Prediction of the continuous probability of sand screen-out based on a deep learning workflow

Full text

* Corresponding author.
E-mail address: lei.hou@warwick.ac.uk (L. Hou).
Prediction of the continuous probability of sand screen-out based on a deep
learning workflow
Lei Hou a, *, Yiyan Cheng b, Derek Elsworth c, Honglei Liu d, Jianhua Ren b
a School of Engineering, The University of Warwick, Coventry CV4 7AL, UK
b Research Institute of Exploration & Development, East China Company of SINOPEC, Nanjing 210011, China
c Energy and Mineral Engineering, EMS Energy Institute and G3 Center, Pennsylvania State University, University Park,
16802, USA
d SINOPEC Research Institute of Petroleum Engineering, Beijing 100101, China
Abstract
Sand screen-out is one of the most serious and frequent challenges that threaten the efficiency and
safety of hydraulic fracturing. Current low prices of oil/gas drive operators to control costs by using
lower viscosity and lesser volumes of fluid for proppant injection - thus reducing the sand-carrying
capacity in the treatment and increasing the risk of screen-out. Current analyses predict screen-out as
isolated incidents based on the interpretation of pressure or proppant accumulation. We propose a
method for continuous evaluation and prediction of screen-out by combining data-driven methods
with field measurements recovered during shale gas fracturing. The screen-out probability is updated,
redefined and used to label the original data. Three determining elements of screen-out are proposed,
based on which four indicators are generated for training a deep learning model (GRU – Gated
Recurrent Units, tuned by the Grid search and Walk-forward validation). Training field records
following screen-out are manually trimmed to force the machine learning algorithm to focus on the
pre-screen-out data, which then improves the prediction of the continuous probability of screen-out.
The Pearson coefficients are analyzed in the STATA software to remove obfuscating parameters from
the model inputs. The extracted indicators are optimized, via a forward selection strategy, by their
contributions to the prediction according to the confusion matrix and root mean squared error
(RMSE). By optimizing the inputs, the probability of screen-out is accurately predicted in the testing
cases, as well as the precursory predictors, recovered from the probability evolution prior to screen-
out. The effect of pump rate on screen-out probability is analyzed, defining a U-shaped correlation
and suggesting a safest-fracturing pump rate (SFPR) under both low- and high-stress conditions. The
probability of screen-out and the SFPR, together, allow continuous monitoring in real-time during
fracturing operations and the provision of appropriate screen-out mitigation strategies.
Keywords: hydraulic fracturing; screen-out; deep learning; continuous probability; pump rate

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1 Introduction
Sand screen-out occurs where the proppant in the fracturing fluid creates a bridge across the
evolving fluid-driven fracture, constricts the flow area (eg. the perforation hole, fractures, etc.) and
results in a rapid rise in injection pressure during hydraulic fracturing (Sun et al. 2020; Economides
and Nolte 1989). Screen-out is considered to be one of the most serious problems that threaten the
safety of equipment and individuals during fracturing, reduce the stimulated production and result in
cost overruns due to the time and material consumption related to wellbore clean-up operations and
equipment maintenance (Cleary et al. 1993; E.V. Dontsov and Peirce 2014).
Previous research on the fracturing of conventional reservoirs suggests that the near-wellbore
tortuosity of fractures may play an important role in causing screen-out, in addition to fluid leak-off,
proppant beach-formation and other factors, according to experiments and field measurements (Barree
and Conway 2001; Aud et al. 1994; Daneshy 2007). Based on these mechanisms, screen-out may be
potentially predicted by interpreting time histories of fracturing pressure based on log-log plots (Nolte
and Smith 1981), calculating the configuration of the proppant distribution in fractures (Cai et al.
2017), diagnosing the connection between wellbore and formation through the perforations based on
acoustic measurements (Merry and Dalamarinis 2020), or inspecting the variation with time of the
treatment pressures (Massaras and Massaras 2012), among other indicators. Data-driven approaches
have also been introduced for prediction by integrating the inverse slope method with deep learning
algorithms (CNN-LSTM) (Sun et al. 2020), predicting the fracturing pressure using the locally-
weighted linear regression and CNN-RNN (J. Hu et al. 2020; Ben et al. 2020), and learning pre-
screen-out patterns in the simulated pressure signals (Yu, Trainor-Guitton, and Miskimins 2020).
For unconventional reservoirs, the screen-out mechanism may be more complex, due to larger
volumes of injection, higher pumping rates, elevated injection pressures and multi-staged operations
in the horizontal wellbore (Weng et al. 2011; Li et al. 2015). The resulting complex fracture networks,
compared with the single high-conductivity bi-wing fracture typical in conventional vertical wells, are
required to maximize the stimulated reservoir volume (Warpinski et al. 2009; Qi et al. 2012). The
pressure fluctuations are also more severe than in conventional reservoirs. Rapid rises and drops in

2
pressure are commonly observed in shale gas fracturing (Roussel, Manchanda, and Sharma 2012),
making the previous recovery of diagnostics from the pressure curve more difficult to recover.
Besides, most of the previous efforts provide the screen-out prediction as a discrete classification
result (i.e. screen-out or non-screen-out). The sudden appearance doesn’t reflect the inducements
before the screen-out and also may reserve limited time for the operator to make judgments and
adjustments.
We, therefore, focus on the continuous diagnosis of screen-out by field data processing, attempting
to improve the fidelity of the early warning and define the form of signals that are precursory and
robustly diagnostic of an impending incident. Since mild screen-out could be useful in increasing the
net pressure in the driven fracture and thereby enhance the stimulated volume of the reservoir
(Massaras and Massaras 2012; E. Dontsov and Peirce 2015), the definition of screen-out is first
constrained into the most critical level where fracturing operations are suspended in the open well by
the release of pressure and cleaning of the wellbore is mandated. The determining-element
mechanisms of screen-out are proposed and used to redefine and label the screen-out probability,
which considers a greater number and broader variety of influence factors compared with previous
efforts that have mainly relied on pressure interpretation or proppant accumulation (Massaras and
Massaras 2012; Cai et al. 2017). The pump rate, one of the determining elements, is fitted for the
safest value where the probability of screen-out approaches the minimum. STATA software is used
for the optimization of the model inputs with a deep learning workflow trained then tested against
rigorously selected field examples with known outcomes. The resulting continuous screen-out
probability monitoring and the safest fracturing pump rate may then be used to improve early warning
of screen-out and allow mitigation in real-time to promote safe and efficient fracturing operations.
2 Methodology
New hypotheses of screen-out are proposed to redefine the screen-out probability and extract
indicators for the screen-out predicting. In this work, the definition of screen-out is constrained to the
most serious condition where open-well flushing is necessary – since this is the basis on which our

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field cases are collected. STATA software and a GRU model are applied to these datasets for
parameter analyses and predictions of screen-out probability.
2.1 Hypotheses of screen-out
(i) Determining elements hypothesis: Three determining elements of screen-out for shale gas
fracturing are proposed – namely, pump rate, fracture volume/capacity and proppant accumulation
(Novotny 1977; Patankar et al. 2002; Dahi-Taleghani and Olson 2011; Aud et al. 1994). The
mechanism of screen-out is presumed to result from parameter mismatch among the determining
elements. New indicators are generated based on the element hypothesis to aid machine interpretation
of the raw data. Screen-out probability is redefined by fixing two of the elements.
(ii) Linear-correlation hypothesis: For shale gas fracturing, the pump rate for proppant injection is
near-constant. We assume that the probability of screen-out has a linear relationship with the injected
volume of proppant under constant pump rate and fixed fracture capacity. Then, the screen-out
probability is defined as the ratio of injected proppant volume to the maximum capacity (total
cumulative volume of injected proppant before the restricted screen-out), which is then used to label
the original data. According to this hypothesis, the ideal screen-out probability curve (probability-vs-
fracturing time) is a smooth and continuous increasing line. However, the fracture is considered to
continue propagating during the fracturing operation, which results in a continuous increase in
fracture volume with time (Manchanda et al. 2020; Dahi-Taleghani and Olson 2011). Therefore, the
actual probability may fluctuate regularly around the ideal curve, but with relatively small departures,
due to this continuing fracture propagation.
2.2 Data preparation
2.2.1 Data collection
The field data are collected based on the restricted definition of screen-out (the fracturing
operation is suspended to release pressure and clean the wellbore). 25 stages of fracturing data are
collected from shale gas wells in the Sichuan basin, China, including ~120,000 groups of field
measurements. The parameters in each group consist of both the geological features (well depth,
vertical depth, minimum horizontal stress) and treatment/fracturing records (pump rate, fluid and
proppant type, wellhead pressure, proppant concentration, shut-in pressure and stage length). The

4
original fluid and proppant types are non-numeric parameters and are replaced by the fluid viscosity
and proppant diameter, as representative parameters of performance, respectively.
The data are split into the training (21 stages) and testing datasets (4 stages) for model training and
prediction, as shown in Table 1. The testing stages are rigorously selected by well locations. The
geological and in-situ stress conditions vary as the increasing well distance, which may increase the
difficulty of model prediction, thus providing a more reliable evaluation of the model performance
and application range. One of them is from the same well (Well A) that is also used for model
training. The other three stages come from new wells different from the training wells, one of which is
from a neighbouring well (Well B), and the other two from remote wells (Wells C and D are more
than 200 km distant from all other wells). All wells, noted in Table 2, are drilled within the same
formation.
Table 1 Division of training and testing datasets
Training sets / stage
Testing sets / stage
Notes
Training wells
21
/
/
Well A
/
1
From one of the training wells
Well B
/
1
From a neighbouring well next to
training wells
Well C
/
1
From a well in a different location
of the basin
Well D
/
1
2.2.2 Data labelling, trimming and extracting
Screen-out probability is calculated and used to label the original field measurements according to
our most severe definition. We truncate the field record following screen-out to direct the machine to
the experience pre-screen-out. Although the training results may be influenced by the missing data, it
boosts the interpretation of the pre-screen-out data, then benefits the continuous monitoring for the
generation of screen-out. It may also prevent the model from cheating by recognizing the overpressure
or pump-off for screen-out, which bypasses the deeper interpretation of data. Similar data processing
is also reported by previous research (Yu, Trainor-Guitton, and Miskimins 2020).
Four new indicators of screen-out are proposed based on the element hypothesis to assist the
model prediction – the downhole pressure after hole perforation (DPP), the ratio of the accumulated

5
volume of injected proppant to that of injected fluid (Vs/Vf), the wellhead pressure change in a unit
volume of injected fluid (ΔP/ΔVf) and the ratio of minimum-horizontal stress to shut-in wellhead
pressure (σmin/Ps). The DPP, calculated from the wellhead pressure, may reflect the pressure variation
induced by fracture propagation and new fracture generation (E.V. Dontsov and Peirce 2014;
Willingham, Tan, and Norman 1993). Details of pressure conversion can be found in Appendix A.
The Vs/Vf ratio represents proppant accumulation in fractures. The ΔP/ΔVf ratio is similar to the
pressure slope returned under a constant pump rate (Massaras and Massaras 2012). The σmin/Ps ratio
reflects the change in in-situ stress due to the material injection (Hayashi and Haimson 1991).
2.3 Data processing tools
The parameter analyses are carried out in STATA 17.0 to assist the selection of model inputs. The
data training and testing are performed using a GRU model built in the Spyder environment. The
GRU algorithm, designed for extracting information from time sequences (Cho et al. 2014), has
performed well in various petroleum engineering applications (Wang et al. 2019; Sun et al. 2020).
According to previous experience (Fan et al. 2021; Sagheer and Kotb 2019), a three-layer (including
the output layer) GRU is established with the activation function ‘ReLu’ operating in each layer (Gal
and Ghahramani 2015). The regularization is performed to avoid overfitting by setting a dropout rate
(of 0.2) behind the first and hidden layers. The ‘Adam’ is selected as the optimizer to compile the
model, where a callback function is applied to return and automatically update the learning rate
(Kingma and Ba 2014; Zeiler 2012). Other hyperparameters, including the number of neural units
(30), epochs (30) and batch size (100) are optimized by the Grid search and Walk-forward validation
(Bergstra and Bengio 2012; M.Y. Hu et al. 1999; Stein 2002). Details of model tuning can be found in
Appendix B.
The workflow of data processing is graphically illustrated in Fig. 1. The original field
measurements and extracted indicators are analyzed by the Pearson correlation coefficients in
STATA. The GRU model is initially trained using the selected original parameters, and the results are
used as a reference. The indicators are appended to the inputs successively for optimization based on
the forward selection strategy. The model performance is promoted by indicator optimization and is
verified by the testing cases. The deep learning workflow proposed in this study has high feasibility

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for different application scenarios if provided with the corresponding datasets for the model training.
It is also possible to promote the performance of the workflow by feeding into new data.
Fig. 1 The workflow of data processing, consisting of data collection, pre-processing and model training.
3 Results
Interfering parameters are removed from the model inputs according to the Pearson coefficient
analyses. The confusion matrix and the root mean squared error (RMSE) are used as criteria for the
model evaluation, in which the RMSE has the same unit as the prediction (Chai and Draxler 2014).
The optimized indicators improve the prediction by halving the reference RMSE and eliminating the
false-negative errors. Successful reports of screen-out and accurate predictions of its probability are
achieved – and may be used in continuous monitoring of fracturing operations.
3.1 Pearson correlation coefficient analyses
The Pearson correlation coefficient is the covariance of the two variables divided by the product of
their standard deviations and is used to quantify the potential interference between variables (Benesty
et al. 2009). The inputs of the deep learning model are analyzed in STATA, and the results are
summarized in Table 2. The higher the coefficient is, the stronger the interference that may exist
between the two variables. Using the coefficient as a reference, we remove the variable that may
significantly interfere with other multiple variables. The Well depth shows high coefficients with the
Vertical depth and Stage length, as well as the Vertical depth with Minimum-horizontal-stress,
Wellhead pressure and DPP. Therefore, the Well depth and Vertical depth are removed from the
inputs of the model training.
The optimization of model inputs is performed with care and with appropriate reference to
engineering experience and preserving as much parameter/information as possible for the GRU

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neuronal units. For instance, the large coefficient linking proppant diameter and proppant
concentration may be due to the characteristics of the data (they are always present in pairs). These
variables are reserved because the diameter and concentration of proppant may each contribute to
screen-out but by different mechanisms (sealing the hydraulic fracture alternately by bridging or
filling, respectively.). There is also a concern that removing the proppant-related features may mislead
future works when collecting the original data.
Table 2 The Pearson correlation coefficients between training variables
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(1)
1
(2)
0.64
1
(3)
0.10
0.44
1
(4)
-0.77
-0.43
0.30
1
(5)
0.13
-0.04
-0.15
-0.20
1
(6)
-0.08
-0.15
-0.14
0.04
-0.21
1
(7)
-0.11
-0.06
0.02
0.14
-0.24
0.51
1
(8)
-0.09
-0.06
0.02
0.11
-0.25
0.50
0.80
1
(9)
0.47
0.70
0.47
-0.18
-0.06
0.25
0.12
0.16
1
(10)
0.30
0.74
0.58
0.00
-0.02
-0.43
-0.19
-0.15
0.71
1
(11)
-0.17
0.03
0.12
0.23
-0.37
0.67
0.54
0.57
0.35
-0.04
1
(12)
0.02
0.02
-0.01
-0.01
-0.01
-0.04
-0.02
-0.02
-0.02
0.01
-0.02
1
(13)
0.43
0.83
0.47
-0.10
-0.07
-0.16
-0.04
-0.05
0.71
0.80
0.05
0.02
1
(14)
-0.03
0.07
0.02
0.01
-0.31
0.55
0.41
0.49
0.41
0.02
0.86
-0.02
0.04
1
Notes: The original measurements: (1) Well depth; (2) Vertical depth; (3) Min-horizontal stress; (4) Stage
length; (5) Fluid viscosity; (6) Pump rate; (7) Proppant concentration; (8) Proppant diameter; (9) Wellhead
pressure. The extracted indicators: (10) DPP; (11) Vs/Vf; (12) ΔP/ΔVf; (13) σmin/Ps. The dependent variable: (14)
Screen-out probability.
3.2 Screen-out prediction based on original measurements
The original field measurements, parameters (3) to (9) in Table 2, are used as inputs to the GRU
model for screen-out probability prediction. The results are shown in Fig. 2, where the time histories
of pump rate, proppant concentration and wellhead pressure are also presented. The confusion matrix
and the RMSE are used as dual criteria for evaluating the predictions. We define that a predicted
screen-out probability higher than 0.9 generates a report of screen-out. The workflow based on the
original parameters fails to give the correct screen-out warning in three of four testing cases. Three
false-negatives (FN error, in Wells A, C and D cases, as shown in Figs. 2 a, c and d), four false-
positives (FP error, in Wells B and D cases, as shown in Figs. 2 b and d) and only one correct

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prediction are reported, as shown in Table 3. There is essentially no pattern for the predicted curves
that produce RMSEs of 0.230 (Well A), 0.236 (Well B), 0.150 (Well C) and 0.369 (Well D),
respectively, compared with the labelled probability.
Fig. 2 Prediction of screen-out probability using the original measurements from (a) Well A, (b) Well B,
(c) Well C and (d) Well D. The blue dashed circle marks the false alarm of screen-out in Wells B and D.
The solid orange line is the labelled screen-out probability curve. The dashed line is the predicted
probability curve. The wellhead pressure, pump rate, proppant concentration are presented to show the
operation procedures.
Table 3 The confusion matrix of the predictions based on original parameters
Predicted events
Screen-out
Non-screen-
out
Actual
events
Screen-out
1 (Correct)
3 (FN error)
Non-screen-
out
4 (FP error)
/

9
3.3 Prediction promotion by optimizing indicators
The predictions are improved by optimizing the extracted indicators compared with the results
based on original measurements. The forward selection strategy is applied for the optimization, during
which the indicator is appended sequentially to the model inputs. The primary indicator that promotes
the prediction is selected, and the others decreasing model performance are abandoned.
The first testing indicator is decided by regression analyses using the OLS (ordinary least squares)
method (executed in STATA) to produce the best prediction with the least indicators. The results are
summarized in Table 4. The Vs/Vf ratio increases the R-squared value more than do the other
indicators (from 0.483 to 0.799), indicating the most significant contribution of Vs/Vf to the screen-out
probability prediction. Therefore, the Vs/Vf is chosen as the first testing parameter for the forward
selection.
Table 4 Regression results between indicators and screen-out probability
Dependent
variable
Screen-out probability
Independent
variables
DPP
-0.001
-0.005
Vs/Vf
21.669
21.914
ΔP/ΔVf
0.000
0.000
σmin/Ps
-0.473
-0.257
Control
variables
Min-horizontal stress
-0.013
-0.01
-0.012
-0.013
-0.013
-0.012
Stage length
0.002
0.003
-0.005
0.002
0.003
-0.003
Fluid viscosity
-0.005
-0.005
-0.001
-0.005
-0.005
-0.002
Pump rate
0.016
0.013
-0.008
0.016
0.009
-0.024
Proppant concentration
-0.005
-0.005
-0.012
-0.005
-0.002
-0.010
Proppant diameter
0.709
0.707
0.283
0.709
0.641
0.233
Wellhead pressure
0.008
0.010
0.003
0.008
0.013
0.012
Constant
0.328
0.328
0.328
0.328
0.328
0.328
R-squared
0.483
0.483
0.799
0.483
0.513
0.821
The results of the forward selection are presented in Table 5, using the confusion matrix and
RMSE as the dual criteria. The introduction of Vs/Vf boosts the model performance by significantly
reducing the RMSE and increasing the number of correct predictions by a single instance. The
combination of Vs/Vf and DPP in the second round selection predicts the ultimate occurrence of
screen-out events in three of four testing cases and halves the number of false-positives. By adding the
ΔP/ΔVf ratio, the workflow successfully reports all of the screen-out events and produces the lowest
RMSE in all testing rounds. Therefore, the indicators in the first three rounds are all selected. The

10
σmin/Ps in the last round is abandoned due to the increasing RMSE and false-negative error, as shown
in Table 5.
Table 5 Results of the indicator optimization by the forward selection
Forward
selection
Indicators appended
to model inputs
FP
error
FN
error
Correct report
/Total event
Averaged
RMSE
Decision
Reference
/
4
3
1/4
0.246
/
Round 1
Vs/Vf
4
2
2/4
0.176
Selected
Round 2
Vs/Vf + DPP
2
1
3/4
0.130
Selected
Round 3
Vs/Vf + DPP +
ΔP/ΔVf
3
0
4/4
0.089
Selected
Round 4
Vs/Vf + DPP +
ΔP/ΔVf + σmin/Ps
6
0
4/4
0.126
Abandoned
The predictions in the third-round test are shown in Fig. 3. Three false-positives are observed for
Wells C and D that are located distant from the training cases (wells), as marked by dashed circles in
Figs. 3 (c) and (d). The false-positive error (the false alarm) is considered less serious than the false-
negative error (the missing alarm) (Pounds and Morris 2003). Besides, the false alarms are reported at
the end of the fracturing operation, and about 15 minutes ahead of the actual screen-out, which may
be acceptable. Therefore, the GRU-based workflow, trained by the original and extracted parameters,
reports accurate screen-out warnings and exerts stable performance in rigorous applications. The
continuous monitoring of screen-out probability allows the field operator to receive pre-warning and
allow rapid response in near-real-time, which is more efficient and practical than the previous discrete
predictions.

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Fig. 3 Promoted predictions of screen-out probability by model inputs optimization based on (a) Well
A, (b) Well B, (c) Well C and (d) Well D. The inputs of the model are consist of the original measurements
and three optimized indicators (Vs/Vf + DPP + ΔP/ΔVf). The blue dashed circle marks the false alarm of
the screen-out in the Wells C and D cases. The solid orange line is the labelled screen-out probability
curve. The dashed line is the predicted probability curve.
4 Discussion
4.1 Inducement analysis based on continuous probability
The probability curve before the screen-out also provides clues for the inducement analysis. In Fig.
3 (a), the long proppant injection slug between 4000s and 5000s increases the screen-out probability
near to the value of 0.8, indicating that the continuous-proppant-injection length may be one of the
key factors causing the screen-out in this case. In Fig. 3 (b), a vertical ascent of probability is
observed around 3000s, when the 40/70 mesh proppant is injected right after the 100 mesh one. The
fracture may not be well cracked with a relatively narrow width that is sensitive to larger proppant
grain. The underdeveloped fracture may be an important inducement for Well B. The pressure
fluctuations in Well A and B also show similar periods to the probability variations.
For Wells C and D, the sign showing in pressure is inconspicuous because it deviates only slightly
from the norm, as shown in Figs. 3 (c) and (d). The probability can still define distinct indications
precursory to screen-out. A long proppant slug may be one of the main reasons causing the screen-out
in Well C, according to the rapid climb in probability between 6000s and 8000s in Fig. 3 (c).
Meanwhile, a different mechanism prompting screen-out is disclosed in Well D. The probability
begins increasing after 2000s when four slugs of fine proppant (100 mesh) are injected. In the 7th, 8th,

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11th and 12th proppant slugs, 100 and 40/70 mesh proppants are successively injected (the short
vertical lines in the middle of those concentration curves denote the switching between proppants),
which all cause significant fluctuations in the probability curve at ~4000s and ~6000s. Conceivably,
fine proppant may have filled micro- and secondary fractures, which should be beneficial to the
stimulation. However, the 30/50 mesh proppant, not commonly used due to its large size, is injected
during the last slug. The larger diameter proppant builds pressure in the main fractures, which may be
difficult to be relieved as a result of staunched flow through the fully-packed minor fractures - hence
triggering a screen-out.
According to the inducement analyses, the proppant may be injected slower to control the slug
length for Wells A and C. Larger proppant may be switched later to allow a sufficient propagation of
fracture for Well B. The amount of fine proppant should be controlled, especially when large diameter
proppant is employed for Well D. However, adopting fine-grained proppant can be a double-edged
sword. Certainly, it fills the minor fractures and boosts the growth of main fractures by increasing the
net pressure. However, conversely, it may also reduce the pressure tolerance and increase the
probability of screen-out, thus should be used with caution.
4.2 Support of the screen-out hypotheses
The predicted probability of screen-out varies in a similar period to the wellhead pressure
variations (Fig. 3), indicating that the GRU model interprets the relationship between wellhead
pressure and screen-out events when the data are manually trimmed. The predicted curves fluctuate
around the labelled curves due to the finite and substantial variation in evolving fracture volume,
which supports the linear hypothesis of screen-out probability. In addition, the Vs/Vf ratio represents
the proppant accumulation in downhole fractures. The DPP and ΔP/ΔVf variations could result from
the pressure response to fracture creation and propagation. The combination of these indicators
significantly promotes predictions, which supports the determining elements hypothesis.
Additionally, the variation of underground fracture is currently difficult to detect and is a non-
directly-adjustable parameter. Proppant accumulation may be the most significant indicative element
considering the RMSE improvement in Table 5. Pumping rate is the single most important element
that may be adjusted to ensure the operation safety. Emergency termination or reduction in pumping

13
rate is commonly used to control the pressure when the first signs of screen-out appear (Yew and
Weng 2014). Therefore, it is essential to reveal the effect of pump rate on screen-out probability based
on both training and testing datasets.
4.3 Effect of pump rate on screen-out probability
A U-shaped correlation between pump rate and screen-out is proposed according to the
observation that both extremely low (aggravating the proppant settling and dune building-up) and
extremely high (increasing the frictions and reshape the proppant dune) pump rates may result in sand
screen-out (Harris and Pippin 2000; Willingham, Tan, and Norman 1993). This is demonstrated by
fitting the correlation between the square-of-pump-rate with screen-out probability in STATA bases
on both training and testing datasets. A small p-value (a smaller p-value reflects stronger evidence in
favour of the hypothesis) and a positive coefficient are obtained, as shown in Table 6, which supports
the U-shaped form hypothesis.
Table 6 Summary of regressions between the squared pump rate and screen-out probability
Dependent
variable
Screen-out probability
Independent
variables
Pump rate
-0.042***
Squared pump rate
0.003***
Control
variables
Mini-horizontal-stress
-0.021***
-0.014***
Stage length
0.004***
0.002***
Fluid viscosity
-0.005***
-0.003***
Proppant concentration
0.817***
0.700***
Proppant diameter
0.003***
-0.007***
Wellhead pressure
0.010***
0.010***
Constant
0.328***
0.281***
R-squared
0.442
0.501
Notes: *** p<0.01, ** p<0.05, * p<0.1.
A flat U-shaped curve is observed with a minimum where the screen-out probability is lowest, as
shown in Fig. 4. The pump rate at this minimum probability is 5.94 m3/min based on the collected
data in this work, which is defined as the safest fracturing pump rate (SFPR). An adjustment in pump
rate is one of the most essential and frequent measures to maintain pressure and ensure safety during
shale gas fracturing (Yew and Weng 2014). The newly defined SFPR can be used as a reference for

14
the real-time pump rate adjustment, which may aid in rapidly reducing the pump rate to the safest
range to prevent or mitigate screen-out.
Fig. 4 U-shaped correlation between squared pump rate and screen-out probability. The vertical
dashed line marks the pump rate at the turning point, which is 5.94 m3/min.
The moderating effects of in-situ stress on the SFPR are studied based on both the low(er) and
high(er) stress datasets, split by the median value (55 MPa) of the minimum-horizontal stress. These
results are presented in Fig. 5. The SFPR moves rightward under the low-stress condition and grows
to 8.33 m3/min at the minimum probability. This reduces to 4.25 m3/min for high(er)-stress
conditions. In addition, the U-shaped curve is steeper for the low-stress condition, indicating that the
probability of screen-out is more sensitive to a variation in pump rate and that the lifting of pump rate
should be pursued with moderation. It is noteworthy that the SFPR may not be the most effective
choice in practice since the operator may be willing to take certain risks to improve the economics of
the stimulation job. However, it could be an important index to prompt pump rate adjustment to
minimize loss when the first signs of the screen-out appear.
Fig. 5 Moderating effects of in-situ stress on the U-shape correlation. The vertical dashed line marks
the extreme point excursion under (a) low-stress and (b) high-stress conditions. The pump rates at the
turning points are 8.33 and 4.25 m3/min, respectively.

15
5 Conclusions
A new awareness of screen-out mechanisms is highlighted by proposing and testing hypotheses
based on a deep learning (GRU algorithm) workflow and the STATA software. Shale gas fracturing
measurements are collected with a strict definition of screen-out applied (when the operation is
suspended for pressure-release and wellbore-cleaning) to allow the binning of data. Time histories of
fracturing parameters are truncated after screen-out to force the GRU model to interpret the pre-
screen-out data – this is shown to improve the prediction of screen-out occurrences. A forward
selection strategy is applied to optimize the model inputs, based on which accurate screen-out
probability predictions are obtained. The major conclusions may be generalized as follows:
(1) By tuning the GRU model and optimizing the inputs, an accurate screen-out probability is
produced in the testing cases for wells at different distances from the training wells. The GRU-based
workflow successfully reports all the screen-out events and constrains the RMSE to ~0.089. The
resulting continuous probability curve aid the field engineer to effectively monitor the evolution of
screen-out, make rapid pre-judgements and prescribe mitigating actions in real-time. Besides, the
variation in probability precursory to screen-out provides valuable clues regarding triggering
mechanisms. For example, the length of the proppant slug, the timing of the switching of proppant
sizes and the use of fine proppant are analyzed for the testing cases based on the evolution of the
probability curves. Explicit strategies are proposed for optimizing the proppant selection and
injection.
(2) Fracture volume, proppant accumulation and pump rate are proposed as three discriminating
elements potentially contributing to screen-out, with these applied in data pre-processing in the
workflow. This presumption is supported by producing the smallest prediction errors in the
optimization of model inputs. Unique features of the mismatch among these elements may provide
simple diagnostics for the mechanism of screen-out for shale gas fracturing. Fracture volume is a non-
directly-adjustable parameter that may be reflected by the pressure variations. Proppant accumulation
may be a significant indicative parameter for screen-out. Pumping rate is shown to be the most
important adjustable element that controls the fracturing pressure. This three-determining-element

16
mechanism extends the characteristic parameters for screen-out study compared with traditional
methods depending on pressure interpretation or proppant accumulation.
(3) A safest-fracturing pump rate (SFPR) is defined by fitting the U-shaped correlation between
the screen-out probability and pump rate – this is 5.94 m3/min based on the collected data. The
moderating effect of in-situ stress on the SFPR shows that conditions of higher-stress reduce the
SFPR. Conditions of lower-stress increase the SFPR, but also increase the relief of the U-shaped
relation, indicating a higher sensitivity to pump rate that requires only a moderate adjustment. The
SFPR may be used as a reference to guide the rapid adjustment of the pump rate into the safest range
to potentially mitigate screen-out.

17
Acknowledgement
This research has received funding from the European Union's Horizon 2020 research and
innovation programme under the Marie Sklodowska-Curie grant agreement No. 846775.

18
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