Explicit Calculation of Expansion Factors for Collision Avoidance Between Two Coplanar Survey-Error Ellipses

Abstract

Summary The positional uncertainty about a point on a wellbore is commonly represented as an ellipsoid. The ellipsoid also accounts for the dimensions of the casing or open hole. With the use of this model, at any time the resulting uncertainty about a wellbore along its trajectory is a curved, continuous cone. To a good approximation, the intersection of the plane normal to a reference well with these cones can be represented as ellipses. This simple geometrical model has been adopted by standards organizations to define minimal acceptable separation distances between wellbores (e.g., the Norwegian NORSOK D-10 Standard and Oil and Gas UK Well Integrity Guidelines). Because of mathematical difficulties, the existing methods for calculating the resulting separation factors are only approximations and may be either too optimistic or too conservative, particularly for ellipses with high eccentricities. This paper presents explicit equations for determining the exact condition in which the ellipses touch, expressing the result as an expansion scale factor. Methods are presented for the expansion of either ellipse or both, together with implementation notes and other associated tools. The new algorithms are only marginally less efficient than the existing approximation methods, and they can be used to increase the allowable proximity of two adjacent wells while satisfying the geometrical and probabilistic constraints. The examples included in the paper illustrate this. The proposed calculation method is consistent with existing industry wellbore uncertainty models. Because the determination of the osculating condition is exact, the calculation is neither too optimistic nor too conservative. This paper is a response to discussions held at the SPE Wellbore Positioning Technical Section meeting on 3 November 2011.

The Scaling Ellipsoid Method to Calculate Wellbore Separation Factors

“…(3) Tactics to narrow the search range Because the basic equation sets, Equation (11) or Equation (12), are quadratic equation sets with three or four unknowns, the multi-solution phenomenon is likely a common question. Now, we take Equation ( 12) as an example.…”

“…It can be deduced that Equation ( 12) likely has one, two, or four solutions. Considering that no matter whether two zoomed error ellipsoids are external or interior contact, they all satisfy Equation (12). However, only the external contact condition satisfies the requirement of SEM; only the scaling factor to the external contact condition can be selected as SESF.…”

“…Based on the whole review of evaluation indexes of wellbore collision risks, it is known that the SF has more advantages and higher recognition degrees than the others. Totally considering the requirements of accuracy and complexity, ISCWSA has recommended three calculation methods for SF, including Center-Vector Method (CVM), Pedal-Curve Method (PCM), and Expansion Ellipse Method (EEM) [12] . However, all recommended methods still evaluate the separation degree of two error ellipsoids on some plane through two wellbore centers, not in 3D space [13][14][15] .…”

“…) have the unknown zoom factor m, it can be converted into a new quadratic equation set with three unknowns, the coordinates of tangent point Po The new equation set can be represented simply by Equation(12).…”

All-Attitude Gyro While Drilling Technology Provides Accurate Surveys in High Angle East/West Directional Wellbores Delivering Reduced Costs and Increasing the Length of the Producing Zone

“…A number of different survey options (MWD, continuous gyro and all-attitude GWD systems) were examined taking careful account of the expected survey accuracy and separation factors (Sawaryn et al, 2013) with respect to existing wells. The Operator's drilling policy stipulates that wells should not be drilled past a minimum 2.0 separation factor without senior management approval.…”