Abnormal surface torque and hook load values are symptoms of downhole drilling condition deterioration which can result in unexpected situations. Usually, friction tests are performed at regular intervals and rig personnel uses these measurements to monitor trend variations in order to detect possible risk of poor hole cleaning or increased borehole tortuousity. The quality of the detection can vary greatly in function of the work load and experience of the drilling staff. The availability of real-time measurements through data servers make it possible to automate and systemize the monitoring process and therefore trigger alarms before drilling problems really occurs. This paper presents a computer system used to systematically analyse real-time data in order to monitor downhole conditions. Such a system can utilize much more data than just the above mentioned friction tests, because mechanical, hydraulic and temperature models can calculate predicted hook load and surface torque in any drilling conditions. The numerical models are automatically calibrated (adjustment of drill-pipe linear weight, factors for mechanical and hydraulic friction and heat generation). The evolution of proper calibration factors is used to detect poor downhole conditions. Automatically generated messages are sent to key personnel who can evaluate the potential problems and take necessary actions. To validate this new methodology, the system has been run on recorded data from three wells on an oil field in the North Sea. A data filtering technique has been developed and applied to solve problems with noisy and erratic real-time signals. With correct input parameters, the system has clearly indicated unexpected measurements several hours before a pack-off problem occurred and therefore proven that the methodology could help in detecting the worsening of downhole drilling conditions. Availability of large amount of real-time data at the rig site or in onshore drilling centres does not necessarily facilitate the recognition of drilling problems. However, online interpretation systems, as the one described above, can systematically analyze the logged data to detect as early as possible the deterioration of hole conditions during drilling operations and corrective actions can be taken before any major problem has really occurred. Introduction Deterioration of downhole conditions during drilling operations can be detected using the hook load and surface torque measurements. Typically, poor hole cleaning, wellbore tortuousity (due to micro-doglegs or larger directional deviation from the planned well path), wellbore instability, formation extrusion, under-gauge hole or junk in hole will have impact on the measured surface torque and hook load. On one hand, poor hole cleaning can result in stuck pipe or indirectly to formation fracturing (due to the increase of downhole pressure in the annulus). On the other hand, increased torque/drag values can hinder reaching the final depth of the well, cause drill-string failure, or prevent from running in the casing/liner string or the tubing string. Therefore it is desirable to monitor those parameters to get an early warning of possible hole condition deterioration.

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The Lehmer-Euclid Algorithm is an improvement of the Euclid Algorithm when applied to large integers. The original Lehmer-Euclid Algorithm replaces divisions on multi-precision integers by divisions on single-precision integers. Here we study a slightly different algorithm that replaces computations on n-bit integers by computations on µn-bit integers. This algorithm depends on the truncation degree µ ∈]0, 1[ and is denoted as the LE µ algorithm. The original Lehmer-Euclid Algorithm can be viewed as the limit of the LE µ algorithms for µ → 0. We provide here a precise analysis of the LE µ algorithm. For this purpose, we are led to study what we call the Interrupted Euclid Algorithm. This algorithm depends on some parameter α ∈ [0, 1] and is denoted by E α . When running with an input (a, b), it performs the same steps as the usual Euclid Algorithm, but it stops as soon as the current integer is smaller than a α , so that E 0 is the classical Euclid Algorithm. We obtain a very precise analysis of the algorithm E α , and describe the behaviour of main parameters (number of iterations, bit complexity) as a function of parameter α. Since the Lehmer-Euclid Algorithm LE µ when running on n-bit integers can be viewed as a sequence of executions of the Interrupted Euclid Algorithm E 1/2 on µn-bit integers, we then come back to the analysis of the LE µ algorithm and obtain our results. B. Daireaux and B. Valléedivision algorithm which is about twice as slow as Karatsuba multiplication -in most of the cases, since there is a small probability of failure.A significant improvement in the speed of the Euclid Algorithm when high-precision numbers are involved can be achieved with the so-called Lehmer-Euclid Algorithm, which uses a method due to Lehmer [18]. Working only with the leading digits of large integers, it is possible to simulate most of the multiple-precision divisions by single-precision divisions, which leads to a significant speed-up of the algorithm. The first version of this algorithm appeared in [18]; then some variants were described in Knuth [16], and finally Collins [7] and Jebelean [14] provided various improvements to the algorithm. Nowadays, most of computer algebra systems and multi-precision libraries use many of these variants. However, there exist very few analyses of the Lehmer-Euclid Algorithm. Sorenson [23] obtained a worst-case analysis of this algorithm, but, to the best of our knowledge, there does not exist any precise average-case analysis of the Lehmer-Euclid Algorithm. It is the purpose of this paper to provide such an analysis. Main resultsThe original Lehmer-Euclid Algorithm replaces divisions on multi-precision integers by divisions on single-precision integers (sometimes double precision is used). Here, we study a slightly different algorithm that replaces computations on n-bit integers by computations on µn-bit integers. This algorithm depends on the truncation degree µ ∈]0, 1[ and is denoted as the LE µ algorithm. This Lehmer-Euclid Algorithm can be viewed as a sequence of executions o...

Summary During drilling operations, downhole conditions may deteriorate and lead to unexpected situations that can result in significant delays. In most cases, warning signs of the deterioration can be observed in advance, and by taking proactive actions, drillers can avoid serious incidents such as packoffs or stuck pipes. A new analysis methodology, relying on an automatic real-time computer system, has been developed to detect those early indicator conditions. The methodology involves constantly computing the various physical forces acting inside the well (mechanical, hydraulic, and thermodynamic). These physical forces are coupled by an automatic model calibration, which then gives a reliable picture of the expected well behavior. Through analysis of the deviations between modeled and measured values, an estimation of the current state of the well is derived in real time. Changes in the well condition are an early warning of deteriorating well conditions. This paper precisely describes the real-time analysis and the results during some drilling operations. The software has been used for monitoring 15 unique wells located in five different North Sea fields. All major situations were signaled in advance at different event time scales: Rapidly changing downhole conditions (such as pulling a drillstring into a cuttings bed) were typically detected 30 minutes ahead of the actual event, medium-duration deteriorations were detected up to 6 hours before the incident, and slow-changing downhole conditions were signaled up to 1 day in advance. Several examples that illustrate the detected incidents over distinct time periods are described. The availability of good-quality real-time data streams makes it possible to implement such analysis tools in an integrated operation setup. Early symptom detection can be used to make decisions in a timely fashion, on the basis of quantitative performance indicators rather than subjective feelings and personal experience.

Newly developed drilling automation systems locate a computer interface between commands issued by the driller and instructions transmitted to the drilling machinery. Such functions are capable of faster and more precise control than can be achieved by an unaided operator and thus can help drilling within narrow margins. To ensure that these systems work properly in all circumstances, an advanced drilling simulator has been developed to enable testing under a wide range of simulated conditions.The environment described in this paper uses hardware in the loop (HIL) simulation to verify that the automation techniques being tested respond correctly in real time. Rigorously validated physical models of the drilling process simulate the response of the well to the commands given to the drilling machines. Abnormal drilling conditions (e.g., packoffs, kicks) and equipment or machine-related problems (e.g., plugged nozzles, power shortage) are convincingly recreated.The drilling simulator models the behavior of surface equipment such as the activation of gate valves to line up different pits or the flow in the mud return. It simulates changes in the drilling fluid properties when mixing additives to the mud. It is therefore possible to focus training sessions on cooperation between different groups at the wellsite. This is particularly useful when planning the introduction of drilling automation that involves new work procedures as a result of automation and adaptation of the drilling team to a new operational environment.Drilling operations are becoming more and more complex. Automation has the potential to provide large improvements in efficiency and safety, but automation technologies must be implemented correctly at the workplace. Just as the aviation industry has used simulated environments for decades, drilling simulation environments are the key to the safe and successful implementation of drilling automation and the development of crew skills to face future challenges.