SPE 146512

Field Development Optimization with Subsurface Uncertainties Michael Litvak, SPE, Jerome Onwunalu, SPE, and Josh Baxter, SPE, BP

Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 30 October–2 November 2011. 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 does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. 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 SPE copyright.

Abstract

This paper outlines a framework for simultaneous optimization of a broad range of field development decisions with subsurface uncertainties.

We optimize discrete and continuous decision variables such as the number of production or injection wells, their locations, perforation intervals, drilling schedules, well rates, etc. As a novel approach, we include additional categorical variables such as depletion strategy, well pattern, or facility size in the optimization process. We consider a limited number of discrete scenarios for each categorical variable (e.g., primary depletion, gas injection, or water injection as three development scenarios).

Field development constraints on well locations, rig schedules, economic risks etc. are incorporated in the optimization. Hydrocarbon recovery or some economic indicator can be used as the objective function for the optimization and applied for ranking the field development options.

Subsurface uncertainties are represented by incorporating multiple reservoir models in the optimization process. Ideally, all reservoir models in the ensemble should be evaluated for every considered field development option to define cumulative probability functions. However, this would make CPU demands very large in some cases. We propose two effective approaches to reduce CPU requirements: (1) one reservoir model is run to test the optimization criterion, and the remaining models are only run if the objective function is significantly improved; or (2) a novel application of a statistical proxy procedure to define a subset of the reservoir model ensemble that is run during the optimization cycle. The efficiencies gained with these techniques allow us to incorporate the additional decision variables in the full optimization process.

Our results indicate that the proposed algorithms sufficiently reduce CPU requirements to effectively handle field development optimization problems with many reservoir models representing subsurface uncertainties. The algorithms have been effectively applied in many fields for simultaneous optimization of well placement, drilling schedule, well production/injection rates, perforation strategy, injection strategy, and facility modifications. They have also been successfully applied in giant oil/gas fields optimizing general field development scenarios.

1. Introduction

Very expensive decisions need to be made in oil/gas field development. These decisions involve a broad range of issues, for example: schedule for reservoir zone development; water/gas injection strategy; number of producers/injectors; well locations, trajectories, perforated intervals, and production/injection rates; artificial lift strategy; facility size, etc. Field experiments evaluating different development options are expensive and, very often, difficult to implement. For this reason, reservoir modeling is widely applied for option evaluation, but only a limited number of available options are “manually” evaluated in most reservoir simulation studies. Frequently, only one reservoir description is applied and impacts of subsurface uncertainties on field development planning are not estimated.

In this paper, we present a general field development optimization technology based on reservoir modeling. The technology provides capabilities for the evaluation of thousands of field development options with multiple reservoir descriptions. It is an extension of BP’s Top Down Reservoir Modeling (TDRM™) technology (Williams et al., 2004). TDRM™ capabilities and workflows for uncertainty estimations and history matching have been extended to the field development optimization. The extension is called TDRM™ Option Evaluation (OE) toolkit (Litvak and Angert, 2009; Litvak et al., 2007a; Litvak, 2006).

TDRM™OE incorporates unique capabilities for optimizing a large range of field development decisions. Specifically, tools are provided for evaluating and optimizing: � Schedule for development of reservoir zones;

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� Number of production and injection wells; � Well completion intervals; � Well locations; � Well trajectories; � Well drilling schedule; � Well types representing design of well tubing strings, artificial lift method, well connections to surface pipeline

network, etc; � Well controls and facility targets; � General field development scenarios, including facility sizing and phasing, depletion strategy, surface pipeline network

structures, etc. There are significant uncertainties in reservoir descriptions even in mature oil/gas fields with extensive well production

and surveillance data. For this reason, computationally efficient and robust procedures for subsurface uncertainty treatment are implemented in TDRM™ OE and presented in the paper.

Significant business value has been demonstrated in many full field applications of the TDRM™ OE technology. Previously published TDRM™ OE applications in oil fields in North Sea, Gulf of Mexico, Russia, and Azerbaijan (Angert et al., 2011; Volz et al., 2008; Litvak et al., 2007b) have illustrated the following: � Field development scenarios have been identified (from evaluations of thousands of options) with significant benefits

in oil recovery and economic indicators as compared to “manually” derived reference cases. � Impacts of subsurface uncertainties on field development decisions have been estimated. � Powerful TDRM™ OE capabilities have been demonstrated.

2. Problem Formulation

The main objectives of TDRM™OE are: a. Select field development decisions that maximize an objective function, honor field development constraints, achieve

high recovery and economic indicators, and ensure acceptable ranges for risks; b. Evaluate many field development options and estimate ranges of uncertainties in predictions for the evaluated

options. Requirements for multiple reservoir simulation models representing subsurface uncertainties are outlined in Section 2.1.

Decision variables and field development constraints are described in Section 2.2. Economic modeling, risk constrains, and objective functions are considered in Section 2.3.

2.1. Multiple Reservoir Models

Multiple calibrated reservoir models representing subsurface uncertainties and their probabilities are the primary input of the TDRM™OE procedure, although it is typical for a single “manual” history match to exist, often referred to as a reference model. If production data are available, an ensemble of history matched models should be generated before a field development evaluation study is initiated. TDRM™ uncertainty estimation and model calibration tools (Williams et al., 2004) are normally applied in this step. In addition, probabilities should be assigned to the selected reservoir models. Bayesian ensemble appraising procedures (Sambridge, 1999a; Sambridge, 1999b; Christie et al., 2002; Litvak et al., 2005) can be applied for the definition of model probabilities if field production data are available for model calibration.

For new fields without any production history, an ensemble of reservoir models should be generated to represent the breadth of subsurface uncertainty before undertaking a filed development study. Here, we use a synthetic three-dimensional example of an oil field to illustrate capabilities of the TDRM™OE toolkit.

2.1.1. Synthetic Example A synthetic oil field with a large aquifer was generated on a 50x32x20 grid (see Figures 1 and 2). Five facies are

represented in the model and are populated using geostatistical simulation. Uncertainties in reservoir description are represented by random porosity, net-to-gross ratio, and permeability multipliers for each facies with triangular probability distributions. Sixteen hundred reservoir models were generated using a Monte Carlo approach for this example.

Two vertical faults are incorporated in the model, separating the reservoir into West, North, and South fault blocks as illustrated in Figure 2. Binary uncertainties in connectivity across these two faults (“sealing” vs. “open”) is considered resulting in four combinations of fault descriptions.

A “manual” or reference field development case with three production wells (see Figure 2) was used to generate 400 simulations for each combination of fault connectivities (1,600 simulations total). For each of the four faulting scenarios, cumulative probability distributions of predicted oil recovery for the reference field development case was built from the 400 simulation runs, then three specific reservoir models corresponding to P10, P50, and P90 recovery percentiles were selected for each fault connectivity combination. This provided us with an ensemble of 12 reservoir models that were used to represent subsurface uncertainties in TDRM™OE applications.

Probabilities were assigned to these 12 synthetic models by assuming that analogue field data plus early exploration and appraisal data had indicated that there was a 90% probability that each fault was sealing. Individual probabilities for the three reservoir models with two sealing faults, six reservoir models with one open fault and one sealing fault, and three reservoir models with two open faults were therefore set to 27%, 3%, and 0.33%, respectively.

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2.2. Decision Variables and Constraints

TDRM™OE can be used to evaluate and optimize a broad variety of field development decisions, although it is typical to have a “manual” or reference scenario in place in undertaking such a study (which is used as an “initial guess”). TDRM™OE

treats field development decisions as decision variables and selects values of these decision variables that honor field development constraints. The TDRM™OE decision variables and constraints are described in this section.

2.2.1. Reservoir Zones

Oil/gas reservoirs with multiple areal zones (compartments) are considered. The TDRM™OE toolkit is designed to evaluate and optimize the order of reservoir zone development.

In our synthetic example, three areal zones (North, South, and West) separated by two faults are simulated (see Figure 2). 2.2.2. Number of Production and Injection Wells

An important objective of TDRM™OE is to optimize the number of producers and injectors that should be drilled in each reservoir zone, as oil/gas recovery and economic indicators are very sensitive to the number of wells and the producer/injector ratio. The total well count, number of injectors, and producer/injector ratio are constrained by specified maximum limits. For example, the maximum well count can be limited by the number of available slots in a production platform.

In our synthetic example, up to six production wells are considered for drilling. 2.2.3. Well Completion Intervals

Oil/gas reservoirs with multiple vertical intervals (sands) are considered. The TDRM™OE toolkit is designed to optimize the selection of initial completion intervals and the subsequent re-completion intervals of wells.

Multiple constraints on the logic of initial completions and re-completions of wells can be incorporated. For example, different combinations of stacked sands might be forced to be completed simultaneously (e.g., vertical Interval 3 can only be completed if Intervals 1 and 2 are also completed); wells can be recompleted only in sequence from the bottom sand to the top sand, etc.

In our synthetic example, two vertical intervals are represented (see Figure 1). The lower interval has significantly higher permeability/porosity but lower initial oil in place volume than the upper interval. The TDRM™OE toolkit could be applied in this case to answer the following question: Should we perforate the lower interval first and recomplete the wells in the upper interval later? Or should we commingle production (and/or injection) from the two intervals?

2.2.4. Well Locations

Potential locations of new or sidetrack wells are selected from discrete sets of points in user specified polygons. Separate sets of potential well locations are defined for producers, water injectors and gas injectors. TDRM™OE selects a producer or an injector for drilling in any point at an intersection of these sets. Any potential well location is defined by X, Y, and Z coordinates corresponding to the well’s top perforation. Well trajectories of potential wells (see next section) are initiated from these potential locations.

Constraints on minimum distances between well pairs, between wells and faults, between wells and aquifer, and between wells and gas-cap are considered. Constraints on maximum distances between sidetrack wells and their parent wellbores, and between new wells and drill sites (platform location) are incorporated. All perforations in a potential well are assumed to be closed if these constraints are violated in some reservoir model.

For our synthetic example, potential well locations generated by TDRM™OE from user specified polygons are shown in Figure 3. X and Y coordinates for top perforations of potential production and injection wells are shown by red and blue symbols, respectively. Sizes of the symbols correspond to Z coordinates of the top perforations. Although not illustrated in Figure 3, some well locations can be common sites where either producers or injectors can be drilled or recompleted.

2.2.5. Well Trajectories Several potential well trajectories can be evaluated. A limited set of potential well trajectories are assigned to each

potential well location, and TDRM™OE selects a well location and a well trajectory from the set assigned to this location. Well perforation input for a reservoir simulator is then automatically generated based on intersections of the selected well trajectories with grid cells.

A series of practical constraints can be applied. For example, a well might only be perforated in grid cells where the product of permeability and net thickness (KH) is above a specified limit, pore volume (PV) is above a certain limit, water cut (WCUT) is below a specified limit, and/or gas-oil ratio (GOR) is below a certain limit. Total well length can be constrained to stay below a maximum limit. Production wells might be considered only if initial oil and gas in place in their drainage radius exceeds certain limits. These constraints are validated for each reservoir model.

In our synthetic example, three potential well trajectories with deviation angles of 00 (vertical), 300, and 600 from vertical

are evaluated. Wells are perforated in grid cells with PV > 1,000 stb and WCUT < 10%. 2.2.6. Well Drilling Schedule

Another important objective of TDRM™OE is the definition of a drilling queue for optimizing scheduling of new wells. The drilling schedule is constrained by the number of available rigs and the well drilling/completion times. TDRM™OE evaluates different orders of wells within the drilling queue. A reservoir simulator represents a) starting production/injection in new wells, and b) shutting down parent wellbores of sidetracks at proper times in accordance with the drilling queue, the available rigs, and the well drilling/completion times.

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In our synthetic example, we assume that one rig is available. Drilling and completion times for new wells with deviation angles of 00, 300, and 600 are set to 90, 100, and 110 days, correspondingly. Different drilling orders of up to 6 production wells are evaluated.

2.2.7. Well Types

TDRM™OE provides capabilities for the selection of well types, which involves evaluating different options for well tubing string design, artificial lift method (e.g. gas-lift versus electrical submersible pumps), well connections to surface pipeline network, etc.

Each well type is represented by a prototype well, with user provided reservoir simulator input for each prototype well. A set of well types are assigned to each potential well location, TDRM™OE selects a well location and a well type from the set assigned to this location. The reservoir simulator input from the corresponding prototype well is automatically applied.

In our example, two well types (gas-lift or natural lift) are evaluated for any potential production well. 2.2.8. Well Controls and Facility Capacities

Parameters controlling well production and restricting facility capacities in the reservoir simulation can be considered as decision variables in the TDRM™OE procedure. For example, variations in maximum well production/injection rates, minimum/maximum tubing head pressure, maximum water cut, maximum gas-oil ratio, facility targets, etc. can be evaluated. Ranges (upper and lower limits) of these decision variables should be specified.

In our example, variations of maximum water cut in production wells in the range from 70% to 95% are evaluated. Wells are shut in if they exceed the maximum water cut.

2.2.9. General Field Development Scenarios As a novel approach, a small number of general field development scenarios can be evaluated in the TDRM™OE

procedure. For example, several facility options (facility sizing and phasing) can be considered. Different injection strategies (primary depletion, water flooding, gas injection, alternative injection patterns, etc) can be evaluated. Surface pipeline network options can be estimated. Capability for the evaluation of general field development scenarios opens the way for the TDRM™OE applications in giant oil fields where optimization at the individual well level may be very CPU time consuming.

To evaluate field development scenarios, categorical decision variables representing field development scenarios are applied and different sets of “include” files (with appropriate simulation keywords) are automatically incorporated in the reservoir simulator input for different field development scenarios.

In our synthetic example, we consider three facility options with different phasing. In the small facility option, initial oil handling capacity of 27,000 stb/d is assumed, with the facility capacity then increased to 41,000 stb/d and 55,000 stb/d after two years and four years, respectively. In the medium facility option, initial oil handling capacity of 41,000 stb/d is assumed with capacity increasing to 55,000 stb/d and 68,000 stb/d in two years and four years, respectively. In the large facility option, initial oil handling capacity of 55,000 stb/d is assumed with the capacity increasing to 68,000 stb/d and 82,000 stb/d in two years and four years, respectively.

2.3. Economic Modeling, Risk Constraints, and Objective Function

2.3.1. Economic Modeling

The TDRM™OE technology can address short-term and long-term field development optimization problems. The short-term problems include optimizations of well rates, gas-lift, well connections to surface pipeline network, etc (Litvak et al., 2002; Wang and Litvak, 2004). The long-term problems incorporate optimization of well locations, zonal completions, well drilling schedule, well types, and field development scenarios.

Economic modeling for short-term field development optimization is not usually required, but it is very important for long-term field development optimization problems for: � Improving project economic indicators along with oil/gas recovery; � Evaluating economic risks of field development decisions; � Representing that oil produced today is more valuable than oil produced in the future.

For these reasons, economic modeling has been implemented as an option in the TDRM™OE toolkit. An economic module is executed for any evaluated field development option and any reservoir model representing subsurface uncertainties. Calculations are based on yearly reports of drilled wells and oil/gas/water production volumes that are automatically extracted from reservoir simulation results. Major economic indicators (e.g. Net Present Value, Internal Rate of Return, Discounted Payback, and Capital Efficiency) are determined from definitions of turnover, operating (OPEX) and capital (CAPEX) expenses, royalty and tax deductions, net cash flow, discounted cash flow, etc.

A number of economic parameters were assumed for our synthetic example to enable a calculation of Net Present Value (NPV). Variable drilling and completion costs for candidate wells depending on their deviation angles were applied.

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2.3.2. Recovery and Risk Constraints

Constraints on minimum hydrocarbon recoveries (oil, gas, or both) from production wells, from reservoir regions, and from the entire field are incorporated. The recovery constraints for a given development scenario must be honored in all reservoir models in the ensemble, and penalties are applied if the recovery constraints are violated in some of the models.

Reservoir simulation predictions from a single reservoir model can be questionable because there are significant uncertainties in reservoir descriptions and simulation parameters. For this reason, there is a risk that field development recommendations based on single model are not valid. The following features can implemented to reduce this risk: � Multiple reservoir models representing subsurface uncertainties can be evaluated during the optimization (Section 2.1). � Risks in predictions of oil/gas recoveries and economic indicators can be constrained. The following procedure is

applied for the validation of the risk constraints for any evaluated field development option: o All reservoir models within the uncertainty ensemble are run; o Cumulative probability distribution functions (CDF) of field oil/gas recovery and economic indicators are

calculated. CDFs are determined from the predicted recoveries and economic indicators in individual reservoir model runs and the probabilities assigned to the models;

o P10, P50, and P90 percentiles of the recovery and economic indicators are determined; o The evaluated field development option is not accepted if relative risk factor (P50 – P90)/P50 for the

recovery or some economic indicator exceeds a user specified limit. � A constraint can be set specifying that predicted oil/gas recovery and economic indicators for all reservoir models in the

ensemble must exceed the corresponding values in the manual or reference case. Any evaluated field development option is not accepted if this constraint is violated. This constraint guarantees that benefits from recommended decisions are predicted by all models.

In our example, minimum oil recovery per well of 3,500 Mstb is assumed and it is requested that predicted field oil recovery and NPV for all 12 candidate models exceed the corresponding values for the reference development case.

2.3.3. Objective Function An objective function for ranking field development options is required only if an optimization workflow (see Section 3

below) is applied. A field development option maximizing the objective function but still honoring constraints should be selected in this case.

Some percentile of an economic indicator or a percentile of hydrocarbon recovery (oil, gas, or oil equivalent) is typically applied as the objective function. A field development option which is the best “on average” (keeping in mind subsurface uncertainties) is selected if the P50 percentile is applied. A field development option which is the best “worse case scenario” is determined if the P90 percentile is used.

In practice, the economic indicator (or recovery) predicted by a specific reservoir model that is closest to the target percentile (e.g., P50) is actually optimized because we are required to provide “base” reservoir model predictions which are used to justify recommended decisions.

In our example, cumulative probability distribution functions of NPV from the 12-model ensemble are calculated for each development scenario considered, and the NPV predicted by the reservoir model closest to P50 is used as the objective function. 3. Workflows

The primary reasons for the successful applications of our field development optimization technology in giant oil fields (Angert et al., 2011; Volz et al., 2008; Litvak et al., 2007b) are the innovative formulation of the problem -- using manageable numbers of decision variables and constraints -- as well as effective workflows implemented for the problem solution. These workflows provide frameworks for the solution of the field development optimization problem and for the evaluation of many field development options with multiple reservoir models representing subsurface uncertainties.

TDRM™OE workflows can be summarized as follows: Initial Set up of Field Development Options: Potential well locations are built from the user specified polygons

(Section 2.2.4). Well perforation input is generated for each potential well location and well trajectory (Section 2.2.5). Constraints on distances from potential wells to existing wells, faults, gas cap, and aquifer (Section 2.2.4) are checked and validated. Well perforation constraints (Sections 2.2.5) are checked.

Search Procedure: In most cases, there are billions of potential field development options. For this reason, a “smart” iterative search of the decision space is implemented for evaluations of “only” a few thousand options. Powerful TDRM™

workflows, e.g. Random Search, Parametric Search, Factorial Search of Full Decision Space, Optimization (Williams et al., 2004), are applied. Discrete decision variables (number of wells, well locations, trajectories, perforation intervals, types, drilling schedule, etc), continuous decision variables (well controls and facility limits), and categorical variables (field development scenarios) are considered in TDRM™OE. A single field development option (from among the billions of potential options) is evaluated in any search iteration as follows:

� Selection of a Field Development Option: Number of wells, well locations, trajectories, perforation intervals, well types, drilling schedule, well controls, facility limits, and field development scenario are selected from corresponding potential sets (Section 2.2). Constraints on distances between new wells are validated (Section 2.2.4).

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� Identification of Reservoir Models for Execution: Normally, all reservoir models from the uncertainty ensemble are executed for each field development option selected. However, two optional procedures described in the next section are implemented to run only a subset of the reservoir models from the ensemble.

� Building Input and Running Reservoir Simulations: Simulator input decks representing the selected field development option are automatically built. Reservoir simulations are executed for the identified reservoir models.

� Validation of Recovery Constraints: Constraints on hydrocarbon recoveries are validated using reservoir simulation results (Section 2.3.2).

� Economic Modeling: Economic indicators are calculated for each reservoir model based on corresponding simulation results (Section 2.3.1).

� Processing of Uncertainties in Prediction Results: CDF and percentiles (P90, P50, P10, etc.) of recoveries and economic indicators are determined (Section 2.3.2).

� Validation of Risk Constraints: Constraints on relative risk factor, incremental recoveries, and incremental economic indicators predicted by the reservoir models are validated (Section 2.3.2).

� Determination of Objective Function: In the optimization workflow, the objective function is determined (Section 2.3.3).

� Workflow Termination: Another field development option is chosen and the process is repeated if the number of iterations is less than a specified maximum limit.

In our synthetic example, the optimization workflow with a Genetic Algorithm (GA) has been applied to determine the

number of production wells, their locations, well trajectories, and well drilling schedule maximizing P50 NPV and honoring all constraints (Section 2.2). The GA was run for 40 generations, with a population of 50 different field development scenarios being evaluated in each generation (2000 field development options). Subsurface uncertainties have been represented by an ensemble of 12 reservoir models (Section 2.1), with all 12 models being run for each of the 2,000 field development options (24,000 simulations in total).

Well locations in the reference (manual) and optimized field development cases are presented in Figure 2. Well names in the Figure reflect suggested well deviation angle (third and fourth symbols, e.g. 00, 30, 60 degrees), reservoir zone (fifth symbol: S-South, N-North, W-West), and drilling order (6th-8th symbols from 001 to 006). The cross plot of P50 NPV versus P50 field oil recovery for the 2000 development options is presented in Figure 4. Numbers of production wells in the evaluated options are represented by colors. Significant increases in oil recovery and NPV in cases with 6 wells in comparison with cases with 3-5 wells are predicted. CDFs of NPV presented in Figure 5 demonstrate that significant increases in NPV are predicted in the optimized field development scenario in comparison with the reference (manual) case for all 12 reservoir models in the ensemble, indicating that the optimal case is robust across the reservoir uncertainty space. Note that the actual objective function for the reference and optimized cases are represented by the discrete points (corresponding to individual reservoir models) on the CDF curves that are closest to the P50 value. Field oil recovery profiles predicted by 12 reservoir models in the reference and optimized cases are demonstrated in Figure 6. Recovery predictions from the reservoir models closest to P50 NPV are represented by darker colors.

4. Uncertainty Treatment Normally, all reservoir models in the ensemble are executed for every evaluated field development option as discussed

above. However, a large number of CPUs may be required if the number of reservoir models representing subsurface uncertainty space is large. In our synthetic example, 50 * 12 = 600 simulation runs were required for each generation of the GA. Depending on the number of available CPUs, progress in performing the field development optimization may be very slow since the GA requires all runs from a single generation to be completed before it can proceed to the next generation.

Two approaches summarized below can be implemented to reduce the CPU requirements with large numbers of reservoir models: Objective Function Estimation and Statistical Proxy.

4.1. Objective Function Estimation

Here, the user-defined reference development case (used as the initial guess) is first evaluated with all candidate reservoir models from the ensemble (representing the subsurface uncertainty). CDFs and percentiles of the recoveries and economic indicators are built and the reservoir model corresponding to the objective function (e.g., P50 NPV) is identified (Section 2.3.3). This specific reservoir model is considered to be the “target” model and the value of the objective function for this model is taken to be the “target” objective function value.

For any subsequent iteration in the optimization workflow, each of which evaluates an alternative field development scenario, the “target” reservoir model is run first. The objective function is estimated from this single simulation and initially assumed to be representative of the P50 for that development scenario. If the value of the estimated objective function is greater than existing “target” value, or is greater than a user-specified threshold, then the following actions occur: � All other reservoir models from the ensemble are also run. CDFs and percentiles are determined and the true objective

function is calculated for the development scenario. � If the true objective function is larger than the “target” value, it becomes the updated “target” value and the specific

reservoir model corresponding to the objective function becomes the updated “target” model.

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Otherwise, if the value of the objective function associated with the “target” reservoir model is below the specified threshold and below the existing “target” objective function value, it is assumed that the field development scenario being evaluated does not hold promise. The remaining candidate simulation models are not run, resulting in CPU savings and the iterative optimization procedure continues by choosing another field development scenario to evaluate.

In our synthetic example we applied the TDRM™OE procedure twice: First, all 12 candidate reservoir models were run for each of the 2000 field development scenarios chosen by the GA (24,000 runs in total). Next, the objective function estimation procedure was used with an NPV threshold of $4,000 Million. The results from this second case produced similar optimized solutions as those presented in Figures 2, 4, 5 and 6. These equivalent results were achieved running all 12 reservoir models in only 1181 of the 2000 development scenarios considered. The total number of reservoir simulations in this second case was fewer than 15,000, a net reduction of 37% in CPU demand.

4.2. Statistical Proxy

Our statistical proxy procedure uses an unsupervised, clustering-based procedure to determine reservoir models that need to be run in any iteration. These decisions are based on constructed statistical correlations between attributes and objective functions (Artus et al., 2006; Onwunalu et al., 2008), where the attributes are the independent variables used in the proxy model. Decision variables and some reservoir properties (e.g. well KH, water saturation, etc) can be applied as the attributes. The dependent variable is the objective function in the optimization. In workflows with multiple reservoir models, multiple proxies are used with each proxy corresponding to a specific reservoir model. The benefits of using this approach compared to a single proxy for all reservoir models are described in Onwunalu et al. (2008).

In the optimization workflow, the proxy attributes and objective function values for each reservoir model are obtained from the outputs of the first generation of the optimizer (GA). They are used as initial input to the corresponding proxies. The attributes and objective function values constitute a proxy’s database and each database is updated as more and more data become available in later iterations of the GA. (for details see Onwunalu et al, 2008). In any iteration, the proxies are used to estimate objective function values in all reservoir models prior to the simulation step. The proxy is then used to select reservoir models that will be simulated based on a threshold of the objective function. A reservoir model is run if the objective function value estimated by the proxy is greater than the threshold. The proxy procedure is set to perform at least three simulations corresponding to the P10, P50 and P90 models (Onwunalu et al., 2008). We use the proxy to reduce the number of simulations while still preserving the main characteristics of objective function CDFs (e.g., NPV, oil/gas recovery).

The proxy procedure has been applied to several field development optimization problems including synthetic and real field applications (Onwunalu et al., 2008). In both applications, we compared the performance of the hybrid procedure (GA plus proxy) to that using only the GA. In the synthetic application, which differs from the synthetic case described earlier, 6 reservoir models were considered in the optimization and we sought to maximize P50 NPV. The optimization using only the GA required over 25,000 simulations while the hybrid procedure with proxy required about 90% fewer simulations and still achieved a solution with a similar NPV.

In the field application, the proxy was applied to maximize incremental NPV in a GOM field. In this case, the proxy procedure found a solution that was similar to using only the GA but required 45% fewer simulations. These examples demonstrate the ability of a proxy to reduce simulations while still providing robust solutions. Furthermore, the CPU requirements of the proxy procedure are minimal compared to the simulation requirements of each reservoir model, since each proxy computation requires only a few seconds. Additional improvements in computational efficiency are obtained by performing the proxy computations in parallel.

We have recently extended the proxy procedure and introduced new features to the overall workflow beyond that described in Onwunalu et al (2008). The latest additions include incorporating enhanced estimation algorithms, improving the accuracy of the estimated objective function values, and the introduction of more robust logic for selecting reservoir models for simulation. These proxy extensions and new field applications will be described in a separate paper.

5. Visualization of Simulation Results

With the sophisticated body of results output from the TDRM™OE procedure, effective visualization becomes extremely important. The primary tool used in this study was Tibco’s Spotfire™ due to its suitability for handling of large data sets and flexible visualization. Spotfire™ not only incorporates the functionality to display two dimensions of data on a two axis plot, but to augment this through dynamic coloring, shaping and sizing of data points. It also includes advanced and highly flexible filtering techniques allowing users to focus on a subset of the large volume of data with ease.

The TDRM™OE procedure includes functionality to create text files including time-variant production profiles, well positions, economic indicators, and objection function values for each field development case and simulation model. With the standard TDRM™OE outputs and the versatility of Spotfire™ it becomes relatively trivial to create the following visualizations that are essential for us to make decisions based on the TDRM™OE process.

• Hydrocarbon recovery versus economic indicator. An example of this visualization can be seen in Figure 4. This scatter plot shows how the P50 NPV of each OE case (field development scenario) varies with the P50 oil recovery. This is

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essential for identifying OE cases that best fit the ultimate objectives of the developing parties and is particularly useful where the balance of prioritising ultimate recovery with NPV is important. In this example, the colouring has been used to identify the number of production wells associated with the P50 outcome.

• CDFs of hydrocarbon recoveries and economic indicators. This visualization is demonstrated in Figure 5, which shows the spread of NPV for two OE cases across the 12 subsurface models used to evaluate each development option. Having identified potential cases of interest from the previous visualization, this plot allows us to focus in on them and study their robustness against the range of subsurface uncertainty. We want to ensure, for example, that, while a development scenario may produce a good P50 result, it does not suffer from excessive sensitivity to the less favourable subsurface descriptions. Shown in Figure 5 are the CDFs for the manual or reference development case as well as the optimized case identified in Figure 4.

• Development case well locations. This visualization is demonstrated in Figure 2, displaying well locations using the X and Y coordinates output by TDRM™OE against the background of an areal view of the reservoir. We take advantage of the sizing feature to show the cumulative production from each well in the visualization. In this way, we can inspect the development case for error checking and refinement to future optimization efforts. Spotfire™’s advanced filtering capability allows us to easily switch from case to case.

• Production or injection profiles for field, regions, and wells. This visualization is demonstrated in Figure 6. These visualizations represent a core of the process of analysis in the TDRM™OE procedure but with the analysis tools

and Spotfire™ these are certainly not exhaustive. In particular, using Spotfire™ line plots to show time variant trends of reservoir pressure decline, GOR, etc, are invaluable to understanding the benefits and drawbacks of each development case and making final recommendations.

6. Full Field Applications

Four studies addressing full-field applications of TDRM™OE have previously been published and are summarized here. Reported business benefits are outlined. Powerful TDRM™OE capabilities are demonstrated. In each case, a manually-derived reference case existed for comparative purposes prior to the initiation of the study.

Field development optimization of a complex Deepwater Gulf of Mexico field containing five stacked hydrocarbon

intervals was presented by Angert et al. (2011). Three gas condensate zones and two volatile oil zones were considered. Subsurface uncertainties were represented by three reservoir models with different interpreted structural characteristics. Locations of 9 wells, their drilling schedule, and the reservoir intervals into which wells were initially completed and then later recompleted were optimized, maximizing net present value while matching field development constraints. Roughly 20,000 field development options were evaluated. As a result, optimized sequencing of completions into the various hydrocarbon bearing zones was proposed which was materially different from that of the reference case. Incremental hydrocarbon recovery of 8% and incremental NPV of 10.5% were predicted in an optimized case as compared with the reference case. In addition, a 4-year extension of the oil plateau and 3-year extension of a drilling holiday were achieved with the optimized case. Results were robust across three candidate reservoir models representing subsurface uncertainties.

Field development optimization of a Siberian giant oil field was presented by Volz et al. (2008). Subsurface uncertainties

were represented by six history matched reservoir models. TDRM™OE capabilities for the evaluation of general field development scenarios were applied to optimize injection patterns (inverted 5-Spot; inverted 7-Spot; line-drive), well spacing, well type (vertical vs. high angle wells), and schedules for zone and pad development. Thousands of field development options were evaluated. As a result, an optimized scheme was suggested for the field development which was substantially different from the planned Technical Development Scheme. Incremental NPV ranging from $1,200 Million to $1,600 Million was predicted for the alternative development scenario, along with incremental oil recovery ranging from 3,300 Km3 to 12,900 Km3. The optimized scheme was accepted for implementation in the field.

Field development optimization of a giant offshore oil field in the Caspian Sea (Azerbaijan) was presented by Litvak et al.

(2007b). Locations of 23 new wells, their drilling schedule, water injection strategy (producer/injector ratio, timing for starting water injection, water injection rates), and locations of sidetrack wells were selected to maximize NPV and honor field development constraints. More than 8,000 field development cases were evaluated. An optimized field development scheme was suggested that demonstrated improved sweep efficiency and predicted a 37% increase in NPV and 12% increase in oil recovery compared with the reference case. Small impacts of uncertainty in oil price on ranking of field development options were also demonstrated. Some recommendations on water injection modifications have been implemented as a result of the study.

Finally, the optimization of a well sidetracking strategy in a mature oil field in the North Sea was presented by Litvak et

al. (2007b). A thin oil zone remains in the reservoir sandwiched between a large gas cap and water leg. The water leg is extensive and water has advanced as a result of continuous production. The remaining oil location is a delicate balance between the largely horizontal water advance and overlying gas cap, together with production offtake points. The

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TDRM™OE optimization procedure was applied to select two wells for sidetracking, horizontal trajectories for the sidetrack wells, perforation intervals, and drilling schedule maximizing oil recovery. Six existing wells were considered as candidates for the sidetracking and 27 potential horizontal trajectories were evaluated for each sidetrack well. Uncertainties in the remaining thin oil zone were represented by 10 history matched reservoir models. An optimized sidetracking strategy was proposed after evaluating 385 options, with the proposed strategy predicting a 53% increase in incremental oil recovery relative to the reference case. 7. Summary � The TDRM™ Option Evaluation technology with unique capabilities for optimizing a broad range of field development

decisions has been developed. � A novel approach for optimizing general field development scenarios opens the way for TDRM™OE applications in

giant oil/gas fields. � Two computationally efficient and robust procedures for subsurface uncertainty treatment in the field development

optimization have been implemented to reduce CPU requirements. � Significant business value associated with the TDRM™OE technology and its powerful capabilities have been

demonstrated in multiple full field applications. 8. Acknowledgements

We thank the management of BP for their support in granting permission to publish this paper. Specifically, we would like to thank Trevor Newley, Scott Lane, and Michael Elliott for their review of the paper and very valuable suggestions. Scott Lane spent significant time editing the paper. His suggestions tremendously improved clarity and readability of the paper. We also thank Patrick Fichtl for providing the reservoir descriptions for the synthetic model example. 9. References

1. Angert, P. F., Isebor, O. J., Litvak, M.L. 2011. “Early Life Cycle Field Development Optimization of a Complex Deepwater Gulf of Mexico Field”, paper OTC 22252 will be presented at the Offshore Technology Conference, Brazil, Rio de Janeiro, Brazil, 4–6 October 2011.

2. Artus, V., Durlofsky, L.J., Onwunalu, J.E., Aziz, K. 2006. “Optimization of nonconventional wells under uncertainty”, Comput. Geosci. 10:389-404

3. Christie, M., Subbey, S., Sambridge, M. 2002. “Prediction under Uncertainty in Reservoir Modeling”, Eight European Conference on the Mathematics in Oil Recovery - Freiberg, Germany, 3-6 September 2002.

4. Litvak, M.L. and Angert, P. F. 2009. "Field Development Optimization Applied to Giant Oil Fields", paper SPE 118840 presented at the 2009 SPE Reservoir Simulation Symposium held in the Woodlands, Texas, USA, 2-4, February 2009.

5. Litvak, M.L., Gane, B., Williams, G., Mansfield, M., Angert, P., Macdonald, C., McMurray, L., Skinner, R., and Walker, G.J. 2007a. “Field Development Optimization Technology”, paper SPE 106426 presented at the 2007 SPE Reservoir Simulation Symposium, Houston, 26-28 February 2007.

6. Litvak, M.L., Gane, B., McMurray, L. 2007b. “Field Development Optimization in a Giant Oil Field in Azerbaijan and a Mature Oil Field in the North Sea”, paper OTC 18526 presented at the 2007 Offshore Technology Conference, Houston, 30 April-3 May 2007.

7. Litvak, M.L. 2006. “Innovative Integrated Modeling Technology”, paper SPE 112811-DL, SPE Distinguished Lecture Presentation during 2006-2007

8. Litvak, M., Christie M., Johnson D., Colbert J., Sambridge M. 2005. “Uncertainty Estimation in Production Predictions Constrained by Production History and Time-Lapse Seismic in a GOM Oil Field”, paper SPE 93146 presented at the 2005 SPE Reservoir Simulation Symposium held in Houston, Texas U.S.A., 31 January 2005 – 2 February 2005.

9. Litvak, M.L., Hutchins, L.A., Skinner, R.C., Darlow, B.L, Wood, R.C., Kuest, J. 2002. “Prudhoe Bay E-Field Production Optimization System Based on Integrated Reservoir and Facility Simulation”, paper SPE 77643 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October 2002.

10. Onwunalu, J., Litvak, M., Durlofsky, L.J., Aziz, K. 2008. “Application of Statistical Proxies to Speed Up Field Development Optimization Procedures”, paper SPE 117323, presented at the 2008 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, 3–6 November 2008.

11. Sambridge, M. 1999a. “Geophysical Inversion with a Neighbourhood Algorithm-I. Searching a parameter space”, Geophysics. J. Int., 138, 479-494, 1999.

12. Sambridge, M. 1999b. “Geophysical Inversion with a Neighbourhood Algorithm -II. Appraising the ensemble”, Geophysics. J. Int., 138, 727-746, 1999.

13. Volz, R., Burn, K., Litvak, M., Thakur, S., Skvortsov, S. 2008. “Field Development Optimization of Siberian Giant Oil Field Under Uncertainties”, paper SPE 116831, presented at the 2008 SPE Russian Oil & Gas Technical Conference and Exhibition held in Moscow, Russia, 28–30 October 2008

14. Wang, P., Litvak, M. 2004. “Gas Lift Optimization for Long-Term Reservoir Simulations”, paper SPE 90506, presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26-29 September 2004.

15. Williams, G., Mansfield, M., MacDonald, D.G., Bush, M.D. 2004. “Top-Down Reservoir Modeling”, paper SPE 89974 presented at the SPE Annual Technical Conference and Exhibition, Houston, 26-29 September 2004.

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Figure 1: Initial saturations and vertical intervals in the synthetic 3-D example

Figure 2: Vertical faults, well locations in the reference and optimized cases in the synthetic 3-D example

X

Z

X

Y

Z

Saturation Volumes Vertical Intervals

Reference Case Optimized Case

North

South

West

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Figure 3: Potential locations of production and injection wells in the synthetic 3-D example

Figure 4: Oil recovery versus NPV in the reference and optimized cases of the synthetic 3-D example.

Optimized Case

Reference Case

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Figure 5: Cumulative Distribution Functions of Net Present Value for the reference and optimized cases of the synthetic 3-D example

Figure 6: Field oil recovery profiles for the reference and optimized cases of the synthetic 3-D example

P50 Reference Case Reference Case P50 Optimized Case Optimized Case