An Improved Method for Calculating Swab and Surge Pressures and Circulating Pressures in a Drilling Well
Authors: Fontenot John E. , Clark R.K. 
Published: December 2007

Abstract
Shortcomings were found in the published techniques for calculating down-hole pressures in a drilling well. An improved method was developed that predicts down-hole pressures in good agreement with those measured in two weighted muds. The new method allows drilling fluid properties to vary with depth and has demonstrated the importance of properly modeling the drilling fluid properties in properly modeling the drilling fluid properties in calculating down-hole pressure changes.

Introduction
Controlling down-hole pressure during drilling is an essential part of well control. Circulating pressures connected with pump operation are usually pressures connected with pump operation are usually calculated using nomographs, slide rules, or simple computer programs. Bottom-hole pressure changes due to drillstring movement (swab/surge pressures) have been described by Clark, Burkhardt, and Moore. These pressure changes are generally calculated using approximate methods developed by Burkhardt (Bingham model) or Schuh (power-law model). The drilling fluid properties are generally assumed to be constant from the top to the bottom of the hole. In applying the conventional methods of calculating down-hole pressures to actual well situations, various shortcomings in the techniques were noted. To overcome these and to obtain as accurate a simulation as possible, a comprehensive theoretical technique using fundamental equations was developed and programmed for computer solution. Downhole pressures were measured in two wells to verify the accuracy of the new program and to provide insight into its shortcomings.

CALCULATION OF PRESSURES
To develop a comprehensive and general approach to calculating down-hole pressures it was decided to consider both the Bingham and the power-law models for the fluids. The works of Burkhardt, Melrose et al. and Dodge and Metzner were used to develop equations for the Bingham model. The equations for the power-law model were developed from the work of Schuh and Dodge and Metzner. In the Appendix we develop and discuss the equations as well as shortcomings found in the work of Burkhardt and Schuh. Equations are provided for the calculation of circulating and provided for the calculation of circulating and swab/surge pressures for both the Bingham and power-law models. This provides a means of power-law models. This provides a means of calculating the downhole pressures under two assumptions. In many cases the results obtained from the two models are in good agreement. The equations in the Appendix were programmed for computer solution. Complex well geometries can be investigated, as the program can handle as many as 10 sections of different geometry, where each section has a uniform description. If required, the maximum number of sections can be increased by minor modifications to the program. The effects of tool joints, drillpipe rubbers, and bit nozzles are included in the calculations. Mud properties are entered as the Bingham-plastic parameters, plastic viscosity and yield point. In parameters, plastic viscosity and yield point. In the power-law portion of the program, the Bingham parameters are converted to power-law constants. parameters are converted to power-law constants. Mud properties are allowed to vary with depth by specifying different fluid properties for each section. This is normally accomplished by allowing the mud properties corresponding to the temperature and pressure at the midpoint of the section to be representative of the whole section. If only surface properties are known, they can be used throughout properties are known, they can be used throughout the well, although pressure predictions will generally not be so accurate. In addition, mud properties can be different inside the pipe and in properties can be different inside the pipe and in the annulus. The program can be used to calculate circulating pressure losses and swab/surge pressures in the pressure losses and swab/surge pressures in the wellbore. If mud flow rates are entered, circulating pressures losses are calculated. If pipe speeds pressures losses are calculated. If pipe speeds are entered, swab/surge pressures are calculated.
SPEJ
P. 451