Drilling Schedule Research Articles

An optimization model for monthly time-step drilling schedule under planned field production

The field production profile over the yearly horizon is planned for a balance between economy, security, and sustainability of energy. An optimal drilling schedule is required to achieve the planned production profile with minimized drilling frequency and summation. In this study, we treat each possible production process of each well as a dependent time series and the basic unit. Then we ensemble all of them into a tensor. Based on formulated tensor calculation and Lasso regularization, a linear mathematical optimization model for well drilling schedule was developed. The model is aimed at minimizing production profile error while optimizing drilling frequency and summation. Although the model proposed in this work requires more memory consumption to be solved using a computer, it is assured as a linear model and could be numerically globally solved in a stable and efficient way using gradient descent, avoiding complex nonlinear programming problems. Main input data and parameters involved in the model are analyzed in detail to understand the effects of different production parameters on the drilling schedule and production profile. The proposed model in this work can evaluate the manual drilling schedule and automatically generate an optimized drilling schedule for the gas field, significantly reducing development plan formulation time.

Physics-based Residual Kriging for dynamically evolving functional random fields

We present a novel approach named Physics-based Residual Kriging for the statistical prediction of spatially dependent functional data. It incorporates a physical model—expressed by a partial differential equation—within a Universal Kriging setting through a geostatistical modelization of the residuals with respect to the physical model. The approach is extended to deal with sequential problems, where samples of functional data become available along consecutive time intervals, in a context where the physical and stochastic processes generating them evolve, as time intervals succeed one another. An incremental modeling is used to account for both these dynamics and the misfit between previous predictions and actual observations. We apply Physics-based Residual Kriging to forecast production rates of wells operating in a mature reservoir according to a given drilling schedule. We evaluate the predictive errors of the method in two different case studies. The first deals with a single-phase reservoir where production is supported by fluid injection, while the second considers again a single-phase reservoir but the production is driven by rock compaction.

A field development strategy for the joint optimization of flow allocations, well placements and well trajectories

One of the major goals that field planning engineers and decision makers have to achieve in terms of reservoir management and hydrocarbon recovery optimization is the maximization of return on financial investments. This task yet very challenging due to high number of decision variables and some uncertainties, pushes the engineers and technical advisors to seek for robust optimization methods in order to optimally place wells in the most profitable locations with a focus on increasing the net-present value over a project life-cycle. The quest to deliver a good quality advice is also dependent on how some uncertainties – geologic, economic and flow patterns – have been handled and formulated all along the optimization process. With the enhancement of computer power and the advent of remarkable optimization techniques, the oil and gas industry has at hand a wide range of tools to get an overview on value maximization from petroleum assets. Amongst these tools, genetic algorithms which belong to stochastic optimization methods have become well known in the industry as one the best alternatives to apply when trying to solve well placement and production allocation problems, though computationally demanding. The aim of this work is to present a novel approach in the area of hydrocarbon production optimization where control settings and well placement are to be determined based on a single objective function, in addition to the optimization of wells’ trajectories. Starting from a reservoir dynamic model of a synthetic offshore oil field assisted by water injection, the work consisted in building a data-driven model that was generated using artificial neural networks. Then, we used Matlab’s genetic algorithm toolbox to perform all the needed optimizations; from which, we were able to establish a drilling schedule for the set of wells to be realized, and we made it possible to simultaneously get the well location and configuration (vertical or horizontal), well type (producer or injector), well length, well orientation – in the horizontal plane –, as well as well controls (flow rates) and near wellbore pressure with respect to a set of linear and nonlinear-constraints. These constraints were formulated so as to reproduce real field development considerations, and with the aid of a genetic algorithm procedure written upon Matlab, we were able to satisfy those constraints such as, maximum production and injection rates, optimal wellbore pressures, maximum allowable liquid processing capacity, optimal well locations, wells’ drilling and completion maximum duration, in addition to other considerations. We have investigated some scenarios with the intention of proving the benefits of development strategy that we have chosen to study. It was found the chosen scenario could improve NPV by 3 folds in comparison to a base case scenario. The positioning of the wells was successful as all producers were placed in zones having initial water saturation less than 0.4., and all injectors were placed high water saturation zones. Moreover, we established a procedure regarding well trajectory design and optimization by taking into account, minimum dogleg severity and maximum duration for a well to be drilled and completed with respect to a time threshold. The findings as well as the workflow that will be presented hereafter could be considered as a guideline for subsequent tasks pertaining to the process of decision making, especially when it has to do with the development of green oil and gas fields and will certainly help in the placement of wells in less risky and cost-effective locations.

Depositional features of the Middle Jurassic formation of Field N and their influence on optimal drilling schedule

The Middle Jurassic formation of Field N represented by 4 hydrodynamically connected layers (J5-6, J4, J3 and J2) contains 42% of the field STOIIP. The J2-6 formation is characterized as a gas-oil-condensate massive lithologically and tectonically screened accumulation with a gas cap (J2, J3 layers) and bottom water (J5-6 layer). Oil is predominantly in the J3 and J4 layers. There is a high risk of early gas coning from gas-bearing layers to oil producing wells determined on the basis of production test results, which can significantly decrease the life of the well. To select a more optimal drilling schedule, it is necessary to take the risk of early gas coning into account and determine distinctive features within the gas- saturated zone that can reduce it. The presence of a thick shale barrier between the J2 and J3 layers with thicknesses varying from 0 to 30 m is recognized as the beginning of a transgression cycle, and if the gas cap is only in the J2 layer, this barrier with the thickness of more than 5 m can extensively prevent early gas coning into oil producing wells. The integration of geological information represented by the probability map constructed and petrophysical information represented by the kh map provide the more precise determination of an optimal drilling schedule.

Optimized Reservoir Management With Mixed Linear Programming

Summary Reservoir engineers face a large number of possible development plans for major offshore oil fields. Some of the factors affecting development include product-processing capacities, drilling-rig availability, extended use of existing platforms, enhanced-recovery options, and subsidence-avoidance requirements. Reservoir simulation is an accepted technique for estimating production from oil and gas fields. Each possible development scenario is simulated separately to obtain future oil- and gas-production estimates from wells included in the scenario. Simulation results are analyzed for each run, and the optimal plan is selected. Enumerating all the possible drilling schedules is a difficult task, and, even with clusters of advanced scientific workstations, the computational requirements of simulation can be overwhelming. This paper describes the application of linear mixed integer programming (MIP) to the combinatorial problem of generating the optimal redevelopment scenario for the Ekofisk field in the Norwegian sector of the North Sea. The MIP model determines the optimal redevelopment program and drilling schedule while maintaining operationally feasible product-processing requirements, drilling-rig use, and well/platform relationships. Optimality is based on the net present value (NPV) of the estimated production forecasts for the wells selected. Total recovered reserves is an alternative optimization criterion. Reservoir simulations generated the estimated production forecasts used in iterative runs of the optimized model. We discuss success of the approach and extensions.

Assessing the Impact of Trajectory on Wells Drilled in an Overthrust Region

Abstract Drilling in the Cusiana Field, which is located in the tectonically active foothills of the Casanare region of Colombia, has proved to be extremely difficult. The geological setting has provided a most challenging drilling environment where all aspects of drilling have been tested to the limit. One major contributor to the operational difficulties is poor hole conditions often leading to stuck pipe. However, experience has shown that performance improves when drilling up-dip of the major faults and bedding, with down-dip and cross-dip well trajectories being the most problematic. Computational stress modelling of the geological cross sections indicates that the principal stresses in the Cusiana Field may be rotated significantly from the vertical and horizontal. After adjusting a conventional wellbore stability analysis to allow for stress rotation, a reasonable match is obtained between prediction and field experience on the issue of stability variation with hole trajectory for wells drilled in the region. Introduction In partnership with ECOPETROL, TOTAL and TRITON, BP has been drilling in the foothills of the Casanare region of Colombia (Figure 1) since the late eighties. Both the Cusiana and Cupiagua Fields have now been declared commercial. Development well drilling in Cusiana commenced in late 1993. Appraisal wells are currently being drilled in Cupiagua. An aggressive drilling schedule is now being pursued with ten rigs active. From the earliest well, operational difficulties were encountered. Possibly the biggest problem associated with drilling wells in this region has been wellbore instability. Considerable effort has gone into tackling the problems and improvements have been made, as reported in a companion paper. Here the particular aspect of instability variation with well trajectory is discussed. Background to Wellbore Stability Wellbore instability (Figure 2) can result in lost circulation where tensile failure has occurred, and spalling and/or hole closure in the case of compressive failure of the rock. In severe cases hole instability can lead to stuck pipe and eventually loss of the open hole section. Due to the large costs associated with wellbore instability it has received considerable attention, as is apparent from the number of publications on the subject. No more so is the extent of the problem greater realised than the drilling experiences encountered in the foothills of the Casanare region of Colombia. For example, Figures 3a and 3b show the caliper traces from a Cusiana development well. Figure 3a shows a hole drilled with a 12 1/4" bit that has enlarged to nearly 45" in places. The in-gauge section is a sand interval. Also, as seen in Figure 3b, the large over-gauge reading in one caliper pair accompanied by a relatively in-gauge reading of the other pair suggests that the stresses may be highly anisotropic. Selection of mud types and weights to eliminate hole instability of wells drilled in Cusiana has been found to be impossible. There are frequent occurrences of loss zones, which necessitate a low mud weight, being adjacent to collapse zones, which require a high mud weight. It is not realistic to incorporate sufficient intermediate casing strings to isolate each individual problem zone. Hence, mud weight selections are made in an attempt to minimise the problems, without eliminating them, and it has been necessary to live with a certain degree of hole instability. Wellbore stability theory shows there are many factors, other than mud weight, that are likely to influence the competency of the wellbore wall. Examples are formation pressure, depth, formation strength, stress state, mud cake efficiency and time. Of parameters that can be controlled by the operator, theory shows that well trajectory has a significant influence on stability. Field experience from wells in the Cusiana Field also indicates that trajectory has a significant influence on hole stability. In cases where optimising mud weights cannot alone reduce instability to acceptable levels, then attention to optimising well trajectory to further reduce or at least limit the extent of problems is necessary.

A Simulation Model Solved the Problem of Scheduling Drilling Rigs at Clyde Dam

The Clyde Dam in New Zealand is located in an area more unstable than was thought when it was designed. Therefore, Electricorp has taken additional precautions to ensure the stability of the hillsides surrounding it, constructing an underground grout curtain of 1,362 meters along the Clutha River. A grout curtain is constructed by drilling holes in the rock and injecting concrete into them. With a budget of millions of dollars for hiring drilling rigs, the construction company wanted to minimize the idling time of the drilling rigs and finish the project quickly. We developed a simulation model that enabled it to find an efficient drilling schedule, saving about NZ$580,000 on hiring costs for drilling rigs (seven percent of drilling hours hired) and 10 weeks (about 26 percent of project completion time).

Scientific plans for deep sea drilling

The Deep Sea Drilling Project is about to launch phase IV of its drilling operations, known as the International Phase of Ocean Drilling (IPOD). Plans for the first year of IPOD are well under way and a preliminary drilling schedule for the first four years has been drawn up. At this stage it is appropriate to inform the scientific community in general of these plans and to invite comment and suggestions. As in the past the scientific planning is carried out by the Joint Oceanographic Institutions for Deep Earth Sampling (JOIDES). This organisation, international from the outset, will through its various panels continue to provide scientific advice to DSDP for the IPOD programme as it has to the previous phases of drilling.

A Note on Offshore Oil Field Development Problems and Suggested Solutions

This Note reviews some aspects of an approach to modeling the problem of developing offshore oilfields. An alternative method of solution is suggested and an associated problem, that of determining an optimal drilling schedule, is described.

A Monte Carlo Approach to Optimal Drilling

Abstract The variable weight-speed optimal drilling problem has been soloed rigorously using a Monte problem has been soloed rigorously using a Monte Carlo scheme to vary the drilling schedule toward the least cost per foot. Constraints are readily accommodated and the global nature of the optimum can he checked by starting with different initial paths. paths. Examples are given of optimal drilling schedules that lie partially interior to the feasible region as well as on upper weight or speed constraints. Comparison with the variational method of Galle and Woods showed good agreement using drilling equations presented here. However, in all cases studied, it was found that variable weight-speed optimization offered very little advantage over the simpler constant weight-speed approach. In view of ibis, a last computer program was developed for the constant weight-speed case using the powerful conjugate-gradient technique. This method should be very effective in connection with field applications. Introduction Although numerous papers discuss drilling optimization or provide optimization techniques based on field experience, it appears that the first analytical approach to the problem was published by Moore. He used drilling equations that were so simple it was possible to calculate directly the optimum weight corresponding to a given rotary speed. In 1959, Graham and Muench used what is sometimes called the "graphical" approach, together with more realistic drilling equations, to calculate optimum combinations of weight and speed to bearing failure. In their paper, cost per foot is computed vs weight for various depths at fixed speed. This is repeated for various speeds until the optimum is found for each depth. The most significant contribution to the field appeared in 1960. This paper by Galle and Woods culminated years of drilling mechanics research, reducing it all to a concise set of drilling equations. Necessary conditions for the optimal variable weight-speed path are found using the classical calculus of variations with integrated drilling equations acting as constraints. The final result is obtained using a numerical procedure. One conclusion was that, in most cases, the variable weight-speed method would effect a saving of at least 10 percent over the best constant weight-speed schedule. Although we do not want to detract from the importance of this work in any way, it is subject to question on two counts. First, the method of solution requires weight and speed to vary continuously as a function of time. Second, it is recommended that bearing-wear-limited schedules be computed using tooth-wear-limited theory. In 1962, Billington and Blenkarn used the equations and techniques developed by Galle and Woods to optimize the variable weight schedule when speed is fixed by rig limitations. They concluded there was little cost advantage in using a variable weight-speed schedule in preference to a constant speed program. In 1963 the second contribution of Galle and Woods to optimal drilling appeared. In this paper ordinary constrained calculus is used to solve the two-dimensional best constant weight-speed problem. They also provide the best speed for a given weight and the best weight for a given speed. Charts are furnished so that hand calculations can be rapidly made. In the introduction, Galle and Woods note that, in certain cases, the procedures in which both weight and rotary speed are varied or where weight alone is varied result in only slightly lower cost than if the bit were properly operated at constant weight and rotary speed. We have therefore seen a transition from the belief that in most cases variable weight-speed is at least 10 percent better than constant weight-speed to the opinion that there is very little difference between the two methods. At this point, one is not certain what to conclude. In this paper a new, rigorous method of optimization is developed. It provides an independent check on the approximations involved in the variational approach of Galle and Woods and compares optimal variable weight-speed schedules to the corresponding optimal constant weight-speed programs.

An Approach to Locating New Wells in Heterogeneous, Gas Producing Fields

A two-dimensional numerical calculation of semi-steady-state flow in a gas field can be used to determine the best possible drilling schedule for developing the remainder of the field. The technique can be used also to estimate gas field performance under alternate spacings, to examine lease-line drainage, and to determine the degree of drainage or depletion of different portions of a field. Introduction The decline of average field pressure during the producing life of a gas field causes a corresponding producing life of a gas field causes a corresponding decline in well deliverability. Additional wells are therefore drilled during the producing life to maintain the desired or contractual total field producing rate. Maximizing the economic return from the producing operation requires minimizing the number of wells drilled. Even if a fixed total number of wells are to be drilled (ultimately), the usual discounted cash flow or present-value analysis dictates that the wells be drilled as late as possible in project life. This paper treats the problem of determining an optimum drilling schedule for remaining field development, starting from an initial (present) time corresponding to an arbitrary degree of depletion and arbitrary number and locations of existing wells. This optimum schedule consists of specified well locations to drill and the time at which each is to be drilled. Conventionally, additional well requirements for maintenance of field productivity are determined from back-pressure curves that relate well deliverability to the difference between average field pressure and flowing wellbore pressures. The assumptions involved in this approach render it satisfactory for only a homogeneous field with regularly spaced wells having equal producing rates. The method described here minimizes new well requirements at each successive stage of depletion by selecting optimal locations for additional wells. The method accounts for the effects on well deliverability of reservoir heterogeneity, irregular spacing, and well interference. Following sections state the problem more fully, describe the conventional and proposed methods of solution, and present example applications. The Appendix describes in detail the mathematics involved in the proposed technique for determining optimal well locations. The Problem The development drilling program necessary to meet contractual producing rates from a gas field is characterized by a plot, such as Fig. 1, of cumulative wells drilled vs time or vs remaining gas reserves. Time and gas in place are related through the specified field producing rate. An obvious economic incentive exists to keep this curve as "low" as possible. Thus Curve 2 is preferable to Curve 1 even though the total number of wells drilled over project life is the same in both cases. Curve 3 is preferable to both of the other curves. A lower limit on the number of wans drilled is imposed by the requirement of a specified total field deliverability, which may vary with time. The problem is to meet this required field productivity problem is to meet this required field productivity with as few wells as possible. The degrees of freedom or decision variables in attacking this problem are the locations of new wells. JPT P. 549

The Use of Linear Programming and Mathematical Models in Under-Ground Oil Production

This paper describes how linear programming models can be used to solve crude-oil producing problems for the purpose of economic planning of coordinated operations. Although the methods of linear programming have been used extensively in the oil industry, very little work has been reported to date in extending these methods to the area of underground oil production. Two separate models are presented. The first model schedules production and assumes either a completely developed field, or, in the case of only partially developed fields, it assumes a given drilling schedule. The second model schedules drilling-rig operations when it is assumed that the production from a given well follows a specified production-decline curve. Consideration also is given to a means for optimizing the investors rate of return which appears as a nonlinear parameter in the objective function.