A New Wellbore Position Calculation Method

Abstract

A method is described for combining multiple wellbore surveys to obtain a single composite, more accurate, well position. Established methods for defining the wellbore position, and its associated uncertainty, rely upon accepting the position obtained from the most accurate survey instrument used in each section of the wellbore. This position is then assigned an uncertainty based on the information from this single survey instrument run. Today, when a modern wellbore is constructed, each section may be surveyed for position many times using one or more magnetic, gyroscopic or inertial survey instruments. By statistically combining the wellbore positions obtained from all of the survey instruments run in a given section of the wellbore a new position, designated the ‘Most Accurate Position’ (MAP), is calculated. The main advantage of the MAP is that its uncertainty is smaller than the uncertainty of any of the constituent surveys. The major benefits of this technique will be to facilitate the drilling of smaller targets at greater distances, allow the drilling of new wellbores in closer proximity to existing wellbores while maintaining accepted safety clearance rules, and improved reservoir delineation. Describing Well Position The wellbore trajectory is defined as a series of surveyed points in three-dimensional space typically described in a North, East and Down reference system. These points are joined together to form a continuous trajectory using a geometrical calculation method1. Most magnetic or gyroscopic survey instruments in use today provide a survey point that is referenced to measured [or along hole] depth that is obtained from the driller's pipe tally, or from a wireline spooling measurement. The survey instrument provides inclination (hole angle) and azimuth (direction) measurements. When these parameters are used to calculate trajectory with an assigned survey depth, the horizontal displacement [or North and East coordinates] from the origin, and the vertical depth [or Down coordinate] from the elevation reference can be derived. Alternatively, some inertial survey instruments measure displacement in three-dimensional space from a known initialization point, and from which all of the above parameters [including depth] can be obtained to achieve the same purpose. Wellbore Position Uncertainty Wellbore survey requirements are typically driven by the need to guide the well to a geological target, to avoid other wells, to ensure that property boundaries are respected, and to record the position of the wellbore for future reference. In order to visualize and quantify our ability to hit a target or avoid colliding with another well, position uncertainty is assigned to wellbore trajectories. This position uncertainty represents our modeled knowledge of the collective errors arising from both the intrinsic performance limitations of the survey sensors and those induced by the operating environment2. This uncertainty is defined as a statistical confidence region with an associated confidence level. In three dimensions the confidence region is most often depicted as an ellipsoid3 because ellipsoids are the constant value contours of the three-dimensional Guassian probability density function. Such a confidence region is commonly referred to as an ‘Ellipsoid of Uncertainty’ (EOU). The EOU is used in target analysis, for example, by reducing the size of the geological target by the size of the EOU to define a drilling target. In this fashion, the geological target will be achieved if the wellbore penetrates the drilling target. Likewise EOUs are used to assess collision risk by considering the proximity of the EOUs from adjacent wells.

Optimization of Well Placement and/or Borehole Trajectory for Minimum Drilling Cost (A Critical Review of Field Case Studies)

“…By using Equations (5), (6) and (7), by equating Equations (4) and (8) with the denominator of Equation (4) being equal to 1 and by using the available data between two points, the coefficients in Equations (4) to (7) and the inclination and azimuth can be obtained. Such computations usually start from a reference point (say at the surface) where all the relevant data are known and the survey point after the reference point, where relevant data are not available.…”

“…Chia et al (7) developed a method, called the MAP -"most accurate position" technique, similar to that by Williamson (6) . The method entails statistical combination of surveys from several wellbore survey instruments to generate a single, composite, more accurate wellbore position.…”

“…For brevity, details of the technique are not provided here and can be found in reference 7. The main advantage the MAP technique is that "its uncertainty is smaller than that of the individual constituents surveys" (7) . By reducing positional uncertainty associated with survey trajectories, well can be drilled to geological targets more accurately and collision with another well can be easily be avoided.…”