Joint Optimization of Well Placement and Controls Applied to a Real Field Case
3.6 Discussion and suggestions for further work
In this final section of this chapter, we treat some of the topics arising from the optimiza-tion work and applicaoptimiza-tion process. The following topics are discussed: role of embed-ded control routine during well placement search; role of non–linear constraints during well placement optimization; critique of sequential constraint handling; and collaboration work.
Role of embedded control routine during well placement search
Results from embedded optimization. We have seen that the mean difference between final cost function values obtained using the joint and sequential approaches is of about 7% (see page 93). Furthermore, we have that embedded control optimization provides each well placement iterate an average increase in cost function of somewhat more than 7% (see page 93). A question that will be treated in further work is whether the differ-ence between joint and sequential final cost function values will increase if the embedded control optimization problem is of a more complex nature than the ones dealt with in this work. If the embedded problem is more complex, we might expect a greater gain at each well placement trial solution due to the embedded optimization compared to using fixed controls or a reactive control strategy. Below we briefly discuss the topic of more com-plex formulations for the control optimization problem, and a possible implementation of inflow control valves for the development of the Martin Linge oil reservoir.
Increased gain from embedded control routine due to greater problem complexity.
The topic to be explored in the future is whether there will be a greater benefit from solving the embedded problem through optimization, if the problem involved is more complex. The idea is that the added complexity is likely to make fixed–control settings, or the use of heuristic control strategies, much less effective at a greater number of well placement trial solutions. The most obvious source for increased complexity to the type of continuous control optimization problems treated in this work is the inclusion of non–
linear production constraints. Dealing with a more complex problem is not a point in itself, but rather, it is the result of more interesting, i.e, realistic, production scenarios often requiring more advanced configurations. A single aspect of problem configuration that may become more advanced and require the use of optimization techniques is the formulation of the objective function. For instance, the control problem formulation used in the latter work in this thesis is relatively straightforward, aimed at increasing cumulative oil production only. More interesting problem formulations could simply mean replacing the cost function definition from FOPT to net present value (NPV) as the objective for control optimization. NPV formulations involve computing revenue from total oil pro-duction (often with a discount factor), and may include one or several cost parameters as-sociated with facilities and the production (and injection, if present) of water. As discussed in Chapter 2, these problem configurations are harder to solve for optimally using reactive control procedures. Overall, production problems that involve complex formulations are likely to decrease the effectiveness of simpler, e.g, heuristic, techniques, and this may increase the advantage of implementing a joint approach for well placement and control optimization.
Role of non–linear constraints during well placement optimization
Different well–length constraint implementations. The solutions from this chapter have been developed using different configurations of the well–length constraint. Most of these configurations have implemented the well–length constraint during the optimiza-tion procedure, while an addioptimiza-tional configuraoptimiza-tion imposes the maximum well–length con-straint only after the optimization procedure is completed. The different implementations of the constraint have been applied for both the joint and sequential approaches. From the function evolution curves (see figures 3.16 and 3.17 on page 95), we noticed that the de-crease due to the a posteriori well–length constraint enforcement is somewhat less severe for the two joint runs (runs JNT2M1 and JNT1M1) compared to the drop observed for the sequential solution (FXD1M1). (Note that a new control optimization is performed after the well lengths in these runs are reduced. However, for each graph in question, the increase due to this new control optimization is small compared to the drop in cost function.)
At this point it is important to note that we do not consider the above results to be in any sense sufficient to make any further claims regarding the different constraint imple-mentations. However, these results give us an idea for further work, which we describe below. It could be these results are an indication that cost function values obtained using the joint approach are less susceptible to certain changes in only one type of variable, in this case, changes corresponding to well length. This apparent robustness may be the result of joint solutions effectively integrating well trajectories with individual well con-trol settings. As discussed in Chapter 2, page 15, the joint approach searches the space of control–optimized well locations, and a joint solution can therefore claim (local) op-timality with respect to both types of variables. Consequently, the optimal control part of a joint solution may help mitigate a drop in the final cost function value, if this drop is primarily caused by only a relatively minor change in the well placement part of the solution, i.e., a decrease in well length. The above discussion is solely based on a few data points. Further work is necessary to properly test whether this property is present.
Critique of sequential constraint handling
In this work, the series of projections dealing with non–linear constraints on well place-ment variables has been impleplace-mented as a sequence of projection operators (see Sec-tion 3.4.3: Methodology, page 84). Handling projecSec-tion operators in this manner may not be efficient since a sequential handling of constraints cannot ensure the final projection is orthogonal to the common solution space. An alternative way is to handle the feasibility constraints concurrently. If we treated all constraints associated with well placement co-ordinates, i.e., bounds, well–distance and well–length constraints, as one projection task, we could possibly improve the performance of the constraint–handling procedure. In our case, this would mean including all constraints into a single problem formulation that solved for the minimum distance to the feasibility bound. This reformulation will be the subject for further work.
Collaboration work
Problem translation. To achieve the stated goals for this application (see Section 3.1:
Targets and strategy for application development, page 42), an effective collaboration between research partner and industry operator is key. During the course of this work we established a close collaboration with the group of engineers from Total E&P Norge AS assigned with planning the development of the Martin Linge oil reservoir. This collab-oration enabled us to have ample access to the reservoir model (e.g., both as Eclipse model and as numerous Petrel projects), and facilitated information transfer and quality feed-back. Moreover, the open–ended interaction was important to efficiently set up and treat specific design issues, e.g., we held various meetings and received clear information about the type of constraints that should be applied to the well placement coordinates. Further-more, input from the group was instrumental for the work model validation process. How-ever, despite the steadfast commitment to collaboration work from the operator team, the process of settling on various specific parameters that ultimately define the optimization problem was challenging. The challenges, from our research point of view, were often linked to not having sufficient understanding about the reservoir and/or knowledge about underlying assumptions and motivations regarding the development of the asset8. In the following we offer a broad outline of the tasks of problem definition and knowledge trans-lation, based on the accomplishment of these tasks in this work, and then propose a collab-oration procedure that may improve the performance of these tasks in future applications.
A very broad background for the application work conducted in this thesis is that, to foster innovation within the petroleum industry, research work needs to be challenged with realistic definitions of operation (i.e., real–life) problems (Lægreid, 2001). The gen-eral issue we focus on here is that these operation problems need to be specified as pre-cisely as possible for the application of research to be effective. Based on this background, and our experience during the course of this work, we argue that obtaining a useful so-lution from the application of research on such a problem, requires that we perform a functional translation of the operation problem and the knowledge embedded in it. Im-portantly, with a functional translation we mean a work process that not only transfers the technical description, but also attempts to incorporate the intent and purpose of the operation problem into the end–formulation of the application problem. A primary goal of any collaboration work then, should be that this end–formulation of the application problem, stated using standard notation for mathematical programming, embodies those fundamental aspects mentioned for the operation problem. In our opinion, to achieve this end, a perceptive collaboration effort is required that combines specialized knowledge contributions from both the operator and research side, and that can also facilitate the flow of expert knowledge from one side to the other.
Further work in this regard could be the development of a test procedure where the research and reservoir team would work together on a rough visualization of the (well placement) problem search space. The idea is that over several work iterations the vi-sualization will become a customized problem formulation. We end this section with a suggestion for such an iterative test procedure.
Test procedure for problem definition. The test procedure we are suggesting targets the translation process. The overriding motive is to meet the reservoir team halfway and to
enable them to re–express their conceptualizations within an optimization context. The visual representation is a simple way to make the end–formulation accessible to the engi-neers. For example, for the well placement problem, the visualization would show bounds and non–linear constraints. Importantly, through a graphical user interface, for example, it would enable the engineering team to directly manipulate the shape and parameters of these end–formulation concepts. Using the visualization, well placement constraint pa-rameters, in this example, can then be overlapped with operation problem specifications.
The procedure is thought to be applied in a stepwise manner. Again for the well place-ment problem, once search regions, individual well and inter–well length and distance relationships, in addition to feasible depth intervals, have all been manipulated graphi-cally by the reservoir team, trial optimization runs using the specified constraints would be performed. These runs would not run reservoir simulations. Rather, the optimization algorithm would use random number generators as cost functions, or possibly an analytic function based on the particular problem (without the ambition of being a surrogate). At this point, the idea is to launch a large number of trial optimization runs to resolve any issues that may be linked to the feasible space currently defined, and if possible, make the optimization process more effective, e.g., by tuning. Importantly, the very quick turn–over for each trial runs allows for several instances of the configuration–test cycle to be per-formed, which enables the developing problem formulation to be re–assessed and updated after each instance. This means one testing phase of the procedure would be followed by a new work iteration with the operator team where the current problem formulation would be evaluated. After each instance, the reservoir team would provide feedback, add to and further tune the visualized problem formulation following their own technical specifica-tions, until the knowledge that they consider the most important about the operation prob-lem, including some of the original intent and purpose, are sufficiently represented. At this point we would launch the optimization proper using reservoir simulations. A dedi-cated collaboration test procedure as the one described above could be a way to develop end–formulations that are highly tuned to the business needs of the operator.
The next chapter deals with the testing of obtained solutions on the real field case model.