Content uploaded by Ghazi D. Alqahtani

Author content

All content in this area was uploaded by Ghazi D. Alqahtani on Jan 14, 2016

Content may be subject to copyright.

SPE 160861

Well Optimization Strategies in Conventional Reservoirs

Ghazi AlQahtani, Ravi Vadapalli, Shameem Siddiqui, Texas Tech University; Srimoyee Bhattacharya, University of

Houston

Copyright 2012, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Saudi Arabia Section Technical Symposium and Exhibition held in Al-Khobar, Saudi Arabia, 8–11 April 2012.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been

reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum

Engineers, its officers, or members. Papers presented at the SPE meetings are subject to publication review by Editorial Committee of Society of Petroleum Engineers. Electronic reproduction,

distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not

more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and whom the paper was presented. Write Librarian, SPE, P.O. Box

833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

Well optimization is an important factor in field development strategies targeted to maximizing the hydrocarbon recovery, and

economic feasibility of new field development projects. Particularly, in view of shortage in new oil field discoveries,

maximizing oil production and net present value (NPV) have become critical factors (hereinafter called the "critical factors")

in reservoir engineering. As a result, well optimization research has become a separate field in its own merit. Recent attempts

by academic and industrial researchers converged on the goal to create efficient well optimization models that can predict

strategies for managing the existing oil and gas fields and developing new fields with potential for maximizing the critical

factors.

Important elements in field development optimization include well type, well placement and scheduling. In the last decade,

significant amount of work has been done in the area of well optimization for which both gradient based and gradient-free

optimization methods were used. In gradient-based well optimization methods, the derivative of the objective function with

respect to the decision variables is sought. In gradient-free optimization, a family of algorithms classified as global or

“stochastic” algorithms - such as the genetic algorithm, simulated annealing, and particle swarm optimization - can be

employed. Other algorithms such as local or “deterministic” algorithms (e.g. Generalized Pattern Search, and Hook Jeeves

Direct Search,) are also useful in these studies. These optimization strategies can be applied individually or as an ensemble of

optimization methods to maximize the critical factors in reservoir simulation.

In this paper, we review several of the current optimization techniques, and their application to maximize the critical factors.

In the process, we address the significance of different methods and highlight their limitations. We discuss as well the

challenges associated in extending these methods, and their potential in the future.

Introduction

A field development plan that promote optimized cost, maximize production plateau duration and recovery (maximizing net

present value) is a primary target in all upstream studies. Although simply stated, the scale and complexity of most studies

presents many challenges to a successful study outcome. For example, the potential of various well types such as vertical,

horizontal, and multilaterals., alternative optimization tactics (e.g., well spacing, and well scheduling), and the need to

consider static or dynamic uncertainty factors with a specific study objective function (e.g., recovery, and NPV). In recent

years, adaptation of existing ideas and methodologies from different industries such as the topic of optimization - the central

theme of this paper - and tremendous applications in other disciplines, showed great investment potential in the petroleum

industry especially with respect to the area of wells optimization (AlQahtani et al. 2009 and Elrafie et al. 2008).

The need to find answers for where and when to drill wells in reservoirs with minimum function evaluations is a key factor in

new development projects. In particular, the number and location of wells has a critical impact on hydrocarbon recovery which

can lead to economic gain or loss. This means that it is impractical to locate new wells based on experience, intuition or

primitive tools. Therefore, the demand to generate efficient automation processes for asset teams to facilitate decision making

cycles is paramount. To the best of our knowledge, the first attempt to optimize the well placement problem mathematically

was done by Rosenwald and Green in 1974 when they used mixed integer programming (MIP) to find the best well locations

from predefined well sites. Since then, well placement optimization kept evolving to more involved and sophisticated

2 SPE 160861

optimization models with different types of algorithms in which both gradient based and gradient-free optimization methods

were used with the goal of finding optimal well locations. For instance, the derivative of the objective function with respect to

the decision variables is sought in gradient-based well optimization methods. Whereas in gradient-free optimization, a family

of algorithms classified as global or “stochastic” algorithms - such as the genetic algorithms, simulated annealing, and particle

swarm optimization are used.

This paper will concentrate on well placement optimization techniques that are categorized as derivative free methods (i.e.

evolutionary algorithms, linear and nonlinear global algorithms). Published work in this area is grouped based on the type of

optimization method used in which the significance and limitations will be addressed. Before we further discuss the

optimization research in the area of interest, we’ll provide pertinent information on the optimization theory and the reader is

referred to the references for further details.

What is Optimization?

Optimization in theory is the problem of finding the maximum/minimum of a function over its domain, i.e.:

Objective function maximize or minimize f (x)

Subject to A x ≤ b

x ∈ S

The domain S is defined through a set of (possibly infinitely many) constraints, a point x ∈ S is a feasible solution and the set

S is the feasible set or the set of feasible solutions. A is the coefficient matrix and b is right hand side values of the inequality.

To know a feasible solution that maximizes (minimizes) f (x), in the case of maximization (minimization) problem, is called an

optimal solution or a global optimal solution if the solution satisfies the optimization problem. If the solution is a maximum

(minimum) around a neighborhood, it is called a local optimal solution or a local optimum. If the solution does not satisfy all

the constraints, the problem is infeasible, otherwise it is feasible. Further, if the problem is feasible but the maximum

(minimum), in case of a maximization (minimization) problem, is ∞ (–∞), then the problem is unbounded. In reservoir

engineering, the conductance of optimization evaluations require reservoir simulators to be part of the picture which make the

overall optimization process challenging.

There are different techniques available for the solution of different optimization problems some of them are listed in table 1.

Table1:Listofsomeoptimizationmethods

ConventionalOptimization

Methods

ModernOptimization

Methods

NonlinearProgramming GeneticAlgorithms

QuadraticProgramming SimulatedAnnealing

LinearProgramming AntColonyOptimization

DynamicProgramming ParticleSwarmOptimization

IntegerProgramming NeuralNetworks

MixedIntegerProgramming FuzzyOptimization

MultiobjectiveProgramming

For the well optimization problem, there is a need to define meaningful decision variables, objectives and constraints. The

problem of finding optimum number and placement wells where the maximization of a performance index (i.e. NPV or

cumulative oil production) is sought while minimizing costs and accommodating operating limits and other constraints is

recognized as a nonlinear optimization problem with integer parameters (Cullick et al 2005). The key step into handling this

optimization problem is to find a pragmatic way to solve it. The following section highlights popular algorithms and their use

for wells placement optimization problems in the recent past. . Holistic optimization strategy will be outlined in a separate

section of this paper followed by future directions.

More than forty papers were considered in this review and about nine derivative free optimization methods were used in wells

optimization since the early work of Rosenwald and Green in 1974. These techniques are listed below and their percent usage

in well optimization methods is shown as a Pie chart in Figure 1.

SPE 160861 3

Figure1:PieChartfortheutilizationpercentageofderivative‐freeoptimization

methodspublishedinwellsplacementoptimization

1. Genetic Algorithms (GA)

2. Simulated Annealing (SA)

3. Branch and Bound (B&B)

4. Covariance Matrix Adaptation-Evolution Strategy (CMA-ES)

5. Particle Swarm Optimization (PSO)

6. Spontaneous Perturbation Stochastic Approximation (SPSA)

7. Retrospective Optimization using Hooke Jeeves search (ROHJ)

8. Nelder-Mead downhill Simplex (N-M)

9. Generalized Reduced Gradient (GRG)

Genetic Algorithms

GA is heuristic evolutionary algorithm usually composed of several blocks that need to be addressed to insure suitability to the

problem in hand (Holland 1975). Primarily, the solutions to the optimization problem need to be represented well genetically.

There should be an initial set of population of solutions generated. The function evaluations for solutions are achieved by

means of their fitness. During reproduction, the genetic structure can be perturbated by genetic operators. The last step

contains the parameter values of GA. The advantage of using this type of stochastic search algorithms is their ability to find

global optimum solution. As reported by different published papers, GA is the most widely used method with about 60% of

the total number of methods applied in well placement optimization. Table 2 lists the published work that indicates utilization

of GA in wells optimization. Bittencourt et al. 1997 embarked the use of GA in reservoir development optimization by

generating a hybrid HGA. This HGA system composed of GA, polytope search and tabue search in attempt to utilize the

power of each method. The work was intended to optimize well location, well type and the direction of horizontal wells. Each

optimized set has an economic reflection as a measure of the profitability of the optimized sets. Santelleani et al. 1998

automated an optimization scheme for the placement of vertical wells with reservoir simulator. They addressed risk and

uncertainty by considering different realizations of geological models deterministically into the optimization scheme which

leaded them to obtain low risk set of optimum wells.

Johnson and Rogers 1998 were concerned about the expensive computations in coupling reservoir simulators with

optimization mathematical schemes. For this reason, they used Artificial Neural Networks (ANN) - as a proxy – coupled with

heuristic search methods (i.e. GA and SA). Their objective was to maximize a profit measure by optimizing the location of

injection wells in Pompano field. In this framework, they utilized ANN as a trained data set that can be used to predict model

results and thus linked with GA or SA to predict performance with some profit measures. Their method to reduce the error in

ANN data set was to apprehend simulator forecasts in weights of ANN. Even though the approach was computationally

involved, uncertainty was not carried out in the optimization framework. Guyaguler et al. 2000, used similar framework but

with including kriging method to create proxy as an alternative to ANN. They developed hybrid method of GA linked with

polytope search – as a helper method - and coupled with a proxy. The objective function in this work was to maximize NPV

by finding the optimum injection well locations. Using kriging as a proxy with the hybrid optimization framework reduced the

60%

8%

8%

6%

6%

3% 3% 3% 3%

GA

SA

B&B

PSO

CMA‐ES

N‐M

GRG

SPSA

ROHJ

4 SPE 160861

computational expense considerably. An extended version of this work was carried out in 2001 when they included uncertainty

assessment in economic measures through adaptation of decision trees and utility theories. They established several well

configuration layouts in which the decision tree will result in the configuration that has the higher expected value of return.

Utility functions with risk attribute measures were incorporated in framework and the final outcome of the system will be the

optimum location of wells with high confidence and low risk as in Guyaguler and Horne 2001. Montes et al. 2001 applied GA

to optimize locations of vertical wells and analyze the impact of internal parameters and population size on the performance of

GA.

Table2:PublishedworkthatindicatesutilizationofGAinwellsoptimization

AuthorsYearTitles

BittencourtandHorne1997“ReservoirDevelopmentandDesignOptimization.”

JohnsonandRogers1998“UsingArtificialNeuralNetworksandtheGeneticAlgorithmtoOptimize

Well‐FieldDesign:PhaseIFinalReport.”

Santellanietal.1998“SurvivaloftheFittest’anOptimizedWellLocationAlgorithmfor

ReservoirSimulation.”

Guyaguleretal.2000“SPE63221OptimizationofWellPlacementinaGulfofMexico

WaterfloodingProject.”

GuyagulerandHorne.2001“SPE71625UncertaintyAssessmentofWellPlacementOptimization.”

Montesetal. 2001“SPE69439TheUseofGeneticAlgorithmsinWellPlacement

Optimization.”

Yetenetal.2002“OptimizationofNonconventionalWellType,LocationandTrajectory.”

BadruandKabir2003“SPE84191WellPlacementOptimizationinFieldDevelopment.”

ÖzdoğanandHorne2004“SPE90091OptimizationofWellPlacementwithaHistoryMatching

Approach.”

Ermolaevetal.2006“EfficientWellSpacingAlgorithms.”

Larionovetal.2006“SPE104326MethodologyofOptimalWellPattern,LocationandPathsin

ProductiveFormationsDuringOilandGasFieldsDevelopmentPlanning.”

Túpacetal. 2007“SPE107552EvolutionaryOptimizationofOilfieldDevelopment.”

Maschioetal.2008 “SPE113483ProductionStrategyOptimizationUsingGeneticAlgorithm

andQualityMap.”

Onwunaluetal.2008“SPE117323ApplicationofStatisticalProxiestoSpeedUpField

DevelopmentOptimizationProcedures.”

Túpacetal.2008“SPE112258DecisionSupportSystemforEconomicAnalysisofE&P

ProjectsUnderUncertainties.”

Emerick,etal.2009“SPE118808WellPlacementOptimizationUsingaGeneticAlgorithmwith

NonlinearConstraints.”

Leeetal.2009“SPE125539HorizontalWellDesignIncorporatedwithInterwell

Interference,DrillingLocation,andTrajectoryfortheRecovery

Optimization.”

Bukhamsinetal2010“SPE136944OptimizationofMultilateralWellDesignandLocationina

RealFieldUsingaContinuousGeneticAlgorithm.”

Arsenyev‐obraztsovetal.2011“ImprovementofOilandGasRecoverybyOptimalWellPlacement.”

Hassanietal. 2011“Aproxymodelingapproachtooptimizationhorizontalwellplacement.”

Litvaketal. 2011 “SPE146512FieldDevelopmentOptimizationwithSubsurface

Uncertainties.”

Moralesetal.2011“SPE143617ANewModifiedGeneticAlgorithmforWellPlacement

OptimizationunderGeologicalUncertainties.”

Yeten et al. 2002 used GA to drive the reservoir simulator and find the optimum well type, location and trajectory of

nonconventional wells (NCWs) or Complex Wells. They dealt with the situation of long and large number of runs by using

helper algorithms (i.e. ANN and Hill Climber) to accelerate the optimization procedure. On well level scale, the parameters to

optimize were the coordinates that define the heel and toe of the laterals in a complex well. The optimized wells produced

higher objective functions (cumulative oil or NPV) which depend mainly on type of the reservoir and degree of uncertainty.

Badru and Kabir 2003 extended the work in Guyguler et al. 2000 by including the horizontal wells. They linked the hybrid GA

SPE 160861 5

with Experimental Design (ED) to find uncertainty impact on recovery and the number of wells required. They found that

uncertainty affect recovery but not the number of wells especially for green fields.

Ozdogan and Horne 2004 came up with a workflow to optimize well placement using pseudohistory approach. The idea was to

include data over time to update the history matched models continuously which accounts for time-dependent uncertainty. The

framework starts by conducting an optimization in which the algorithm tries to find different suitable locations with highest

NPV which are called test locations. The optimization scheme used here was a hybrid GA with polytope search linked with

proxies (i.e. kriging and neural networks). The next step is applying gradual deformation algorithm to history match the

production response from the generated realization to the actual response. This will create multiple pseudohistory curves that

were matched as data from new wells became available. At the end of optimization cycle, optimum wells locations will be the

output that honor different realizations and frequent updates over time. There was a huge amount computations performed to

get the recursive history matching steps which bounds the applicability of this approach to small fields with tens of wells.

Ermolaev et al. and Larionov et al 2006 used GA with Ant Colony algorithms to find efficient well spacing and optimal well

patterns for vertical and horizontal wells. The selection criterion for the location of the well was via reserves distribution

which were obtained by 3D geomodels and then upscaled to 2D coarse grids. The Ant Colony algorithm was used to capture

search stages in a collect and analyze fashion of the optimization experience which can reduce the computations time

considerably. Their performance measure was either cumulative oil or NPV.

Tupac et al. 2007 utilized hybrid GA for oil field development to find optimum well types, number and placement with NPV

and cumulative oil as the objective functions. They used proxy models based on approximation functions (i.e. Elman Neural

Networks and Hierarquical Neuro Fuzzy with Binary partition) from simulation output and create a cutoff to determine

whether the proxy or simulator will be used for the function evaluations. It is important to highlight the utilization of Quality

Maps from which they identify the best location to place wells. Quality Maps are a 2D representation of regions goodness for

high potential productivity which was introduced by Cruz et al. 1999. Distance between wells were regulated by constrains

while a maximum well length for horizontal wells was set initially. To overcome the computation expense bottleneck, they

performed their optimization model on parallel processors with the help of a Common Objects Request Broker Architecture or

COBRA. In 2008, the work got extended by adding real options in which the facility expansion option was added to the

optimization framework. This was achieved by installing additional wells under reserve volume uncertainties in the additional

well drainage area. Maschio et al. 2008 integrated the use of Quality Maps with GA to reduce the number of combinations

considered in the optimization. Number of wells and their positions were the optimization variables with NPV as an objective

function. They found that using Quality Maps enabled them to find optimum well positions with decreased number of

simulations.

Onwunalu et al. 2008 combined GA with statistical proxy that was described as a clustering based techniques. This type of

proxy can establish relationship between the variables and the objective function (i.e. NPV) using unsupervised learning

techniques. More details on the proxy can be found in Artus et al 2006. This combined approach was found to reduce the

number of simulation runs required by significant amount of time (up to 91% less computations). Emerick et al 2009

developed a software utilizing GA to optimize number, location and trajectory of production and injection wells. The goal for

their work was to generate a tool that can be used by asset teams in field development projects that can facilitate access to

robust optimization models. They overcome the bottleneck in handling nonlinear constraints of wells placement optimization

problem by applying Genetic Algorithm for Numerical Optimization of Constrained Problems (GENOCOP) technique. The

optimization scheme here was deterministic and utilized the concept of Quality Maps defined earlier. They found significant

increase in NPV values when using their automated approach compared with well position scenarios suggested by simulation

engineer. Lee et al 2009 introduced combined node based well configuration that identify geometric dimensions of horizontal

wells with GA to determine well locations and detailed trajectory. This combined approach is linked to the simulation and the

framework can suggest optimum well locations for vertical and horizontal wells with different trajectories. The effort here

resulted in more realistic horizontal well designed compared to one line horizontal wells used conventionally which showed

improved profit and cumulative oil production.

Bukhamsin et al. 2010 used binary and continuous GA’s to identify a suitable optimization method that can be applied in real

field’s development plan accommodating variables such as well type, well location, laterals number and orientation. The main

findings here were that continuous GA combined with Hill Climbing search can result in optimum answers with application

related to real field studies. Arsenyev-obraztsov et al 2011 leveraged on the GA work conducted earlier by Ermolaev et al

2006 and added Boolean (Integer programming) to make optimum conversion of producer to injector. Hassani et al 2011

developed different proxies and linked them with GA to optimize horizontal well location. The three proxies created were

quadratic, multiplicative and radial basic function models. They found out that quadratic models outperformed other proxies in

fitting the real model and in generating predictions. However, radial basic functions were the best with optimization

operations. Litvak et al. 2011 extended the work in Onwunalu et al. 2008 by including discrete as well as continuous decision

variables (i.e. number of wells, wells placement, well scheduling, well pattern, well rates and facility size). In addition, new

variables were introduced such as depletion strategy (i.e. gas injection or water injection). The goal of this work was to reduce

the expense of computations by objective function estimation and leveraging on the statistical proxy coupling with GA.

Uncertainty in geological parameters and economic terms were included in the optimization scheme which can be taken

6 SPE 160861

further to large scale field optimization. Morales et al. 2011 introduced modified GA for well placement optimization taking

into account geological uncertainty. The modification allows for user defined level of risk to be incorporated in the

optimization scheme to find optimum well locations. The approach was applied to optimize horizontal well placement in gas

condensate reservoir considering different realization and acceptable level of risk by the user.

Simulated Annealing Algorithms

SA is a stochastic metaheuristic algorithm that can find global optimization due to the nature to search in large space (Thomas

2009). The earliest work with SA in well placement optimization was conducted by Beckner and Song 1995. They were

seeking optimal well placement and scheduling by formulating the optimization as a traveling salesman problem. Their

optimization method was linked with a simulator. Table 3 lists the published work that indicates utilization of SA in wells

optimization. Johnson and Rogers 1998 used results of SA optimization scheme as a comparative means to the GA results as

mentioned in the previous section. Norrena and Deutsch 2002 used SA to find good static well placement plans without

coupling optimization to simulator. They selected SA to perform the optimization framework due to its ability to converge to

an optimal result, SA ability to converge quickly and the objective function can be nonlinear or discontinuous. This

methodology can work for vertical wells, deviated and segmented wells where the objective function is a measure of

performance of well plan.

Table3:PublishedworkthatindicatesutilizationofSAinwellsoptimization.

AuthorYearTitles

BecknerandSong1995“FieldDevelopmentPlanningUsingSimulatedAnnealing‐

OptimalEconomicWellSchedulingandPlacement.”

JohnsonandRogers1998“UsingArtificialNeuralNetworksandtheGeneticAlgorithmto

OptimizeWell‐FieldDesign:PhaseIFinalReport.”

NorrenaandDeutsch2002“AutomaticDeterminationofWellPlacementSubjectto

GeostatisticalandEconomicConstraints.”

Branch and Bound Algorithms

B&B is considered as a deterministic global algorithm that can handle linear or nonlinear problems especially in discrete and

combinatorial optimization (Clausen 1999). This type of algorithms is based on partitioning, sampling and subsections of

upper and lower bounds (Thomas 2009). Table 4 lists the published work that indicates utilization of B&B in wells

optimization. The earliest ever work, that we know of, done in wells optimization was the work conducted by Rosenwald and

Green 1974 by developing numerical optimization framework to select optimal positions of wells. They used B&B with mixed

integer programming to determine optimum well locations from predefined location sets. Their technique objective is to

minimize the difference between actual flow curves and the desired (demand curves). Tarhan et al 2009 developed multistage

stochastic optimization scheme to optimize three classes of variables (i.e. decision, resource and state). In decision variables

they aim to find optimum number of wells, well types, well scheduling and facilities to be built by maximizing NPV in

offshore oil and gas field with different reservoirs under uncertainty. Duality based B&B were used to find the optimum

solution that involved nonconvex mixed integer nonlinear programming. This was achieved by calculating upper and lower

bounds in which Lagrange multipliers were incorporated and branching the problem at different levels. The endogenous

uncertainty was represented by initial hydrocarbon maximum flow rate, recoverable hydrocarbon volume and water

breakthrough time in the reservoir. Farmer et al. 2010 developed a proxy from reservoir simulator output by using radial basis

function model. They applied B&B global optimizer to find optimum location and trajectory for multilateral well. They

compared the results of the approach used with GA results and showed considerable increase in cumulative oil production.

Table4:PublishedworkthatindicatesutilizationofB&Binwellsoptimization

AuthorYearTitles

Rosenwaldand

Green

1974“AMethodforDeterminingtheOptimumLocationofWellsina

ReservoirUsingMixedIntegerProgramming.”

Tarhanetal.2009“AMultistageStochasticProgrammingApproachforthePlanningof

OffshoreOilorGasFieldInfrastructureUnderDecisionDependent

Uncertainty.”

Farmeretal.2010“OptimalMultilateralWellPlacement.”

SPE 160861 7

Particle Swarm Optimizations

This type of global optimization belongs to Evolutionary Computation algorithms that are inspired by biological mechanisms

of evolution. Table 5 lists the published work that indicates utilization of PSO in wells optimization. Onwunalu and Durlofsky

2011 developed a novel approach to use this type of optimization algorithm in large scale field development optimization. In

this work they proposed well pattern optimization (WPO) that include well pattern description (WPD) to handle large number

of wells followed by well by well perturbation (WWP) that are incorporated into core optimize (i.e. PSO). The advantage here

is that WPO handles group of wells as pattern compared with single well placement used in conventional methods. Such

technique save time in computational efforts since the number function evaluations is reduced considerably. The overall field

scale optimization was to maximize NPV with optimum number of wells and best well patterns populated into the field. Well

types considered in this work were vertical, deviated, and dual lateral wells. The work was applied with different cases in

which multiple realizations were considered to account for geological uncertainty and the results showed promising potential

when compared with GA method.

Table5:PublishedworkthatindicatesutilizationofPSOinwellsoptimization

AuthorYearTitles

Onwunaluand

Durlofsky

2011“ANewWell‐Pattern‐OptimizationProcedureforLarge‐Scale

FieldDevelopment.”

Wanget

al.

2011“SPE141950OptimalWellPlacementunderUncertaintyusing

aRetrospectiveOptimizationFramework.”

Wang et al. 2011 introduced novel approach to find the optimum well placement under uncertainty using Retrospective

Optimization (RO). RO can be used in conjunction with stochastic or deterministic core optimizers. They used Particle Swarm

Optimization (PSO) as the core optimizer and compare with Simplex Linear Interpolation based gradient search (SLI) as the

deterministic core optimizer. RO utilizes a sequence of realizations to account for geological uncertainty which is conducted

by either random sampling or cluster sampling. The basic idea for the objective function is to be approximated by the average

over the selected number of realizations that evolved and thus new objective functions (i.e. cumulative oil) can be averaged on

a larger number of realizations. As a result, RO does not require large number of computations because the number of

realizations is small but as the number of realizations increase the RO will require many calculations. When the size of the

sample is large objective function calculated will be close to the optimum which has to be confirmed by running the process to

the end.

Covariance Matrix Adaptation-Evolution Strategy

CMA-ES belong to the Evolutionary Algorithms which are inspired by biological means of evolution. This type of algorithm

is designed for multi objective nonlinear optimization problems in continuous domain. It is considered as very powerful

evolutionary algorithm for difficult nonconvex optimization as reported in a benchmark study between different types of

evolutionary computation algorithms in Hansen et al. 2009. Table 6 lists the published work that indicates utilization of CMA-

ES in wells optimization. CMA-ES was used by Ding 2008 to optimize well locations for different types of wells with NPV as

objective function. In this work comparison between CMA-ES and GA showed comparable findings. Sensitivity study was

conducted on CMA-ES and concluded that population size and CMA-ES parameters might affect the performance of the

algorithm. Extended work by Bouzarkouna et al 2011 to well optimization problem utilizing adaptive penalization with

constraint handling. The results of this work showed that CMA-ES outperformed GA method in terms of NPV and

optimization convergence. In addition, quadratic proxy was generated and linked with CMA-ES and result showed lower

computational time by 20% with comparable results to that of CMA-ES without proxy.

Table6:PublishedworkthatindicatesutilizationofCMA‐ESinwellsoptimization.

AuthorYearTitles

Ding,D.Y.

2008“SPE113525OptimizationofWellPlacementUsingEvolutionary

Algorithms.”

Bouzarkounaetal.

2011“WellPlacementOptimizationwiththeCovarianceMatrix

AdaptationEvolutionStrategyandMeta‐Models.”

Other Derivative- Free Optimization Algorithms

In this section, four algorithms will be covered which include Spontaneous Perturbation Stochastic Approximation (SPSA),

Generalize Reduced Gradient (GRG), Nelder-Mead (N-M) and Retrospective Optimization using Hooke Jeeves search

(ROHJ). Table 7 lists the published work that indicates utilization of the above algorithms in wells optimization. The SPSA is

a gradient based algorithm that calculates in random stochastic search an approximated gradient and not the exact one. It was

used by Bangerth et al 2006 to find optimum location of wells and operation parameters that can yield high cumulative oil.

8 SPE 160861

This method was compared with several techniques (i.e. very fast SA, finite difference gradient, N-M and GA) to find out

which algorithm can find the best objective with minimum function evaluations. They found that SPSA and very fast SA

showed better performance for the optimization schemes that were applied on two different test cases. SPSA was able to find

solutions with less function evaluation than very fast SA. However, the later was found more reliable global well locations

than SPSA.

GRG is an optimization algorithm that can handle nonlinear constraints and can transform inequality constraints to equality

ones. This type of algorithm was used by John and Onyekonwu 2010 for well spacing optimization. They derived NPV as

objective function leveraging on oil production decline curves. GRG is built in algorithm in Excel Solver under the category of

nonlinear programming (NLP) engines which was used in this work as an optimizer to find optimum well locations using

simulation results.

Table7:PublishedworkthatindicatesutilizationofSPSA,GRG,N‐MandROHJalgorithmsinwellsoptimization

AuthorYear Titles

Bangerthetal.

2006 “Onoptimizationalgorithmsforthereservoiroilwellplacementproblem.”

Johnand

Onyekonwu

2010 “SPE140674NonLinearProgrammingforWellSpacingOptimizationofOil

Reservoirs.”

Tilkeetal.

2010 “SPE135168AutomatedFieldDevelopmentPlanninginthePresenceof

SubsurfaceUncertaintyandOperationalRiskTolerance.”

Wangetal.

2010 “Useofretrospectiveoptimizationforplacementofoilwellsunder

uncertainty.”

N-M algorithm belongs to direct search methods and it can be referred to as downhill simplex. N-M is a multidimentional

unconstrained optimization that uses the valued of the objective function without derivatives which is suitable for nonsmooth

functions and more details can be found in Thomas 2009. This type of algorithm was used by Tilke et al. 2010 to optimize

well placement planning. They created an automated field development planning workflow that accommodates well locations

optimization under uncertainty. Part of this workflow was a high speed analytical reservoir simulator that was coupled with the

N-M algorithm to find results in short timeframe. The approach used here is to reran optimum result an initial guess for the

next run which helped converging to better objective function (i.e. NPV). The uncertainty in this framework included

geological and economic factors which were taken further identify optimum wells with high or low confidence based on

efficient frontier analysis.

ROHJ algorithm was used by Wang et al. 2010 to incorporate uncertainty in optimizing vertical well locations with NPV as an

objective function. Uncertainty handling here covered parameters such as oil water contact, porosity and permeability. RO

utilizes a sequence of realizations to account for geological uncertainty which is conducted by either random sampling or

cluster sampling. The basic idea for the objective function is to be approximated by the average over the selected number of

realizations that evolved and thus new objective functions (i.e. cumulative oil) can be averaged on a larger number of

realizations.

Optimization Techniques Challenges and Directions

It is important to study the algorithms to be considered in well optimization loop because their performance is very dependent

on the type of problem statement. The techniques presented in this paper are capable of handling discontinuous as well as

nonlinear objective function with multiple local minima or maxima. As mentioned earlier, they are capable of finding best

global solution for the concerned optimization problem. Investigation is needed for some of the algorithms in terms of their

sensitivity to the number of decision variables, constraints and internal parameters of the optimization scheme.

Derivative-free optimization algorithms are observed to be very suitable for this kind of problem statement where model is

black box to the optimization algorithm. On the other side, the issues with using derivative based methods are their

inflexibility to handle possible discontinuities in the objective function and nonlinearities in constraints. Derivative based

methods increase complexity to the optimization problem especially when objective function is nonlinear in nature with

respect to the decision variables.

One common challenge for wells placement optimization with any algorithm was the unavoidable numerous number of

simulation runs and computations expense. In fact, using derivative-free optimization algorithm requires lot of simulations

before giving optimal solutions and also, they face with the problem of convergence. Therefore, combination of global search

and local search method might be the way to approach the well placement optimization problem in the time effective manner.

The use of proxies in place of reservoir simulators was found to be very significant to reduce the expense of computations.

Figure 2 shows a bar chart for the methods used to generate proxy models for wells placement optimization. The need to

experiment with different methods to find a reasonable solution surface that can expedite the cycle of decision making process

SPE 160861 9

with asset teams is paramount and requires additional studies. Therefore, it would be reasonable to use appropriate proxy

model and update it as and when needed. There is no doubt that an optimum result of an optimization framework is to have it

automated with easy access to project development teams with average or even minimum skills in using the computing

environments. In addition, further extension for the current methodologies to be applied for different types of reservoirs is

needed. As seen in the reviewed papers, more constraints are taking place with more involved optimization algorithms. This

can indicate that decisions need to go earlier in the optimization loop in order to link the technical results to business.

Therefore, more complex optimization schemes are expected to translate inputs from the management teams into bounds and

constraints. Large scale wells optimization could provide significant insights to the optimum development strategies and NPV.

However, such studies will be computationally challenging and may need supercomputing (Vadapalli et al. 2008, Vadapalli et

al. 2010) capabilities such as cluster, grid and cloud computing. On the other hand, a small scale well level optimization could

be misleading especially when the results are extended to represent large scale wells optimization scenarios.

Figure2:Barchartforthefrequencyofthemethodsusedtogenerateproxymodelswithreferencetothe

reviewedworkinwellplacementoptimization.

Reservoirs are heterogeneous in character areally and vertically. The depletion, sweep and productivity of a reservoir can vary

markedly from region to region. In turn, this will have a bearing on the most appropriate well technology, design and

completion strategy to be used throughout each of these different regions. If the reservoir can be defined in terms of behavior

regions, then these can be extracted as sector models and developed using a narrower range of well types and completions

under uncertainty. This aids in identifying the most appropriate and cost beneficial well and completion technology. However,

uncertainty adds to the computational complexity further and might warrant for use of supercomputing environments.

Figure 3 shows general flowchart for well optimization algorithm with uncertain inputs. There are mainly two types of inputs

for any kind of well optimization. Input to optimization module which includes number of design variables along with their

bounds and other design constraints imposed on objective function or other variables. Input to the reservoir model includes

reservoir properties obtained from various sources like well logs, well testing etc. along with the economic parameters for

NPV calculation. Uncertainty on above variables can also be included in the calculation by providing distribution of them.

Optimization module includes optimization algorithm which uses reservoir model to evaluate objective function. Finally, we

will get the best design with certain distribution because of uncertainty in the input parameters. Therefore, best design with

certain confidence interval is obtained.

0% 3% 6% 9% 12% 15% 18% 21% 24%

LeastSquares

Multiplicative

Regression

NeuroFuzzy

Quadratic

Radialbasicfunction

Statisticalcorrelations

ANN

Kriging

10 SPE 160861

Conclusion

Well optimization offers incremental potential to significantly increase ultimate hydrocarbon recovery by generating an

affirmative picture for development plans with the virtue of many alternatives being evaluated. We reviewed published work

in the area of wells optimization and highlighted the major trends achieved and the challenges associated with the utilized

approaches. Small scale well optimizations could be misleading especially when the results are used to represent large scale

well optimizations. These simulations are computationally challenging and therefore, employing supercomputing

environments to study the scalability and efficiency of these algorithms for large scale well optimization studies will be

necessary.

In a nutshell, some of the points which are found to be the core of the optimization decision making process are:

1. Choice of appropriate design variables

2. Inclusion of uncertainty of important variables

3. Objective function

4. Design constraints based on various operational or geometric limitations

5. Type of optimization algorithm

6. Use of proxy (metamodels)

Figure 3: Flowchart for Well Optimization

1. Reservoir Properties

2. Economic parameters

3. Probability distribution of

Uncertain Variables

Optimum Design

with distribution

Reservoir Model Input

Reservoir / Proxy

Model

Objective Function

O

p

timization Module

1. Design Variables

2. Design / Bound Constraints

Optimization Module Input

SPE 160861 11

References

AlQahtani,G.D.,Elrafie,E.A.,Abbas,R.T.,Ikuku,C.E.,Hogg,M.F.,andRincon,A.,2009,SPE120050ComplexWell

ModelingWorkflowEnablingFullFieldOptimizationandForwardDecisions:SPELatinAmerica&Caribbean

PetroleumEngineeringConference,p.1‐14.

Arsenyev‐obraztsov,S.S.,Ermolaev,A.I.,Kuvichko,A.M.,Naevdal,G.,andShafieirad,A.,2011,Improvementof

OilandGasRecoverybyOptimalWellPlacement:16thEuropeanSymposiumonImprovedOilRecovery,no.

April2011,p.12‐14.

Badru,O.,andKabir,C.S.,2003,SPE84191WellPlacementOptimizationinFieldDevelopment:SPEAnnual

TechnicalConferenceandExhibition.

Bampi,D.,andCosta,O.J.,2010,SPE139376MarlimField:AnOptimizationStudyonaMatureField:Latin

America&CaribbeanPetroleumEngineeringConference,no.December,p.1‐3.

Bangerth,W.,Klie,H.,Matossian,V.,Parashar,M.,andWheeler,M.F.,2005,AnAutonomicReservoirFramework

fortheStochasticOptimizationofWellPlacement:ClusterComputing,v.8,no.4,p.255‐269,doi:

10.1007/s10586‐005‐4093‐3.

Bangerth,W.,Klie,H.,Wheeler,M.F.,Stoffa,P.L.,andSen,M.K.,2006,Onoptimizationalgorithmsforthe

reservoiroilwellplacementproblem:ComputationalGeosciences,v.10,no.3,p.303‐319,doi:

10.1007/s10596‐006‐9025‐7.

Beckner,B.L.,andSong,X.,1995,FieldDevelopmentPlanningUsingSimulatedAnnealing‐OptimalEconomic

WellSchedulingandPlacement:SPEAnnualTechnicalConferenceandExhibition,.

Bittencourt,A.C.,andHorne,R.N.,1997,ReservoirDevelopmentandDesignOptimization:SPEAnnualTechnical

ConferenceandExhibition,.

Bouzarkouna,Z.,Ding,D.Y.,andAuger,A.,2011,SPE143292PartiallySeparatedMeta‐modelswithEvolution

StrategiesforWellPlacementOptimization:SPEEAGEAnnualTechnicalConferenceandExhibition,.

Bouzarkouna,Z.,Yu,D.,andAnne,D.,2011,WellPlacementOptimizationwiththeCovarianceMatrixAdaptation

EvolutionStrategyandMeta‐Models:ComputationalGeosciences,,p.1‐17.

Bukhamsin,A.Y.,Farshi,M.M.,andAziz,K.,2010,SPE136944OptimizationofMultilateralWellDesignand

LocationinaRealFieldUsingaContinuousGeneticAlgorithm:SPEAnnualTechnicalConferenceand

Exhibition,.

Burak,Y.,Durlofsky,L.,andKhalid,A.,2002,OptimizationofNonconventionalWellType,LocationandTrajectory:

SPEAnnualTechnicalConferenceandExhibition,,doi:10.2523/77565‐MS.

Clausen,J.,1999,BranchandBoundAlgorithms‐PrinciplesandExamples.:Computer,,p.1‐30.

Chvatal,Vasek.,1983,LinearProgramming.,Freeman&Co.

Cruz,P.S.,Horne,R.N.,Stanford,U.,Deutsch,C.V.,andAlberta,U.,2004,TheQualityMap:AToolforReservoir

UncertaintyQuantificationandDecisionMaking:SPEAnnualTechnicalConferenceandExhibition,,no.

December2003,p.3‐6.

Cruz,P.S.,Horne,R.N.,andDeutsch,C.V.,1999,SPE56578TheQualityMap:AToolforReservoirUncertainty

QuantificationandDecisionMaking:SPEAnnualTechnicalConferenceandExhibition,.

Cullick,A.S.,Narayanan,K.,andGorell,S.,2005,SPE96986OptimalFieldDevelopmentPlanningofWellLocations

WithReservoirUncertainty:SPEJournal,,p.1‐12.

Ding,D.Y.,2008,SPE113525OptimizationofWellPlacementUsingEvolutionaryAlgorithms:SPEEAGEAnnual

TechnicalConferenceandExhibition,,no.June,p.9‐12.

Eide,A.L.,Holden,L.,andAasen,J.D.,1995,SPE30710OptimizingReservoirPerformanceUnderUncertaintywith

ApplicationtoWellLocation:SPEAnnualTechnicalConferenceandExhibition,,p.67‐76.

12 SPE 160861

Elrafie,E.,AlQahtani,G.D.,Agil,M.,Rincon,A.,andColomar,F.M.,2008,SPE117630FieldDevelopmentPlans

OptimizationbyModelingFluidsFlowImpactandAssessingIntelligentWellsonReservoirPerformance:SPE

InternationalPetroleumExhibitionandConference,.

Emerick,A.A.,Silva,E.,Messer,B.,Almeida,L.F.,Szwarcman,D.,Pacheco,M.A.C.,andVellasco,M.M.B.R.,2009,

SPE118808WellPlacementOptimizationUsingaGeneticAlgorithmwithNonlinearConstraints:SPE

ReservoirSimulationSymposium,,p.1‐20.

Ermolaev,A.I.,Larionov,A.S.,andNifantov,A.V.,2006,EfficientWellSpacingAlgorithms:10thEuropean

ConferenceonMathematicsofOilRecovery,,no.September.

Farmer,C.L.,Fowkes,J.M.,andGould,N.I.M.,2010,OptimalMultilateralWellPlacement:OxfordUniversity

MathematicalInstitute,,no.10,p.1‐13.

Gen,M.,andCheng,R.(2000).GeneticAlgorithmsandEngineeringOptimization.Engineering,JohnWiley&Sons,

Inc.

Guyaguler,B.,andHorne,R.N.,2001,SPE71625UncertaintyAssessmentofWellPlacementOptimization:SPE

AnnualTechnicalConferenceandExhibition,.

Guyaguler,B.,Horne,R.N.,Rogers,L.L.,andRosenzweig,J.J.,2000,SPE63221OptimizationofWellPlacementin

aGulfofMexicoWaterfloodingProject:SPEAnnualTechnicalConferenceandExhibition,v.63,p.1‐10.

Hansen,N.,Auger,A.,Ros,R.,Finck,S.,andPošík,P.,2009,ComparingResultsof31AlgorithmsfromtheBlack‐

BoxOptimizationBenchmarkingBBOB‐2009:Idea,.

Hassani,H.,Sarkheil,H.,Foroud,T.,andKarimpooli,S.,2011,Aproxymodelingapproachtooptimization

horizontalwellplacement:RockMechanicsSymposium,,no.1999.

Holland,J.,1975,AdaptationinNaturalandArtificialSystems:AnIntroductoryAnalysiswithapplicationsto

Biology,ControlandArticialIntelligence.TheMITPress,London,U.K.

Ierapetritou,M.G.,Floudas,C.A.,Vasantharajan,S.,andCullick,A.S.,1999,OptimalLocationofVerticalWells:

DecompositionApproach:v.45,no.4.

John,U.M.,andOnyekonwu,M.O.,2010,SPE140674Non‐LinearProgrammingforWellSpacingOptimizationof

OilReservoirs:InternationalConferenceadnExhibition,,no.August.

Johnson,V.M.,andRogers,L.L.,1998,UsingArtificialNeuralNetworksandtheGeneticAlgorithmtoOptimize

Well‐FieldDesign:PhaseIFinalReport:Optimization,,no.March.

Larionov,A.,Nifantov,A.,Itkin,V.,andAlexandrov,V.,2006,SPE104326MethodologyofOptimalWellPattern,

LocationandPathsinProductiveFormationsDuringOilandGasFieldsDevelopmentPlanning:SPERussian

OilandGasTechnicalConferenceandExhibition,.

Lee,J.W.,Park,C.,Kang,J.M.,andJeong,C.K.,2009,SPE125539HorizontalWellDesignIncorporatedwith

InterwellInterference,DrillingLocation,andTrajectoryfortheRecoveryOptimization:SPEEAGEReservoir

CharacterizationandSImulationConference,,no.1997.

Litvak,M.,Onwunalu,J.,andBaxter,J.,2011,SPE146512FieldDevelopmentOptimizationwithSubsurface

Uncertainties:SPEAnnualTechnicalConferenceandExhibition,,no.November.

Maschio,C.,Nakajima,L.,andSchiozer,D.J.,2008,SPE113483ProductionStrategyOptimizationUsingGenetic

AlgorithmandQualityMap:SPEEAGEAnnualTechnicalConferenceandExhibition,,no.June,p.9‐12.

Montes,G.,Repsol,F.,Bartolome,P.,andUdias,A.L.,2001,SPE69439TheUseofGeneticAlgorithmsinWell

PlacementOptimization:SPELatinAmerica&CaribbeanPetroleumEngineeringConference,,p.1‐10.

SPE 160861 13

Morales,A.N.,Nasrabadi,H.,andZhu,D.,2011,SPE143617ANewModifiedGeneticAlgorithmforWell

PlacementOptimizationunderGeologicalUncertainties:SPEEAGEAnnualTechnicalConferenceand

Exhibition,.

Norrena,K.P.,andDeutsch,C.V.,2002,SPE78996AutomaticDeterminationofWellPlacementSubjectto

GeostatisticalandEconomicConstraints:SPEInternationalThermalOperationsandHeavyOilSymposium,.

Onwunalu,J.E.,andDurlofsky,L.J.,2011,ANewWell‐Pattern‐OptimizationProcedureforLarge‐ScaleField

Development:SPEJournal,,no124364.September.2011.

Onwunalu,J.,Litvak,M.,Durlofsky,L.J.,andAziz,K.,2008,SPE117323ApplicationofStatisticalProxiestoSpeed

UpFieldDevelopmentOptimizationProcedures:InternationalConferenceadnExhibition,.

Ozdogan,U.,andHorne,R.N.,2006,OptimizationofWellPlacementUnderTime‐DependentUncertainty:SPE

Journal,v.3,no.April,p.26‐29.

Pan,Y.,andHorne,R.N.,1998,SPE49055ImprovedMethodsforMultivariateOptimizationofFieldDevelopment

SchedulingandWellPlacementDesign:SPEAnnualTechnicalConferenceandExhibition,.

Rosenwald,G.W.,andGreen,D.W.,1974,SPE3981AMethodforDeterminingtheOptimumLocationofWellsin

aReservoirUsingMixed‐IntegerProgramming:SPEJournal,v.255.

Santellani,G.,Hansen,B.,andHerring,T.,1998,“SurvivaloftheFittest”anOptimizedWellLocationAlgorithmfor

ReservoirSimulation:SPEAssetmanagmentConference,.

Tarhan,B.,Grossmann,I.E.,andGoel,V.,2009,AMultistageStochasticProgrammingApproachforthePlanning

ofOffshoreOilorGasFieldInfrastructureUnderDecisionDependentUncertainty:,p.1‐61.

Tilke,P.G.,Banerjee,R.,Halabe,V.B.,Balci,B.,Thambynayagam,M.,andSpath,J.,2010,SPE135168Automated

FieldDevelopmentPlanninginthePresenceofSubsurfaceUncertaintyandOperationalRiskTolerance:SPE

AnnualTechnicalConferenceandExhibition,,p.1‐8.

Túpac,Y.J.,Faletti,L.,Pacheco,M.A.C.,andVellasco,M.M.B.R.,2007,SPE107552EvolutionaryOptimizationof

OilfieldDevelopment:SPEDigitalEnergyConferenceadnExhibition,.

Túpac,Y.J.,Lazo,J.G.,Faletti,L.,Pacheco,M.A.,andVellasco,M.M.B.R.,2008,SPE112258DecisionSupport

SystemforEconomicAnalysisofE&PProjectsUnderUncertainties:IntelligentEnergyConferenceand

Exhibition,.

VadapalliR.,LuoP.,KimT.,KumarA.,andSiddiquiS.,2008,DemonstrationofGrid‐enabledEnsembleKalman

FiltersDataAssimilationMethodologyforReservoirCharacterization,Proc.of15thACMMardiGras:

WorkshoponGrid‐enablingApplications,Feb29‐Mar1(2008).

VadapalliR.,SillA.,SiddiquiS.,SolimanM.,andDeimbacherF.,2011,UncertaintybasedOptimizationof

SubsurfaceReservoirs,SIAMConferenceonMathematical&ComputationalIssuesintheGeosciences,Mar

21‐24,LongBeach,CA.

Wang,H.,Ciaurri,D.E.,Durlofsky,L.J.,andCominelli,A.,2011,SPE141950OptimalWellPlacementunder

UncertaintyusingaRetrospectiveOptimizationFramework:SPEReservoirSimulationSymposium,.

Wang,H.,Ciaurri,D.E.,andDurlofsky,L.J.,2010,Useofretrospectiveoptimizationforplacementofoilwells

underuncertainty:WinterSimulationConference,,p.1750‐1757.

Weise,T.(2009).GlobalOptimizationAlgorithms:TheoryandApplication.it‐weise.de(self‐published),Germany.

Özdoğan,U.,andHorne,R.N.,2004,SPE90091OptimizationofWellPlacementwithaHistoryMatching

Approach:SPEJournal,.