Mathematical Modelling of the Drilling Process for Real-time Applications in Drilling Simulation, Interpretation and Assistance

For the last thirty years, mathematical modelling has been used to develop software solutions that support drilling engineering activities at the planning stage of drilling operations. But it is only for the last decade that mathematical models have been used for the real-time support of drilling operations. Moving from a pure engineering perspective to having models that can respect real-time requirements, necessitates many improvements of the subjacent mathematical modelling of the drilling process. First, it is not anymore possible to ignore transient behaviors that were somewhat irrelevant at the planning stage. Second, there is a need for solutions that should be fast enough to cope with the real-time constraints of the drilling process. With the perspective of creating applications that can support the drilling process in real-time, the following mathematical models have been developed: • Drilling fluid behavior. The properties of drilling fluids depend on their composition and pressure-temperature conditions. For instance, the pressure-temperature dependence of the mass density of drilling fluids, depends on the individual PVT-properties (Pressure-Volume-Temperature) of each of the components and their relative volume fractions. Therefore, the addition of drill-cuttings in the drilling fluid also changes the drilling fluid PVT-behavior. Furthermore, the rheological behavior of drilling fluids depends also on its composition. We have found that the rheological behavior of a KCl/polymer water-based mud is simultaneously modified by the relative proportion of barite and sand. Furthermore, it is known that drilling fluids are thixotropic. Yet, we found that the thixotropic behavior of drilling fluids is different from the one of other thixotropic fluids and we have determined that one of the causes for the discrepancy is related to the presence of solids in the fluid mix. We have developed a method to estimate the rheological behavior and its associated uncertainty, as a function of the modification of the solid proportions. • Drill-string mechanical sub-models coupled with hydraulic effects. Hydraulic pressure has also an impact on drill-string mechanical forces not only because the fluid mass density modifies buoyancy but more generally because viscous pressure gradients generate net forces along the drill-string. These hydraulic related forces are superposed to those engendered by mechanical friction and elastic deformation. • Steady state and transient drill-string mechanical models. Steady state torque and drag models utilizing the above-mentioned drill-string mechanical sub-models can be used to assess some characteristics of the drilling process when constant velocities are prevalent. But, during a drilling operation, there are many moments during which the drill-string displacement is in transient mode. Therefore, it is also important to have access to transient torque and drag models with a fast response time. • Transient cuttings transport model. The transport of cuttings is obviously influenced by hydraulic circulation but also drill-string rotational speed, at least in the deviated parts of a well. On the other hand, the presence of drill-cuttings in suspension or settling on the low-side of the borehole, influences pressure losses and mechanical forces along the drill-string. Therefore, the estimation of the transient displacement of drill-cuttings plays an important role in the overall estimation of the actual drilling conditions during a drilling operation. However, a transient cuttings transport model shall also be sufficiently fast, especially when it is used in real-time applications. Equipped with such models of the drilling process that are compatible with real-time constraints, then it is possible to solve problems that are relevant for the assistance of drilling operations. A first domain of application is related to the estimation, in real-time, of surface and downhole sensor values as a function of external commands like the block position and speed, the top-drive rotational velocity and the pump rates. We will refer to this domain of application as “drilling simulation”. However, comparison of measured values with simulated ones, require the proper modelling of the sensors and the impact of their actual position on the readings. For instance, drilling fluid is retained in the flowline and mud treatment equipment. Therefore, to simulate pit volumes, it is important to model the retention mechanism. Transient hydraulic, mechanical and heat transfer models, associated with precise modelling of sensor measurements, can then be used to interpret the current actual drilling conditions, because if their estimated parameters differ from the measurements, then a possible reason is that something unexpected is happening downhole. However, such drilling symptom detection method necessitates two additional conditions to be fulfilled: • The models shall be calibrated. Regardless of the quality of the drilling models, the inputs to these models are always known with a limited degree of accuracy and therefore their outputs may differ from measurements for that simple reason. However, it is important to distinguish between uncertainties that are related to properties that do not change substantially during a given drilling operation, from those that can change at any time. To avoid influencing the calibration of time invariant properties with possible side effects of the deterioration of the drilling condition, it is important to utilize drilling conditions by which undesirable side effects have no or little influence on the measurements that are used to calibrate the property. • Uncertainty of the modelled outputs shall be estimated. Calibration may reduce the uncertainty on the model outputs, but it does not eliminate it completely. It is therefore important to estimate the uncertainty of the predicted values. To achieve this, it is necessary to capture the precision by which the inputs of the process are known and to propagate that uncertainty throughout the modelling of the outputs. With continuously calibrated models and an estimation of the current downhole conditions, then it is possible to address some preliminary drilling process assistance functions: • Safety triggers. During the execution of automation functions, the situation awareness of the driller is reduced as he does not drive the drilling machines himself. Therefore, it shall not be attempted to automate any functions before a minimum set of protection functions are in place. Such safety triggers shall detect and react to incidents related to the axial and rotational movement of the drill-string and, of course, associated with pressure. Example of such safety triggers are: o Reactions to overpulls and set-down weights. o Reactions to abnormal torques. o Reactions to abnormal pressures. • Safeguards. Any drill-string or drilling fluid movements shall not generate a drilling incident. Therefore, commands to the drilling machines shall be kept within safe operational envelopes. For instance, upward movement of the drill-string shall not decrease the downhole pressure below the pore pressure or the collapse pressure of the open hole formations. Similarly, the applied flowrate combined with a possible downward movement and rotation of the drill-string shall not overpass the fracturing pressure of open hole formation rocks. • Automated procedures. Protected by safety triggers and operating within acceptable safeguards, then it is possible to automate some standard procedures. However, such automatic procedures must continuously be adapted to the current drilling conditions. For instance, the length of a friction must be modified to account for the current drill-string length and mechanical friction, or the flowrate applied during the ream-down sequence of a reciprocation procedure shall be reduced as a function of the current potential surging risk

Whirling dynamics of a drill-string with fluid–structure interaction

Fluid–structure interaction models for drill-string vibrations are often of reduced order. However, both the structure and the surrounding fluid are non-linear, which can lead to complex coupled dynamic. In this paper, a coupled fluid–structure model is developed, where the flow is reduced to multiple cross-sections and solved with the lattice-Boltzmann method, while the finite element method is employed to discretize a region of the drill-string. In sequence, the whirling dynamics and the fluid forces are analyzed for different configurations. The process is repeated disregarding the fluid-interaction with the aim of evaluating the fluid forces. The fluid forces estimated through the solution of the Navier–Stokes equation shows that the fluid acts in both dissipation and excitation of the vibrations. The dissipation is seen when high frequency dynamics is expected, whereas the lower frequencies are excited.publishedVersio

Application of the quemada viscosity model for drilling fluids

A number of different models are used to describe the shear rate dependent viscosity of drilling fluids. Most, such as the Herschel-Bulkley model, have a purely empirical basis. The Quemada model, while still empirical, is based on physical principles. It is based on the notion that structural units develop in the fluid at low shear rates which are then partially broken down as the applied shear rate increases. In the current work, drilling fluid rheological data are fitted to the Herschel-Bulkley and the Quemada model. The development of the Quemada model and the calculation of each model parameter are presented. We show that the Quemada model better fits measurements over a wider range of shear rates than the Herschel-Bulkley model. We describe how to select the parameters of the Quemada model. Knowing the difficulty of obtaining a known shear rate for fluids with yield stresses, we discuss how this can affect the quality of the Quemada model fit. Furthermore, in principle, the Quemada model is not applicable in presence a non-zero yield stress. Therefore, we show how to handle the yield stress using a (very high) zero shear rate viscosity.acceptedVersio

Automatic Measurement of the Dependence on Pressure and Temperature of the Mass Density of Drilling Fluids

Drilling fluids are subject to substantial variations in pressure and temperature while they are circulated in a well. These changes are so great that the mass density of the drilling fluid varies significantly during circulation. Accurate estimation of the hydrostatic and hydrodynamic pressures therefore requires a reliable model of the pressure and temperature dependence of the mass density of the drilling fluid. Usually, the mass density of a drilling fluid is measured manually with a mud balance. The pressure and temperature dependence of the mass density of the fluid, i.e., its PVT behavior, is then calculated from a PVT model of its components and their relative proportions. However, variations in the composition of the fluid mix and uncertainties in the PVT behavior of each component, may lead to inaccuracies. To overcome these limitations, an apparatus has been designed to measure the PVT behavior of the drilling fluid directly and automatically. The setup measures both the mass density and the speed of sound of the fluid at specific conditions of pressure and temperature. It is possible to estimate the adiabatic compressibility from the speed of sound in the liquid mix. The device utilizes a heat exchanger from which the specific heat capacity of the drilling fluid can be derived. The isothermal compressibility can be calculated by combining the specific heat capacity and the adiabatic compressibility. While estimating the specific heat capacity using the heat exchanger, the thermal conductivity of the fluid is also estimated as a byproduct. A PVT model of the drilling fluid is obtained by combining measurements made at different conditions of pressure and temperature. The automatic and continuous provision of drilling fluid PVT behavior enhances the precision of model predictive drilling control systems and at the same time, can simplify their configuration, therefore making them more accessible to any drilling operation.Automatic Measurement of the Dependence on Pressure and Temperature of the Mass Density of Drilling FluidspublishedVersio

eLAD: Well simulator specifications

eLAD is a laboratory for evaluating new drilling automation tools, new drilling advisory systems, new work processes within drilling operations, the consequences of wired pipe telemetry. The kernel of the laboratory is a well simulator which is behaving as a well would have under the simulated drilling circumstances. This document describes the requirements of such a well simulator.NFR, Statoil, ConocoPhillip

Precise Method to Estimate the Herschel-Bulkley Parameters from Pipe Rheometer Measurements

Accurate characterization of the rheological behavior of non-Newtonian fluids is critical in a wide range of industries as it governs process efficiency, safety, and end-product quality. When the rheological behavior of fluid may vary substantially over a relatively short period of time, it is desirable to measure its viscous properties on a more continuous basis than relying on spot measurements made with a viscometer on a few samples. An attractive solution for inline rheological measurements is to measure pressure gradients while circulating fluid at different bulk velocities in a circular pipe. Yet, extracting the rheological model parameters may be challenging as measurement uncertainty may influence the precision of the model fitting. In this paper, we present a method to calibrate the Herschel-Bulkley rheological model to a series of differential pressure measurements made at variable bulk velocities using a combination of physics-based equations and nonlinear optimization. Experimental validation of the method is conducted on non-Newtonian shear-thinning fluid based on aqueous solutions of polymers and the results are compared to those obtained with a scientific rheometer. It is found that using a physics-based method to estimate the parameters contributes to reducing prediction errors, especially at low flow rates. With the tested polymeric fluid, the proportion difference between the estimated Herschel-Bulkley parameters and those obtained using the scientific rheometer are −24% for the yield stress, 0.26% for the consistency index, and 0.30% for the flow behavior index. Finally, the computation requires limited resources, and the algorithm can be implemented on low-power devices such as an embedded single-board computer or a mobile device

The Effect of Thixotropy on Pressure Losses in a Pipe

Drilling fluids are designed to be shear-thinning for limiting pressure losses when subjected to high bulk velocities and yet be sufficiently viscous to transport solid material under low bulk velocity conditions. They also form a gel when left at rest, to keep weighting materials and drill-cuttings in suspension. Because of this design, they also have a thixotropic behavior. As the shear history influences the shear properties of thixotropic fluids, the pressure losses experienced in a tube, after a change in diameter, are influenced over a much longer distance than just what would be expected from solely entrance effects. In this paper, we consider several rheological behaviors that are relevant for characterizing drilling fluids: Collins–Graves, Herschel–Bulkley, Robertson–Stiff, Heinz–Casson, Carreau and Quemada. We develop a generic solution for modelling the viscous pressure gradient in a circular pipe under the influence of thixotropic effects and we apply this model to configurations with change in diameters. It is found that the choice of a rheological behavior should be guided by the actual response of the fluid, especially in a turbulent flow regime, and not chosen a priori. Furthermore, thixotropy may influence pressure gradients over long distances when there are changes of diameter in a hydraulic circuit. This fact is important to consider when designing pipe rheometers

Measurement of Drilling Fluid Rheology and Modeling of Thixotropic Behavior

Drilling fluids perform a number of important functions during a drilling operation, including that of lifting drilled cuttings to the surface and balancing formation pressures. Drilling fluids are usually designed to be structured fluids exhibiting shear thinning and yield stress behavior, and most drilling fluids also exhibit thixotropy. Accurate modeling of drilling fluid rheology is necessary for predicting friction pressure losses in the wellbore while circulating, the pump pressure needed to resume circulation after a static period, and how the fluid rheology evolves with time while in static or near-static conditions. Although modeling the flow of thixotropic fluids in realistic geometries is still a formidable future challenge to be solved, considerable insights can still be gained by studying the viscometric flows of such fluids. We report a detailed rheological characterization of a water-based drilling fluid and an invert emulsion oilbased drilling fluid. The micro structure responsible for thixotropy is different in these fluids which results in different thixotropic responses. Measurements are primarily focused at transient responses to step changes in shear rate, but cover also steady state flow curves and stress overshoots during start-up of flow. We analyze the shear rate step change measurements using a structural kinetics thixotropy model

Autonomous Decision-Making While Drilling

The drilling process is complex because unexpected situations may occur at any time. Furthermore, the drilling system is extremely long and slender, therefore prone to vibrations and often being dominated by long transient periods. Adding the fact that measurements are not well distributed along the drilling system, with the majority of real-time measurements only available at the top side and having only access to very sparse data from downhole, the drilling process is poorly observed therefore making it difficult to use standard control methods. Therefore, to achieve completely autonomous drilling operations, it is necessary to utilize a method that is capable of estimating the internal state of the drilling system from parsimonious information while being able to make decisions that will keep the operation safe but effective. A solution enabling autonomous decision-making while drilling has been developed. It relies on an optimization of the time to reach the section total depth (TD). The estimated time to reach the section TD is decomposed into the effective time spent in conducting the drilling operation and the likely time lost to solve unexpected drilling events. This optimization problem is solved by using a Markov decision process method. Several example scenarios have been run in a virtual rig environment to test the validity of the concept. It is found that the system is capable to adapt itself to various drilling conditions, as for example being aggressive when the operation runs smoothly and the estimated uncertainty of the internal states is low, but also more cautious when the downhole drilling conditions deteriorate or when observations tend to indicate more erratic behavior, which is often observed prior to a drilling event

Connecting Multilayer Semantic Networks to Data Lakes: The Representation of Data Uncertainty and Quality

Drilling oil and gas wells is a complex process involving many disciplines and stakeholders. This process occurs in a context where some pieces of information are unknown, or are often incomplete, erroneous, or at least uncertain. Yet, during drilling engineering and construction of a well, drilling data quality and uncertainty are barely addressed in an auditable and scientific way. Currently, there are few or no placeholders in engineering and operational databases to document uncertainty and its propagation. The Society of Petroleum Engineers (SPE) has formed a cross-disciplinary technical subcommittee to investigate how to describe and propagate drilling data quality and uncertainty. The subcommittee is a cooperation between the drilling system automation, wellbore positioning, and drilling uncertainty prediction technical sections. As the topic is vast and complex, a systematic method was adopted, where multiple user stories or pain points were generated and ranked with the most compelling user story analyzed in detail. From this approach, a series of multidisciplinary workflows (drilling data generators) can now be captured and described in terms of data quality and propagation of uncertainty. The paper presents details of one user story focused on capturing the description of the quality and uncertainty of depth measurements. Multiple use cases have been extracted from this single user story exemplifying how multiple stakeholders and disciplines manage, communicate, and understand the notion of wellbore depth and its relative uncertainty. Current data stores have the main objective of recording the results of processes but have very limited capabilities to store how the interdisciplinary processes generated and cross-related these results. The study explores the use of semantic networks to capture those multidisciplinary data relationships. A minimum vocabulary has been created using just a few tens of concepts that has sufficient expressiveness to describe all the extracted use cases, showing that the semantic network method has the potential to describe a broad range of complex drilling-related processes. The study also demonstrates that use of a multilayered graph, employing other notions that do not expressly refer to the processes that generated the data, can capture the description of how uncertainty propagates between each of those concepts.Connecting Multilayer Semantic Networks to Data Lakes: The Representation of Data Uncertainty and QualitypublishedVersio