paper

1. Estimation of underground interwell connectivity: A data-driven
technology
Ehsan Jafari Dastgerdia
, Ali Shabanib,
*, Davood Zivarc,
*, Hamid Reza Jahangirid
a
Department of Petroleum Engineering, Khazar University, Baku, Azerbaijan
b
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran
c
Special Core Analysis Lab, Petro Makhzan Kav (PMK), Tehran, Iran
d
Department of Chemical and Petroleum Engineering, Iran University of Science and Technology, Tehran, Iran
A R T I C L E I N F O
Article History:
Received 21 August 2020
Revised 17 October 2020
Accepted 9 November 2020
Available online xxx
A B S T R A C T
Water injection into petroleum reservoirs is widely performed around the world for enhancing oil recovery.
Understanding the underground fluid path is an important factor in improving reservoir performance under
waterflooding operation. This may be used to optimize subsequent oil recovery by changing injection pat-
terns, assignment of well priorities in operations, recompletion of wells, targeting infill drilling, and reduce
the need for expensive surveillance activities. Most of the hydrocarbon reservoirs are equipped with sensors
that measure the flow rate, pressure, and temperature in the wellbores continuously. Valuable and useful
information about the interwell connections can be obtained from the measured data. In the present paper, a
novel data-driven approach is developed that contributes to estimating the underground interwell connec-
tions through analyzing and processing the injection and production data of a petroleum reservoir. This novel
data-driven technology is named Detection of Events (DoE) and combines with the Capacitance Resistance
Model (CRM) to quantify the connections between injectors and producers. The proposed approach has been
applied to both synthetic and field cases. The results of the method show a good agreement between CRM
and DoE for the field case (75%), and present a good insight into the better understanding of the underground
connections.
© 2020 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.
Keywords:
Data-driven approach
Capacitance resistance model (CRM)
Detection of events (DoE)
Interwell connections
1. Introduction
Data acquisition systems are used in the petroleum industry to
monitor the field operation continuously. The gathered data can be
used for the well-log prediction, risk analysis, reservoir management,
drilling engineering, and uncertainty analysis through applying dif-
ferent data-driven methods [1,3,4,24,25]. Injection of water into the
oil reservoirs for enhancing oil recovery is widely used around the
world since the early days of the petroleum industry. Increasing the
oil recovery by waterflooding can prolong the life of a petroleum res-
ervoir. Waterflooding needs detailed management and continuous
monitoring. During a waterflooding operation, understanding the
underground fluid paths is necessary information for the efficient oil
displacement, determination of infill drilling, and injection-produc-
tion pattern. This information depends on the quality of the connec-
tion between wells of the reservoir. There are different methods to
quantify the underground connection among the wells including tra-
ditional simulators, tracers, and data-driven approaches
[2,8,12,15,17,30,31,33]. Traditional simulators have been used by the
petroleum companies as a standard reservoir evaluation method.
However, due to the limitations of the modeling techniques, reservoir
simulators might not fully represent the true reservoir performance.
Besides, maintaining a truly representative full reservoir simulation
model for the routine and frequent analysis of waterflood perfor-
mance prediction is a challenging process. Nowadays, using tracers is
not common in the petroleum industry, because it takes a long time
for the tracers to breakthrough, which makes the procedure time and
money consuming.
Over the past few years, several data-driven approaches based on
available reservoir data have been introduced and developed for pre-
diction of the production rates and the connections between wells
[5,23,37]. Some researchers used a data-driven interwell numerical
simulation model (INSIM) for modeling waterflooding [9,39]. Other
researchers used spearman rank correlations to find the connectivi-
ties between injectors and producers of a field [10,27,28,32].
Recently, capacitance resistance models were introduced for water-
flooding studies and were used widely by companies and researchers
for estimating the connections between the wells of a reservoir
[6,7,16,1821,23,29,36,38]. This intuitive and numerically fast tech-
nique utilizes only the injection and production data. It exhibits the
* Corresponding authors.
E-mail addresses: alishabani.sharif@gmail.com (A. Shabani), Davood_zivar@yahoo.
com (D. Zivar).
https://doi.org/10.1016/j.jtice.2020.11.008
1876-1070/© 2020 Published by Elsevier B.V. on behalf of Taiwan Institute of Chemical Engineers.
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2. strengths of the injector-producer connections without geological
information [35]. Izgec and Kabir [11] introduced the CRM as a reli-
able method that its results have a good agreement with traditional
reservoir simulations [11]. Moreno [22] and Zhao et al. [39] tried to
find the connectivity in multi-layer systems [22,39]. Shabani et al.
[31] used CRM for understanding the injectors’ efficiency and analyz-
ing the interwell connections. The neural network also can be used
for prediction of the production rate and the interwell connections
[5,26,34]. Artun [5] used weight factors achieved from the neural net-
work to define the quality of connections between injectors and pro-
ducers of a synthetic reservoir [5]. As the neural networks are not the
physics based methods, they cannot estimate the interwell connec-
tions as efficient as CRMs [13,14,26]. Jahangiri et al. [12] developed
and applied Top-Down WaterFlood (TDWF) diagnostics and optimi-
zation method for the North Sea and used it as a “virtual” interwell
tracer. As demonstrated for the North Sea field, the efficiency of the
most recent injector in the field will be understood without the need
to await the results of a tracer program.
In this paper, we present a novel approach named Detection of
Events (DoE), based on relating the injection and production data of a
real reservoir. The proposed approach complements CRM by data
mining techniques to quantify and validate the CRM injector-pro-
ducer connection estimates. This has implications when it comes to
prioritizing water injectors when optimizing injection under various
water constraints (e.g. individual well, well pad and/or total vol-
umes). The proposed method is tested for the synthetic and real res-
ervoirs, then the results are compared with the results of CRM. The
structure of the paper is as follows: Section two presents the mathe-
matical methodology. Results and discussions of the proposed
method are presented in section three, and section four presents the
conclusions.
2. Mathematical methodology
Understanding the underground interwell connections presents
valuable information about the performance of a waterflooding
operation. For estimating the interwell connections in the present
study, both analytical capacitance resistance model (CRM) and detec-
tion of events (DoE) approach are used. These two complementary
data-driven methods, which do not require any geological or
dynamic reservoir models, quantify the underground connections
between the injectors and the producers.
2.1. Capacitance resistance model (CRM)
A detailed methodology of the capacitance resistance model is
presented in this section. Capacitance resistance models are used in
most engineering fields including electrical, chemical, petroleum, etc.
In the petroleum industry, CRM enables a reservoir engineer to esti-
mate production rates of producers, and understand the under-
ground connection between each pair of injector-producer through
history matching of the production data [22,29].
By assuming different control volumes, different forms of the CRM
can be developed, including CRMT, CRMP, and CRMIP [29]. Among
different forms of CRM, the CRMP (CRM Producer) can be used for a
system of multi-well. It can estimate the production rate of producers
and the quality of the underground connection between each pair of
injector-producer. By assuming a constant productivity index (J), and
a step variation of the injection rate and production pressure in the
time interval of Dtk, the production rate of each producer can be esti-
mated by the underlying equation [29]:
qjðtkÞ ¼ qjðtk1Þe
Dtk
tj þ 1e
Dtk
tj
X
Ninj
i¼1
fijIi
k
Jjtj
DPk
w;j
Dtk
#
ð1Þ
In this equation, qj, tj, and Jj are the production rate, the time con-
stant, and the productivity index of the jth producer respectively. fij is
the connection factor between the ith injector and the jth producer, Ii
is the injection rate of the ith injector, and Njnj is the number of active
injectors. The connection factor (fij), time constant (tj), productivity
index (Jj), and the primary production rate of the producer (q0) are
estimated using the optimization process. It is obvious that the sum
of the connection factors between an injector and other producers
must be less than one as presented below (Npro is the number of
active producers in the reservoir):
X
Npro
j¼1
fij1 ð2Þ
The calculated connection factors (fij) create a matrix and are used
for identification of the quality of the connection between each pair
of injector-producer. The high value of the connection factor means
that there is a stronger underground connection between the injector
and producer. According to the magnitude of the connection factor
between each pair of injector-producer, the quality of the connection
is defined as presented in Table 1.
2.2. Detection of events (DoE)
DoE is a quantitative method for identifying the flow path
between injectors and producers of a reservoir. This method is based
on finding relations between injection and production events. A flow
rate or a pressure event is defined as the certain changes in that flow
rate or pressure in a certain period of time. For determination of the
Nomenclature
AP Agreement parameter
fij Fraction of the rate of injector i that is towards to the
producer j
Ii Injection rate of the ith injector (STB/Day)
Jj Productivity index of the jth producer (STB/Day.psi)
Ninj Number of injectors
Npro Number of producers
ng Number of the elements in the green squares of the
Boston matrix
no Number of the elements in the orange squares of the
Boston matrix
nr Number of the elements in the red squares of the
Boston matrix
Pw Wellbore pressure (psi)
Q Flow rate (STB/Day)
qj Production rate of the jth producer (STB/Day)
Scoreij Score of the connection between the injector i and
the producer j in DoE
Tmin Minimum time lag for an event of an injector to be
seen in a producer (Days)
Tmax Maximum time lag for an event of an injector to be
seen in a producer (Days)
T Time (Days)
a Constant variation derivate (STB/Day2
or psi/Day)
b Minimum event variation
Table 1
Quality of the connections according to the connection factor
matrix in CRM.
Amount of the connection factor Quality of the connection
fij 0.2 Weak
0.2 fij 0.5 Medium
0.5 fij Strong
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3. quality of connection between each pair of injector-producer, DoE
detects injector and producer events, then it identifies that every one
of the producer events is due to changes in producer choke valve or
caused by the certain injector event. According to the number of evi-
dences that represent the connection between each pair of injector-
producer, an interwell connection will be assumed for these wells.
In order to discriminate between non-connection events (trig-
gered by an operator intervention at the surface) and connection
events (due to the reservoir response to other inputs), evidence for
operator action is required. When the operator changes the choke
valve size, the flow rate and wellbore pressure change simulta-
neously. These variations lead to non-connection events that are not
representative of a connection between wells. DoE requires injection
rates of the injectors for identification of event start date and dura-
tion. But in producers, DoE requires flow rate and wellbore pressure
in order to check whether the events are made by a change in the
choke valve or not.
DoE is implemented in 3 steps including, 1) detection and evalua-
tion of the events in the injection rates of the injection wells, 2)
detection of the events in the production rates and bottom-hole pres-
sure (BHP) of the production wells, and 3) comparison and evaluation
of the event in order to find the connectivity and association between
each pair of injector-producer. The steps of a DoE algorithm are pre-
sented below:
2.2.1. Detection and evaluation of the events in the injectors
In the first step, the events of injection rates are identified. The
event of an injector rate means a sharp change in injection rate, shut-
in of the injector, or its constant flow rate (during a certain period of
time). For an injection flow rate, four types of events exist, including
Increases, Decreases, No flow, and Smooth. In Table 2 and Fig. 1, four
types of these events have been presented.
No flow events are detected easily from the injection data. In
order to detect other types of events, it is required to define a crite-
rion (based on derivate of flow rate), to find out whether the flow
rate is increasing, decreasing, or constant. For this purpose, it is
required to define a parameter named constant variation derivate
(a). A constant variation derivate is a constant number (derivate) for
determining types of changes in the wellbore flow rate. The slope of
the flow rate diagram versus time (@Q
@T ) is compared with the value of
a in order to recognize the type of events in each day, as presented in
Table 3. In Table 3,Q is the flow rate and T is the time.
After finding the type of events in each day, the same and sequen-
tial daily events are merged. For example, 2 sequential increasing
events in each day are merged to have an increasing event that lasts
for 2 days. Then, in order to find the considerable Increasing and
Decreasing events, the absolute change of flow rate to its primary
value is compared with a parameter named minimum event variation
(b) as presented in Table 4. Those events that their absolute variation
is less than b are excluded from the Increasing and Decreasing events
and allocated to the Smooth events.
2.2.2. Detection of the events in the production rate and pressure of the
production wells
For each producer, daily events of production rate and wellbore
pressure are detected using the method presented in the previous
section (same procedure as the injection flow rate). For daily events
of wellbore pressures, the value of constant variation derivate (a) is
different from the one for flow rates. No merging will be done for the
events of production wells, and there is only daily events for the pro-
duction rate and wellbore pressure. This is because these daily events
are required to detect the events which are created by the operator
(changing choke valve size). For instance, if the operator is opening
the choke valve (Increasing event of the production rate in the pro-
ducer), the pressure of the producer is decreasing so rapidly
(Decreasing event of the pressure in the producer). This escalation in
the production rate of the producer is not representative of an inter-
well connection because it is not created by increasing the injection
rate of other injectors.
Fig. 2 shows an example of a change in choke valve size. The rate
of the injector i is decreasing on day 62, and it seems that with 5 days
lag time the flow rate of producer j is decreasing too (due to the injec-
tor i). But, the pressure of the producer j is increasing. This means that
the reduction in the producer rate is due to the choke valve closing by
the operator, and these events are not representative of the connec-
tion between injector i and producer j.
2.2.3. Comparison and evaluation of the events to find the connection
between each pair of injector-producer
As discussed in the previous section, although some events in the
production wells are created by the operator, there are some other
events in the production wells that have been created by the injec-
tion wells as presented in Table 5.
For instance, as can be observed in Fig. 3, the production rate
event in the producer j is increasing (on day 110), meanwhile the
pressure event of the producer is constant. If this increment in the
producer rate was due to the opening of the choke valve, the pressure
of the producer would be decreasing so rapidly which is not the case
here. This means that an external factor is supporting the producer.
In this situation, if the injection rate event in the injector (with a
proper lag time) is increasing too, this pair of injector-producer will
be assigned one score. As shown in Fig. 3, there is an increasing event
in the injector i on the 100th day, so this pair of injector-producer
will be assigned one score in DoE. The minimum lag time (Tmin) and
the maximum lag time (Tmax) after the beginning of the injector event
are selected as the boundaries for evaluation of producer events. Only
the production rate and pressure events that their start time is in this
timespan will be considered for scoring. The values of Tmin and Tmin
depends on the size of the reservoir, and are as the input parameters
determined by the user. In Fig. 4, two sequences of events that show
the connection and non-connection between one pair of injector-
producer (for a real case), have been presented.
After surveying all of the events between each pair of injector-
producer, a score matrix with Ninj columns and Npro rows is produced.
Then, according to the 10 percentile and 50 percentile of the score
matrix, the quality of the connection is determined as presented in
Table 6.
3. Results and discussions
For analysis the correctness of the proposed method, both syn-
thetic and real waterflooding cases were studied in this section. For
each case, CRM and DoE are run to find the connection between
wells. Then, the estimated interwell connections of both methods are
compared and discussed.
3.1. Synthetic case
A simple synthetic waterflooding case was used in this section to
perform a detailed analysis of the results of the DoE. The synthetic
case is a homogeneous 1D reservoir that has been flooded for 100
Days. It consists of only one injection well and two production wells
as presented in Fig. 5. For simplicity of the synthetic case, the
Table 2
Events of the flow rate.
Event name Definition
Increasing An increase in flow rate
Decreasing A decrease in flow rate
No flow Shut-in well
Smooth Flow rate is almost constant
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4. bottom-hole pressure of both producers is constant during water-
flood operation, so the last term of Eq. (1) in CRM and the pressure
events in DoE can be neglected.
3.1.1. Results of CRM for the synthetic case
As was discussed in Section 2.1, the connection factors of CRMP
(producer base representation of the CRM) can be used to find the
quality of the connection between injectors and producers. Hence,
this model is run for finding the interwell connections in the syn-
thetic reservoir. History matching of injection and production data
leads to a connection factor matrix (fij) with Ninj columns and Npro
rows as presented in Table 7. Fig. 6 presents the simulated (from
CRMP) and observed total (oil+water) production rate of the syn-
thetic reservoir. According to Table 7, the connection factor between
injector 1 and producer 1 (I1 P1) is 0.65, and for injector 1 and pro-
ducer 2 (I1 P2) is 0.35. It means that there is a strong connection for
the first pair and a medium connection for the second one (according
to Table 1). This is because of the producer 1 closeness to the injector
1 in comparison with the producer 2.
Fig. 1. Different types of events for the flow rate.
Table 3
Daily event detection.
Criterion Event type
@Q
@T a Increasing event
@Q
@T a Decreasing event
a @Q
@T a Smooth event
Table 4
Detection of Smooth events.
Criterion Event type
j Q2Q1
Q1
jb Increasing or Decreasing event
j Q2Q1
Q1
j b Smooth event
Fig. 2. Events those are not representative of the connection between injector i and
producer j.
Table 5
Events that present the connection between a pair of injector-producer.
Production pressure event Production rate event Injection rate event
Increasing Increasing Increasing
Smooth Increasing Increasing
Increasing Smooth Increasing
Decreasing Smooth Decreasing
Decreasing Decreasing Decreasing
Smooth Increasing Smooth
Decreasing Decreasing No flow
Decreasing Smooth No flow
Fig. 3. Events that are representative of the connection between injector i and pro-
ducer j.
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5. 3.1.2. Results of DoE for the synthetic case
According to the discussions in the DoE methodology, some con-
stants are needed for running a DoE. For the synthetic case, a is
selected 50 (STB/Day2
), b is 0.2. Tmin and Tmax are selected according
to the size of the injectors events (Tmin = 0 Days and Tmax = 5 Days).
Fig. 7 presents the events of the injector 1 versus the events of pro-
ducers 1 and 2. Also, the details of these events have been presented
in Table 8 and Table 9. Note that for the simplicity smooth events
have not been reported here, because they don’t affect the connec-
tions in this case. For the big data containing a huge number of
events, a code can be developed for the detecting and scoring the
events as described in Section 2.2.
As presented in Fig. 7, there are 2 Increasing-Decreasing events in
the injector. The magnitude of the first Increasing-Decreasing events
are too large, so they create Increasing-Decreasing events in both
producers. Hence, according to the size of these events (duration),
the score of the first events are allocated to both pair of injector-pro-
ducer (see Table 9). The second Increasing-Decreasing events are
small, so they cannot be detected in producer 2 (a 50), and the sec-
ond producer receives no score from these events.
The score matrix (achieved from DoE) for the synthetic case is pre-
sented in Table 10. According to the 50 percentile of the score matrix
(see Table 6), producer 1 shows a strong connection with injector 1,
while a medium connection is observed between producer 2 and the
injector. Therefore, both of CRMP and DoE are in agreement and pres-
ent the same results about the connections of the synthetic case.
Fig. 8 presents the connection map of DoE and CRMP for the synthetic
reservoir. In this figure, different connection strengths are shown by
the line width. A thick line represents a relatively strong connection,
and a medium line represents a medium connection.
3.2. Real case (field case)
In this section, the injection and production data of a real res-
ervoir have been studied. Workflows are implemented in this res-
ervoir to continuously improve their performance. In the real
case, it is important to highlight key assumptions to ensure
higher confidence in results, especially in the application of CRM.
One requirement is the judicious selection of the time interval for
the study. The selected data should include a minimum of
120 days of injection and production (to ensure that the wells
have affected each other), with a relatively constant number of
the active injector and producer wells.
The studied reservoir consists of several production and injec-
tion wells, but only for 250 days, the number of active wells in
this field is constant (no new well is drilled or perforated, and
there are 6 active producers and 4 active injectors). So, we use
the injection and production data of this specified timespan for
DoE and CRM analyses. The schematic of the real reservoir has
been presented in Fig. 9.
3.2.1. Results of CRM for the real case
Similar to the synthetic case, CRMP is used for finding the inter-
well connections in the real reservoir, and then the results are com-
pared with the results of the DoE method. Fig. 10 shows the
simulated (from CRMP) and observed total (oil+water) production
rate of the entire reservoir. According to the high value of R-squared
(0.916) presented in Fig. 10, the results of the simulated production
rate (CRM) show a good agreement with observation data. Fig. 11
shows the connectivity map of the field achieved by CRM (according
to Table 1). As presented in Fig. 11, CRMP estimates that there is a
strong underground connection between injector 1 and producer 5
(I1 P5), and injector 3 and producer 3 (I3 P3).
Fig. 4. Two sequences of connection and non-connection events in a real case.
Table 6
Quality of the connections according to the score
matrix created by DoE.
The value of the score Quality of the connection
Scoreij P10 Weak
P10 Scoreij P50 Medium
P50 Scoreij Strong
Fig. 5. Schematic of the synthetic reservoir (red circles are the producers and the blue
triangle is the injector).(For interpretation of the references to color in this figure leg-
end, the reader is referred to the web version of this article.)
Table 7
Connection fac-
tor matrix for
the synthetic
case.
fij I1
P1 0.65
P2 0.35
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6. 3.2.2. Results of DoE for the real case
Sensible values must be selected for each one of the DoE parame-
ters. In the real case, a is 300 STB/Day2
for the flow rate events, and
50 psi/Day for the pressure events. b is 0.1, Tmin is 2 Days and Tmax is 8
Days. In Fig. 12, the results of the connectivity map of the DoE for the
entire field have been shown. As presented in Fig. 12, DoE estimates
that there is a strong underground connection between injector 2
and producer 3 (I2 P3), injector 3 and producer 3 (I3 P3), and injec-
tor 3 and producer 4 (I3 P4). Injector 3 and producer 3 (I3 P3), was
reported to have a strong connection by both DoE and CRM. DoE
Fig. 6. Total production rate of the synthetic reservoir.
Fig. 7. Events of the injector 1 versus the events of producers 1and 2 in the synthetic case.
Table 8
Events of the injector 1 in the synthetic case.
No. Event type Duration (Days) a b
E1 Increasing 914 600 3
E2 Decreasing 1419 600 3
E3 Increasing 4951 200 1
E4 Decreasing 5156 200 1
Table 9
Events of the producers in the synthetic case.
Well No. Event type Duration a b Connection Score Total score
P1
E5 Increasing 915 195 1.74 Yes 6
28
E6 Decreasing 1526 103.7 0.61 Yes 11
E7 Increasing 4955 67.3 0.62 Yes 6
E8 Decreasing 5661 55.9 0.26 Yes 5
P2
E9 Increasing 1015 104.5 1.11 Yes 5
11
E10 Decreasing 1622 77 0.46 Yes 6
E11 Increasing 5055 37.7 0.51 No 0
E12 Decreasing 5661 26.4 0.23 No 0
Table 10
Score matrix for
the synthetic case.
Scoreij I1
P1 28
P2 11
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7. considers the connection between injector 2 and producer 3 (I2 P3)
as a strong connection, while CRM expresses that this connection is
medium. CRM estimates that there is a strong connection between
injector 1 and producer 5 (I1 P5), while DoE estimates that this is a
weak connection.
It is time-consuming for analyzing one by one of the estimated
connections for a real reservoir. Hence, the Boston matrix has been
used in order to have a quick and fair comparison between the con-
nections calculated by CRM and DoE (see Table 11). In the Boston
matrix, as the higher number of elements are on the main diagonal,
the results are in a better agreement. The green squares show the
number of pairs that have been estimated similarly by CRM and DoE
(for example, 14 pairs with a weak connection are recognized by
both CRM and DoE). The red squares show where the two models dis-
agree with each other (for example, there is a pair that CRM considers
Fig. 8. Connection map of the synthetic reservoir (estimated by CRMP and DoE).
Fig. 9. Schematic of the real reservoir.
Fig. 10. Total production rate of the entire reservoir.
Fig. 11. Underground connection map of the real reservoir (estimated by CRMP; a
thick line represents a relatively strong connection, a medium line represents a
medium connection, and a thin dashed line signifies a weak connection).
Fig. 12. Underground connection map of the reservoir (estimated by DoE).
Table 11
Results of CRM and DoE in Boston matrix.
Connection Weak (CRM) Medium (CRM) Strong (CRM)
Weak (DoE) 14 1 1
Medium (DoE) 4 1 0
Strong (DoE) 1 1 1
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8. as a strong connection, but DoE considers weak. Also there is another
pair that DoE considers a strong connection while CRM considers
weak). The orange squares show the connection strengths that are in
slight disagreement (CRM considers a connection medium strength,
while DoE considers the connection to be a weak connection).
A criterion was developed to express the agreement between two
approaches in the Boston matrix. In the developed criterion, each
square with specific color awards a specific point. For example, 3
points are awarded to the pairs which are located in the green
squares of the Boston matrix, 1 point to the pairs of the orange
squares, and no points are awarded to the pairs located in the red
squares. Based on this criterion, it can be inferred that what percent
the estimated connection strength by DoE confirms the estimated
connection strength by CRM. The agreement parameter (AP) between
2 methods is calculated using the equation presented below:
AP ¼
3ng þ no
3ðng þ no þ nrÞ
100 ð3Þ
where, ng is the number of pairs in the green squares, no is the num-
ber of pairs in the orange squares, and nr is the number of pairs in the
red squares. According to the Table 11, 16, pairs are in the green
squares, 6 pairs in the orange squares, and 2 pairs in the red region.
Consequently, there is 75% agreement between CRM and DoE in the
studied case.
Another advantage of using this method is the confidence about
the true underground interwell connections. For example, a strong
connection has been estimated between injector 3 and producer 3
(I3 P3) in both methods. So, this strong connection can be reliable.
CRM estimates there is a strong connection between injector 1 and
producer 5 (I1 P5), while DoE estimates that this connection is
weak. Hence, the connection between this pair is not trustable and
requires more surveillance techniques. According to the long distance
between injector 1 and producer 5 (see Fig. 12), the distrust about
this pair is not weird. The fact that events on an injection well are
correlated in time with events on a separate producer well does not
provide a predictive mechanism for how future production from that
well might usefully vary. However, a strong association is still indica-
tive of a communication path between the wells and this insight
could be great information to develop the reservoir in the future.
3.2.3. Comparison of DoE and ANN
Artificial neural networks (ANNs) also is used as a data-driven
method for estimating the underground interwell connections [5]. In
the present section, a comparison is performed between the ANN
and DoE approaches in terms of accuracy, data requirements, exper-
tise requirements, training algorithm, and processing times. To do so,
ANN was applied for the real case (field case) using the backpropaga-
tion algorithm and 1 hidden layer. Then, the normalized ANN connec-
tions compared with the CRM connections and presented in the form
of the Boston matrix (Table 12).
Accuracy: It is believed that CRM presents more reliable interwell
connections in comparison with ANN, as CRM is a physics-based
approach [13,14,26]. Therefore, the value of the agreement with CRM
(Eq. (3)) is selected as the accuracy criteria in this section. Regarding
Table 12 and using Eq. (3), there is a 68% agreement between the
obtained result from CRM and ANN. As the agreement parameter for
CRM and DoE was 75%, it can be inferred that the DoE is more consis-
tent with the CRM (more precise) in this studied case.
Data requirements: In terms of required data, both DoE and ANN
required the same set of data (the injection and production data).
Expertise requirements: When it comes to working with ANNs,
deep knowledge of the ANN theory and training parameters is cru-
cial. On the other hand, DoE does not requires any optimization algo-
rithm and only needs the proper identification of the parameters
used for the detection of the events.
Training algorithm: No training algorithm is required for the DoE,
while the performance of the ANN strongly depends on the training
algorithms.
Processing time: Both DoE and ANN methods are fast, where the
CPU time is less than a few minutes.
According to all these terms, it seems that DoE is more efficient
than ANN. DoE is in a better agreement with CRM and is easier to
apply. However, DoE only can be used for estimation of the interwell
connections and cannot predict the production rate of the reservoir.
4. Conclusions
In this paper, a novel data-driven approach (DoE) was proposed in
order to find the underground connections between injection and
production wells. The proposed method is based on finding the
impact of injection rate fluctuations on the production rates and scor-
ing the relevant impacts. Then, by establishing an effective calibration
between CRM and DoE, the confidence about the estimated under-
ground connections were analyzed. The proposed method was suc-
cessfully tested for both synthetic and real reservoirs, and the
estimations of these two methods (CRM and DoE) showed a good
agreement with each other (75%).
The proposed method can be used by reservoir engineers for
understanding the underground path of the injected fluid, and deci-
sion-making about the future. Although there is a high degree of sim-
ilarity between DoE and CRM, it is highly recommended to integrate
this methodology with other existing surveillance techniques, such
as tracer, streamline modeling, and 4D seismic to evaluate and moni-
tor the waterflooding process more accurately.
Declaration of Competing Interest
None.
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