into training, validation, and test data.
each neuron. These different conditions can lead to various different solutions
for the same problem. It is mandatory to train several networks to
4.1 Hydraulics Prediction Using NNs. It is well known that ensure that a network with great generalization is discovered.
calculation of hydraulics behavior along wellbore has been an Each time an ANN is trained, the ANN can result in a different
extreme challenge for decades. Large amounts of mathematical solution due to different initial weights, bias values, and different
models have been developed to simulate the actual downhole con- divisions of data into training, validation, and test sets. As a result,
ditions ([27,28]). Based on those background theories, the overall different ANNs trained on the same problem can present different
objective of this project is to predict pump pressure accurately outputs for the same input. To ensure that an ANN of good
using NNs approach. Yanfang and Salehi presented results of accuracy has been found, the NN must continue training several
hydraulic optimizations based on collected data for few wells times.
[29]. The study here builds on the previous work with providing At each training run, the performance of the created ANNs is
results validation with actual collected field data. Throughout this scaled by mean squared error which then would be generated by
particular study, an ANN model was implemented through the fit- MATLAB after each training. During this project for each genera-
ting tool of MATLAB. The total 12 input parameters were used as tion, the maximum mean square error, minimum mean square
model inputs to train the NNs, and the output parameter was the error, values of training, validation, and test dataset are recorded
pump pressure. This ANN model can predict the pump pressure in and compared. The NN with the lowest performance is the one
real-time accurately and this prediction can be used as a reference that is generalized best to the data set.

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 4.1.3 The Problem of Overfitting. To determine the optimal Table 2 Input and output parameters applied in this modeling
size of the ANN model is a heuristic approach, we can try two or
more hidden layers if the results with one are still not competent. Input Output
However, one hidden layer usually creates positive results.
Torque Pump pressure
Increasing the number of hidden layers or the number of neurons
Rotational speed (RPM)
in the hidden layer, increases the power of the network, yet still Flow rates (measured at the surface)
requires more calculations to make it more likely to produce over- Active PVT
fitting. The error on the training data set is driven to a very small Pump stroke speed 1 (SPM1)
value but when new data is presented to the network, the error is Pump stroke speed 2 (SPM2)
then massive. A too complex network has the tendency to memo- Pump stroke speed 3 (SPM3)
rize the data but has not learned to generalize to new issues. It Total pump speed
focuses excessively on the data given for learning and leans Hook load
toward modeling the noise. ROP
Differential pressure
To avoid overfitting data, the technique called early stopping is
Depth
used. Within this study, the field data was divided into three sub-
sets: training subset constitutes 75% of the total data, validation
subset 15% of the total data, and testing subsets that include 10%
of the database. The training set is used to mark the model. It is MSE versus depth plot and UCS versus depth plot were created
used for computing the gradient and upgrading the network using actual field drilling datasets. Due to the content of this pro-
weights and biases. The validation set is used to ensure the general- ject, results from well 3 were only included in this paper, denoted
ization of the developed network during the learning phase. The as Figs. 2 and 3, respectively. The calculation procedures should
validation error usually will decrease during the initial process of be similar to well 3, if well 1 and well 2 are analyzed.
training, as does the training set error. However, when the network 4.2.2 Methodology of Building Model. Training and obtaining
begins to overfit the data, the error on the validation set begins to an optimal network model is a challenging task. In this project, an
grow. The network weights and biases are preserved at the mini- acceptable approach is to train several networks with increasing
mum of the validation set error. The testing set is used to observe complexity using a learning subset of the training data and con-
the last performance of the network and compare different models. currently observing the error of a validation subset. After training
is completed, the network with the lowest validation error is the
4.2 Modeling preferred one. An extra testing subset of the data is used to mea-
4.2.1 Drilling Data Used for the Analysis. In this project, dril- sure the generalization of the developed model.
ling dataset from actual wells called well 1, well 2, and well 3 was Prior to training the ANNs, the data of well 1, well 2, and well
all collected and trained. These three wells were drilled in similar 3 were partitioned randomly into training, validation, and testing
geological areas. Both controllable and uncontrollable parameters subsets. For the model building process, the available dataset
were included. Controllable parameters and uncontrollable param- consisted of 75% for the pure network learning process, 15% for
eters were shown in Table 2. There are overall 12 drilling parame- validation (making decisions with respect to oversizing), and 10%
ters as input parameters and pump pressure as the only output in for testing purposes. This error of the data subset used for testing,
the paper. denoted as test-error, was used as a measure for the model quality.
So far, many investigations had been conducted to calculate Multilayer network architecture was used to build the model in
mechanical specific energy (MSE) [31,32] and unconfined compres- this study. Starting from generation 4 to generation 15, 12 genera-
sive rock strength (UCS) [33]. The MSE surveillance process pro- tions of networks were trained. Each generation of multilayer
vides the ability to detect changes in the efficiency of the drilling network had one more hidden unit than the previous generation.
system. Recently, Mohan et al. [34] introduced a new term called To prevent from trapping in local error minima, we trained in
hydro mechanical specific energy to identify inefficient drilling con- each generation ten differently initialized networks. A total of 120
ditions by including hydraulic energy term. This has improved per- networks were trained for that problem, the network yielding
formance by allowing the optimum operating parameters to be the lowest validation error was finally selected as best model.
identified easily, and providing the quantitative data needed to cost- Figure 4 sketches a summary of the particular model errors
justify design changes to extend the current limits of the system. In obtained during the first training run. The black curves indicate
general, MSE analysis has resulted in redesign in areas as diverse as the MSE errors from the learning data subset, the red curves
well control practices, bit selection, BHA design, makeup torque,
directional target sizing, and motor differential ratings. To obtain the
rock strength parameters along the wellbore is another critical focus.
Rock strength logs are used to conduct different types of analysis
such as preventing wellbore failure, deciding on completion design
methods, and controlling sand production.
In this study, MSE and UCS were calculated using the equa-
tions mentioned as below:

Input Energy
MSE  (2)
Output ROP

480  Tor  RPM 4  WOB

MSE ¼ þ (3)
Dia2  ROP Dia2  p

S ¼ S0 ð1 þ aS  pebS Þ (4)
 1
aS2 db3 b cdb3 lMW
where ROP ¼ b 2
þ þ
RPM WOB RPMdb 0:000516qqn
(5) Fig. 2 MSE versus depth from well 3

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 Fig. 5 ANN architecture diagram. The optimal network size is
the one which has 11 hidden neurons.

Fig. 3 UCS versus depth from well 3

Fig. 6 Performance plot of the developed optimal ANN. Epoch

80 means 80 iterations. MSE of validation error has the lowest
value after 80 iterations.

Fig. 4 Summary of model errors. Generation represents the

number of hidden neurons.

indicate the errors from the validation subset, and the blue curves
indicate the errors from the test data subset. The dashed lines indi-
cate the maximum errors of the ten networks per generation and
the solid lines denote the minimum errors of the ten networks per
generation. The red line at the bottom with yellow dots indicates
the errors for the corresponding network in each generation with
the lowest validation errors. The white diamond indicates the best
model, the network that has the overall lowest validation error.
The most common ANN architecture is the feed-forward
ANN that is a network structure in which the information will
propagate in one direction, from input to output. While develop-
ing, the networks among two-layered, three-layered, and four-
layered networks, the three-layered showed the lowest network Fig. 7 Error histogram of the developed optimal ANN
error. Different structures in three-layered have been tested
as well. Finally, comparison of 120 created ANNs made us con-
clude that a three-layer ANN with 11 hidden neurons in hidden performance of the network training. Performance of the best
layer is the best model. As it is shown in Fig. 5, a three-layer ANN is shown in Fig. 6, which means this model gets the lowest
feed-forward network with “tansig” activation function for hidden validation error after 86 iterations
layer and “purelin” for output layer and full connection topology
between layers is used. Back-propagation algorithm with 1X G X m  2

Levenberg–Marquardt training function has been used for train- MSE ¼ Yj ðkÞ  Tj ðkÞ (6)
ing. This algorithm can approximate any nonlinear continuous 2 k¼1 i¼1
function to an arbitrary accuracy [35].
We evaluated the simulation performance of the ANN model where m is the number of output nodes, G is the number of train-
on the basis of MSE and efficiency coefficient “R.” The MSE of ing samples, Yj ðkÞ is the expected output, and Tj ðkÞ is the actual
the network is defined as Eq. (6), which is used to show the output.

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 model. Since there is no analytical answer available, a heuristic
approach called forward regression has been used in this study,
which was also borrowed from the study of Fruhwirth et al. [26].
Forward regression, also called forward selection [36], is a step-
wise model building method in statistics. The main approach is to
start with no variables in the model, testing the addition of each
variable using a chosen model comparison criterion, adding one
variable each time that improves the model the most, and repeat-
ing this process until none improves the model.
In this study, our approach is to start with one input in the
model. So, we trained in the first step several networks in the
same way as demonstrated in Sec. 4.2.2 using only depth as input,
then the same procedure using hook load (hkld) as input and con-
tinued until the last of the 12 input parameters was used as single
model input. For each of the 12 training runs, we trained 12 gener-
ations with the ranges of hidden neurons from 4 to 15 in the net-
work, with ten different initialized networks in each generation to
prevent against trapping too much in local error minima. So, a
total number of 1440 networks were generated. The minimum
error of each parameter obtained by the above procedure is
sketched in Fig. 9. It is easy to recognize from that sketch that the
model with depth as single input yields the lowest validation error.
So, we denoted depth as the input that has the most impact to the
model.
The second step, we made 11 training runs with depth as
fixed input and adding exactly one of the remaining parameters
Fig. 8 Regression plot of the developed optimal ANN as second input. In each training run, we trained again 12 gener-
ations with the ranges of hidden neurons from 4 to 15 in the
network to find the optimal network size. Finally, the input
The error histogram plots can also be used to validate network together with depth yielding the lowest MSE was total pump
performance. Figure 7 shows the distribution of the best network speed (totalspm).
errors. The third step, we did the same procedure as above holding
Figure 8 shows the regression plot of predicted ROP against depth and totalspm as fixed input and adding one of the reminding
field data. The efficiency coefficient value R of training, validation parameters as a third input. We performed the same procedures
and testing subsets shown in the diagram is 0.99912, 0.99919, and for the rest steps, adding one input in each step until all parame-
0.99891, respectively. The overall efficiency coefficient R is ters were used as model input. Since the whole training process
0.9991. At the testing regression result, the regression equation is was repeated exactly 12 þ 11 þ 10… þ 1 ¼ 78 times, a total of
9360 networks were trained to obtain as result the ranking of the
Output ¼ 1  Target þ 0:0018 (7) input with respect to the model error. In Fig. 10, the results are
sketched, depth at the very left has the leading impact followed by
which means the best model does not have overfitting problem. totalspm, diff press, etc. The first error values in Fig. 10 give us
the model errors using only depth as input, the second values the
4.2.3 Input Sensitivity Analysis on This Model. It is always a errors using depth & totalspm as input, the third values the errors
challenge to determine which parameters have impact on the using depth & totalspm & diff press, etc.

Fig. 9 Ranking of model input, one single input channel. This figure indicates that when depth
is the input, the ANN gives the lowest MSE, which means depth is the leading factor of this
model.

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 Fig. 10 Ranking of model inputs. MSE has rapidly decreased when the parameters have been
added as inputs.

4.2.4 Comparisons of Parameters’ Ranks Between This Model To have a comprehensive understanding of input impact on the
and The Model of Fruhwirth et al. As we know, dataset used in model, it is also important to do parameter selection procedures
this model was based on three different vertical wells but drilled [37]. Any procedure for parameter selection should have two
in the similar geological areas. This dataset included 12 input components: First, a criterion must be defined by which it is possi-
parameters in total. As a reference, the model of Fruhwirth et al. ble to judge whether one subset of parameters is better than
was based on two different directional wells which drilled in the another and second, a systematic procedure must be found for
similar geological areas. That model included 17 input parameters searching through candidate subsets of parameters. It is possible
in total. Although a model can be created with different selections that the created model can be more reliable if we combine all the
of drilling parameter packages, the ranks of drilling parameters related parameters together for consideration. That means the
should not have large variety when we compare the shared input more comprehensive dataset we have, the more reliability the cre-
parameters by two models. ated model would have.
To verify our created model, we compared the ranks of those
shared input parameters between our model and the model of 4.2.5 Simulation to Verify the Quality of the Developed
Fruhwirth et al. The ranks result of the model of Fruhwirth et al. Model. After the process of determining the optimal network
is shown in Fig. 11. By comparing Figs. 10 and 11, the shared model and input parameter impact on the proposed model, we
input parameters are measured depth, hook load, RPM, ROP, and used 180–200 data points from the rest of field data for simulation,
flow rate. From the trending curves of these two figures, we which was selected from well 1, well 2, and well 3, respectively.
conclude that measured depth has higher rank than other shared Figure 12 gives the simulation result of well 1. Figure 13 gives
parameters in both models. Moreover, parameters like hook load, the simulation result of well 2. Last but not least, Fig. 14 gives the
RPM, ROP, and flow rate have more or less the same degree of simulation result of well 3. These results demonstrated that the
significance in both models. Due to the fact that different field proposed model has predicted accurate pump pressure and
datasets have been used by these two models, it is pointless to matched concisely with the actual field data.
compare all the input parameters. The above observations give us Figure 15 shows a plot of the overall simulation results from a
the conclusion that these two models have good agreement. different perspective. From this diagram, we can see for well 1,
well 2, and well 3, the ANN-simulated pump pressure values are
approximately the same as the measured pump pressure values.
Moreover, it proves that not only the predictive model is

Fig. 12 Simulation cross-plot for well 1 (actual pump pressure

Fig. 11 Ranking of model inputs from the model of Fruhwirth versus predicted pump pressure). The MSE error line is very
et al. close to the zero line.

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 Fig. 13 Simulation cross-plot for well 2 (actual pump pressure
versus predicted pump pressure). The MSE error line is very
close to the zero line.
Fig. 15 The overall simulation results for well 1, well 2, and
well 3
promising but also the division of field data into three subsets is
excellent as well.
needs to overcome the limitations of available data, well condi-
tions, as well as the selections of representative wells.
5 Discussion
Due to boundary conditions in underground while drilling [38], 6 Conclusions
such as in situ mud rheology, well geometry, and pipe roughness,
This paper provides an approach using neural computing meth-
the following assumptions have been made for this application.
ods such as multilayer ANN modeling to predict nonlinear drilling
For a certain NN model, data sets should be selected at normal
optimization problems. The proposed model can not only predict
drilling conditions. Since data collection is extremely significant
pump pressure as a reference range value accurately but also pro-
in the modeling, field data that is reasonable during normal dril-
vide the impact of each input parameter on this particular model.
ling conditions should only be considered. Therefore, in conclu-
The novelty is this paper is validation of computer models with
sion, wrong data, repeated data, and unusual data need to be
actual field data collected from an operator in LA. A very good
deleted before it is used to train the NNs.
agreement between the developed model’s results and actual field
A created model should be considered to be applied for a simi-
data was observed. Following specific conclusions were made
lar geographic field and homogeneous formation. Since field data
based on results of this study:
from well 1, well 2, and well 3 are only selected as data samples,
the proposed model is capable as a predictive tool in similar wells • High accuracy for pump pressure prediction using selected
or similar fields. Moreover, considering more different wells can parameters illustrates that they have essential role in drilling
improve the generalization of the developed model. operation efficiency. The performance of the network model
Throughout this study, only vertical well drilling is considered. depends largely on the size and accuracy of the database and
Due to the limitation of available field data, well drilling records the variables selected for the analysis.
related to inclination angle, dog leg severity, and vertical depth • The application of different drilling parameters data set col-
are not included in the whole data set. For this project, depth lection is suggested in the field of study in order to find the
refers to measured depth as well as vertical depth only if the wells most consistent model. The application of NN for prediction
studied are vertical wells. Further development of this approach of pump pressure showed more confident results, since it

Fig. 14 Simulation cross-plot for well 3 (actual pump pressure versus predicted pump pres-
sure). The MSE error line is very close to the zero line.

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