## Optimization Framework Improves Mariner Field Development

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The growing popularity of model-based optimization work flows has resulted in an increase in their application to field cases. In the complete paper, the authors present the challenges, results, and learnings from a 2-year robust multiobjective optimization application at the Mariner heavy-oil asset in the UK sector of the North Sea. The authors used the efficient stochastic simplex approximate gradient technique (StoSAG) to achieve optimization incorporating geological and petrophysical uncertainty. Depending on the problems, significant increases of between 5 and 20% in the expected value of the objective function were achieved. For the multiobjective optimization cases, nontrivial optimal strategies reduced gas production by 40% with less than 1% loss in the economic objective.

## Introduction

To date, most studies of single- and multiobjective optimization have focused on a single study with a specific purpose. Very few studies have used these work flows in an operational setting (i.e., during the field-development-planning stage at an asset tackling a variety of problems).

Including uncertainty is an important step in decision making during field-development planning, especially because uncertainty is so extensive at this stage in the life cycle of a field. Considering a range of potential development scenarios that will provide the necessary tools to enable robust decisions is imperative. These scenarios should also account for the fact that different objectives often conflict with one another. Thus, there is a need for multiobjective optimization under uncertainty, which can be applied in an operational setting.

Adapting model-based optimization work flows requires computational efficiency. While the adjoint-based gradient method is computationally very efficient, it is not suitably flexible to incorporate different types of control variables and requires access to the simulation source code as well as a significant implementation effort. Thus, in this paper, the authors use the StoSAG technique. They chose to use an approximate gradient method for the optimization instead of a derivative-free technique because the computational costs for derivative-free methods are usually higher when uncertainty, in terms of different model realizations, is considered.

StoSAG is an approximate-gradient-based approach that has proven practical for optimization under uncertainty. A user must decide on the ratio of geological model realizations to control perturbations. The authors used a ratio of 1:1 for all experiments unless otherwise specified, making the number of control perturbations equal to the number of geological realizations. This is computationally the most-efficient approach for large-scale optimization under uncertainty when using high-fidelity, full-physics-simulation models. The objective function is the usual expression for (simple) net present value as used in life-cycle-optimization studies.

## Multiobjective Optimization

For field-development planning, multiple objectives are usually defined as long-term objectives from a reservoir-engineering viewpoint, and short-term objectives from a production-engineering viewpoint. However, it is important for the methods to be independent of the type of objectives to be able to account for any type of objectives in an optimization framework.

## Controls

The authors use two main types of controls: drilling order and well-trajectory control. Each well is assigned a priority value. Wells are then drilled in order of their priority, with the highest-value wells drilled first. The drilling times for the individual wells are also accounted for, making the dates at which the wells are drilled variable. Therefore, a change in drilling order also leads to a change in the times at which wells are opened in the simulation.

A parameterization developed elsewhere in the literature is used to optimize a control vector that defines the positions of an a priori defined number of target points that define a well trajectory. The choice of the number of target points to be used within the optimization is user-dependent, and the number provides the optimization flexibility to find optimal and nontrivial well paths. A minimum of two target points (heel and toe, start and end) are, however, necessary to optimize the trajectory of a well. The first target point is defined as the spatial coordinates for the well, with three variables—*x, y, *and *z. *Every other point following the first point is defined in terms of an azimuth, angle, and measured depth with respect to the previous target point. Therefore, the second point will be defined with respect to the first, and the third will be defined with respect to the second. As an example, for a choice of four well target points for a single well, the authors will have defined 12 control variables.

The allowable changes in the target points can be variable and controlled by a user to ensure well drillability. Usually, the first target point can move during the optimization more than the other points to avoid the generation of infeasible well trajectories. Large changes to the angles are permitted near the heel of the well, but changes for subsequent points are limited. With the target points defined as described, the well trajectory is generated using root mean square, ensuring that the well path passes through all selected target points. An automated work flow was developed wherein the well path intersects the grid and the connection transmissibility factors are calculated for use in the dynamic flow simulation. Each time the optimizer adapts the well target points, new well paths are generated with the corresponding well-connection transmissibility factors.

## Mariner Heavy-Oil Field

The Mariner field, discovered in 1981, is approximately 150 km east of the Shetland Islands. The producing reservoir sections, with an estimated 2 billion barrels of oil in place, are located at depths of approximately 1200–1500 m, in approximately 100 m of water. The field was planned to begin producing in 2017–2018.

The oil is heavy, ranging from 12–15 °API, and highly viscous (67 to 500 cp), depending on the reservoir formations. Traditionally, such heavy-oil reservoirs face production problems because of increased water production from the aquifers below. This is especially true when the viscosity of the oil is very high. Additionally, produced-water reinjection for pressure maintenance is the drainage strategy being implemented in this field.

The field consists of upper and lower reservoir zones. The lower reservoir section consists of lower Paleocene, delta-fed, sand-rich turbidite channels interspersed with sand-rich turbiditic sheet-lobes and mixed sand-mud turbidites. The upper reservoir is believed to consist of channel-like disconnected sand bodies. It is estimated that the reserves of the upper reservoir are larger than those of the lower section. Both sections are relatively faulted, adding to their geological complexity. Additionally, it is uncertain at this stage whether there is any communication between the two reservoir sections.

The lower section is approximately 1400 m beneath the seabed, with marginally lighter but much-less-viscous oil properties than the upper section. Additionally, there are different gas/oil ratios between the lower and upper reservoirs.

The field is being developed using a two-stage approach, with the development of the lower reservoir planned first. More than 70 wells are planned to be drilled over a 10-year development campaign.

## Simulation Models and Numerical Experiments

The paper describes the simulation models for the lower and upper reservoirs and then discusses a series of different numerical optimization experiments linked to drilling order; multiple objectives (drilling order and gas production) for the combined field model; and well-trajectory optimization, including structural uncertainties for a sector of the upper reservoir model. **Fig. 1** shows an oil-production comparison from one model from the ensemble of model realizations.

The initial strategy called for drilling 27 single-bore producers and 12 injectors, with no multilaterals planned for the first 5-year time horizon. However, a detailed analysis of the strategy revealed that it would be better to drill four multilateral wells within the first 5 years in combination with 8 injectors and 21 single-bore producers, indicating that pressure support is an important mechanism to improve long-term reservoir management.

Designing optimal well trajectories usually is performed one well at a time and usually on a single model realization. This practice might lead to relatively optimal strategies for the single well on a single model realization. When such a strategy is tested against known sources of uncertainty through an ensemble of models, the strategy for each well may or may not be optimal. Additionally, interaction between wells is not accounted for, which is another drawback of the localized, single-well, sequential approach to well placement. This interaction between wells and the aim for the overall project objective to be achieved suggests the application of a more-global approach, wherein the trajectories of all wells being considered are optimized simultaneously, instead of the localized sequential approach.

## Conclusions

- Well-trajectory optimization under uncertainty can be used efficiently in a multiobjective optimization framework to obtain nontrivial solutions of significant practical value.
- Robust multiobjective optimization work flows can achieve results of significant practical value in an operational asset.
- The multiobjective optimization framework not only is able to handle different objectives, but also can provide asset engineers with multiple scenarios for improving field-development planning and decision making under uncertainty.

*JPT*Technology Editor Judy Feder, contains highlights of paper SPE 193883, “Robust Multiobjective Field Development Optimization for the Mariner Asset,” by

**Remus Gabriel Hanea,**SPE,

**Ole Petter Bjorlykke, Yastoor Hasmi,**and

**Tao Feng,**Equinor, and

**Rahul Mark Fonseca,**TNO, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, USA, 10–11 April. The paper has not been peer reviewed.

Optimization Framework Improves Mariner Field Development

01 September 2019

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