Some of the most important and expensive activities in onshore oil and gas field development involve the use of drilling rigs. Using a production systems perspective, this paper presents a method to optimize onshore drilling rig fleet size and schedule considering reservoir management and operational objectives, namely maximizing production volume, meeting production targets and/or minimizing rig costs. An example of industry application is presented involving a field with 237 wells located in the northern United States. Results demonstrate that given a fixed fleet size, optimizing for rig utilization or cost does not best satisfy production objectives. Furthermore, significant variations in production rates (30%) and costs (19%) are possible depending on fleet size and schedule. The results suggest that providing decision support and optimization to assist with determining rig fleet size and schedule is not only likely to reduce planning and response time, but also bring the overall development operation better in line with key performance objectives.
Key Words: Drilling; Drill Rigs; Scheduling; Optimization; Oil and Gas; Production Control in Onshore Field Development
In an environment of diminishing reserves and low commodity prices, oil and gas operators are under increasing pressure to produce the maximum volume of oil and gas at the lowest possible cost. Some of the most important and expensive activities during the reservoir development and production phases involve the use of drilling rigs. These rigs are used for both drilling wells and maintenance activities. This paper concerns the use of rigs for drilling wells. Given the high cost of acquiring and operating land-based rigs, which, depending on the price of oil, can command daily rates of up to $22,000 USD [1], operators use relatively few of them as compared with the number of wells that need drilling. Thus, immediate allocation is not always possible, resulting in queues of wells awaiting rigs. The problem of determining the sequence of wells to be drilled by each rig is called the Rig Scheduling Problem (RSP) [2].
ig scheduling requires coordination between two main entities involved with oil and gas field development within an operator’s organization: reservoir management and operations [3]. These groups typically have different goals and responsibilities, which are traditionally addressed sequentially. The primary objective of the reservoir management team is to maximize the production volume or meet production targets by creating an operating plan that defines which wells to drill and how to drill them. The operations team then takes the operating plan created by the reservoir management team and creates a rig schedule (by assigning rigs to wells) that aims to minimize rig costs and overall operations costs while meeting production targets.
Commonly, the operating plans provide envelopes that define a time range in which each well is expected to be drilled. If the operating envelopes are too narrow to create feasible rig schedules, the reservoir management team must iteratively adjust the operating plan until rig scheduling is feasible. This is problematic because the process is time consuming and reservoir management and operations teams are often under intense time pressure to complete their work. To minimize scheduling time, the operating plan is often created with substantial slack to avoid the iterative process described above, which may result in highly suboptimal schedules [4].
By considering the entire workflow from the perspective of a production system, this paper presents a method to optimize drill rig fleet size and schedule that considers both reservoir management and operational objectives, namely maximizing production volume, meeting production targets and/or minimizing drilling and completion costs.
A group of drilling rigs with different specifications must drill a set of wells that have varying characteristics. Multiple wells are often drilled from a single, compact piece of land called a pad. Doing so saves time and money that would otherwise be spent packing and moving the rig and preparing a new drilling site.
It is important to determine the rig fleet size and to create a schedule in order to assign a specific set of pads to each drilling rig in the fleet in a specific order. The decision variables for the RSP as well as objectives and constraints are defined below.
These are factors that the decision maker is willing and able to vary to influence the RSP outcome:
| Rig Fleet Size | The number of drilling rigs available to be scheduled |
| Rig Schedule | The sequence of pads to be drilled by each rig |
| Pad Drill Strategy | The method of drilling a set of wells on a given pad |
For a description of the candidate pad drill strategies used in the example application, see Table 1 below. The acronyms in Table 1 signify the different types of steps that can be taken in going from one well to the next. For example, MTVL signifies rig Move; drill Top Hole; drill Vertical section; drill Lateral section.
Table 1: Example of different inter-pad drilling strategies
The RSP can also be affected by different and unrelated factors, namely drilling rig factors, well factors and other factors which are summarized below [5].
| Objectives | There are two fundamental metrics used to evaluate the quality of a given RSP solution |
|
| Constraint | This metric is used to evaluate the feasibility of a given solution to the RSP |
Quarterly production rate target: The desired production rate for each financial quarter |
| Drilling Rig Factors | Factors affecting the Drilling Rig Schedule that relate directly to drilling rig specifications |
Rig Capability: Each rig has a horsepower rating that affects the maximum depth it can drill
Rig Cost Rate: Daily cost of employing the drilling rig Rig Speed: Speed of the rig while moving between wells Rig Maintenance requirements: Frequency and duration of maintenance activity which prevent the rig from being in operation |
| Well Factors | Factors affecting the Drilling Rig Schedule that relate directly to well characteristics |
Well Drilling Time: Time needed to drill the well
Well Completion Time: the time required to complete the well after drilling is finished Well Production Profile: The amount (barrels) of fluid that a well is expected to produce as a function of time Pad Assignment: Multiple wells are often drilled from a single, compact piece of land (the pad). Doing so saves time and money that would be spent packing and moving the rig and preparing a new drilling site. The pad assignment defines the particular pad where the well is |
| Other Factors | Oil Price: The price of oil as a function of time |
As rig fleet size, well counts, and the distance between wells continues to increase, the challenges
involved in drill rig scheduling grow exponentially [6]. Therefore, ensuring that the right rig is in the right
place at the right time becomes increasingly difficult to manage using a manual approach. Several
researchers have developed computation approaches to address the RSP in order to reduce planning time,
improve responsiveness to changing information and/or improve the quality of solutions generated.
One class of approaches can be called “Operations-based optimization.” For example, one heuristic
minimizes the total distance traveled by the rig as a proxy for minimizing cost, subject to satisfying the
production target constraints [6]. Another approach called simultaneous sizing and scheduling minimizes
the total number of rigs while maximizing the utilization of each rig using a mathematical programming
model [7]. A final approach formulates an optimization objective of the cost of the drilling rig schedule,
considering both moving and drilling costs [5].
A second class of methods can be termed “Reservoir management-based optimization”. An example
draws an analogy between the Rig Scheduling Problem and the Vehicle Routing Problem (VRP) [8]. The
objective is to maximize the cumulative NPV of the portfolio of wells, where the portfolio NPV is based
on the NPV of each well in the period within which it is drilled. Variables include the number of rigs and
the drilling sequence. For the optimization problem to be well posed, individual well NPVs must vary
with the drilling period but they cannot all vary at the same rate with respect to the drilling period. The
work shows that by application of simulated annealing to optimize the objective, portfolio NPV can be
improved by as much as 30 times compared to traditional methods [8]. Another method in this class is to
minimize oil loss by varying the number of rigs and schedule [9].
A final family of methods involves “combined optimization.” An example from this family of methods is
the Rig Activity Scheduler. The objective is to schedule the rigs to minimize the transportation cost, while
meeting or exceeding the target production delay [4]. Higher performing wells are scheduled as early as
possible, and a roughly equal number of wells is assigned to each individual rig. A penalty function to
penalize, for instance, downtime of wells, is used with the cost being the well downtime multiplied by the
potential production rate.
A second example of “combined optimization” integrates drilling rig scheduling with reservoir simulation
[10]. The algorithm aims to maintain overall field production, while seeking to reduce the net distance
travelled by the rigs and the number of rigs used. As for well statistics on production, it assumes wells
have a normal and a maximum production rate. While we classify this as a “combined optimization”
algorithm, no actual optimization is used. Instead, the work focuses on reducing the net distance
travelled [10].
This paper presents the first stochastic approach to dealing with the problem of planning and scheduling a
fleet of onshore oil rigs where service times are assumed to be uncertain.
The literature highlights three primary challenges with the Rig Scheduling Problem. First is the
complexity of the optimization problem, because of the number of variables. Even with the
simplifications described in order to arrive at a well-posed problem, the high dimensionality of the phase
space (i.e., the high number of variables), together with the combinatorial complexity of the problem
causes the number of combinations and permutations of variables to be investigated to grow rapidly as the
range of parameters grows.
A second challenge, exemplified by a number of cited references, is that typical approaches do not align
reservoir management objectives with operational objectives, or at the very minimum, clarify the
tradeoffs between the two considerations. For instance, reservoir management objectives to honor well
release preferences and constraints, together with production targets is at odds with operations objectives
to minimize total cost incurred and honoring rig fleet management constraints. Approaches have typically
made simplifying assumptions without systematically quantifying the tradeoff between various
constraints to optimize overall system objectives. An example is the approach to maximize rig utilization,
assuming that will result in maximizing production and minimizing total cost.
A final challenge is that most approaches are deterministic, and do not account for variability and
statistical variation that occurs throughout operations. This includes variability in task execution times,
variability in times when resources are available, and variability in resource capacity. It is necessary for
the model of the problem to be able to accommodate this variability and uncertainty in planning
assumptions across the entire system of tasks in the rig scheduling workflow.
Figure 1: Block diagram illustrating components of the model for the Rig Scheduling Problem
Figure 1 shows a flow chart of process steps in the model and information dependencies (i.e., coupling). Coupling is represented by arrows between components. Coupling above the diagonal indicates sequential execution while coupling below the diagonal indicates iteration. Table 2 below gives a text description of information dependencies.
Table 2: Description of process components as well as the information inputs and outputs for each component
The incorporation of uncertainty in the different parameters is summarized in Table 3, which summarizes the key pieces of information needed for the analytical model. It is important to note that this comprehensive listing of key parameters and their ranges is facilitated by the production systems’ formulation of the problem.
Table 3: Description of process information requirements
Putting Tables 3 and 4 together with Figure 1 results in Figure 2, the proposed optimization process, consisting
of a combination of interdependent iterations, manual, sequential and automated. Below Figure 2, each block in
the overall optimization process is described.
Figure 2: Overview of the proposed optimization process
Pad Drilling Sequence: Defines the overall drilling sequence based on a list of candidate pads
Rig Allocation: Allocates rigs to each pad based on overall drilling sequence and the
rig count
Well Delivery Schedule: Calculates the well delivery schedule based on the pad schedule for each rig
Inter-Pad Drill Strategy: Defines the drill strategy for each pad. Three different inter-pad drilling strategies were considered, shown in Table 1
Project Production: Calculates the oil or gas resource production for the project over time. This is a function of time
Project Cost: Calculates the oil or gas resource production for the project over time. This is a function of time
Optimizer: Systematically generates and evaluates alternative production scenarios based on the problem formulation provided
Table 4: Example of task duration time input into process
Figure 3: Example well production curve
The first example modeled is a site in the Northern United states, with 237 wells and 103 pads. The
maximum distance between any two wells is 316 km (196 miles). A map of the well locations is shown in
Figure 4.
Figure 4: Map of the 203 well locations in the example application
The first problem formulation aimed to minimize production cost (US$/BOE) while maximizing production rate (average BOEPD – barrels of oil equivalent per day). Three types of variable were considered in the problem:
Algorithms considered in this experiment were the DAKOTA multi-objective genetic algorithm and the Monte Carlo DOE. Simulation results are summarized in Figure 4, which illustrates the Pareto frontier demonstrating the tradeoff between production rate and production cost, separating feasible combinations of production rate and cost from infeasible combinations.
Figure 5: Pareto front of solutions illustrating the trade-off between the competing objectives –
production rate and cost
A second experiment was to minimize production cost (in US$ per BOE) while honoring constraints on meeting quarterly production targets (in thousands of BOEPD). The variables in the problem were the same as in Experiment 1: the number of rigs, three different types of pad drilling sequence (shown in Table 1), and the sequence of pads ranging from pad 1 through to pad 103. The contrast between imposing the constraints and not imposing them is shown in Figure 6, where the unconstrained formulation yields solutions that fail to meet the quarterly production targets.
Figure 6: Production flow rate for two different drilling rig schedules. Note that the unconstrained
minimum rig cost solution does not meet the quarterly production rate targets
This paper addresses the Rig Scheduling Problem (RSP) by taking a production systems perspective to incorporate more systematically variable uncertainty, and coupling between reservoir management objectives and operation objectives in applying simulation-based optimization.
Case study data supports the hypothesis that the commonly used heuristic of optimizing for rig utilization / cost does not necessarily best satisfy project production rate objectives. Significant variations in production rate (30%) and costs (19%) are possible depending on management decisions.
Practical benefits of using the production systems model with numerical simulation and optimization included reduced planning time and increased response time – the time it takes to handle schedule revisions due to changes in inputs. Additional contributions include reduction in scheduling errors.
Several areas for further work are suggested from this preliminary work. More detailed modeling of well completion activities can yield a more accurate model of the overall process. The work can benefit from a better analysis and representation of solution uncertainty. The algorithms used in the modeling can be improved to reduce feedback latency.
Finally, it is possible to have more systematic coverage of input parameters and their uncertainty. Some of the above attributes (such as geographic coordinates and water depth) are deterministic; others (such as presence of H2S and depth) are uncertain, but may be treated as roughly deterministic; and others (such as an oil potential and service time) are severely probabilistic. Uncertainty is a central issue in oil exploration and production. Thus, in order to define a profitable drilling strategy for oil wells, it is fundamental that the used methods take this component into account.
The author’s work was supported by a gift from the Project Production Institute.
