simulation optimization of water-alternating-gas process...

Scientia Iranica C (2019) 26(6), 3431{3446

Sharif University of TechnologyScientia Iranica

Transactions C: Chemistry and Chemical Engineeringhttp://scientiairanica.sharif.edu

Simulation optimization of water-alternating-gasprocess under operational constraints: A case study inthe Persian Gulf

S. Sadeghnejada;�, M. Manteghian, and H. RouzsazDepartment of Petroleum Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran.

Received 30 August 2018; received in revised form 13 December 2018; accepted 25 June 2019

KEYWORDSWater-Alternating-Gas (WAG);EOR;Optimization;Simulated annealing;Operationalconstraints.

Abstract. The optimization of the e�ciency of Water Alternating Gas (WAG) oodingprojects can guarantee the success of these projects. Many operational constraints canindirectly a�ect ooding e�ciency. Their e�ects are not normally considered during routineoptimizations. The main aim of this study is to determine the inuence of these constraints(e.g., maximum water-cut, maximum Gas-Oil Ratio (GOR), and minimum Bottom HolePressure (BHP) during the WAG process). Implementing a reservoir simulator coupledwith Simulating-Annealing (SA) enables us to discover the e�ects of these constraints duringsimulation optimization. The developed optimizer is applied to a case study from an Iranianformation located in the Persian Gulf. The recovery factor of WAG ooding is comparedwith that of the conventional waterooding and gas injection. Moreover, the optimizationof individual and simultaneous WAG parameters is analyzed. Results indicate that: (a)Operational constraints can not only alter the production mechanism but also directly a�ectthe ultimate recovery factor; (b) The recovery factor of simultaneous optimization of allWAG parameters is higher than that of individual parameter optimization; (c) Irrespectiveof the approach to parameter optimization, WAG ratio (or the volume fraction of injectedwater to gas) remains almost constant during all optimizations, showing the inuence ofthis parameter during WAG ooding scenarios.

© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

Waterooding and gas injection are well-establishedtechniques for production enhancement. However, dueto the mobility ratio of both injection phases, the�ngering e�ect is a common problem during oodingthat can a�ect the recovery factor. Di�erent methodshave been introduced to reduce the drawbacks of these

*. Corresponding author.E-mail address: [email protected] (S.Sadeghnejad)

doi: 10.24200/sci.2019.51680.2311

methods [1-5]. In order to make use of the bene�t ofthe simultaneous injection of both uids, WAG oodingwas introduced [6,7]. In this method, by stabilizingthe injection front, the remaining oil saturation of theformation decreases. In addition, gas injection reducesthe oil saturation in bigger pores, whereas water

ooding reduces the oil saturation in smaller pores[8]. Thus, WAG ooding can squeeze more volume ofhydrocarbon out of a reservoir by combining factorsincluding better mobility control, sweeping un-sweptzones (i.e., macroscopic displacement), and improvedmicroscopic displacement e�ciency [9,10].

WAG can be ooded in both miscible and immis-cible approaches. It is notable that 79% of the WAG

3432 S. Sadeghnejad et al./Scientia Iranica, Transactions C: Chemistry and ... 26 (2019) 3431{3446

projects are miscible, highlighting the popularity ofthis approach [9]. Among miscible ooding processes,CO2-water-alternating injection has greater popularitynowadays [11,12]. The most important criterion formiscibility determination is the Minimum MiscibilityPressure (MMP). If a reservoir pressure reaches MMP,CO2 ooding is miscible. CO2-water-alternating in-jection can e�ectively enlarge swept volume and oildisplacement e�ciency [13]. The injection of CO2into oil reservoirs has two advantages: increasing oilproduction and sequestering CO2 as an environmentalmeasure [14]. Yan et al. studied the displacementprocess and exquisite interaction mechanism on a porescale by analyzing the adsorbed oil layer during CO2-WAG injection [15]. Liu and Zhang simulated theinjection of CO2-CH4 mixtures [16]. They showedthat the rhythmic injection of these uids could o�er abetter mobility ratio and delay water breakthrough.

There are very good case studies for the appli-cation of optimization algorithms in the petroleumliterature [17-20]. However, the related studies of�nding the optimal conditions in WAG processes arerestricted to parameter sensitivity analysis via non-systematic approaches. In these studies, a limitedquantity of simulation runs (i.e., without implement-ing any optimization algorithm) were conducted todetermine an optimum condition. For example, anintegrated approach to reservoir modeling was usedto evaluate the performance of the miscible WAGprocess in Alaska [21]. Bedrikovetsky et al. de-veloped an analytical model for a tertiary miscibleCO2-WAG [22]. A simulation study using full-�eldcompositional reservoir modeling was undertaken tomanually optimize (i.e., without implementing anyoptimizer) the design of miscible or immiscible CO2-water-alternating ood in a pilot located in Jilin oil�eld [23]. Ghomian et al. investigated the e�ect ofhysteresis, WAG ratio, slug size, and heterogeneityon CO2-WAG ooding without the implementation ofany optimization tool [24]. Furthermore, Alizadeh etal. (2014) conducted a series of numerical sensitivitystudies to determine the magnitude of scaling groupsand their interaction with recovery factors duringimmiscible WAG displacement processes [25]. Liu etal. (2016) investigated the parameters inuencing WAGfor CO2 ooding by only using a numerical simulationpackage in a low permeability block of Jilin oil �eld [26].Chen et al. developed a multi-level programming modelfrom a life-cycle perspective for implementing the shalegas supply chain system. A set of leader-follower-interactive objectives with emphasis on environmental,economic, and energy concerns was incorporated intothe synergistic optimization process [27]. Moreover,an inexact multi-criteria decision-making model withconsideration of shale gas production pro�les andrecoverable reserves was analyzed in detail [28].

It is crucial to optimize operational parametersbased on the overall economy (e.g., net present value,overall project economy, and oil recovery) in WAGprojects [29]. There are some studies in the WAGliterature that have implemented optimization andarti�cial intelligence algorithms in their applicationsduring WAG ooding, but without emphasizing therole of production mechanisms imposed by productionconstraints. For example, Yang et al. implementedsimulated annealing and genetic algorithm and an-alyzed the capability of these techniques in WAGprocess optimization [30]. Moreover, a 3D reservoirsimulator integrated with an EOR expert system wasused to determine the reservoir strategies to optimizethe oil recovery from a carbonate reservoir with WAGtechniques [31]. Esmaiel and Heeremans introduceda response surface proxy model using optimal designthrough decision-making during WAG ooding in orderto reduce the number of required simulation runs [32].Ma (2010) used a commercial simulator and a neuralnetwork toolbox to build an arti�cial neural networkmodel for screening and designing WAG processes [33].Odi and Gupta simulated a CO2-WAG core oodresults by applying non-adjoint-based optimization al-gorithms to �nd an optimal WAG con�guration [34]. In2013, a heuristic simplex algorithm was used to �nd themaximum NPV and the best injection scenario in themixed-integer nonlinear problem optimization duringWAG processes [35]. Moreover, Mohagheghian utilizeddi�erent evolutionary algorithms to optimize hydrocar-bon WAG performance in a real case study [36]. Hetested the optimization tools with di�erent controllingvariables (e.g., injection rates, cycle ratio, time, etc.)to compare the performance, convergence speed, andthe quality of the optimal solutions found by thosealgorithms. The previous studies paid insigni�cantattention to the role of operational constraints duringthe optimization of WAG scenarios. These parameters,as operative limitations, would alter the productionmechanism of a �eld. Thus, ignoring them during

ooding scenarios might result in the misleading ofoptimization results.

The factors that can a�ect the success of WAGprojects can be categorized into two groups: reservoirparameters (e.g., heterogeneity, petrophysical proper-ties, and uid properties) and operational parameters(e.g., injection pattern, injection rate, WAG cycle,cycle time, etc.) [36]. The focus of this study is onthe optimization of the later parameters. As a casestudy, the dataset of an Iranian o�shore heavy oilformation located in the Persian Gulf was nominated.By coupling a reservoir simulator with a SimulatedAnnealing (SA) optimization algorithm, di�erent pro-duction/injection scenarios are investigated. In oursimulation-optimization approach, we have consideredsome injection/production parameters as variables and

S. Sadeghnejad et al./Scientia Iranica, Transactions C: Chemistry and ... 26 (2019) 3431{3446 3433

the ultimate oil recovery as an objective function.The main objective of this research is to reveal therole of operational constraints during optimizationand evaluate their e�ects on the optimization results.Subsequent to the natural production period of the�eld, the injection rates of water and gas oodingare optimized. Afterward, the optimizations of theWAG ooding parameters (e.g., injection rates, WAGratio, and cycle time) are considered in detail. Theultimate recovery factors of the individual and simul-taneous optimization of these parameters are comparedtogether. During all simulation optimization scenarios,the e�ect of operational constraints on �nding theoptimal scenario with the maximum recovery factor isdiscussed in detail.

2. Material and methods

2.1. Statement of the problemSimulation can be considered as an e�ective tool toanalyze the details of a production process [37] andpredictions of its future behavior. In petroleum en-gineering, production optimization plays an importantrole in increasing the amount of produced hydrocarbonand increasing its recovery factor. Optimization is oneof the best ways to �nd a proper solution withoutthe need to investigate all possible statuses duringsimulations [38]. The purpose of this study is toinvestigate the role of operational constraints in theultimate oil recovery of a WAG ooding project duringthe production optimization process.

Because of either facility limitations (both down-hole and surface) or economic issues, many restrictionsshould be considered during a simulation-optimizationscenario. For example, during the simulations, eachwell can operate at a speci�c target value, includingoil/water/gas ow rate or bottom-hole/tubing-headpressure. Changing the control mode of a well from aprimary mode to other modes is a routine to meet theoperational constraints. For example, due to reservoir

pressure reduction, the well may not produce morehydrocarbons at the initial rate with a BHP abovethe minimum BHP-limit set by the user. Therefore,the producing well with an oil-ow-rate target may beconverted to a �xed BHP mode. The well control modeis then changed automatically to maintain a constantBHP, wherein the oil production rate will decline. Thisprocess can be reversed when the oil production of thiswell exceeds the oil-rate target by any reason, e.g.,well stimulation, secondary recovery, or EOR scenarios.Furthermore, drilling the best location of injection andproducing wells is a challenging task that can a�ectthe reservoir connectivity between wells [39-44]. Inaddition, a well or its connections might automaticallybe closed due to the violation of some other economicconstraints. For example, the surface facility of a wellis designed to work under a speci�c gas (or water)-to-oil ratio limit (i.e., an operational limit), and itcannot process excess gas (or water). Examples ofsuch economic well constraints include lower econom-ical limit for hydrocarbon production rate, maximumwater cut (or water-hydrocarbon ratio), and maximumGas-Oil-Ratio (GOR). Overlooking the aforementionedconstraints during any EOR optimization de�nitelyalters the �nal results. Therefore, the operationalconstraints should be considered for the proposedcase studies. These targets can be considered viaconstrained optimization approaches.

In order to investigate the role of operational con-straints in this study, di�erent scenarios are consideredand the results are compared together (Figure 1). Inthe �rst scenario, natural production from the �eldunder study is discussed as a base case. The objectiveof this scenario is to �nd an optimum productionrate with the ultimate maximum recovery, consider-ing the operational constraints. In the second andthird scenarios, the optimum injection rates duringwaterooding and gas injection into the �eld areinvestigated. The injection in these scenarios startswith a lag of 28 years after the natural production

Figure 1. Scenarios considered during simulation optimization.


period. Furthermore, the optimization of injectioncycle time, injection ratios, and water/gas injectionrates during WAG ooding are examined. Theseparameters are individually optimized and, during eachoptimization scenario, the optimized values from theprevious results are implemented. At the �nal stage,the simultaneous optimization of all parameters isperformed, and its results are compared with individualparameter optimizations.

2.2. Goal and scopeThe primary goals of this study can be summarized asfollows:

(a) Coupling a simulated annealing simulator with ablack oil simulator to �nd the best productionscenario;

(b) Finding the best injection-production scenarioduring natural production, waterooding, gas in-jection, and WAG ooding in the case under study;

(c) Investigating the role of operational constraintsin the production optimization of the de�nedsimulation scenarios;

(d) Investigating the role of individual and simultane-ous optimization of WAG parameters during theultimate recovery.

These goals can be achieved by:

(a) Finding the e�ect of the following operationalconstraints: lower economical-limit for the hydro-carbon production rate, maximum water cut (orwater-hydrocarbon ratio), and maximum GOR;

(b) Finding the optimum production rate, water in-jection rate, and gas injection rate during naturalproduction, waterooding, and gas injection sce-narios, respectively;

(c) Finding optimum water and gas cycle time, waterinjection rate, and gas injection rate during WAG

ooding scenarios.

2.3. Simulated Annealing (SA) optimizerOptimization algorithms o�er a potential for a sys-tematic investigation of a broader set of productionscenarios under a given condition. These algorithmstogether with the experienced-judgment of specialistsallow for a better assessment of formation uncertaintyand signi�cantly reduce possible risks in decision-making. Consequently, there is an increasing interestin the implementation of optimization algorithms inthe oil industry. However, the selection of an appro-priate optimization algorithm, runtime con�guration,and the dynamic optimization of a reservoir remain achallenging problem [45].

In this study, the SA optimization algorithm isselected as an e�cient optimization method. This op-timization algorithm is implemented in the petroleum

literature for many di�erent applications [46-49]. SAwas �rst introduced by Kirkpatrick et al. [50] and Cerny[51]. This method is motivated by an analogy to solidannealing and is classi�ed as a heuristic method [52].In order to apply the SA method to a speci�c problem,di�erent parameters should be speci�ed including costfunction (i.e., objective function), random neighboringsolution, acceptance probability function, and anneal-ing schedule temperature (i.e., cooling schedule). Thedetails of this algorithm and the parameters usedin our speci�c simulation-optimization approach arementioned in Appendix A.

2.4. Simulation assumptionThe key assumption during simulations includes:

Three-dimension three-phase simulation is per-formed on the �eld scale;

The black oil uid model is considered in which theoil and gas properties may change with time andpressure, but their composition is constant;

The uid model is considered to be slightly com-pressible in which uid compressibility is constantin a certain range of pressures;

Corner-point gridding based on the notion of co-ordinate lines and corner depths with non-uniformgrids is used during simulations;

A heterogeneous rock model is considered, in whicheach grid cell has its own porosity and permeability;

A �ve-point stencil scheme is used for discretizingthe simulation partial di�erential equations;

Reversible rock compressibility is considered else-where.

An E100 package was used as the simulator of thisstudy. The input data �le was written based on thedata from one of the Iranian formations.

2.5. Coupled simulation optimization approachTo determine an optimum solution, a simulator shouldbe coupled with an optimizer. Figure 2 illustrates thecommunications between the implemented simulatorand the optimizer. The optimizer package and therelated input/output programs are coded in Matlab.The protocol concerning these communications be-tween the optimizer and the simulator was made byreading/writing on ASCII �les.

The algorithm starts with the de�nition of inputparameters for both optimizer and simulator. The op-timizer parameters include initial temperature, coolingschedule, equilibrium condition, and �nal terminationcondition. The simulator parameters consist of thenumber of injection and production wells, decisionvariables, and well constraints. Appendix A discussesthe details of the SA approach.


Figure 2. Schematic illustration of the coupled simulator-optimizer algorithm. The optimization and simulation sectionsare shown with �lled green and blue boxes, respectively.

Figure 3. (a) Porosity map of the formation under study. (b) Selected sector of the �eld showing the initial saturation ofthe reservoir for three available phases (i.e., oil, water, and gas).

During the optimization of each scenario, theSA optimizer is responsible for generating randomneighbor solutions and requesting the simulator toevaluate the objective function value (i.e., ultimaterecovery factor). The simulator tries to compute theultimate recovery of the �eld at a �xed time after thestart of the production (e.g., 50 years) by applyingthe operational constraints. The optimizer calls thesimulator for so many times to reach an optimumcondition in each scenario.

2.6. Case studyAs a case study, an Iranian o�shore oil reservoir hasbeen used (Figure 3(a)). A sector is selected throughthe entire reservoir with 7 � 7 � 20 blocks (the totalnumber of blocks is 980). The dimensions of theblocks in the x-, y-, and z-directions are 128, 177, and3.5 m, respectively. The reservoir under study has aninitial pressure of 19.3 MPa and contains 680,599 m3of oil originally in place. Two wells on either side ofthe model were considered (Figure 3(b)). During the


Table 1. Rock and uid properties of the reservoir under study.

Property Amount Property AmountPorosity (%) 3-32 Oil density (kg/m3) 935.96Horizontal permeability (�10�11m2) 0-1.35 Gas density (kg/m3) 1.3Vertical permeability (�10�11m2) 0-0.13 Water density (kg/m3) 1140.03Rock compressibility (1/Pa) 8:7� 10�10 Oil viscosity (mPa.s) 3.65Bubble point pressure (MPa) 18.62 Water viscosity (mPa.s) 0.55Initial reservoir pressure (MPa) 19.31 Gas viscosity (mPa.s) 0.02

natural production period, both wells were producingand, in the other scenarios, one of them was consideredas an injector of water and/or gas. Table 1 summarizesthe rock and uid properties.

Figure 4 depicts the water-oil and gas-oil drainagerelative permeability data of the formation. Sincethe intersection of the relative permeability curvesof the water and oil phase is at a point lower than(but close to) a water saturation rate of 50%, thereservoir rock is neutral-wet. During WAG ooding,three-phase ow conditions and, especially, hysteresise�ects become relevant in the recovery process [53].Hysteresis e�ects become larger in processes with uid

ow reversal as in the case of WAG injection. Inorder to consider this phenomenon, the hysteresiscapability of the simulator based on the methodologyof Aziz and Settari [54] was implemented during oursimulations.

Table 2 summarizes the well production/injectionparameters during all scenarios. In this study, theparameters such as maximum water-cut, maximumGOR, minimum BHP, and minimum oil ow ratewere investigated as e�ective operational constraints.The values of these parameters were set based onthe operational values of the �eld under study (i.e.,�eld readings). The considered control modes and

Figure 4. Relative permeability and capillary pressuredata used during simulations.

well constraints during our simulation are shown inTable 3.

3. Results and discussion

3.1. Optimizing natural production scenarioThe type of energy (i.e., production mechanism) avail-able for moving hydrocarbon uids to the production

Table 2. Production/injection parameters considered during the optimization of water ooding, gas injection, and WAGinjection scenarios.

Well production/injection parameters Value ScenariosWater ooding Gas injection WAG

Production rate (m3/d) 238.48p p p

Maximum injection BHP (MPa) 20.68p p p

Water injection rate (m3/d) 238.48 { {p

Gas injection rate (m3/d) 18,405 { {p

Table 3. Well operational constraints in the �eld under study.

Well constraints limit DescriptionOil ow rate for each well (m3/d) < 31:80 The well is closed if this limit is brokenBottom hole pressure (MPa) < 6:20 Production changes from a constant rate mode to a constant BHP modeWater cut (%) > 50 The worst-o�ending connection in the well is closedGas-oil-ratio (m3/m3) > 356:2 The worst-o�ending connection in the well is closed


Figure 5. Production rate optimization of 652simulations during natural production. The optimum rate(390.63 m3/d) is shown with a red cross. The recoveryfactor of rates from 360 to 420 m3/d (distinguished by twodashed lines) behaves di�erently from the other regions.

wells is quite important for determining the amountof recovery factor during natural production [55].Moreover, reservoirs are usually subjected to di�erentproduction mechanisms that may change during theirproduction lifetime. The primary production mecha-nisms of the reservoir under study are compaction-driveand solution-gas-drive mechanisms. Pressure depletioncauses the gas phase to appear in the formationbecause of the release of dissolved gas once the pressurefalls below the bubble point pressure. Gas releasingin the reservoir can have either positive or negativee�ects. The negative factors include the following:Either increasing the gas-oil-ratio in production wellsmay cause some operational problems or the reservoirpressure decreases more rapidly than the pressure dropof an under-saturated reservoir. Nevertheless, if theproduced gas has su�cient time to develop a secondarygas cap in the formation, then the rate of pressure dropreduces as the gas cap expansion can compensate forthe pressure drop rate of the formation (i.e., a positivefactor).

Figure 5 displays the results of the applied opti-mization to evaluate the optimum production rate ofthe reservoir under study during natural production.Each point in this graph represents the result of asingle simulation run, which was called by the SAoptimization algorithm. The �gure outlines the resultof 652 simulations (i.e., function calls) with di�erentproduction rates in the range of 48 to 636 m3/d.

As the production rate increases, more gas isproduced; in addition, a modest downward trend inrecovery factor is observed in Figure 5. However, thereis an unconventional rise in the recovery factor curvefrom 360 to 420 m3/d (distinguished by two dashedlines in Figure 5), in which the ultimate recoveryreaches a peak of 28.9% at a rate of 390.63 m3/d. Thedominant production mechanism for the production

Figure 6. Comparison of average reservoir pressure andcumulative gas production of two di�erent productionscenarios with production rates of 47.70 and 390.63 m3/d.

rates less than 360 m3/d is solution-gas-drive, whereasthe production is limited by the �eld maximum GOR,caused by the surface facility limitations at rates overthan 420 m3/d. At the optimum production rate of ourstudy (i.e., 390.63 m3/d), the operational constraintshelped the formation have a higher recovery factor.During the production, the upper perforations of thewell were automatically closed due to high-productionGOR (i.e., > 356:2 m3/m3 from Table 3); therefore,the lower perforations only continued to produce morehydrocarbon. The closure of the upper perforationsresulted in ceasing gas production and, consequently,developing a secondary gas cap in the reservoir. Thus,the expansion of this gas cap can maintain the reservoirpressure as the dominant drive mechanism. In thissituation, the recovery factor of the reservoir reachesits maximum value of 28.9%.

To validate the creation of the secondary gas capin the reservoir, Figure 6 shows the reservoir averagepressure and cumulative gas production for productionrates of 48 and 390 m3/d. For the former productionrate, the reservoir pressure falls steadily, while, for thelater production rate, pressure dramatically slumps inprimary steps (t < 1200 days) and moderately declinesafterward. This sudden reduction in the pressure droprate results from the release of the solution gas. After1200 days, gas production rise continues, but with arate more moderate than before. This is because ofthe closure of the upper perforations and the creationof the secondary gas cap that can displace oil belowgas-oil-contact in a piston-like manner toward the opencompletions.

3.2. Optimizing waterooding scenarioThe aim of this scenario is to �nd the optimum water-injection rate. During waterooding, the productionwell produces at a rate of 238.48 m3/d. The results of659 simulations with di�erent water injection rates areillustrated in Figure 7. The optimum injection rate iscalculated to be 164.55 m3/d with a recovery factor of35.5%, which is almost 6.6% higher than the naturalproduction.


Figure 7. Optimization of the water injection rate in thewater ooding scenario. The optimum injection rate(164.55 m3/d) is shown with a red cross. The recoveryfactor behaves di�erently in the three de�ned injectionrate ranges with the vertical dashed lines.

Figure 8. Comparison of production water cut atdi�erent injection rates of 164.55, 238.48, 362.49, and397.47 m3/d. Injecting with higher rates decreases waterbreakthrough time.

At low injection rates (qinj < 120 m3/d), theinjected water could not compensate the reservoir pres-sure drop due to the production (i.e., weak water-drivemechanism); therefore, the recovery factor remainedalmost constant irrespective of the water injection rate.On the contrary, water broke through at high injectionrates (qinj > 370 m3/d). After the breakthrough ofwater in the production well, no more oil could beproduced and the sweep e�ciency remained almostconstant irrespective of the injection rate, becausethe completions reached their maximum-water cutconstraint in these cases (i.e., 50% in Table 3) and wereclosed. This behavior can easily be seen in Figure 8,where an increase in the injection rate (e.g., injectionrate of 264.55 to 397 m3/d) resulted in a dramatic risein well water-cut in preliminary time steps. Thus, thewell completions automatically were closed, and water-cut plummeted to zero.

Furthermore, Figure 7 shows a declining trendof recovery factor from an injection rate of 120 to370 m3/d. This is because of the availability of a

Figure 9. Average gas saturation of reservoir, �Sg, fordi�erent water ooding scenarios with an injection rate of143, 164.55, 174.89, and 238.48 m3/d. The optimuminjection rate, 164.55 m3/d, behaves di�erently from theother scenarios.

balance between injection and production rates (i.e.,strong water drive mechanism). This balance pro-longed the breakthrough time and increased the piston-like movement behavior of the injected uid. However,a sharp jump in the recovery factor is observable inthis �gure around an injection rate of 164.55 m3/d.Since this injection rate was lower than the productionrate (i.e., 238.48 m3/d), the injected water could notmaintain the reservoir pressure and, �nally, gas wasreleased from the formation uid (i.e., P < Pb). Theexpansion and migration of this gas to the formationgas-cap could support the reservoir pressure; therefore,the maximum recovery of 35.5% could be achieved.

Figure 9 depicts the average gas saturation, �Sg,of the reservoir at di�erent injection rates. At allinjection rates (except 164.55 m3/d), as the injectionrate increases, �Sg falls because the injected watermay support the pressure reduction. The �Sg of theformation rose in the primary steps (t < 11000 days)and before gas breakthrough. After gas breakthrough,due to the formation depletion and gas production,�Sg decreased. The trend of �Sg at an injection rateof 164.55 m3/d is di�erent from that in the otherscenarios. At this rate, �Sg of the reservoir went upover time. During waterooding with this rate, theupper perforations quickly reached the maximum GORconstraints (i.e., in Table 3) and were automaticallyclosed. In this situation, the released gas could not beproduced. Increasing �Sg resulted in the creation of asecondary gas cap in the reservoir and, consequently,a rise in recovery factor. Thus, �Sg of the formationrocketed despite the trend of the other scenarios.Again, this phenomenon emphasizes that the opera-tional constraints can inuence the production results.

3.3. Optimizing gas injection scenarioFigure 10 depicts the result of 699 simulations duringthe SA optimization of gas injection rates. Theoptimum ultimate recovery (39.1%) was obtained ata gas injection rate of 18,122 m3/d, which was 10.2


Figure 10. Recovery factor versus gas injection rateduring optimization. The optimum gas injection rate(18,122 m3/d) is shown with a red cross. Three di�erentrecovery factor behaviors can be seen (distinguished bytwo vertical dashed lines).

Figure 11. Field gas production for three di�erent gasinjection scenarios with injection rates of 8495, 14158, and18122 m3/d.

and 3.7% higher than the natural production and water

ooding scenarios, respectively.

The trend of Figure 10 can be classi�ed into threeregions. The gas �ngering e�ect and breakthroughcontinuously reduced the formation recovery factor atinjection rates higher than 18,000 m3/d. At higherinjection rates, gas �ngering reduced the injectionsweep e�ciency and the recovery factor, too. Therecovery factor curve reached its highest point, 39.1%,at a gas injection rate of 18,122 m3/d. In addition,the recovery factor curve surged at low gas injectionrates (qinj < 12; 000 m3/d). The reason for thisbehavior is that, prior to gas breakthrough, highergas injection rates could compensate for more reservoirpressure drop due to the production. The furtherincrease of the gas injection rate from 12,000 to 18,000m3/d resulted in reaching the operational gas-oil-ratiolimit in the production well (Table 3), wherein theproduction ceased. In this case, the recovery factorsigni�cantly dropped.

Figure 11 illustrates the cumulative gas produc-tion curve versus reservoir average saturation for three

di�erent gas injection scenarios (i.e., 8,495, 14158,and 18,122 m3/d). At the same average gas satu-ration value, the scenario with an injection rate of18,122 m3/d produced less gas than the scenario withan injection rate of 8,495 m3/d. Therefore, the formerscenario could have a higher recovery factor. In thescenario with an injection rate of 14,158 m3/d, theinjected gas and the released solution gas broke throughvery soon in the production well, and the productionwell ceased to produce more hydrocarbon due to themaximum GOR constraint limit.

3.4. Single-parameter optimization of theWAG ooding scenario

3.4.1. WAG cycle time optimizationDi�erent WAG ratios introduce various mixture zonesand displacement mechanisms in a formation. Varyingcycle time obviously changes the number of cycles,which might a�ect the ultimate recovery of a oodingprocess. Figure 12 depicts the result of about 1500simulations during the SA optimization of WAG cycletime with a �x slug size. As is clear, the optimizationof more parameters (i.e., water and gas cycle time)sharply increases the number of function calls (i.e.,1500 simulations) during the optimization.

The optimum recovery factor, 43.3%, was ob-tained at a point with water and gas injection cycletimes of 81.5 and 180 days, respectively. A closer lookinto the available results reveals that some realizationshave a better ultimate recovery factor than the otherrealizations. Figure 12(b) shows this signi�cant trend.These points are some local minimum of the objectivefunction that lies on a straight line, which passesthrough the origin of this �gure. The global minimumat the highest recovery value (i.e., 43.3%) also lieson this straight line. Considering the water andgas injection rates (238.48 m3/d and 18,405 m3/d,respectively) along with the computed optimum cycletimes resulted in the optimum WAG ratio of almost 1:1(in �eld unit MSCF/STB).

WAG Ratio =Volume of injected waterVolume of injected gas

� 1:70m3m3

= 1STBMSCF

: (1)

3.4.2. Water injection rate optimization in WAGscenario

The second scenario during the proposed WAG opti-mization involves the optimization of the water injec-tion rate while keeping the cycle times and gas injectionrate from the previous scenario constant. Figure 13illustrates the function calls during the SA optimiza-tion. The behavior of this �gure can be divided intothree subsections (distinguished by two vertical dashed


Figure 12. (a) Recovery factor from 1000 simulations based on di�erent water and gas injection cycles. In each scenario,values of 238.48 m3/d and 18,405 m3/d were considered for water and gas injection rates, respectively. (b) Top view of (a)showing a trend between gas and water injection cycles with a higher recovery factor.

Figure 13. Recovery factor from 560 simulations withdi�erent water injection ow rates during WAG ooding.A value of 18,405 m3/d and 238.48 m3/d was consideredfor gas injection rate and production, respectively, duringall simulations.

lines). Before the injection rate of 160 m3/d and dueto the insu�cient pressure maintenance, the recoveryfactor was low (i.e., weak water drive mechanism).The optimum injection rate was achieved at a valueof 242.6 m3/d with a recovery factor of 43.4%. Inaddition, the recovery factor plummeted by a greaterincrease in the water rate after 270 m3/d due tothe quick breakthrough of the water phase in theproduction well. It is worth noting that the calculatedoptimum injection rate of 242.6 m3/d is very closeto the optimum injection rate from the wateroodingscenario (i.e., 238.48 m3/d). In addition, this value is inagreement with the result of the optimum WAG ratioof 1:1 from the previous section.

3.4.3. Gas injection rate optimization in WAGscenario

In this scenario, an optimum condition for the gasinjection rate during the WAG ooding is investigated.

Figure 14. Gas injection rate optimization of WAG

ooding scenario (751 simulations). The optimum gasinjection rate of 18,859 m3/d with the ultimate recoveryfactor of 43.5% is shown with a red cross.

During the optimization, the optimized values of thewater injection rate and cycle times from the previousanalyses were implemented. An optimized gas injectionrate of 18,859 m3/d was found with a maximumrecovery factor of 43.5% (Figure 14). The interestingpoint of the computed optimum rate is that this value isagain very close to the optimum WAG ratio (i.e., 1:1 in�eld unit) calculated from the section \WAG cycle timeoptimization". It indicates that the optimum injectionrates of water and gas should be in agreement with theoptimum WAG ratio.

3.4.4. Simultaneous parameter optimization of WAGparameters

In contrast to the previous sections in which WAGparameters were individually optimized, the aim of thissection is to optimize the WAG ooding parameters(i.e., water and gas injection rates and water and gasinjection cycles) simultaneously. Since the result of fourparameters cannot be depicted in a single �gure, waterand gas slug sizes (i.e., injection rate � cycle time)


Figure 15. (a) Recovery factor (FOE) of nearly 2800 reservoir simulations for di�erent water and gas slug sizes. Duringthe optimization, all WAG parameters were considered simultaneously. (b) Top-view of (a) and by only �ltering thesimulation results with more than 38% recovery factor. The simulation results lie on a straight line, showing a WAG ratioof 1:1.

Table 4. Summary of the optimization results.

Scenario Optimization parameter Optimum parameter Recoveryfactor (%)

Incrementalrecovery (%)�

Natural production Production rate 390.63 m3/d 28.9 {Water ooding Injection rate 164.55 m3/d 35.5 6.6Gas injection Injection rate 18,122 m3/d 39.1 10.2

Individual WAGparameter optimization

Water and gas cycle time 81.5 days, 180 days 43.3 14.4Water injection Rate 242.61 m3/d 43.4 14.5Gas injection rate 18,859 m3/d 43.5 14.6

Simultaneousparameter optimization

Water injection rate,Water cycle,Gas injection rate,Gas cycle

88.23 m3/d,181 days,26,023 m3/d,110 days

46 17.1

� Incremental recovery with respect to the primary production.

were used to show all simulation results in a 3D graph(see Figure 15(a)). The optimum scenario resulted in arecovery factor of 46% for the water injection rate andcycle time of 88.24 m3/d and 181 days, respectively,and the gas injection rate and cycle time of 26,023 m3/dand 110 days, respectively. The �rst interesting issuewith the computed results is that the simultaneousoptimization of the WAG parameters results in theultimate recovery factor that is almost 3% higher thanthat in the individual optimization results. Second,in compliance with our previous results, the optimumWAG ratio in this optimization scenario is again 1:1(in �eld unit). This behavior is well illustrated inFigure 15(b), in which the top view of Figure 15(a)is shown for those simulation points with a higher

recovery factor (e.g., > 38%). All simulation resultslie on a straight line, showing a WAG ratio of 1:1.This shows that, during WAG optimization, WAG ratiocan be an important parameter and will remain almostconstant irrespective of the manner of optimizations.

3.5. SummaryTable 4 summarizes the optimization results of allscenarios. Recovery factor increases from waterood-ing to gas injection and rises even more during WAG

ooding. As is shown, the simultaneous optimization ofall parameters has the highest ultimate recovery factor.

Figure 16 depicts the average reservoir pressureduring all optimum-ooding scenarios. As can be seen,subsequent to the natural production period, all scenar-


Figure 16. Average reservoir pressure for di�erentoptimized scenarios, including natural production (withthe rate of 390.63 m3/d), water ooding (with an oodingrate of 164.55 m3/d), gas ooding (with an injection rateof 18,122 m3/d), and WAG ooding (simultaneousoptimization of all parameters) showing pressuremaintenance of the reservoir during all ooding scenarios.

ios result in nearly constant reservoir pressure mainte-nance in the formation. In other words, the oodingprocess could maintain the reservoir pressure after thenatural production period with a constant trend.

4. Conclusion

In this study, a simulated annealing optimizer wascoupled with a reservoir simulator to investigate thee�ciency of di�erent production-injection scenarios.The recovery factor was selected as an objective func-tion. The considered scenarios include optimizationof natural production, waterooding, gas injection,individual WAG parameters, and simultaneous WAGparameters. The developed model was then appliedto a case study from an Iranian o�shore formation.The role of di�erent operational constraints includingproduction mode change (i.e., from constant rate toconstant BHP), closing perforations above a maximumwater-cut, or GOR limit was analyzed. The obtainedresults indicate that:

(a) The operational constraints could considerablyalter the production characteristics of a oodingscenario by changing the production mechanism(e.g., from solution-gas-drive to secondary-gas-cap-drive). Therefore, these production restric-tions could alter the �nal optimal scenario andshould always be analyzed;

(b) The recovery factor of the optimized WAG sce-nario (46%) was clearly higher than that of theoptimized natural production (28.9%), waterood-ing (35.5%), and gas injection (39.1%);

(c) The ultimate recovery factor of the individualWAG parameter optimization (in average 43.4%)

was certainly less than the simultaneous opti-mization of all parameters (46%). This revealsthat to �nd the best scenario during simulationoptimization, all parameters should be optimizedtogether;

(d) Irrespective of the number of variables duringoptimizations, the WAG ratio (i.e., the volumefraction of injected water to gas) remains almostconstant and equal to 1:1 in the �eld unit.

The obtained results can facilitate:

(a) Finding the role of operational constraints duringoptimization of primary production, secondaryrecovery, and WAG ooding scenarios;

(b) The manner of optimization of inuential param-eters during ooding scenarios.

However, during a production-optimization process,many uncertain parameters are available where ascenario-based model cannot completely address them.These uncertainties cause non-uniqueness of solutionsthat should be obtained with a probabilistic methodwithout overly exhausting simulation resources [56].Thus, future studies are required to reveal the e�ect ofdi�erent uncertain inputs on the result of simulation-optimizations. One possible approach could be �ndingthe e�ect of these uncertainties through the implemen-tation of the Monte Carlo simulations during simu-lation optimizations. Finding a proper optimizationalgorithm that can handle the non-linearity of complexhydrocarbon formations and reduce the computationtime is worthy of research. Furthermore, in this study,only the role of operational parameters was consideredduring the task of �nding the success of the WAG

ooding project, while the e�ect of reservoir param-eters (e.g., heterogeneity, petrophysical properties, and

uid properties) [36] is open for further investigations.Finally, in this study, a rather simple objective function(i.e., recovery factor) was studied. The implementationof more complicated objective functions (e.g., netpresent value) and multiple-objective functions can bethe title of future research.

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Appendix A

A.1. Simulated annealing strategySimulated Annealing (SA) is a probabilistic techniquethat was originally inspired by the process of metalannealing in metallurgy. This method attempt tomodel the controlled heating and cooling process ofa material in order to change its physical properties(e.g., increasing the size of its crystals) by altering itsinternal structure (i.e., minimizing its thermodynamicfree energy).

Figure A.1 depicts the optimization procedureof SA. The algorithms start with setting the initialtemperature and generating a random solution. Next,


Figure A.1. Flow chart of the simulation annealing procedure.

the objective function value is evaluated for the randomsolution. Subsequently, a random neighboring solutionshould be generated by making a small change to thecurrent solution. The new solution's cost is calculated,and a decision will be made whether to move thissolution (i.e., new state) based on an acceptance prob-ability function. This procedure continues reachingthe equilibrium condition (i.e., in practice, repeatingthe process for a large value). Then, the system tem-perature is decreased based on an annealing scheduletemperature, and the previous steps are repeated untilthe stop condition (termination condition) is met.

A.2. Annealing temperatureSA incorporates a temperature parameter, T , intothe minimization procedure. T is initially set high(T0) and, then, is allowed to slowly `cool' as thealgorithm runs. At high temperatures, the algorithmwill be allowed to accept worse solutions, which oftenguarantee to avoid being trapped in local optimums.Thus, accepting worse solutions allows the algorithmto extensively search for optimal solutions. As thetemperature declines, the chance of accepting worsesolutions reduces; therefore, the algorithm focuseson search spaces that may contain �nal optimumsolutions. Moreover, in each �xed number of steps, theannealing parameters are set to lower values than thatof iteration number (i.e., T increases). This process

is called restarting or re-annealing that again helpsthe algorithm to escape local solutions. In our case,we run the re-annealing module every 130th iteration.This parameter was tuned by trying a couple ofsimulation-optimization runs.

A.3. Acceptance probabilityAn acceptance distribution probability (p) is de�ned,which depends on the di�erence between the new costfunction value, Enew, and the current saved cost value,Ecurrent, and also the system temperature, T . In ourmethodology, achieving the maximum ultimate recov-ery is de�ned as a cost function (E = recovery factor).The acceptance probability, p, decides probabilisticallywhether to stay in the current state or to bounce out ofit. In our model, if the new state (i.e., the new recoveryfactor) is better than the current state, it becomes thenext solution, while if the new state is worse than thecurrent state (i.e., the new recovery factor is lowerthan the current recovery factor), the algorithm canstill consider it as the next point with the acceptanceprobability of:

p =1

1 + exp(�ET ); (A.1)

where �E = Enew�Ecurrent. The acceptance probabil-ity is between 0 and 1/2. Lower temperature results in


lower acceptance probability, and vice versa. Moreover,larger �E leads to lower p.

A.4. Annealing scheduleCarefully controlling the rate of cooling of the tem-perature can guarantee to reach more optimum condi-tions. The cooling rate should be low enough for theprobability distribution of the current state to be closeto the thermodynamic equilibrium. The algorithmsystematically lowers T and stores the best state foundso far. In our algorithm, the cooling rate follows thefollowing equation:

T = T0 � 0:95k; (A.2)where T0 is the initial temperature of the system, and kis the same as the iteration number until re-annealing.For better optimization purposes, T0 is selected insuch a way that the algorithm is able to explore theentire search space better before any cooling. Thevalue of T0 clearly depends on the scaling of �E and,thus, is problem-speci�c. To determine T0 in ouroptimization, an 80% acceptance chance is consideredfor a change that increases the objective function atinitial temperatures. By conducting an initial searchof our simulation-optimization approach, T0 of 150 Kis selected based on the speci�ed criteria.

A.5. Generating neighboring solutionDuring the optimization, the new solutions, xnew, aregenerated from the current solution, xcurrent, accordingto the formula:

xnew = xcurrent +D �R; (A.3)where x is the vector of variables. During ourproduction-injection scenario, parameters such as pro-duction rate, water/gas injection rates, or cycle timeswere considered as our decision variables. R 2 [�1;+1]is a vector of random numbers and D is a diagonalmatrix, which de�nes the maximum allowable changesin each variable. D is updated after an acceptable

change in the state of the solution as follows:

Dnew = (1� �)Dcurrent + �Dsuccess: (A.4)� is the weighting factor (0.85 was considered in ouralgorithm), and Dsuccess consists of the magnitudeof the changes in each control variable in the newsuccessful state. This equation controls the maximumstep size associated with each control variable.

A.6. Terminating conditionThe �nal T in our algorithm was determined when thesystem su�ciently cooled or the search ceased makingprogress. In other words, it is either no improvementbeing found at each temperature or the acceptanceratio falling below a small value (i.e., 10�6 in ouralgorithm).

Biographies

Saeid Sadeghnejad is an Assistant Professor ofPetroleum Engineering, Tarbiat Modares University,Iran. His research interests include formation char-acterization using pore-scale methods and EOR. Heholds a BS degree in Chemical Engineering, and MSand PhD degrees in Petroleum Engineering from SharifUniversity of Technology, Iran.

Mehrdad Manteghian is a Professor of ChemicalEngineering, Tarbiat Modares University, Iran. Hisresearch interests include industrial crystallization andmass transfer. He holds a BS degree in chemicalEngineering from AmirKabir University and MS andPhD degrees in Chemical Engineering from UMISTUniversity, UK.

Hossein Rouzsaz obtained his MSc degree inPetroleum Engineering from Tarbiat Modares Univer-sity, Tehran, Iran. His study area is EOR. Mr. Rouzsazholds a BS degree in Petroleum Engineering, fromPetroleum University of Technology, Iran.

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