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
