# Arch. Min. Sci., Vol. 52 (2007), No 4, p. 457–481

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Arch. Min. Sci., Vol. 52 (2007), No 4, p. 457–481

. Arch. Min. Sci., Vol. 52 (2007), No 4, p. 457–481 457 HERNAN DIAZ*, MENGJIAO YU*, STEFAN MISKA*, NICHOLAS TAKACH* MODELING OF ECD IN CASING DRILLING OPERATIONS AND COMPARISON WITH EXPERIMENTAL AND FIELD DATA MODELOWANIE ECD W WIERCENIU Z RÓWNOCZESNYM RUROWANIEM WRAZ Z PORÓWNANIEM DANYCH EKSPERYMENTALNYCH I TERENOWYCH Three modeling approaches to the determination of equivalent circulating density (ECD) in Casing Drilling1 operations are considered in this study; viz., hook-load measurements, pump-pressure measurements and conventional hydraulic models. The bottom-hole pressure is obtained by adding the calculated annular pressure losses to the hydrostatic pressure. Since the annular clearance is very small in casing drilling, a narrow-slot flow approximation model is adopted that takes into account the effect of pipe rotation. A Yield-Power-Law (YPL) drilling fluid is considered in this study. Results from each of the three approaches are compared with experimental and field data. The differences between the calculated and measured bottom-hole pressures (hence ECD) are within a range of about ±8%. In terms of the frictional pressure losses in the annulus, this range increases to about ±60% in some instances. It is shown that pipe rotation plays an important role in determining ECD. The experimental data indicate an increase in the annular pressure losses with increasing pipe rotary speed. The hook-load measurements correlate well with flowing bottom-hole pressures. Keywords: ECD, Casing Drilling, Modeling, Field Data W artykule rozważono trzy podejścia do modelowań wykonywanych w celu określenia ekwiwalentnej gęstości cyrkulacyjnej (ECD) w operacjach wiercenia z równoczesnym rurowaniem1; poprzez pomiary obciążenia haka, pomiary ciśnienia pomp oraz zastosowanie konwencjonalnych modeli hydraulicznych. Ciśnienie na dnie otworu otrzymywane jest przez dodanie obliczonych strat ciśnienia w przestrzeni pierścieniowej do ciśnienia hydrostatycznego. W przypadku rur okładzinowych wielkość przestrzeni pierścieniowej jest bardzo niewielka, dlatego zaadaptowano model wąskiej szczeliny, uwzględniający efekt rotacji rur. W artykule rozważano płuczkę opisywaną modelem reologicznym Herschela Bulkleya (YPL). Wyniki zastosowania wymienionych trzech podejść zostały porównane z danymi doświadczalnymi i terenowymi. Różnice pomiędzy wartościami ciśnienia obliczonego i zmierzonego na dnie otworu (a więc * THE UNIVERSITY OF TULSA, TULSA, OK 74104-3189, USA 1 Casing Drilling is a registered trademark of Tesco Corp. 458 i ekwiwalentnej gęstości cyrkulacyjnej) pozostają na poziomie ok. ±8%. W przypadku strat ciśnienia w przestrzeni pierścieniowej w niektórych przypadkach wartość ta ulega zwiększeniu do ok. ±60% Zwrócono uwagę, że rotacja rur odgrywa dużą rolę w określaniu ekwiwalentnej gęstości cyrkulacji. Dane doświadczalne wskazują na wzrost strat ciśnienia w przestrzeni pierścieniowej wraz z rosnącą prędkością obrotową rur. Uzyskano dobrą korelację między pomiarami obciążenia haka i ciśnienia przepływu na dnie otworu. Słowa kluczowe: ECD, wiercenie z równoczesnym rurowaniem, modelowanie, dane terenowe Nomenclature A − annular area, L2, in2 Ai − area of casing based on internal diameter, L2, in2 An − area of drill bit nozzles, L2, in2 Ao − area of casing base on outside diameter, L2, in2 Cv − in situ cuttings concentration, dimensionless D − depth, L, ft Deff − generalized “effective” diameter, L, in Dh − wellbore diameter, L, in Dhy − Do-Di, hydraulic diameter, L, in Di, Di1, Di2 − casing internal diameter, L, in Do − casing O.D., L, in Fb − force due to buoyancy, mL/t2, lbf Fbit − jetting force, mL/t2, lbf Fd − drag force, mL/t2, lbf − hook load, mL/t2, lbf Fh Fp − force due to piston effect, mL/t2, lbf f − friction factor without pipe rotation, dimensionless f’ − friction factor with pipe rotation, dimensionless fh − friction factor at the borehole wall, dimensionless fo − friction factor at the casing wall, dimensionless g − acceleration due to gravity, L/t2, 9.81 m/s2 K − Consistency index, mtm–2/L, lbf sm/ft2 Lj − section casing length, L, ft m − flow behavior index of Yield Power Law model, dimensionless N − Generalized flow behavior index, dimensionless NRe − Reynolds number, dimensionless Ph − hydrostatic pressure, m/Lt2, psi Q − flow rate, L3/t, gal/min ReYPL − Reynolds Number for Yeild-Power-Law fluids, dimensionless ri − casing radius, L, in rpm − casing rotary speed, rev./min 459 u − mean tangential velocity, L/t, ft/s vsp − superficial cuttings velocity, L/t, ft/s vslip − slip velocity, L/t, ft/s − mixture velocity, L/t, ft/s vm v − mean axial velocity, L/t, ft/s Wc − casing weight in the air, mL/t2, lbf Wj − unit weight of casing, m/t2, lbs/ft wob − weight on bit, mL/t2, lbf (∆P)ω=0 − pressure drop without pipe rotation, m/Lt2, psi (∆P)ω − pressure drop with pipe rotation, m/Lt2, psi (∆P)bit − pressure drop through the bit, m/Lt2, psi ∆Pfa, ∆Pa − frictional pressure losses, m/Lt2, psi æ wr æ a = arctan ç i ç è 2v è γw − shear rate, t–1, s–1 η − apparent viscosity, m/Lt, cp µ − viscosity, m/Lt, cp π − 3.14159… − equivalent density due to frictional pressure losses, m/L3, lbm/gal ρfa ρι − density inside casing, m/L3, lbm/gal ρ1 − mud density, m/L3, lbm/gal ρmh − mixture density, m/L3, lbm/gal ρο − density outside casing, m/L3, lbm/gal ρp − cuttings density, m/L3, lbm/gal τi − wall shear stress in pipe, m/Lt2, psi τo − average wall shear stress in annulus, m/Lt2, psi − wall shear stress, m/Lt2, psi τw τy − yield stress, m/Lt2, psi ω − angular velocity, rad/s 1. Introduction Casing drilling uses a casing string to drill, evaluate and case a well simultaneously. This technology bypasses some time-consuming steps of conventional drilling that may take up to 35% of the total time to drill a well (Tessari, 1999; Tarr, 1999). It has been estimated that casing drilling has the potential to reduce the costs of conventional rotary drilling by approximately 15% (Tarr, 1999). The well geometry in casing drilling is a major difference from conventional drilling. The ratio of hole to pipe diameter is close to unity. The internal diameter of a casing is 460 large so that there is relatively little pressure loss inside the casing. However, the casing drilling annulus provides more restricted flow so that higher than normal pressure losses are encountered. Analogies can be drawn to slim-hole hydraulics. It is well documented (Tao, 1954; DiPrima, 1960; Ustimenko, 1964; Cartalos, 1993; Haciislamoglu, 1994; Hansen, 1999; McCann, 1993) that the narrow clearance between drill pipe and the wellbore plays an important role in determining the frictional pressure losses in slimhole drilling. The determination of the flowing bottom hole pressure (hence ECD), during drilling operations, is an important task of the drilling engineer. In most casing drilling situations the ECD will be higher than the ECD in conventional drilling, even though a lower flow rate may be used. ECD is determined using the following equation: ECD = Ph + D Pfa Dg = rmh + rfa (1) The hydrostatic pressure is determined by the average density of mud and cuttings in the annulus. The frictional pressure losses depend on the borehole geometry, the flow regime, pipe rotation and drillstring dynamics. In the case of casing drilling the in situ cuttings concentration may be higher than in conventional drilling due to lower flow rates and the frictional pressure losses are higher than conventional drilling because of the narrow clearance between casing and the wellbore. And while the influence of drill pipe rotation on hole cleaning and ECD has been widely recognized in conventional drilling (Walker, 1970; Luo, 1989; Lockett, 1993; Hansen, 1995; Wei, 1997; Ooms, 1999; Sterri, 2000; Bailey, 2000), very little is known about the effects of pipe rotation on ECD in casing drilling operations. Although casing drilling has been identified as a technology that can potentially solve many problems in conventional drilling operations, a better understanding of hydraulics is needed to improve the efficiency of this technology (Tarr, 1999). In order to obtain a better understanding of the factors that affect ECD in casing drilling operations, experimental and field data provided to the authors are analyzed using the models presented in this paper. Particular emphasis is placed on the effect of pipe rotary speed on ECD. 2. Mathematical Modeling 2.1. Calculation of Hydrostatic Pressure The hydrostatic pressure can be computed from: Ph = g ( rl (1 - CV ) + rp CV ) D (2) where the in situ cuttings concentration in an annulus, CV, can be determined by the following equation: 461 2 CV = æ æ vsp 1 æ vM 1 æç vM - 1ç + - ç - 1ç 4 çè vslip çè vslip 2 çè vslip çè (3) For small values of Cv, the average slip velocity, vslip, can be assumed to equal the terminal settling velocity. In this paper the settling velocity was calculated from Chien’s (Chien, 1992) correlations. A detailed derivation was provided by Diaz (Diaz, 2002) 2 . 2 . C a l c u l a t i o n o f A n n u l a r P r e s s u r e L o s s e s f o r a Yi e l d - P o w e r Law Fluid with Pipe Rotation Using Narrow Slot Approximation Tao and Donovan (Tao, 1954) proposed the following equation to determine the pressure losses in a small clearance for a Newtonian fluid. (D P)w = f ' (D P)w = 0 f cos a (4) This model can be extended for a non-Newtonian fluid if f, f’ and (∆P)ω are calculated using a model for non-Newtonian fluid flow in the annulus. In our study Tao and Donovan’s model was extended to calculate frictional pressure losses in the annulus for Yield Power Law fluids using the narrow slot approximation approach. A computational procedure is shown in Appendix A. 2.3. Calculation of Annular Pressure Losses Using Hook Load Measurements During casing drilling operations a noticeable reduction in the hook-load is observed. This reduction is caused by the upward forces on the outside surface of the casing due to fluid flowing in the annulus. Thus, this hydraulic lift may be used to estimate the pressure losses in the annulus. In order to develop the relationship between hook-load and annular pressure we assume a casing string composed of two casing sizes, with different lengths and unit weights. The densities inside and outside the casing are different due to the presence of cuttings in the annulus. Steady state flow is assumed and convective acceleration terms are neglected. From a force balance of the casing drilling string we obtain (see Appendix B): Fh = Wc Fb Fd Fp – Fbit wob (5) The contribution of the factors that cause the reduction of hook load is shown in Fig. 1. Calculations were done for a depth of 6720 , weight on bit of 10780 lbs, flow rate of 351 gpm and rate of penetration of 57 ft/hr. The values of these parameters change 462 as the well is drilled. However, the distribution of the effects on the hook load does not change much. Therefore, the trend can be extended to different conditions. The principal causes of reduction of hook load are buoyancy, weight on the bit and the piston effect. From the result obtained with Equation 5, the jetting force is too small to be considered an important factor. In addition, the contribution of drag force in reduction of the hook load is not large. The difference of pressure at the end of each section, which causes the piston effect, depends on many variables such as hole geometry, hole eccentricity, drill string dynamics and pipe rotation. Thus, in casing drilling operations the hook load measurement offers a way to estimate the bottom hole pressure. 14000 36.1% 12000 31.4% Ibs 10000 24.3% 8000 6000 4000 7.8% 2000 0.4% 0 bouyancy drag piston jetting force wob effect Fig. 1. Factors causing reduction in hook load Rys. 1. Czynniki wpływające na zmniejszenie obciążenia haka The average shear stresses at the casing wall, τoj, can be related to the annular pressure drops, ∆Paj, through a force balance of forces acting on casing in the annulus (see Appendix B). Equation 5 can be written in a general form for a casing string composed of “m” sections as: m Fh = å [w L j j - g ( roj Aoj - r i Aij ) L j - j =1 p Dh Doj D Paj ] - D Pbit An - wob 4 (6) Equation 6 can be used to obtain an expression for the change in hook load, ∆Fh, due to fluid flowing in the annulus. For a string composed of one casing size the change in hook load can be determined by the following equation: D Fh = p Dh Do D Pa 4 Warren (2001) derived a similar equation for the same case (7) 463 æ æ ç ç 2 2 ç p ç Dh - Do + Do2ç D Pa D Fh = ç 4 ç æ fh æ æ Dh æ ç 1+ ç çç ç ç ç f çç D ç ç è è o èè o è è (8) where fh and fo are the friction factors at the borehole wall and casing wall, respectively. Instead of defining an average friction factor, Warren (Warren, 2001) used different friction factors for the borehole and the casing wall. Both friction factors were calculated using the same Reynolds number, but different wall roughness. When fh and fo are equal (as is the case when assuming an average friction factor) Equation 8 reduces to Equation 7. 2.4. Calculation of Bottom Hole Pressure Using Surface Pump Pressure Measurements Bottom hole pressure can be calculated from surface pump pressures. Pressure losses inside the casing are computed using the conventional model for flow in pipes. The pressure drops through the bit and the surface equipment are calculated using the methods provided in Applied Drilling Engineering (Bourgoyne, 1986). The bottom hole pressure can be determined by subtracting all these pressure losses from the pump pressure. 2.5. Experimental Data The Baker Hughes Experimental Test Area (BETA) is located about 20 miles south of Tulsa, Oklahoma. The data was collected by MoBPTeCh Alliance and provided to TUDRP (The University of Tulsa Drilling Research Project) as a courtesy of Hughes Christensen. 2 . 5 . 1 . C a s e d H o l e Te s t s The well bore schematic is shown in Fig. 2. Three predetermined flow rates, 550 gpm, 450 gpm and 350 gpm of water, were used with the casing rotating at different rates (0, 60, 120 and 180 RPM). The test was repeated using bentonite/water muds of 9 ppg and 10 ppg. Down hole and standpipe pressures were recorded during these tests. 2 . 5 . 2 . D r i l l i n g Te s t s During the test the flow rate was kept constant at 540 gpm and the rpm and WOB were changed. The BHA was comprised of the 12 Ľ” bit with TFA 0.746. More detailed information can be found in Diaz s work (Diaz, 2002). 464 Flow outlet @ -1.50’ Hole cased with 13 1/4 ”, 68 #/ft Ground level @ -12’ 11 3/4 ” drilling casing Length = 201.13’ BHA length = 60.6’ Bottom of bit @ -282.85 Top of cement @ -300.29’ Casing Shoe @-325’ Fig. 2. Schematic of BETA Wellbore. (Courtesy of BETA facilities) Fig. 2. Schemat otworu BETA (za zgodą firmy BETA) 2.5.3. Calculation of Bottom Hole Pressure Three methods were used to estimate the bottom hole pressure. The results of each method were compared with the field data obtained from the MDP tool. The bottom hole pressure was finally obtained by adding the calculated annular pressure losses to the hydrostatic pressure. These methods are as follows: Method 1: The annular pressure losses are obtained from the measured hook load using Equation 8. Method 2: The annular pressure losses are obtained from the measured hook load using Equation 7. Method 3: The annular pressure loss is calculated using a narrow slot flow approximation for a Yield-Power-Law fluid. The effect of pipe rotation is included using an extension of Tao-Donovan s (Tao, 1954) approach for non-Newtonian fluids (Appendix A). 2.6. Field Data BP drilled 15 gas wells (Shepard, 2001 and Shepard 2002) using the Tesco Casing Drilling process in the Wamsutter area of Wyoming. Data was collected while the production hole was drilled. This data is from a well that we call “Well 1”. The pump pressure, rpm, ROP, flow rate and hook load measurements were recorded. A schematic of the well is shown in Fig. 3. Casing string configuration, drilling fluid properties, and cuttings properties can be found in Tables 1 and 2. 465 4 1/2 ’’, 11.6 ppf casing 7’’,23ppf @1179’ 6 1/4 ’’ Hole 5’’,23ppf casing L1 = 1536’ Fig. 3. Schematic of Well 1 Rys. 3. Schemat otworu 1 TABLE 1 Casing String Data TABLICA 1 Dane techniczne kolumny rur okładzinowych section no 2 1 Bit O.D in 4.50 5.00 6.25 I.D. Unit Weight in lbs/ft 4.00 11.60 4.04 23.20 ( 2x13/32 + 3x14/32) Length ft to surface 1536 TABLE 2 Fluid and Cuttings Properties TABLICA 2 Właściwości płynu i zwiercin Fluid Density ppg 8.33 Viscosity cp 1 Cutting Specific Gravity Diameter in 2.6 0.25 466 The data collected in the tests was provided to TUDRP (The University of Tulsa Drilling Research Project) as a courtesy of BP-Tesco. 2.6.1. Calculation of Bottom Hole Pressure In order to analyze this field data, Methods 2 and 3, described in the previous section, are used. The pump pressure measurements were also used to estimate the BHP. This approach is referenced to as Method 4. 3. Discussion of Results Water and two muds, Muds A and B, were used in the tests. The average rheological properties of these fluids are listed in Table 3. The Reynolds numbers for different flow rates and types of fluids were calculated and are shown in Table 4. The flow regime is fully turbulent for water at all flow rates. For Mud A the flow regime is also turbulent, but close to the transitional region. The flow regime for Mud B is laminar below 450 gpm and transitional to turbulent above this flow rate. TABLE 3 Average Properties of Muds TABLICA 3 Średnie właściwości płuczek Fluid Density (ppg) A B 8.7 9.8 600 11 35 Fann Viscometer Reading 300 200 100 6 7 6 4 1 23 18 12 3 3 1 3 TABLE 4 Generalized Reynolds Number TABLICA 4 Uogólniona liczba Reynoldsa Q (GPM) 350 450 550 Water 29836 38360 46885 Generalized Reynolds Number Mud A Mud B 4972 1765 7089 2500 9402 3298 Figs. 4 to 6 show the bottom hole pressure as a function of the casing rotary speed at different water flow rates (350 gpm, 450 gpm and 550 gpm). Both model predictions show a similar trend compared to the experimental data: the annular pressure losses increase 467 as pipe rotary speed increases. The results obtained from the hook load measurement show a better agreement with the experimental data as compared to the predictions using the narrow slot approximation. Bottom hole pressure, psi 140 136 132 128 MDP tool Method 1 Method 2 Method 3 124 120 0 60 120 180 RPM Fig. 4. Bottom hole pressure vs. rotary speed. Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Rys. 4. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Bottom hole pressure, psi 145 140 135 MDP tool Method 1 Method 2 Method 3 130 0 60 120 180 RPM Fig. 5. Bottom hole pressure vs. rotary speed. Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm Rys. 5. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm 468 Bottom hole pressure, psi 160 155 150 145 MDP tool Method 1 Method 2 Method 3 140 135 0 60 120 180 RPM Fig. 6. Bottom hole pressure vs. rotary speed. Water, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm Rys. 6. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Woda, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm The differences between the calculated and measured bottom-hole pressures (hence ECD) are within a range of about ±8%. However, in terms of the frictional pressure losses in the annulus, this range increases to about ±60%. Similar tests were conducted using Muds A and B. Figs. 7 to 9 show the bottom hole pressure as a function of rotary speed. The model predictions and measured data show trends similar to those observed in the water tests. Again, the results obtained from the hook load measurements show better agreement with the experimental data as compared to the narrow slot approximation. The difference between the calculated and measured bottom-hole pressures are within a range of about ±8%. However, in terms of the frictional pressure losses in the annulus, about ±40% difference is obtained. Another fluid, Mud B, was tested in this study at the same flow rates (350 gpm, 450 gpm and 550 gpm). Fig. 10 shows the bottom hole pressure as a function of rotary speed at a flow rate of 350gpm. The axial flow is laminar under this test condition. The predicted pressure losses obtained from Method 3 decrease as pipe rotary speed increases. These results agree well with the theoretical (Haciislamoglu, 1994; Hansen, 1995) and experimental (Cartalos, 1993; Luo, 1989) results for laminar helical flow of a shear thinning fluid in a concentric pipe. However, the experimental data shows an increase in the annular pressure losses when the casing rotary speed increases. The flow of Mud B becomes less laminar with increasing rotary speeds of the casing. Again, a better agreement was obtained from the hook load measurements. 469 Bottom hole pressure, psi 145 141 137 133 MDP tool Method 1 Method 2 Method 3 129 125 0 60 120 RPM Fig. 7. Bottom hole pressure vs. rotary speed. Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Rys. 7. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Bottom hole pressure, psi 155 150 145 140 MDP tool Method 1 Method 2 Method 3 135 0 60 120 180 RPM Fig. 8. Bottom hole pressure vs. rotary speed. Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm Rys. 8. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm 470 Bottom hole pressure, psi 170 165 160 155 MDP tool Method 1 Method 2 Method 3 150 145 0 60 120 180 RPM Fig. 9. Bottom hole pressure vs. rotary speed. Mud A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm Rys. 9. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka A, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm 168 Bottom hole pressure, psi 164 160 156 152 MDP tool Method 1 Method 2 Method 3 148 144 0 60 120 180 RPM Fig. 10. Bottom hole pressure vs. rotary speed. Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Rys. 10. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 350 gpm Figs. 11 and 12 show the results for Mud B at the flow rates of 450 gpm and 550 gpm, respectively. The flow regime is turbulent when the flow rates go beyond 450 gpm. 471 Similar trends were observed and the results using hook load data are better than the predictions using narrow slot approximation. 190 Bottom hole pressure, psi 185 180 175 170 MDP tool Method 1 Method 2 Method 3 165 160 0 60 120 180 RPM Fig. 11. Bottom hole pressure vs. rotary speed. Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm Rys. 11. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 450 gpm Bottom hole pressure, psi 205 200 195 190 185 MDP tool Method 1 Method 2 Method 3 180 175 0 60 120 180 RPM Fig. 12. Bottom hole pressure vs. rotary speed. Mud B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm. Rys. 12. Zależność ciśnienia na dnie otworu od prędkości obrotowej. Płuczka B, Dh = 12.715”, OD = 11.75”, TD = 283’, Q = 550 gpm 472 The differences between the calculated and measured bottom-hole pressures are within a range of about ±20% for Mud B. However, in terms of the frictional pressure losses in the annulus, this range increases to about ±40%. A flow test was conducted in which the flow rate was kept constant at 540 gpm but the rotary speed and WOB were changed. The properties of the fluids used are shown in Table 5. TABLE 5 Properties of Muds Used in Drilling Test TABLICA 5 Właściwości płuczek użytych w badaniach wiertniczych Fluid Density ppg C D 9.3 9.7 600 18 29 Fann Viscometer Reading 300 200 100 6 10 7 4 1 19 13 9 1 3 1 1 The measured and calculated bottom hole pressure for the interval from 435’ to 665’ are shown in Fig. 13 when Mud C was used in the test. Both Method 2 and Method 3 over-predict the bottom hole pressure. 400 Bottom hole pressure, psi 380 360 340 320 300 280 260 240 MDP tool Method 2 Method 3 220 200 415 465 515 565 615 665 715 Depth, ft Fig. 13. Bottom hole pressure vs. depth. BETA drilling tests. Mud C, Interval: 435’-665’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm Rys. 13. Zależność ciśnienia na dnie otworu od głębokości. Badanie otworu BETA. Płuczka C, Interwał: 435’-665’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm 473 Similar tests were conducted with Mud D. Fig. 14 shows the bottom hole pressure, measured and calculated values for the interval from 665’ to 887’ (TD). Both models under-predict the bottom hole pressure in this interval. Bottom hole pressure, psi 600 550 500 450 400 350 650 MDP tool Method 2 Method 3 700 750 800 850 900 Depth, ft Fig. 14. Bottom hole pressure vs. depth. BETA drilling tests. Mud D, Interval: 665’-887’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm Rys. 14. Zależność ciśnienia na dnie otworu od głębokości. Badanie otworu BETA. Płuczka D, Interwał: 665’-887’, Dh = 12.25”, OD = 10.75”, Q = 540 gpm 5000 Bottom hole pressure, psi 4500 4000 3500 3000 2500 Method 2 Method 3 Method 4 2000 1500 2800 3800 4800 5800 6800 7800 8800 Depth, ft Fig. 15. Bottom hole pressure as a function of depth. Well 1. Water, Interval: 2850’-9070’, Dh = 6.25”, OD1 = 5”, OD2 = 4.5” Rys. 15. Ciśnienie na dnie otworu jako funkcja głębokości. Otwór 1. Woda, Interwał: 2850’-9070’, Dh = 6.25“, OD1 = 5“, OD2 = 4.5“ 474 Fig. 15 is a plot of the bottom hole pressure as a function of depth for the interval from 2850 ft to 9070 ft. Water was used as the drilling fluid in this test. The results obtained using Methods 2 and 3 are similar. The bottom hole pressure obtained from Method 4 (using pump pressure measurements) is greater than the values obtained from the other two methods (using hook load measurements and narrow slot approximation). 4. Concluding Remarks Three modeling approaches are proposed and evaluated in this paper for estimating ECD in Casing Drilling operations: 1. A mathematical model for estimation of bottom hole pressure using hook load measurements; 2. An extension of Tao and Donovan s method for calculating pressure losses, using the narrow slot approximation approach; 3. Use of surface pump pressures for estimation of bottom hole pressure. Experimental data was analyzed to estimate the bottom-hole pressure by adding the calculated annular pressure losses to the hydrostatic pressure. Comparisons of the models with the experimental data show good agreement. The differences between the calculated and measured flowing bottom hole pressure are within a range of about 8%. However, in terms of the frictional pressure losses in the annulus, this range increases up to about 60%. These frictional pressure losses represent about 10-30% of the total bottom hole pressure. It is shown in this study that pipe rotation plays an important role in determining the Equivalent Circulating Density in the annulus of a wellbore. The experimental results indicate that an increase in the annular pressure losses is observed with increasing pipe rotary speed. The hook-load measurements correlate well with flowing bottom-hole pressures. Hook load measurements as well as surface pump pressure measurements can be used to determine the bottom hole pressure (hence Equivalent Circulating Density) in casing drilling operations. Acknowledgement We would like to express our appreciation to Peter Bern of BP, Allen Sinor of Hughes Christensen, Tommy Warren of Tesco, the MoBPTeCh Alliance and Tulsa University Drilling Research Projects for making this study possible. This paper was originally presented as SPE 87149 at the SPE IADC Meeting held in Dallas TX in March 2-4 2004. 475 REFERENCES B a i l e y W.J., P e d e n J.M., 2000. A Generalized and Consistent Pressure Drop and Flow Regime Transition Model for Drilling Hydraulics, SPE 62167 Drill & Compellation 15. B o u r g o y n e A.T., M i l l h e i m K.K., C h e n e v e r t M.E., Y o u n g F.S., 1986. Applied Drilling Engineering, SPE Text book Series. C a r t a l o s U., 1993. An analysis Accounting for the combined Effect of drillstring Rotation and eccentricity on Pressure Losses in Slimhole Drilling, SPE 25769 presented at the Annual Meeting. C h i e n S.F., 1992. Settling Velocity of Irregularly Shaped Particles, SPE 26121. D i a z H., 2002. Field Experimental Study and Modeling of ECD in Casing Drilling Operations, Master s Thesis, The University of Tulsa. D i P r i m a R.C., 1960. The stability of a viscous fluid between rotating cylinders with an axial flow, Journal of Fluid Mech., 9, p. 621. H a c i i s l a m o g l u M., C a r t a l o s U., 1994. Practical Pressure Loss Prediction in Realistic Annular Geometries, SPE 28304, presented at the Annual Meeting. H a n s e n S., 1995. Drill pipe Rotation Effects on Frictional Pressure Losses in Slim Annuli, SPE 30488. Presented at the annual technical conference. H a n s e n S.A., et al., 1999. A new Hydraulic Model for slim Hole Drilling Applications, SPE 57579 presented at the Annual Meeting. L o c k e t t T.J., et al., 1993. The Importance of Rotation Efficient Cutting Removal During Drilling, SPE 25768 presented at the Annual Meeting. L u o Y., P e d e n J.M., 1989. Laminar Annular Helical Flow of Power-Law Fluids; SPE 20304, presented at the Annual Meeting. M c C a n n R.C., et al., 1993. Effects of high Speed Pipe Rotation on Pressure in Narrow Annuli; Paper SPE 26343, presented at the Annual Technical Conference. O o m s G. et al., 1999. Influence of Drillpipe Rotation and Eccentricity on pressure Drop over Borehole during Drilling, SPE 56638, presented at the Annual Meeting. S h e p a r d S.F., R e i l e y R.H., W a r r e n T., 2001. Casing Drilling: An Emerging Technology, paper IADC SPE 67731, 2001 IADC/SPE Conference, Amsterdam, February 27 March 1, 2001. S h e p a r d S.F., R e i l e y R.H., W a r r e n T., 2002. Casing Drilling successfully applied in Southern Wyoming, World Oil, p. 33-41, June 2002. S t e r r i N., S a a s e n A., A a s B., H a n s e n A.S., 2000. Drill String rotation Effects on Axial Flow of Shear Thinning Fluids in an Eccentric Annulus, Oil gas Magazine, p. 30-33. T a o L.N., D o n o v a n W.F., 1954. Through-Flow in concentric and Eccentric Annuli of Fine Clearance With and Without Relative Motion of the Boundaries; Assoc. Mem. ASME, 54 A-175, presented at the Annual Meeting, p. 1291. T a r r B., S u k u p R., 1999. Casing-while-Drilling: The Next Step Change in Well Construction, World Oil, Oct. T e s s a r i R.M., M a n d e l G., 1999. Casing Drilling A Revolutionary Approach to Reducing Well Cost, SPE/IADC 52789, presented at the SPE/IADC Drilling Conference, Amsterdam, Mar. 9-11, 1999. U s t i m e n k o B.P., Z m e i k o v V.N., 1964. Hydrodynamics of a flow in an annular channel with an inner rotating cylinder , Institute of power Engineering academy of Sciences, Vol 2, No. 2, p. 259-250. W a l k e r R., Al R a w i O., 1970. Helical Flow of Bentonite Slurries, SPE 3108, presented at the Annual Meeting. W a r r e n T., 2001. Casing Drilling Engineering Manual, Tesco Corporation, 2001 edition. W e i X., 1997. Effect of drillpipe Rotation on annular Friction Pressure Loss (AFPL), in laminar Helical Flow of Power Law Fluids in Concentric and Eccentric Annuli Master s thesis petroleum department University of Tulsa. Received: 03 September 2007 476 Appendix A Procedure for calculating effect of pipe rotation on pressure losses Suppose we have a yield power law fluid and are given the following data: Do, Di, Q, ρ, k, m, τy and rpm. Then we: Calculate the angular velocity, ω 2p rpm 60 A.1 Q A A.2 w ri w Di = 2 4 A.3 w= Calculate mean axial velocity, ν: v= Calculate mean tangential velocity, u: u= Calculate shear stress at the wall, τw from: 1+ m (t w - t y ) m æ 3m æ æ 12v m æ = t yç ç ç çt w + 1 Do - Di 1+ m è è 1 + 2m è è K m t w2 A.4 Calculate wall Shear Rate, γ·w: 1 æt -t æ m g&w = çç w y çç è K è A.5 Calculate Generalized Fluid Behavior Index, N from: g&w = 1 + 2N 12V 3 N Do - Di A.6 Calculate Reynolds Number, ReYPL: N Re, slot = Deff r v h A.7 477 where: Deff = 3N æ 2 æ ç Dh y ç 1 + 2N è 3 è h= t w , av gw A.8 A.9 Determine whether flow is Laminar or Turbulent: If N Re, slot < (N Re )cr Þ Laminar flow Otherwise, flow is Turbulent Calculate friction factor, f: For laminar flow, f = 2t w 16 = 2 N Re, slot rV A.10 For turbulent flow, find f from: N é 1- ù 1 4 0.4 = 0.75 Log10 êRe YPL f 2 ú - 1.2 N f êë ûú N A.11 æ dP æ Calculate annular pressure drop gradient without rotation, ç ç : è dl èw = 0 4t 2 fr v 2 æ dP æ ç ç = w = Dhy è dl èw = 0 Dhy A.12 Where Dhy is hydraulic diameter Do – Di Calculate annular pressure drops, (dP)ω=0: (dP)w = 0 = 2 fr v 2 dL Dhy A.13 Calculate v' = v sec α, where æ wr æ a = arctan ç i ç è 2v è A.14 We substitute v = v' and repeat the above calculations. The annular pressure loss with the effect of pipe rotation is: (dp)w = f ' (dP)w = 0 f cos a A.15 478 APPENDIX B Relationship between hook load and annular pressure drops In order to develop this relationship we assume: • Casing string composed of two casing sizes, with different lengths and unit weights. • The densities inside and outside the casing are different, due to the presence of cuttings in the annulus. • Steady state and acceleration terms are neglected. From force balances at different sections of a casing drilling string we obtain: At the bottom of the first section (Fig. B.1): F b + (P b + D Pbit)( Ai1 - An ) - P b (Ao1 - An ) = 0 B.1 F b = P b(Ao1 - Ai1) - D Pbit (An - Ai1) B.2 At the top of the second section (Fig. B.2): F T - P T Ai 2 - Fh = 0 B.3 F T = P T Ai 2 + Fh B.4 From a force balance of the whole string, we get (Fig. B.3): Fb Fb Fh PT pump Pcb wob PB Ft Ft Fig. B.1. Boundary condition at the bottom of the 1st section Fig. B.2. Boundary condition at the top of 2dn section Rys. B.1. Warunki graniczne w dolnej części 1-ej sekcji przewodu Rys. B.2. Warunki graniczne w górnej części 2-giej sekcji przewodu 479 F T - w1 L1 - w2 L 2 + Pc12 (Ai1 - Ai 2) - Po12 (Ao1 - Ao 2 ) + to1p Do1 L1 - t i1p Di1 L1+ t o 2 p Do 2 L 2 - t i2p Di 2 L 2 + F b = 0 B.5 where: P T = D Pc1 + D Pc 2 + D Pbit + D Pa1 + D Pa 2 + g ( ro1 - ri ) L1 + g ( ro 2 - ri ) L2 B.6 P b = D Pa1 + D Pa 2 + g ro1 L1 + g ro 2 L 2 B.7 Pc12 = D Pc1 + D Pbit + D Pa1 + D Pa 2 + g ( ro1 - ri ) L1 + g ( ro 2 - ri ) L2 + g ri L2 Pa12 = D Pa 2 + g ro 2 L2 Ft W2 t o2 t i2 Section 2, L 2 Pa12 Pc12 t o1 W1 Section 2, L 1 Fb Fig. B.3. Force balance of a casing string Rys. B.3. Bilans sił działających na przewód rur okładzinowych B.8 B.9 480 From a balance of viscous forces acting on a fluid element in the pipe the following equations are obtained (Fig. B.3): t i1p Di1 L 1 = D Pc1 Ai1 B.10 t i 2 p Di 2 L2 = D Pc 2 Ai 2 B.11 Combining Eqns. B.1 to B.11 we have: Fh = Wc Fb Fd Fp – Fbit wob B.12 WC = w1 L1 + w2 L 2 B.13 Fb = g ( ro1 Ao1 - ri Ai1)L 1 + g (ro 2 Ao 2 - ri Ai ) L 2 B.14 Fd = t o1p Do1 L1 + t o 2p Do 2 L 2 B.15 Fp = D Pa1 Ao1 + D Pa 2 Ao 2 B.16 Fbit = D Pbit An B.17 where Casings weight in air: Buoyancy effect: Fluid drag: Piston effect: Jetting force The average shear stresses at the casing wall, τoj, can be related to the annular pressure drops, ∆Paj, through a balance of forces acting on a fluid element in the annulus. See Fig. B.4. t oj P+D Paj P rh t oj roj Fig. B.4. Forces acting on a fluid element in the annular space Rys. B.4. Rozkład sił działający na element płynu w przestrzeni pierścieniowej 481 Then, for annular flow: t oj p (Dh + Doj ) L j @ D Paj p 2 (Dh - Doj2 ) 4 B.18 Thus, Eqn. B.15 can be rewritten as: Fp = Do1 p (Dh - Do1 ) D p (Dh - Do 2) D Pa1 + o 2 D Pa 2 4 4 B.19 Combining Eqn. B.19 and Eqns B.12 through B.17 and rearranging: Fh = w1 L1 + w2 L2 - g ( ro1 Ao1 - ri Ai1) L1- g ( ro 2 Ao 2 - ri Ai ) L2 - p p Dh Do1 D Pa1 - Dh Do 2 D Pa 2 - D Pbit An - wob 4 4 B.20 In general, for a casing string of m sections: Fh = m å[ w L j j =1 j - g ( roj Aoj - ri Aij ) L j - p Dh Doj D Paj ] - D Pbit An - wob 4 B.21