Design Automation for Interwell Connectivity Estimation in ... · analytics in the Oil and Gas (O&G) ﬁeld. ... During the drilling ... tion II presents the preliminaries of the

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCAD.2016.2584065, IEEETransactions on Computer-Aided Design of Integrated Circuits and Systems

1

Design Automation for Interwell ConnectivityEstimation in Petroleum Cyber-Physical Systems

Xiaodao Chen, Dongmei Zhang, Lizhe Wang, Senior Member, IEEE Ning Jia, Zhijiang Kang, Yun Zhang,and Shiyan Hu, Senior Member, IEEE

Abstract—In a petroleum Cyber-Physical System(CPS), interwell connectivity estimation is critical forimproving petroleum production. An accurately esti-mated connectivity topology facilitates reduction in theproduction cost and improvement in the waterfloodmanagement. This work presents the first study focusedon Computer Aided Design for a Petroleum Cyber-Physical System. A new Cyber-Physical System frame-work is developed to estimate the petroleum well con-nectivities. Such a framework explores an innovativeWater/Oil index integrated with the advanced crossentropy optimization. It is applied to a real industrialpetroleum field with massive petroleum CPS data. Theexperimental results demonstrate that our automatedestimations well match the expensive tracer based trueobservations. This demonstrates that our framework ishighly promising.

Index Terms—Interwell Connectivity, PetroleumCyber-Physical System, Cross Entropy, Optimization,Design Automation.

I. Introduction

Petroleum engineering research and practice are in thestage to embrace various emerging advanced computa-tional technologies for the investigatations on variouspetroleum activities. Examples include large-scale detailedreservoir simulations, and petroleum data processing andanalytics in the Oil and Gas (O&G) field. A criticalproblem among them is to present a thorough study onthe interconnections among wells. Since the industrial(O&G) wells are widely dispersed all over the oil field,individual well interacts with each other strongly. Thus,understanding the interconnections among wells can helpthe (O&G) field people to manage the reservoir in ascientific way.

X. Chen and N. Jia are with the School of Computer Science, ChinaUniversity of Geosciences, Wuhan, China 430074.

D. Zhang (corresponding author) and L. Wang (correspondingauthor) are with the School of Computer Science, China Universityof Geosciences, Wuhan, China 430070.

X. Chen D. Zhang and L. Wang are also with Hubei Key Labora-tory of Intelligent Geo-Information Processing, China University ofGeosciences, Wuhan 430074, China.

Z. Kang and Y. Zhang are with the Petroleum Exploration andProduction Research Institute of SINOPEC (PEPRIS), Beijing, Chi-na.

S. Hu is with the Department of Electrical and Computer Engi-neering, Michigan Technological University, Houghton, MI, 49931,USA.

Corresponding Author: Dongmei Zhang (E-mail: [email protected]) and Lizhe Wang (E-mail: [email protected])

Oil ProductionWell

Water InjectionWell

Water Pipe

Oil Pipe

Oil

Water

Fig. 1. An illustration on the interwell connectivity

The interwell connectivity characterizes the oil reservoirin terms of flow conduits, communication barriers and in-jection imbalance properties among wells [1]. Refer to Fig-ure 1 for an example of how interwell connectivity impactsthe oil field. In Figure 1, there are three production wellsand one injection well. Two of the production wells andthe injection well are connected underground, while theleft most production well is isolated. During the drillingprocess, after water is injected from the injection well intothe ground, oil can be pushed out of the two productionwells connecting to it. The knowledge of interconnectionsamong wells, which is the main target of the intertwellconnectivity, is highly beneficial to the petroleum indus-try. With such knowledge, the underground conductivityparameters of permeability and anisotropy knowledge ofthe oil field can be estimated. The practical implication isthat well injection rate can be set such that the cost fordrilling is reduced [2].

Some recent works such as [3] analyze the petroleumdata to estimate the interwell connectivity. The tech-nique proposed in [3] is not only non-scalable but alsoimpractical due to the fact that that approach cannothandle bottom pressure as indicated in [3]. Scalabilityis a critical problem. There are massive interaction datasuch as the injection/production rate, well pressure, andWater/Oil (W/O) rate which need to be processed. Inaddition, the petroleum data usually span over decadesand they exhibit the properties of high heterogeneity (frommultiple well sources) and high dimension. Traditionally,the petroleum data are almost always processed manually.Various geographic properties in the petroleum filed are



2

Well

Control Unit

Data Transmission

Control Flow

Petroleum Data Analysis Center

Well Production Control Center

Production Data Acquisition Center

Historical Petroleum Database

Fig. 2. Embedded Cyber-Physical System (CPS) control scheme

analyzed by those petroleum experts according to theirexperiences. These properties can be handled when a smallpart of a petroleum field is given. However, for a completepetroleum field, petroleum data are significantly larger andthus it is not feasible to carry out the manual analysis.This necessitates the innovative Computer Aided Designmethodology for the interwell connectivity study.

When the interwell connectivities are determined, apreliminary production optimization can be performedon the (O&G) filed. This optimization takes incomingpetroleum data, especially the daily injection data anddaily production data as input. Using these data, theconnectivity value accuracy can be improved. With betterquality of interwell connectivity values, the profit of thewaterflooding can be further improved. The above proce-dure exhibits all essential properties of a Cyber-PhysicalSystem (CPS). Refer to Figure 2. In this petroleum CPS,production data from petroleum wells are collected by thedata acquisition center node. With data from historicalpetroleum database, the petroleum data analysis centercan perform the interwell connectivity study. Historicalpetroleum database includes historical production data,as well as the geographical information of the petroleumfield. When the connectivity values are computed, thepetroleum data analysis center can operate productionwells accordingly through the control center unit. Themain purpose of the control center unit is to make thedecision of injection rate and production rate. Clearly,the above system forms a control and feedback loop whichuniquely characterizes a CPS. As shown in Figure 3, thepetroleum CPS recursively optimizes the injection rateflow to achieve a high quality of waterfloor managementin a reservoir. To the best of our knowledge, this work isthe first study on the CAD for petroleum Cyber-PhysicalSystems.

There are limited research efforts on modeling inter-well connectivity. Existing models include the CoupledGeomechanical-Fluid Flow Model [4], the MultivariateLinear Regression (MLR) Model [5] and the popular Ca-pacitance Model (CM) [6]. Based on these models, the

Production Optimization

Petroleum Data Acquisition

InterwellConnectivity

Analysis

Fig. 3. Cyber-Physical System (CPS) control and feedback loop

interwell connectivity can be estimated applying linearor least square regressions on the injection rate and theproduction rate of well groups [7]. However, in practicepetroleum data are massive, multi-dimensional and highlyheterogenous, while all previous works only focus on asmall set of wells with a limit time span. Their tech-niques are not scalable and thus can not be applied tothe practical field. In addition, when the mathematicalregression is applied on the real data, it often returnsunrealistic interwell connectivity values. For example, inpractice only interwell connectivity values between 0 and1 are meaningful where 0 and 1 denote no connection andfull connection respectively. However, the mathematicalregression sometimes can return a large connecitivity valuewhich is far outside [0, 1]. Thus, a salient technique whichcan handle large-scale realistic petroleum data is highlynecessary.

In this work, a new algorithm to determine the interwellconnectivity value based on the flow patterns of bothinjection wells and production wells is proposed. Thealgorithm is also applied to a real (O&G) field in theNorth of China. The contribution of this paper can besummarized as follows.• A new interwell connectivity cyber-physical system

framework is developed to determine the connectivityof petroleum wells such that the production cost canbe significantly reduced.

• An innovative Water/Oil index driven advancedcross entropy optimization technique is proposed forachieving the high performance interwell connectivityestimation.

• The proposed scheme is applied to a real industrialpetroleum field with massive petroleum CPS data.Our experimental results demonstrate that our es-timations well match the true observations of thetracer, which indicates that the proposed techniqueis highly promising.

The remainder of the paper is organized as follows. Sec-tion II presents the preliminaries of the interwell connec-tivity analysis and the production optimization. SectionIII gives the theoretical foundations of the cross entropymethod. Section IV describes the proposed the Water/Oil



3

(W/O) index driven Cross Entropy algorithm. The fieldapplication is analyzed in Section V. A summary of workis given in Section VI.

II. PreliminariesWith the production data and injection data from oil

reservoir field, the interwell connectivity can be estimatedand the waterfloor management can be achieved by theCapacitance Model (CM) which is widely used in theliteratures. The production rate of a well i can be com-puted as Equation (1) [6], where q(t) denotes the rateof the production at the time stamp t, q(t0) denotes theinitial production rate, J denotes the productivity index,pwf denotes the bottom well pressure of the well at thetime stamp t, and τ is the time constant. Note that τcan be calculated by using the total compressibility, thepore volume and the productivity index J . Literature [8]discretizes the time interval such that

qi(t) = χ · qi(t0)e(t0−t)/τp +j=Ω∑j=1

λijw′ij(t) (2)

where i denotes the index of the primary productionwell, Ω denotes connecting well set to the well i and jdenotes the index, χ denotes the impact value from theprimary production well i, and λij denotes the interwellconnectivity value. w′ij(t) can be calculated by

w′ij(t) =L∑l=1

[e(tl−t)/τij − e(tl−1−t)/τij

]wij(t) (3)

where wij(t) denotes the injection rate of injector well j,l denotes the time step and n is the total amount of thetime step. Using Equation (2), the primary well productionrate is linear in terms of the injection rate of its connectingwells. In each time step, all values above are known exceptthe connectivity value λ or the impact value χ.

A simple example is used to illustrate those equationsas follows. If the total time is three days and the timeinterval is one day, the equation array from Equation(2) for the three time intervals can be presented as:qi(t1) = χ · qi(t0)e(t0−t1)/τp +

∑j=Ωj=1 λijw

′ij(t1), qi(t2) =

χ · qi(t0)e(t0−t2)/τp +∑j=Ωj=1 λijw

′ij(t2) and qi(t3) = χ ·

qi(t0)e(t0−t3)/τp +∑j=Ωj=1 λijw

′ij(t3), where t1, t2 and t3

denote day 1, day 2 and day 3 respectively. Note that λ isin between [0, 1], where 0 and 1 denote no connection andfull connection between two wells, respectively.

Refer to Figure 4. The petroleum production system isanalogous to a circuit with a capacitance, which is whythis model is named the capacitance model. In Figure 4,the total production amount qj is equivalent to the outputcurrent Ioutput and the injection amount at each well withits connectivity is equivalent to the input current valueIinput. The electrical charge energy of the capacitance isequivalent to the pressure p and the capacitance value isequivalent to the permeability volume Vp multiplied by thetotal compressibility Ct.

IinputC

λ1qw1(t)+λ2qw2(t)

Ioutput qj

VpCt

qj

qw1(t)

λ1 λ2

qw2(t)

E p

Fig. 4. Equivalent CM circuit example for a three wells petroleumproduction system

According to the first order oscillation circuit property,this petroleum injection-production system can be formu-lated as Equation (4) [9].

CtVpdp

dt+ qjt =

∑∀i

λijqwi (4)

Based on it, reference [8] proposed the capacitancemodel which has been summarized in Equation (1-3).

After the connectivity values of wells are computed, theprofit in a reservoir can be computed by [10]:

Pro = OpN∑i=1

∫t∈φ

roi(ε)dε−WpM∑j=1

∫t∈φ

rwj(ε)dε (5)

where Op and Wp denote the oil/water price per barrelrespectively, N and M denote the numbers of productionand injection wells respectively, ro and rw denote theproduction rate and injection rate respectively and φdenotes the time interval for profit optimization. Note thatthe connectivity value are used to calculate the ro togetherwith the value of rw. In other words the connectivitystudy can help to determine and optimize the cost of thepetroleum production.

A. Problem FormulationOur problem formulation can be presented as follows.

Given a petroleum field, Np production wells and Niinjection wells, both of which have production data withgeographic data, the interwell connectivity analysis asksto determine the connectivity value λij of connected wellsi and j of that petroleum field.



4

q(t) = q(t0)e(t0−t)/τ + e−tτ

τ

∫ ξ=t

ξ=t0eξτ w(ξ)dξ + J

[pwf (t0)e(t0−t)/τ + pwf (t) + e−

tτ

τ

∫ ξ=t

ξ=t0eξτ pwf (ξ)dξ

]. (1)

III. The Cross Entropy MethodThis paper uses the advanced cross entropy frame-

work for the estimation of inter-well connectivities. Crossentropy framework is initially proposed in [11] and anoverview of this framework is presented as follows.

A. Cross-Entropy Theoretical FoundationCross Entropy method is a framework to compute the

approximate to the optimal solutions of NP-Hard problem-s, such as the traveling salesman problem, the quadraticassignment problem and DNA sequence alignment prob-lem. As a meta heuristic, it optimizes the initial solutioniteratively using the Monte Carlo method and ImportanceSampling (IS) [11], [12], [13], [14], [15], [16], [17]. The briefintroduction to Cross-Entropy method is presented herefor completeness. Refer to [18], [6], [19] for further details.

Suppose that the optimization target is to minimizef(x),

ω∗ = minx∈χ

f(x), (6)

where ω∗ denotes the minimum value of f(x) over themultidimensional variable x defined in space S. The prob-ability that f(X) is below the threshold ω is defined as`(ω),

`(ω) = Pu(f(X) ≤ ω) = EuIf(X)≤ω (7)

in which X is a set of random samples defined in space S.It is generated based on the Probabilistic Density Function(PDF) g(x, p). I· is the indicator function such thatIf(X)≤ω = 1 if and only if f(X) ≤ ω holds. TheCross-Entropy method adjusts ω at every iteration suchthat it becomes closer to ω∗. The target is to maximizeω such that `(ω) approaches 0. This iterative procedurecan be viewed as a stochastic Lagrangian relaxation. Theprobability that f(X) ≤ ω is estimated by

ˆ= 1N

N∑i=1

If(Xi)≤ω (8)

There exists a technical challenge in finding ˆ. Whenit approaches 0, the Monte Carlo simulation method re-quires N to be sufficiently large to estimate ˆ accurately.Since f(X) ≤ ω becomes a rare event, the Monte Carlosimulation method is computationally expensive.

To tackle this technical challenge, IS is introduced.According to IS, Equation (8) can be rewritten as [11]

ˆ= 1N

n∑i=1

If(Xi)≤ωg(Xi)k(Xi)

(9)

where k(x, p) is the new PDF that alleviates the require-ment on the large number of samples. There exists anoptimal k∗(x, p) leading to Equation (10) [11].

`(ω∗) = 1N

n∑i=1

If(Xi)≤ωg(Xi)k∗(Xi)

= ˆ (10)

Cross Entropy method aims at using k(x, p) to approxi-mate k∗(x, p) such that the cross entropy between k(x, p)and g(x, p) is minimized. The cross entropy is defined inEquation (11) [11].

H(f, g) = Ef lng(x)k(x) =

∫g(x)lng(x)dx

−∫g(x)lnk(x)dx

(11)

Minimizing the Cross Entropy H(f, g) is equivalent tofinding v for maximizing [11]

maxv

∫k(x)lng(x, v)dx, (12)

This is equivalent to maximizing [11]

maxvEuIf(x)≥ωlnk(x, v) (13)

B. Limitation of the Standard Cross Entropy Method

The standard Cross Entropy method can approximatethe optimal solution when there is plenty of samples areused. The initial solution PDF needs to ensure the coev-erage of the whole solution space, such that the optimalsolution is not excluded. Samples generated by the PDFare employed in the cross entropy technique to find atrajectory pointing to the optimized solution. Given amassive petroleum data set, a large number of samplesare needed to cover the input parameter combinations andthe solution space. For this reason, the standard CrossEntropy method is computationally expensive for handlingthe large data set. Thus, it is necessary to integratethe cross entropy technique with additional features toeffectively reduce the solution space while still keepingsolutions with a certain quality. Such a feature needs toexplore the unique nature of the problem.

To improve the standard Cross Entropy method, aWater/Oil (W/O) index driven Cross Entropy method willbe proposed. The W/O index is used to reduce the solutionspace which has been illustrated in Figure 5. In Figure5 (a), the starting point of the approach is the point inpurple, the circle is the solution space, and the optimalsolution is the point in red. To search the solution inthis case, the traditional Cross Entropy method requires alarge number of samples to cover the whole solution space,due to the large solution space. In contrast, the CrossEntropy method with W/O index guidance in Figure 5(b) first computes the W/O index value according to theproperties of petroleum CPS, and obtains a new startingpoint for the search. It then computes the solution usingthe new starting point with smaller search space, whilestill maintaining the solution quality.



5

(a) The cross entropy method without W/O guidance

(b) The cross entropy method with W/O guidance

Fig. 5. W/O index guidance impacts the Cross Entropy method.

IV. Algorithmic Framework

A. Algorithmic Overview

At a high level, the Cross Entropy framework is toiteratively approximate optimal solutions through utilizingthe importance sampling based Monte Carlo simulations.Figure 6 shows the work flow of the Cross Entropy method.The Cross Entropy method first initializes the solutionPDF over the solution space θ. A number of samples canbe generated according to this PDF. Comparing samples,those with better objective values are selected, which arepresumably closer to the optimal solution than others.Subsequently, the solution PDF is characterized usingthose samples. After the solution PDF is updated, thealgorithm proceeds to the new iteration with the newsolution PDF. When this Cross Entropy Method appliesto solve the interwell connectivity problem, the optimalsolution is a set of λij values that best fit the Equation(2). However, the solution space is very large. The reasonis that the connectivity value in practice can be anywherebetween 0 to 1, and there can be exponential number ofpotential combinations of connectivies among wells. Thus,it is very expensive to start from a solution PDF whichcovers the whole solution space. This motivates us to de-sign a W/O index driven Cross Entropy (WOCE) methodto effectively reduce the solution space and thus reducethe number of samples in each iteration to accelerate thealgorithm.

B. W/O index Analysis

This work utilizes the Water/Oil Ratio (WOR) of theproduction well to reduce the solution space and to im-prove the standard Cross Entropy method. The W/Oration curve of each production well has been studied, andpetroleum connection features are discovered. As shownin Figure 7, when water is injected in the injection well

-50

0

50

100

150

200

250

2009/4/17 2009/4/27 2009/5/7 2009/5/17 2009/5/27 2009/6/6 2009/6/16 2009/6/26 2009/7/6

Injectionton

-20

0

20

40

60

80

100

120

2009/4/17 2009/4/27 2009/5/7 2009/5/17 2009/5/27 2009/6/6 2009/6/16 2009/6/26 2009/7/6

W/O ratePercentage

Fig. 7. Injection impacts WOR

around May 2009, the WOR curve of the connected pro-duction well becomes active with some delay. Intuitivelyspeaking, when the water injection starts, connected pro-duction wells would be impacted. Thus, how a connectedwell is impacted can form a W/O index value for the con-nectivity analysis. The impact degree can be establishedusing WOR sequence values.

In this work, the raw WOR sequence S is first purifiedto form a refined sequence S using a high pass filter.After the refinement, the proposed algorithm calculatesthe summation of gradient values of S at each time stepwithin a time window Φ1 as shown in Equation (14). Notethat this time window is formed after the injection.

IΦ1 =∑t∈Φ1

(dSdt

) (14)

The proposed algorithm shifts the time window to Φ2.After a certain number of iterations, there are a numberof Ii values obtained. The injection impact values can becomputed as

I = maxIΦ1 , IΦ2 , IΦ3 , ..., IΦk (15)

where k denotes the number of time windows. In theimplementation, the time window is set to be 60 dayswhich quite fits the target reservoir zone. Each timewindow is shifted 2 days ahead, and there are 60 shiftsin total. The value of I is the W/O index value of theinterwell connectivity value λ between an injection welland a production well. Large value of I implies the strongconnection between the injection well and the productionwell.

C. WOCE Method for Interwell Connectivity AnalysisThe W/O index driven Cross Entropy (WOCE) method

for interwell connectivity analysis is summarized in Algo-



6

Initialize Solution PDF f(θ)

Solution Space θ

Solution Space θ

Solution Space θ

Solution Space θ

Elite Samples

f(θ) f(θ) f(θ) f(θ)

GenerateSolution Samples

EvaluateSolution Samples

Update Solution PDF f(θ)

Fig. 6. Cross Entropy Method Scheme

Algorithm 1 The W/O index driven Cross Entropy(WOCE) Method.

1: Compute the W/O index values of every pair of wells.2: Initialize the mean of the connectivity PDF for all

pairs of wells according to their W/O index: ~µ =µ(1)

1 , µ(1)2 , µ

(1)3 , ..., µ

(1)N where µ(i)

1 is the mean valueand N denotes the number of pairs of potential con-nected wells.

3: Initialize the variation of the connectivity PDF for allpairs of wells: ~σ = σ(1)

1 , σ(1)2 , σ

(1)3 , ..., σ

(1)N , where σ is

the standard variation.4: Set k = 1.5: Generate M connectivity samples according to the

connectivity PDF parameters µ(k) and σ(k)

6: Evaluate generated connectivity samples:sp1, sp2, sp3, ..., spM through computing theright hand side of the Equation (2).

7: Select top M elite samples sp1, sp2, sp3, ..., spM bythe deviation which is generated by each sample.

8: Update PDF parameters µ(k+1), σ(k+1) : µ(t+1)i = µti+∑M

j=0(spj−µti)

Miand σ(t+1) =

√∑M

j=0(spj−µ(t+1)

i)2

Mi∀i ∈

[1, N ].9: t= t + 1;

10: Check the stop criteria with the updated connectivityPDF.

11: Repeat 5 to 10 till the converge criteria is satisfied.

rithm 1. The details of the algorithm can be summarizedas follows:

The proposed algorithm computes the Water/Oil indexvalue of wells according to the method which has beendiscussed in section IV-B. After that, it initializes con-nectivity PDF parameters for every pair of wells. Notethat there is a connectivity PDF associated with everypair of wells. The connectivity PDF of two wells denotesthe connectivity strongness between that pair of wells.In practice, it has a range between the value 0 and thevalue 1, where 0 denotes no connection between wellsand 1 denotes the full connection. The W/O index valueguides to set the mean value of the PDF. After thePDF parameters are determined, the algorithm proceedsiteratively. In each iteration, it starts with interconnect

samples sp generation according to interconnect PDFs. Forevery group of production and injection wells, there are acertain amount of connectivity sample groups generated inpractice, and large number of samples can help the algo-rithm to achieve better solution qualities. In each samplegroup, there are connectivity values for every two wells.All these values of a group are carried into the Equation(2) for the evaluation. In the evaluation procedure, samplevalues of each group are used to calculate the right handside of the Equation (2). The proposed algorithm thencomputes the difference of the right hand side and theleft hand side of the Equation (2). A small differencevalue denotes a good sample quality. By now, samples ofeach group can be evaluated by these values, and elitesample thus can be selected. Elite samples are utilizedto update the PDFs of interconnect wells according to

µ(k+1), σ(k+1) : µ(t+1)i = µti +

∑M

j=0(spj−µti)

Miand σ(t+1) =√∑M

j=0(spj−µ(t+1)

i)2

Mi∀i ∈ [1, N ]. Note that, elite samples

increases the mean value µ of PDFs which makes the pairof associated wells have large probability of generatinglarge values of connectivity. In this way, The sigma valueare reduced in each iteration which leads the proposedalgorithm to meet the convergence. Note that, the totalnumber of iteration is set to be 20 in the experiment.

In Figure 8, an example is presented to illustrate theproposed W/O index driven Cross Entropy (WOCE)method. In this example, there are two production wellsconnected to the injection well, and connectivities betweenthe injection well and production wells are denoted by λ01and λ02, respectively. In this case, the PDFs of connec-tivities are initialized to Gaussian distributions where themean value and standard deviation are set to be 0.5 and0.53 respectively. Thus, the connectivity ranges from 0 to 1.

Samples can be evaluated using Equation (3). Assumingthat sample 1 and 2 are top 2 samples, they are selected forPDF updating. As a result, the mean value of the λ01 inthe second iteration can be calculated as 0.70 = 0.65+0.75

2and the standard deviation value in the second iterationcan be calculated as 0.75−0.70

3 .The control scheme for the Petroleum CPS system can

be summarized in Figure 9. The control scheme firstcollects the static and dynamic petroleum CPS data. TheW/O rate index values are then calculated for all pairs



7

qj

qw1

λ0,1 λ0,2

qw2

1,0 2,0

0 0.5 1 0 0.5 1

0 0.7 0 0.25

Initial PDF

Connectivity Samples

1,0Sample 1: ( =0.75, =0.20)2,01,0Sample 2: ( =0.65, =0.30)2,01,0Sample 3: ( =0.50, =0.70)2,01,0Sample 4: ( =0.85, =0.45)2,0

Updated PDF

Elite SampleElite Sample

Fig. 8. An example on Cross Entropy Method

Retrieve Static Petroleum CPS Data

Retrieve Dynamic Petroleum CPS Data

Calculate W/O Index Values

Analysis Interwell Connectivity Degrees

Modify Production Controls

Fig. 9. The Control Scheme for the Petroleum CPS

of wells. After that, it proceeds to compute interwell con-nectivities according to which the petroleum productioncontrols are modified. The updated petroleum productioncontrols can take new incoming Petroleum CPS data in thenext iteration. Note that the proposed method describedin Algorithm 1 is an essential part of the Petroleum CPSsystem. Algorithm 1 consists of two core steps in thePetroleum CPS system as shown in Figure 7, which are“Calculate W/O Index Values” and “Analysis InterwellConnectivity Degrees”, respectively.

V. Field Application

The proposed WOCE method for interwell connectivityanalysis is implemented in C++ and is applied to anindustrial petroleum field located in North of China. Thepetroleum data includes the injection value, productionvalue and geological map information. According to themap and the reservoir report from that area, the oil fieldis based on the dissolution of soluble rocks, and there aresinkholes and dolines under the ground. The productiondata span over 7 years from 2005 to 2012 with relatedgeographical parameters. A dell workstation with Inteli7 3.07 GHz CPU and 24G memory is employed for thepetroleum data analysis.

In the O&G field, there are two groups of wells whichhave tracer response reports. The tracer is chemical fluidwith space color modular which can be observed manually.In this O&G field, the tracer is chemical fluid with spacecolor modular which can be observed manually. The traceris labeled as ”BY-1” and main chemical composition isC28H20N305. When it is injected to the injection well,the observations are made at some neighbouring wells.Once the color tracer is observed, connections between theinjection well and the observing production well can be de-termined. Usually it reveals the connectivity relationshipamong a group of wells. However, it costs expensively interms of facilities and human labor. In fact, sometimesit cannot fully extract the connections among wells, e.g.,when a production well is not producing oil during theobservation period. In addition, the tracer is not ableto provide connectivity values λ. Therefore, the traceris usually used in practice as a qualitative tool to checkif wells are connected or not. It is not able to provideinformation about the connectivity values.

In the experiments, we compare the proposed WOCEmethod and the tracer result. To illustrate our compar-isons, two injection wells of the field are selected for theinvesitgation of its connecting wells. Refer to Figure 10and Figure 11, in which wells are presented according tothe their real geographical locations. There are three typesof wells, which are an injection well, connected productionwells and isolated production wells. For the wells in Figure10, the tracer are injected with water at the injection wellW12 in the year 2008. The tracer observations on wells 3,5, 7, 8, 9 and 16 confirm the connections as shown in Figure10 (a). However, according to the tracer report observedtracers are less than the total injected tracers. Thus, wecannot conclude that well 3, 5, 7, 8, 9 and 16 representthe complete set of connected production wells. It wouldbe possible that there are further connections. Figure 10(b) shows the result from the proposed WOCE scheme,in which connected wells are well 5, 6, 7, 8, 9 and 16.Comparing to the tracer results, our technique connectsthe production well 6 but not the production well 3 to theinjection well W12.

For the case in Figure 11, the tracers are injected twiceat the well 11 in 2009 and 2010, respectively. However, theobservation results do not match with each other. In 2009,



8

W1

W2W4

W5W6

W7

W8

W9W10

W11W12

W13W14

W15

W16

W3

(a) Tracer result

Injection Well

Connectivity

Connected Production Well

Unrelated Well

W1

W2W4

W5W6

W7

W8

W9W10

W11W12

W13W14

W15

W16

W3

(b) WOCE result

Fig. 10. A comparison between the proposed WOCE result and the tracer result with the injection well W12

(a) Tracer result

Injection Well

Connectivity

Connected Production Well

Unrelated Well

(b) WOCE result

W9W10

W11W12

W13W14

W15W16

W17W18

W19W20

W21 W22 W23

W25

W9W10

W11W12

W13W14

W15W16

W17W18

W19W20

W21 W22 W23

W25

Fig. 11. A comparison between the proposed WOCE result and the tracer result with the injection well W11

tracers are observed at well 16 19 and 20, while in 2010,tracer is observed at well 9 15 16 and 18. The industrialpractice in handling them is to combine the tracer resultsas shown in Figure 11 (a). The WOCE result is shown inFigure 11 (b), it shows no connection between the well 11and the well 14, while it shows the connection between thewell 11 and the well 13. The indistrial experts from Sinopecconfirm that our results can be classified as having onlyminor errors which can be readily used in practice [20].

We have applied the WOCE method to 6 test groups ofwells. According to [21], crude oil price per barrel is set to$38, one barrel is set to be 42 US gallons (34.97 imp gal)[22] and the injection water cost is set to be $0.6 per ton[23]. The rest of production procedure costs are $0.098/bblfor lifting cost, $0.086/bbl for separation cost, $0.122/bblfor de-oil cost, $0.084/bbl for filtering cost, $0.159/bbl forpumping cost and $0.03/bbl for injection cost [24]. Thetotal available injection water is set to be 10 tons for eachgroup. We compare the uniform injection method with outproposed WOCE guided injection method. The productionsituation are summarized in Table I. Note that in each testgroup there are two injection wells and only one of them is

connected with the production well. We make the followingobservations.• There are normally 5 to 8 production wells in the test

groups. The water injection quantities highly dependon the connectivity value, the production rate, andthe cost of water.

• Our proposed method can obtain monetary profitsvarying from $631.5 to $1753.7. It significantly out-performs the baseline uniform injection method, withup to $882.7 improvement in the monetary profit.The reason is that our method well estimates theconnectivity degrees between wells. With this criticalinformation in hand, one can easily determine the bestoil fields to perform production, which are the oneswith the large connectivity and low W/O rate. Recallthat W/O refers to the ratio of production water overproduction oil, and a low W/O ratio means that it ismore cost effective since more production oil can begenerated.

We also investigate the run time complexity over differ-ent iterations for the proposed technique. The results areshown in Figure 12. The proposed algorithm is performed



9

TABLE IWOCE Method Field Application on an Oil Field in North China.

Group Index Wells in Group Uniform Injection WOCE guided Injection Improvement ($)Monetary Profit ($) Monetary Profit ($)1 W1, W3, W4, W7, W10 522.7 1057.2 534.52 W1, W3, W6, W7, W12, W16 433.2 878.2 445.03 W13, W14, W15, W23, W25 694.4 1400.5 706.14 W13, W16, W17, W19, W20, W27 871.0 1753.7 882.75 W9, W16, W18, W19, W20, W22, W24, W27 455.4 922.5 467.16 W9, W15, W16, W20, W22, W25, W26, W27 309.9 631.5 321.6

Number of iterations

Number of iterations

Con

necti

vit

y D

egr

ee

Runt

ime

(s

)

(a)

(b)

Fig. 12. Computing Analysis with different number of iterations

over different number of iterations which is ranging from 5iterations to 25 iterations. The connectivity values becomestable after 15 iterations. The runtime of the algorithmare monotonically increasing with respect to the numberof iterations as shown in Figure 12 (b). According tothese properties, the proposed algorithm can be tuned inpractice according to different attributes of well groups.

VI. ConclusionIn this work, a new computer-aided design technique for

cross entropy based interwell connectivity cyber-physicalsystem framework is developed to determine the connec-tivity of petroleum wells for the production cost mini-mization. Such a framework processes the petroleum datawith an innovative Water/Oil index driven advanced crossentropy optimization technique for interwell connectivityestimation. Its application on a real industry oil field

demonstrates that our automated estimations well matchthe expensive tracer based true observations. This demon-strates that the proposed framework is highly promising.

AcknowledgementThis study was supported in part by the National

Natural Science Foundation of China (No. 61501411) andthe National Science and Technology Major Project ofChina (No. 2016ZX05014-003-003).

References[1] M. Soroush, D. Kaviani1, and J. L. Jensen, “Interwell connectiv-

ity evaluation in cases of changing skin and frequent productioninterruptions,” Journal of Petroleum Science and Engineering,vol. 122, pp. 616–630, 2014.

[2] A. Dinh and D. Tiab, “Analytical determination of interwellconnectivity based on flow rate fluctuations in waterflood reser-voirs,” Journal of Petroleum Science and Engineering, DOI:10.2118/164481-MS.

[3] D. Kaviani, J. L. Jensen, and L. W. Lake, “Estimation ofinterwell connectivity in the case of unmeasured fluctuatingbottomhole pressures,” Journal of Petroleum Science and En-gineering, vol. 90-91, pp. 79–95, 2014.

[4] K. Heffer, R. Fox, C. McGill, and N. Koutsabeloulis,“Novel techniques show links between reservoir flow direc-tionality, earth stress, fault structure and geomechanicalchanges in mature waterfloods,” SPE Journal, vol. 2, pp.http://dx.doi.org/10.2118/30 711–PA, 1997.

[5] A. Albertoni and L. W. Lake, “Inferring interwell connectivityonly from well-rate fluctuations in waterfloods,” SPE ReservoirEvaluation and Engineering, vol. 6, 2003.

[6] J. J. A.A. Yousef and L. Lake, “Analysis and interpretationof interwell connectivity from production and injection ratefluctuation using a capacitance model,” SPEREE 9(5):630-646.SPE-95322-PA, 2006.

[7] A. Albertoni and L. Lake, “Inferring connectivity only from well-rate fluctuations in waterfloods,” SPE Reservoir Evaluation andEngineering Journal, vol. 6, pp. 6–16, 2003.

[8] P. G. A.A. Yousef, J. Jensen, and L. Lake, “A capacitance modelto infer interwell connectivity from production and injection ratefluctuations,” SPE Annual Tehcnique Conference and Exhibi-tion, 2005.

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[20] Personal communication with Sinopec experts, 2015.[21] oil price, http://www.oil-price.net/.[22] Wikepedia, https://en.wikipedia.org/wiki/Barrel.[23] Altxw, http : //www.altxw.com/news/content/2015 −

10/16/content9411355.htm.[24] B. Bailey, M. Crabtree, J. Tyrie, J. Elphick, F. Kuchuk, C. Ro-

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Xiaodao Chen received the B.Eng. degreein telecommunication from the Wuhan Uni-versity of Technology, Wuhan, China, in 2006,the M.Sc. degree in electrical engineering fromMichigan Technological University, Houghton,USA, in 2009, and the Ph.D. in computerengineering from Michigan Technological Uni-versity, Houghton, USA, in 2012. He is cur-rently an Associate Professor with School ofComputer Science, China University of Geo-sciences, Wuhan, China. His research interests

include Design Automation for petroleum system, High PerformanceComputing and Optimization.

Dongmei Zhang received the Ph.D. degreefrom China university of Geosciences, Wuhan,China. She is currently a Professor with Schoolof Computer Science, China University of Geo-sciences, Wuhan, China. Her research interestsinclude Multi-Objective Optimization and 3DVisualization in Geosciences.

Lizhe Wang (SM’ 2009) received the B.Eng.degree (with honors) and the M.Eng. degreeboth from Tsinghua University, Beijing, Chi-na, and the Doctor of Engineering in appliedcomputer science (magna cum laude) fromUniversity Karlsruhe (now Karlsruhe Instituteof Technology), Karlsruhe, Germany.

He is a ”ChuTian” Chair Professor at Schoolof Computer Science, China University of Geo-sciences, Wuhan, China.

Prof. Wang is a Fellow of IET and Fellow ofBCS.

Ning Jia received the bachelor’s degree incomputer science and technology from ChinaUniversity of Geosciences, Wuhan, China, andnow studying in the China University of Geo-sciences for the master’s degree in ComputerScience.

Zhijiang Kang received the Ph.D. degreefrom China university of Geosciences, Wuhan,China. is currently working in Petroleum Ex-ploration and Production Research Instituteof SINOPEC (PEPRIS). His research interestsincludes Reservoir Exploration, Interwell Con-nectivity Study and Production Optimization.

Yun Zhang is currently a Senior Engineerof Petroleum Exploration and Production Re-search Institute of SINOPEC (PEPRIS). Heis Postdoctoral for 2008-2011 in PEPRIS. Hegraduated from China University of Petroleumof Development of Oil and Gas Engineering in2008. His research interests includes NumericalSimulation and Petroleum System Simulation.

Shiyan Hu (SM’ 2010) received his Ph.D. inComputer Engineering from Texas A&M U-niversity in 2008. He is an Associate Professorat Michigan Tech. where he is Director of Cen-ter for Cyber-Physical Systems and AssociateDirector of Institute of Computer and Cyber-systems. He has been a Visiting Professor atIBM Research (Austin) in 2010, and a Visit-ing Associate Professor at Stanford Universityfrom 2015 to 2016. His research interests in-clude Cyber-Physical Systems, Cybersecurity,

Computer-Aided Design of VLSI Circuits, and Embedded Systems,where he has published more than 100 refereed papers.

He is an ACM Distinguished Speaker, an IEEE Computer SocietyDistinguished Visitor, an invited participant for U.S. National Acade-my of Engineering Frontiers of Engineering Symposium, a recipient ofNational Science Foundation (NSF) CAREER Award, a recipient ofACM SIGDA Richard Newton DAC Scholarship (as the faculty advi-sor), and a recipient of JSPS Faculty Invitation Fellowship. He is theChair for IEEE Technical Committee on Cyber-Physical Systems. Heserves as an Associate Editor for IEEE Transactions on Computer-Aided Design, IEEE Transactions on Industrial Informatics, andIEEE Transactions on Circuits and Systems. He is also a GuestEditor for 7 IEEE/ACM Transactions such as IEEE Transactionson Computers and IEEE Transactions on Computer-Aided Design.He has served as chairs, TPC chairs, TPC track chairs and TPCmembers for numerous conferences.

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