This article provides a brief overview of the MWD STD approach to correcting BHA sag, but for more detailed information, please refer to this material.
For BHA sag correction, MWD STD Basic utilizes the method of energy minimization formulated in [1]. For a certain BHA design we define the energy function:
The energy function considers the gravity energy, bending energy, and WOB deflection energy:
Where x – high-side coordinate; z – along borehole coordinate; g – the Earth’s gravity; q – linear weight normalized for the inclination and the mud weight; EI – bending stiffness; dls – drillstring dogleg severity; θ – drillstring bending angle; wob – weight on bit.
Deflection of the drillstring x(z) is found within constrains (borehole wall, motor bend) with minimization of E(x, z) function by the coordinate descent method [2]. Unlike the Lubinski method [3], this method does not require assuming the contact points of the drillstring with the borehole walls, but calculates such points in the process of solving.
The results of the method were compared with the Lubinski method for a simple BHA (bit and drillpipe). Both methods demonstrated a high degree of agreement. Also, the method is consistent with commercial software for BHA modeling.
Additionally, the method was tested on experimentally collected data [4]: for a complexly deviated borehole drilled in cement blocks, the actual curvature was measured using a laser surveying system, which made it possible to obtain a true micro-profile of the borehole with high accuracy, then the borehole was re-measured by a BHA with an MWD tool, where measurements were subject to sag and misalignment. Further, the MWD tool data were corrected by the proposed method and compared with the true micro-profile. The results of the comparison are shown on the figure below:
1. Brands, S., et al., 2012, Scaled Tortuosity Index: Quantification of Borehole Undulations in terms of Hole Curvature, Clearance and Pipe Stiffness, IADC/SPE 151274
2. https://en.wikipedia.org/wiki/Coordinate_descent
3. Lubinski, A., Woods, H. B., 1953, Factors Affecting the Angle of Inclination and Dog-Legging in Rotary Bore Holes, API 222-150
4. Stockhausen, E., et al., 2012, Directional Drilling Tests in Concrete Blocks Yield Precise Measurements of Borehole Position and Quality, IADC/SPE 151248