Investigation of Drill Bit Heave Response to Drill Rig Heave Excitation

Investigation of Drill Bit Heave Response to Drill Rig Heave Excitation Liqing Huang, Galin V. Tahchiev and Yusong Cao MARINTEK USA Inc 263 Augusta Drive, Suite 2, Houston, Texas, 7757, USA ABSTRACT Managing bottom hole pressures within acceptable limits when drilling from a floating drill rig has become one of the facing challenges for the Managed Pressure Drilling (MPD) in deep waters. When adding a new segment to the drill string, the drill string is set on the slips and the entire drill string moves vertically with the heave of the rig. This can cause high surge and swab pressures in the borehole and may lead to lost circulation of drilling fluid or an influx of formation fluid. The drill string is very long (up to several thousand meters) and is surrounded by the drilling fluid. In addition to the material properties of the drill string, the frictional drag along the string, as well as the reaction of the fluid to the motion of the drill bit at the borehole, will have significant influence on the vertical motion response of the drill bit to the heave of the drill rig. This paper presents an investigation on the vertical motion of the drill bit to the heave motion of the floating drill rig using a simplified elastic string model. The computer software RIFLEX and SIMO are employed in conducting the nonlinear dynamic response analysis of the drill string dynamic system and sensibility study of the important factors (parameters) on the response of the drill string. The drill bit heave Response Amplitude Operator (RAO) curves obtained would reveal the relation between the motion of the drill bit and the heave motion of the floating rig. KEY WORDS: Managed Pressure Drilling (MPD); surge and swab pressures; drill bit motion; floating drill rig; Finite Element Method (FEM); heave Response Amplitude Operator (RAO) curve; parametric study. INTRODUCTION Managed Pressure Drilling (MPD) and early kick detection applications have been successfully applied on many onshore and offshore drilling operations. In deepwater drilling and depleted reservoirs, one of the main limitations is the narrow margin between pore and fracture pressure gradients. MPD may be a solution to this but one of the challenges faced in offshore managed pressure drilling operations, especially when trying to hold constant bottom hole pressure, and also in early kick detection operations is the heave motion of the floating vessels. Maintaining constant bottom hole pressure or managing bottom hole pressure within acceptable limits when drilling from a floating rig (such as a semi-submersible rig) is more complicated due to the heave caused by ocean waves. During drilling and tripping mode the heave compensators located on these rigs control the altitude of the drill string. However, during connections, the drill string is set on the slips and the entire drill string moves vertically with the heave of the rig. This can cause high pressure surge and swab at the borehole, which will affect the bottom hole pressure and may in turn lead to lost circulation or an influx of formation fluid (Sensoy and Roy, 29; Syltøy, 28). The faster the drill string moves with the drill rig, the higher the surge and swab pressure will be (refer to APPENDIX). The motion of the drill string depends on the frequency and amplitude of the heave motion of the drill rig, the material properties of the drill string, the frictional drag along the string, the viscosity of the drill fluid, as well as the reaction of the fluid to the motion of the drill bit at the borehole. The heave caused by ocean waves that have an average time period of more than 5 seconds, creates surge/swab pressure in wellbore while the drill string is sitting on the slips (Grusso, 1972). Studies (Wagner et al., 1993) show that pulling the pipe with a velocity of.5 m/s creates swab effect of 15 3 psi (134 268 kpa) depending on the Bottom Hole Assembly (BHA), casing, and drilling fluid configuration. For example, pressure surge due to heave effects ranging between 75 15 psi (517 134 kpa) depending on the BHA and casing sizes has been observed in Kristin Deepwater Field in North Sea (Solvang et al., 28). Especially, harsh weather conditions in the North Sea amplify the heave effects on wellbore dynamics. The objective of this study is to conduct an investigation on the vertical motion of the drill bit to the heave motion of the floating drilling rig using a simplified model of a vertical drill string. The heave RAO curves of the drill bit obtained from the dynamic analysis of the drill string would provide the information on the relation between the motion of the drill bit and the heave motion of the floating rig. The motion information can then be used by the drilling contractors for more accurate determination of the surge and swab pressure due to the

heave motion of the rig, ultimately having a better control of maintaining the bottom hole pressure. SOFTWARE The nonlinear dynamic response analysis of the drill string is performed by using the commercially available computer software: RIFLEX, a time domain simulation program for static and dynamic analysis of slender marine structures, such as mooring lines, umbilicals, and also for steel pipelines and conventional risers; SIMO, a time domain simulation program for dynamic analysis of motions and stationkeeping behavior of complex systems of floating vessels and suspended loads. Coupled analysis (Stansberg, 1999) is performed following a procedure using the software above. Compared to traditional separated two-step global response analyses of floating structures, the coupled analysis introduces the total loads (dynamics included) from the slender body members (mooring lines/risers) as a force directly into the large body model of the floater in the time domain. The forces on the floater include (among others) frequency dependant 1st and 2nd order wave forces. In this way, the full interaction is taken into account, and accurate floater motions and dynamic loads in the mooring lines and risers are obtained simultaneously. NUMERICAL MODELING Modeling Assumptions For the present investigation of the drill bit motion, the whole drill string dynamic system is simplified as a vertical slender elastic rod with a lumped point mass (representing the BHA) attached to the bottom of the rod. The rod is subjected to a prescribed harmonic heave excitation at the top. The following assumptions and modeling are used (1) Vertical drilling is considered. The slightly curved drill string and well casing can be stretched to be vertically straight without introducing additional bending moments and torque, and the drill string initially stays at the central axis of the well casing without any pipe-inpipe contact; (2) The strengthening effect of the connecting joints of the drill string is small and can be neglected and the whole drill string can be simplified as a long homogeneous pipe with the same geometric shape and material properties; (3) The BHA at the bottom of the drill string can be simplified as a lumped point mass without the geometry shape. As the drill bit moves, the axial load on the drill bit due to the drilling fluid (mud) pressure change is applied; (4) The well casing can also be simplified to a homogeneous pipe with a relatively thicker pipe wall. The pipe is assumed to have the same material properties as the drill string; (5) The drill string and the well casing are assumed being totally submerged in the drilling fluid (mud), and the interior of the drill string is also filled with the drilling fluid; (6) The internal drilling fluid (mud) within the drill string is assumed to move with the same velocity/acceleration as the drill string, so that the internal fluid is modeled as additional mass attached to the drill string; horizontally, so that they are only allowed to move in the vertical direction; (8) The hydrodynamic force by the drill fluid on the drill string in the axial direction is assumed to be composed of two components, one is proportional to the square of the local vertical velocity of the string and the other one is proportional to the vertical acceleration. The hydrodynamic force can be expressed as, Fz ( s) Cd z 2 = ( s) + Ca z ( s) (1) where z ( s) is the vertical velocity of a point on the string at location s (distance from the top of the string) and z ( s) is the vertical acceleration of the point. Cd and Ca are referred as drag coefficient and added-mass coefficient, respectively. (9) The load on the drill bit by the fluid F can be decomposed and bz expressed as, Fbz = k( zb zbo ) Bb z b Ab z b (2) where zb is the vertical position of the drill bit and z bo is the vertical position of the drill bit at the static equilibrium. The first term represents the hydrostatic restoring force (to be further explained later), the second term is the damping force and the third term is the inertial force. k, B b and Ab are referred as the hydrostatic stiffness, damping, and added mass, respectively, for the drill bit. The assumptions above are only applied to the vertical drilling cases or close to vertical (slightly inclined) drilling cases. For curved drilling, some of the assumptions need to be lifted, and more sophisticated model has to be used. FEM Models Based on the assumptions above, three FEM models from the simplest to the most complicated (shown in Fig. 1) are introduced and compared in this study: (a) One vertical drill string with distributed buoyancy force, (b) One vertical drill string with concentrated buoyancy force at the bottom end, (c) One vertical drill string with pipe-in-pipe contact with the well casing and concentrated buoyancy force at the bottom end. MODEL (a) In MODEL (a), the whole drill string/ BHA system is totally submerged in the drilling fluid. The concept of weight in fluid (= weight in air the buoyancy) is used to account for the hydrostatic load on the string. MODEL (b) In MODEL (b), the load at the bottom of the drill bit due to the hydrostatic pressure is modeled as a concentrated force using a Global Spring or External Force. This force varies linearly with the depth of the drill bit. It acts like a linear spring providing a restoring force to the motion of the drill bit. Note that due to the modeling of the concentrated buoyancy force at the drill bit, the true weight (weight in air) rather than the weight in fluid should be used in the modeling of the whole drill string dynamic system. The schematic diagrams for the two methods are shown in Fig. 2. (7) Both ends of the drill string and the well casing are constrained

Modeling in air Depthdependent Pressure p = ρga (RIFLEX Default Buoyancy Model) df = pdz (RIFLEX/SIMO Coupling with External Functions) Concentrated Buoyancy Force, F B = ρgal Pipe-in-pipe Contact Concentrated Buoyancy Force, F B = ρgal Global spring force, F s k Equivalent system External force, F e MODEL (a) MODEL (b) MODEL (c) Fig. 1. Schematic diagrams of the three FEM models The restoring force (F s ) in the Global Spring is expressed as: Fs = k( z z ) F (3) s where z and z are the current depth and initial depth of the drill bit respectively, F s the initial force of the Global Spring. The External Force (F e ) is expressed as: F e = ρga( z z ) ρgaz (4) where ρ is the density of the drilling fluid (mud), g the acceleration of gravity, and A the cross-section area of the drill string including the mud inside. For the two equivalent systems, we have the spring stiffness (k) and initial force (F s ) for the Global Spring as follows: k = ρga (5) F s = ρgaz (6) Note that the hydrodynamic parameters for MODEL (b) modeled in air should be α times of those for MODEL (a) modeled in drilling fluid, and the specific ratio α is defined as: ρ α = (7) ρ air MODEL (c) In Model (c), the well casing is also modeled as one ideal pipe (slave pipe) outside the drill string (master pipe). The axial friction coefficient between the drill string and well casing is set to zero in order to have an equivalent model as the previous two simplified models. Thus, the well casing in MODEL (c) can only constrain the lateral motion of the drill string and has no effect on the heave motion of the drill string. Further, the FEM model (c) could be extended to include the swab and surge pressure model to conduct the dynamic-hydraulic coupled analysis under the real sea states. Fig. 2. Schematic diagrams of the two equivalent systems for MODEL (b) SIMPLIFIED EXAMPLE Sample Data The MPD design data and the drill string properties used for the present numerical study as listed in Table 1 and Table 2 are close to those of some practical vertical drilling well located in Norwegian North Sea. Static Analysis Table 1. MPD design data Activity: Water Depth: Bit Depth: Water Density: Air Density: Steel Density: Steel Elastic Modulus: Steel Shear Modulus: Drilling Fluid: Mud Density: Dynamic Viscosity: Kinematic Viscosity: Pump Pressure: Bit Pressure Loss: Bit Pressure: Flow Rate: Drill 8 1/2" MPD 19 m 5215.42 m 125 Kg/m^3 1.25 Kg/m^3 7874 Kg/m^3 2.1E+11 Pa 7.93E+1 Pa CsK Formate mud 182 Kg/m^3 7.E-3 Pa.s 3.846E-6 m^2/s 2.45E+7 Pa 9.972E+6 Pa 1.453E+7 Pa 2.13E-2 m^3/s In the static analysis, the distributed buoyancy force and effective tension along the length of the drill string are calculated at the static equilibrium state. Since the static results of the three equivalent models are the same, only MODEL (a) is shown in Fig. 3 for brevity.

Table 2. Drill string properties Drill Pipe: Outer Diameter: 127. mm Inner Diameter: 18.61 mm Thickness: 18.39 mm Equivalent Density: 13.483 Kg/m^3 Hydrodynamic Diameter: 127. mm BHA Total Mass: 7.65E+4 Kg Vertical Added Mass: 2.35E+3 Kg Vertical Drag Coefficient: 8.33E-2 KN/(m/s) 2 Hydrostatic Force: 6.64E+2 KN Global Spring Stiffness: 3.68E-1 KN/m Well Casing Outer Diameter: 716. mm Inner Diameter: 216. mm Thickness: 5. mm Equivalent Density: 8.865 Kg/m^3 Hydrodynamic Diameter: 716. mm 26 Static forces, line 1 After load step 2 EFF. TENSION minimum dynamic displacements. The RAO of the drill bit could further be calculated by dividing the average dynamic amplitude by the prescribed heave amplitude. Table 3 summaries the maximum, minimum and average values of heave amplitude and RAO of the drill bit. The RAO versus frequency curve of the drill bit is plotted in Fig. 7. Amplitude.3.2.1. -.1 Displ z-dir INODE 1 Displ z-dir INODE 1 -.3 1 2 3 4 5 6 7 8 9 1 Time Fig. 4. Prescribed harmonic heave excitation applied at the top end for MODEL (a) Effective tension [KN] 24 22 2 18 16 14 12 1 8 Amplitude.3.2.1. -.1 6 1 2 3 4 5 6 Line length [M] Fig. 3. Effective tension along line length at static equilibrium state for MODEL (a) -.3 1 2 3 4 5 6 7 8 9 1 Time Fig. 5. Dynamic displacement time history at drill bit for MODEL (a) Dynamic Analysis In the dynamic analysis, a prescribed harmonic heave excitation with amplitude of.2 m and frequency of.1 Hz (shown in Fig. 4) is applied to the top of the drill string/ BHA system. Fig. 5 shows the dynamic response time histories at the drill bit for MODEL (a). Time histories of the drill bit motion were obtained using MODEL (a) for various excitation frequencies ranging from.1hz to 1 Hz with the rig heave excitation amplitude fixed at.2m. The plots of the time histories are shown in Fig. 6. The analyses were performed using hydrodynamic parameters C a =.1 and C d =.1. The value of C a (added-mass coefficient along the axial direction) is chosen empirically based on the experimental results of circular cross-section riser and mooring line, for the cross-section of drill pipes are usually circular, they should have similar hydrodynamic parameters with circular crosssection riser and mooring line. The value of C d (drag coefficient along the axial direction) is randomly picked based on the following sensitive study of hydrodynamic parameters. Ignoring the initial transient response, the dynamic amplitude of the drill bit motion could be calculated by the average of the absolute values of the maximum and.1.8.6.4.2 -.2 -.4 -.6 -.8 ( A =.2 m; f = 1 Hz ) -.1 1 2 3 4 5 (a) f = 1 Hz

.3 ( A =.2 m; f =.5 Hz ).4.3 ( A =.2 m; f =.66667 Hz ).2.2.1 -.1.1 -.1 -.3 -.3.5.4.3.2.1 -.1 -.3 -.4 2 4 6 8 1 (b) f =.5 Hz ( A =.2 m; f =.2 Hz ) -.5 5 1 15 2 (c) f =.2 Hz -.4 -.5 1 2 3 4 5 6.3.2.1 -.1 -.3 (e) f =.66667 Hz ( A =.2 m; f =.5 Hz ) 1 2 3 4 5 6 7 8 (f) f =.5 Hz.8.6.4 ( A =.2 m; f =.1 Hz ).3.2 ( A =.2 m; f =.4 Hz ).2.1 -.1 -.4 -.6 -.8 5 1 15 2 25 3 35 4 (d) f =.1 Hz -.3 2 4 6 8 1 (g) f =.4 Hz

.3.2.1 -.1 -.3 ( A =.2 m; f =.33333 Hz ) 2 4 6 8 1 Table 3. Summary of nonlinear dynamic response analysis for MODEL (a) with hydrodynamic parameters C a =.1 and C d =.1 Case Amplitude Period Frequency Max Heave Min Heave Avg Amplitude RAO 1.2 1. 1..73436 -.7343.73434.367171 2.2 2..5.233537 3354.233537 1.167683 3.2 5..2.3599 -.3591.3599 1.529544 4.2 1..1.428997 -.429.428997 2.144986 5.2 15..67.266323 6633.266328 1.33164 6.2 2..5.234462 344.234429 1.172146 7.2 25..4.22892 283.22859 1.14296 8.2 3..33.214856 1521.21531 1.75154 9.2 5..2.28822 84.28612 1.4362 1.2 1..1.25784 425.2517 1.2586.25.2.15.1.5 -.5 -.1 -.15 (h) f =.33333 Hz ( A =.2 m; f =.2 Hz ) Fig. 7. RAO curve of drill bit for MODEL (a) with hydrodynamic parameters C a =.1 and C d =.1.25.2.15.1.5 -.5 -.1 -.15 2 4 6 8 1 (i) f =.2 Hz ( A =.2 m; f =.1 Hz ) 2 4 6 8 1 Table 4. The results summary of nonlinear dynamic response analysis for MODEL (b) with hydrodynamic parameters C a =.1 and C d =.1 Case Amplitude Period Frequency Max Heave Min Heave Avg Amplitude RAO 1.2 1. 1..24583.12581.71251.356256 2.2 2..5.267472 -.13517.21321 1.663 3.2 5..2.31431 9728.35793 1.528966 4.2 1..1.437225 -.4219.42879 2.143545 5.2 15..67.27468 5765.266167 1.33834 6.2 2..5.242854 2577.23431 1.17155 7.2 25..4.229177 129.22635 1.13174 8.2 3..33.22317 638.214745 1.73726 9.2 5..2.21733 -.19955.2829 1.41452 1.2 1..1.214332 -.1956.24964 1.24819 (j) f =.1 Hz Fig. 6. Dynamic displacement time histories at the drill bit for MODEL (a) with hydrodynamic parameters C a =.1 and C d =.1 The summary tables of the maximum, minimum and average values of heave amplitude and RAO of the drill bit for MODEL (b) and MODEL (c) are given in Table 4 and Table 5 respectively. The heave RAO versus frequency curves of the drill bit for MODEL (b) and MODEL (c) with hydrodynamic parameters C a =.1 and C d =.1 are plotted in Fig. 8 and Fig. 9 respectively. Fig. 8. RAO curve of drill bit for MODEL (b) with hydrodynamic parameters C a =.1 and C d =.1

Table 5. Summary of nonlinear dynamic response analysis for MODEL (c) with hydrodynamic parameters C a =.1 and C d =.1 Case Amplitude Period Frequency Max Heave Min Heave Avg Amplitude RAO 1.2 1. 1..86162.499181.181219.9697 2.2 2..5.968792.431438.268677 1.343383 3.2 5..2.314311 9728.35793 1.528966 4.2 1..1.437226 -.4219.42879 2.143544 5.2 15..67.27468 5765.266167 1.33834 6.2 2..5.242854 2577.23431 1.17155 7.2 25..4.229178 129.22635 1.13175 8.2 3..33.22317 638.214745 1.73726 9.2 5..2.21733 -.19955.2829 1.41452 1.2 1..1.214333 -.1956.24964 1.2482 Heave Peak RAO 2.2 2.1 2 1.9 Heave Peak RAO of Drill Bit ( C a =.1 ) INODE2711 1.8.2.4.6.8 1 C d Fig. 1. Effect of drag coefficient on the heave peak RAO for MODEL (a) with added-mass coefficient C a =.1 Heave excitation amplitude effect Fig. 9. RAO curve of drill bit for MODEL (c) with hydrodynamic parameters C a =.1 and C d =.1 Sensitivity Study Hydrodynamic parameter effect In order to investigate the effect of the hydrodynamic parameter on the RAO curves, the hydrodynamic coefficients for MODEL (a) are varied while fixing the heave excitation amplitude and frequency at the top of the drill string. It is known that the added mass coefficient can greatly affect the heave peak frequency, while the drag coefficient has more effect on the heave peak RAO value. Since the drag force is proportional to the square of velocity, the effect of drag coefficient is important to be investigated here. Table 6 shows the heave peak RAO value changes with the varying drag coefficient for the 7 cases. As seen in Table 6 and Fig. 1, the heave peak RAO value decreases from 2.15 to 1.84 as C d increasing from.5 to 1., which indicates that the drag coefficient plays a significant role in determining the heave peak RAO. Table 6. Summary of the effects of the drag coefficient for MODEL (a) Case Amplitude Period Freq. Ca Cd Max Heave Min Heave Avg Amplitude Peak RAO 1.2 1..1.1.5.429987 -.43.429992 2.14996 2.2 1..1.1.1.428997 -.429.428997 2.144986 3.2 1..1.1.2.425954 -.42595.425954 2.129772 4.2 1..1.1.3.42825 -.4283.42826 2.14128 5.2 1..1.1.4.414738 -.41474.414738 2.73691 6.2 1..1.1.5.47643 -.4764.47644 2.38218 7.2 1..1.1 1..368655 -.36866.368655 1.843277 In order to investigate the effect of the heave excitation amplitude on the RAO curves, the heave excitation amplitude at the top of the drill string for MODEL (a) is varied from.1 m to 5. m while fixing all the other parameters. Table 7 shows the peak RAO values changes with the varying heave excitation amplitude for the 18 cases. Fig. 11 indicates that the peak RAO value decreases slowly from 2.15 to 1.42 with the increasing of the heave excitation amplitude from.1 m to 5. m, showing a strong nonlinearity of the system. CONCLUSIONS / DISCUSSIONS In this preliminary study, a simplified analytical method is introduced to investigate the heave response of the drill bit to the drill rig heave excitation. In the numerical modeling, three FEM models are built to conduct the nonlinear dynamic response analysis of the drill string dynamic system; the sensitivity studies of some key parameters are also conducted to obtain a series of the heave RAO curves of the drill bit. As a result, several conclusions could be reached as follows: Table 7. Summary of heave excitation amplitude effect for MODEL (a) with hydrodynamic parameters C a =.1 and C d =.1 Case Amplitude Period Freq. Max Heave Min Heave Avg Amplitude Peak RAO 1.1 1..1.214993 15.214995 2.149953 2.2 1..1.428997 -.429.428997 2.144986 3.3 1..1.641585 -.64159.641586 2.138619 4.4 1..1.851891 -.85189.851892 2.12973 5.5 1..1 1.5939-1.594 1.5939 2.11879 6.6 1..1 1.26244-1.26241 1.26245 2.148 7.7 1..1 1.462913-1.46291 1.462913 2.89875 8.8 1..1 1.658811-1.65881 1.658811 2.73514 9.9 1..1 1.849855-1.84986 1.849855 2.55395 1 1. 1..1 2.37944-2.3795 2.37945 2.37945 11 1.5 1..1 2.99868-2.9987 2.99868 1.939912 12 2. 1..1 3.685364-3.68537 3.685364 1.842682 13 2.5 1..1 4.3826-4.3826 4.3826 1.75214 14 3. 1..1 5.12313-5.1231 5.12313 1.67771 15 3.5 1..1 5.59272-5.59272 5.592721 1.59792 16 4. 1..1 6.12938-6.1294 6.12939 1.53226 17 4.5 1..1 6.629865-6.62987 6.629866 1.47333 18 5. 1..1 7.1397-7.1397 7.1397 1.42794

Heave Peak RAO 2.2 2 1.8 1.6 Fig. 11. Effect of heave excitation amplitude on the heave peak RAO for MODEL (a) with hydrodynamic parameters C a =.1 and C d =.1 (a)the nonlinear dynamic response results obtained from the three FEM models using the simplified method are quite close to each other, which indicates that the distributed buoyancy model is accurate enough to predict the dynamic responses of the concentrated buoyancy model which has more physical meanings than the former. (b) The drag coefficient of the drill pipe plays a significant role in determining the nonlinear dynamic response of the drill bit s heave motion to the drill rig s heave motion. Besides, the drill string dynamic system shows strong nonlinearity in the relationship between the drill rig s motion excitation and the drill bit s motion response. The effect of the damping and added mass of the drill bit on the dynamic response of the drill bit remains to be examined. In the future work, a sensitivity study should be performed. The drag coefficients and added-mass coefficients of the drill string, as well as the damping and added mass of the drill bit, should be calibrated based on the available test data to provide more accurate estimation of the drill bit s heave response. Additionally, the modeling should be extended for analysis of curved drilling with centralizers inserted to analyze and assess the real drilling operations. ACKNOWLEDGEMENTS The authors sincerely thank Knut Steinar Bjørkevoll, senior scientist in SINTEF Petroleum Research for providing the design data of the example drill string and helping to build the numerical models. REFERENCES Heave Peak RAO of Drill Bit ( f =.1 Hz ) INODE2711 1.4 1 2 3 4 5 Heave Excitation Grusso, J.A. (1972). An Analysis of Well Kicks on Off Shore Floating Drilling Vessels, SPE Conference Paper No. 4134. Kelly, M. Swab/Surge Pressures. http://infohost.nmt.edu/~petro/ faculty/kelly/swab.pdf Sensoy, T. and Roy, A. (29). Surge and Swab Effects due to the Heave Motion of Floating Rigs. Draft report of Weatherford International LTD, pp 1-3. Solvang, S.A., et al. (28). Evaluation Managed Pressure Drilling Resolves Pressure Depletion Related Problems in the Development of HPHT Kristin Field. SPE/IADC Conference Paper No. 113672, January 28. Stansberg, C.T. (1999). VERIDEEP, Act. 2.1, Practical Procedure for Coupled Analysis of Floating Offshore Structures. MARINTEK (NORWAY) Report No. 5139.41.2, June 1999. Syltøy, S., et al. (28). Highly Advanced Multi-Technical MPD Concept Extends Achievable HPHT Targets in the North Sea, SPE Conference Paper No. 114484, January 28. Wagner, R.R., Halal, A.S. and Goodman, M.A. (1993). Surge Field Tests Highlight Dynamic Fluid Response. SPE/IADC Conference Paper No. 25771, February 1993. APPENDIX Swab/Surge Pressures (Kelly, 28) The movement of the drill string when pulling out of the borehole causes the pressure decrease on the bottom of the borehole due to the friction between the movement of the pipe and the stationary drilling mud. This is referred to as swab pressure, P swab. The reverse is also true, running in the borehole the pressure will increase due to the pipe movement, this is called surge pressure, P surge. The swab and surge pressure need to be control so the well does not form a kick or break down the formation. For a Newtonian fluid, the friction gradient caused by the pipe movement using the slot flow approach to laminar flow can be derived µ ( va.5v p ) Pfsp = (a) 1( dh d p ) where µ is the dynamic viscosity of the drilling fluid, v a the flow velocity of drilling fluid in the annulus of pipe, v p the velocity of drill pipe in the hole, dh and d p the diameters of the hole and the drill pipe. For the closed end pipe, the flow rate in the annulus is equal to the rate of the fluid being displaced by the pipe 2 πd p v p Qa = (b) 4 2 d pvp va = (c) 2 2 dh d p Substituting Eq. (c) into Eq. (a), we have 2 d p µ v p.5 2 2 dh d p P fsp = (d) 1( dh d p ) Thus, for a specific drilling operation ( dh and d p are fixed), the friction gradient is only depending on the dynamic viscosity of the drilling fluid and the velocity of drill pipe in the hole. As long as the dynamic motion of the drill string is known, the swab and surge pressure can be accurately determined.