Instrument Performance Models and Their Application to Directional Surveying Operations

Abstract

Summary. When planning, monitoring, or checking the results from a directional surveying program, one must be able to predict the probable errors associated with the different survey tools used. An "instrument performance model" is a mathematical algorithm that, when combined with a set of independently validated parameters describing the particular survey instrument in question and information about the well, enables the directional uncertainty to be computed at any point in a survey run. Randomization caused by axial rotation of the tool significantly affects the size of the predicted errors. The analysis accounts for rotation and incorporates a new depth-measurement-error treatment. Performance models have many practical uses in survey operations management and wellsite quality control. They enable research to be focused accurately and objective comparisons to be made between different instruments. Introduction The main difficulty for drilling engineers concerned with running a directional survey program has been the lack of literature describing a coherent structure that brings together instrument selection, operations planning, data analysis, and performance modeling into a single discipline that can be routinely applied to all wells. Thorogood introduced one approach to the problem of specifying and implementing well surveys. Within that framework, the service contractor is responsible for calibrating, maintaining, and operating survey tools to a level of accuracy and reliability defined by an instrument performance specification. The operator of a well is responsible for creating an environment in which successful surveys can be run. Therefore, the operator must monitor the performances of contractors carefully and control other factors that may performances of contractors carefully and control other factors that may significantly affect survey accuracy and instrument reliability. At each step in the process of managing an operation, it is necessary to be able to predict the behavior of the instruments and to quantify the possible errors resulting from their use. These ends can be achieved with instrument performance models. This paper shows how such models can be constructed and demonstrates their application to directional-surveying-operations management. A new method for the treatment of depth-measurement errors based on Wolff and de Wardt'S work is proposed, and the analysis is extended to consider errors that vary randomly between stations. Error-Analysis Background Analytic methods to quantify survey errors were originally developed by Waistrom et al. in the late 1960's and early 1970's. Their model is based on the assumption that errors vary randomly between stations throughout a survey. Errors predicted with this approach are far smaller than differences observed between surveys. Wolff and de Wardt postulated that although measurement errors may vary randomly between surveys, they tend to be systematic within a survey. Predictions made with their method were found to be more consistent with field experience than those calculated by the Waistrom method. In 1981, Warren analyzed survey errors resulting from measurements taken during a relief-well drilling operation. He presented a new method for extracting the random and systematic errors presented a new method for extracting the random and systematic errors from survey results, confirmed that both systematic and random errors occurred in the data sets, and showed that the systematic errors caused much larger positional errors than the random errors. Most survey tools in routine use during the development of the Wolff-de Wardt method were photomechanical devices comprising noninertial-grade sensors. Errors caused by the instrument could typically be on the order of several tenths of a degree of inclination and several degrees of azimuth. Errors resulting from external effects (such as axial misalignment of running gear, deflections of the drilling assembly, or uncertainty in the reference direction) could not easily be distinguished from those associated with the directional sensors. For these systems, Wolff and de Wardt's simple empirical formulations were quite appropriate. The new generation of inertial-grade gyroscopic and solid-state magnetic sensors, however, is capable of resolving direction to the order of 0.05 degrees of inclination and 0.1 degrees of azimuth. The same general external error-producing mech-anisms still apply and have a much greater impact on the overall performance of the surveying system. Consequently, a more rigorous approach is required to quantify both the external effects and the error characteristics of the new high- accuracy gyroscopic systems and solid-state magnetic devices. Stephensons analyzed sensor systems and showed how their performance is a function of not only borehole deviation but also performance is a function of not only borehole deviation but also geographical location. Formulation of the performance modeldescribed below enables these dependencies to be considered explicitly. Their complexity should not be a deterrent to their use because of the wide availability of computer systems. Instrument Performance Models An instrument performance model is a mathematical description of the error sources specific to a particular survey instrument. The model enables one to calculate the measurement uncertainty for an instrument under specific downhole conditions. In computer terms, an instrument performance model is a subroutine that presents a standard interface to a range of applications. This idea is illustrated in Fig. 1. The concept of a standard interface is very important because, by decoupling the instrument performance description from its end use, the model can be derived, performance description from its end use, the model can be derived, maintained, modified, or extended independently of the main code within which it is embedded. Incorporation of instrument-specific terms directly into the mathematics for error propagation is a significant practical shortcoming of the Wolff-de Wardt analysis. practical shortcoming of the Wolff-de Wardt analysis. To compute values of measurement uncertainty, an instrument performance model requires two sets of data: a list of parameters performance model requires two sets of data: a list of parameters to calibrate the model and specific details of the well at the point of the measurement. The parameter list is a set of constants that describes the magnitude of the different error sources applicable to the particular survey. Representative values of parameters are given for a typical attitude-referencing gyroscopic system (Table 1) and for a magnetic measurement-while-drilling (MWD) device (Table 2). The parameters may vary according to how the tool is run. Consider, parameters may vary according to how the tool is run. Consider, for example, geomagnetic uncertainty and drillstring magnetic interference. Where the geomagnetic field is known accurately from direct on-site measurement, drillstring interference-compensation methods can be applied validly. Under these conditions, performance levels approaching those of gyroscopic survey tools can be obtained from magnetic instruments. SPEDE P. 294