SPE 16613 Evaluation of Annular Pressure Losses while Casing Drilling Vahid Dokhani, Mojtaba P. Shahri, SPE, University of Tulsa, Moji Karimi, SPE, Weatherford, Saeed Salehi, SPE, University of Louisiana at Lafayette Copyright 213, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 3 September 2 October 213. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 3 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract Casing Drilling is an innovative drilling method wherein the well is drilled and cased simultaneously. The small annulus of Casing Drilling can create a controllable dynamic ECD (Equivalent Circulating Density). Casing Drilling technology permits the same desired ECD as conventional drilling to be achieved using a lower, but optimized, flow rate, rheological properties, and mud weight. In this paper, the frictional pressure loss during Casing Drilling operation is evaluated using Computational Fluid Dynamics. Annular pressure losses have received substantial attention in theoretical analyses, laboratory assessment and actual well measurements. Combinations of casing motion, annular eccentricities, wall roughness and fluid temperatures along the length of the annulus affect fluid flow regimes that control annular pressure losses. Current analytical solutions have limited applicability for complex conditions with pipe rotation and eccentricity. In this study, the pressure losses during Casing Drilling operation are investigated using computational fluid dynamics. The results are compared against the available analytical solution and field data. The effect of pipe rotation and eccentricity on the frictional pressure loss is investigated as well. According to the simulation results, the pipe rotation reduces the frictional pressure loss for Yield-Power-law fluid which would be beneficiary during the casing drilling operation. It is found that the pipe eccentricity has a significant effect on the ECD calculation. The industry is moving towards more challenging jobs in narrow pressure window scenarios such as deep-water and HPHT applications. Drilling with casing/liner is among the primary options to complete these sections due to strengthening effects associated with plastering the wellbore wall and also eliminating conventional drill pipe trip. Having accurate models for ECD including the effects of pipe rotation and eccentricity in the narrow annulus is essential to the success of these challenging jobs. Introduction Casing Drilling is a process in which a well is drilled and cased simultaneously. The idea builds on experience gained from drilling liners to the bottom in troublesome holes. It was implemented for drilling a sequence of highly pressured shale formation following by a depleted reservoir (Vogt et al. 1996). The major problem related to the depleted reservoirs is narrow operational mud window (Shahri et al. 213). Extensive research and development in late 199 s led to commercialize casing drilling technology where the first fully retrievable casing drilling system was introduced in 1999 (Tessari and Madell, 1999). With the advances in top-drive systems, retrievable BHA, and PDC bits, the technology made it possible to complete a well using casing as the drillstring (Shepard et al. 22). The original purpose of developing Casing Drilling was to eliminate Non Productive Time (NPT) associated with tripping and running casing. In this method the well is drilled and cased at the same time, casing is conveyed to the bottom by circulating, reciprocating, and rotating simultaneously, eliminating drillstring tripping and its associated problems. By replacing conventional drillpipe with standard oilfield casing and cementing it in place after the well is drilled, Casing Drilling reduces the time spent on drilling operation and running casing up to 3% (Tessari and Madell, 1999, Skinazi et al. 2, Shepard et al. 22). The Casing Drilling system has been employed in many fields around the world where it has demonstrated its advantages and applications to reduce non-productive time. Here, we are going to briefly discuss lessons learned from Casing Drilling operation around the world. Implementing Casing Drilling in the Lobo field in south Texas could prevent well control problems associated with the lost circulations as well as improving gas production in another field through less fluid invasion (Warren and Tessari, 24). Several tests performed both on land and offshore Brazil, where those runs were targeted to
2 SPE 16613 overcome borehole stability and loss circulation zones. Although sliding ROP was similar for both conventional drilling and Casing Drilling, rotating ROP is reported to be higher while Casing Drilling (Placido et al. 25). Using Casing Drilling mitigated the lost returns and reduced the formation damage in a depleted coal formation in New Mexico (Robinsot et al, 28). Casing Drilling was employed to drill the surface section of a new well in Foukanda field offshore Congo. It enabled the operator to drill six extra wells from a platform that had no more empty slots on the template (De Luca and Aliko, 29). According to Sanchez et al. (21) drilling surface sections through troublesome shale formations in Oman was successful using Casing Drilling operation. It is also reported that this technique reduced drilling phase about 4% in this area. By reducing exposure time of reactive shales to aqueous fluids, the technique improved the wellbore stability and thus eliminated conditioning trips. Feasibility of Casing Drilling operation was testified in both vertical and directional sections in Maranon basin in Peru. It is shown that the technique is less risky for drilling surface and intermediate holes (Beaumont et al., 21). Casing Drilling technology was implemented in Saudi Arabia aiming to cure complete losses. It is reported that the technique was partially successful to reduce losses, although they had few casing fatigue failures in high torque and total loss environment (Chima et al. 212). Casing Drilling can be utilized in high pressure high temperature drilling operations as well (Shadravan and Amani 213). One of the most reported benefits associated with Casing Drilling is that it can significantly reduce the lost circulation problems. The wellbore plastering effect of the Casing Drilling offers the possibility to drill depleted zones with less formation damages (Warren and Tessari, 24). Plastering effect also enhances the pressure containment of the wellbore by smearing the drill cuttings in to the formation pore spaces. Smaller particle sizes are generated by Casing Drilling operation confirms the smearing effect of the casing string (Karimi et al. 211). During early implementation of the technology, other benefits were seen while drilling with large diameter casing. It was originally thought that drilling with the larger pipe would induce more drilling problems, where in practice fewer problems were observed (Karimi et al. 212). A typical configuration of casing drilling operation versus conventional method is shown in Figure 1. Casing Drilling Conventional Method Figure 1: Casing Drilling and Conventional Drilling Configuration (Top view) In the past researchers tried to provide prediction of pressure losses while Casing Drilling using field data or numerical methods to answer the true response of non-newtonian fluids. It is expected to have a higher frictional pressure drop with the smaller clearance space between inner casing and the wellbore wall. It is speculated that the casing may be offset to an unknown value. Combination of pipe rotation and eccentricity helps to form a highly effective seal to minimize fluid losses. Eccentric configuration of Casing Drilling is supported through some observations by several publications (Salehi et al. 213). Smaller cutting size or casing wear is attributed to the eccentric configuration of Casing in the wellbore (Fontenot et al. 24, Karimi et al. 212). Ozbayoglu et al., (21), and Osgouei (21) measured some data for estimating total pressure drop and cuttings concentration in narrow eccentric horizontal and inclined annuli from cuttings transport experiment. Results from their study indicate that drillpipe rotation speed does not have significant influence on pressure drop for constant rate of penetration (ROP) and flow rate. This paper aims to simulate Casing Drilling operation through CFD modeling in order to evaluate the combined effect of eccentricity and pipe rotation on velocity profile of a non-newtonian fluid. To achieve that, we briefly review some publications. Azouz et al. (1992) investigated numerical modeling of laminar flow of non-newtonian fluids in eccentric annuli using a mathematical expression for effective viscosity. They studied a special eccentric geometry in which the smaller space of the annulus is partially blocked due to cutting accumulation. Their numerical results predict that the pressure gradient is not much affected by the cutting bed thickness for the case of Power-Law fluid, whereas for Newtonian fluids the pressure gradient gradually increases with the increase of cutting bed height (Azouz et al. 1992). Escudier and Gouldson (1992) showed through their experimental investigation that the effect of inner pipe rotation on friction factor in a concentric annular is marginal. In addition, their experimental data signifies that for moderate Reynolds number (except Re < 1), rotating the inner pipe up to 8 rpm does not generate any axial velocity fluctuation for non-newtonian fluid. Hansen and Sterri (1995) investigated the effect of pipe rotation on frictional pressure loss in slim annuli where they compared their experimental results with CFD predictions. The authors selected a laminar flow regime for CFD modeling of Power-Law fluids in presence of pipe rotation and eccentricity. Comparing the absolute effect of rotation on pressure losses for a given eccentricity value with CFD prediction, indicates that CFD model underestimate the frictional pressure drop at lower flow rates. It is concluded that when the Reynolds number and Taylor number is less than their critical values, the frictional pressure drop are reduced in comparison with that of no pipe rotation.
SPE 16613 3 Comparing the experimental data and numerical results presented by Nouar et al. (1998) for concentric flow of a non- Newtonian fluid at very low Reynolds number show that; (1) the experimental results does not satisfy the slip velocity assumption at the wall, and (2) inducing a very low pipe rotation tends to destroy the plug region as well as creating a velocity peak to close to the inner pipe region. Note that the second observation confirms the statement by Escudier and Gouldson (1992). Escudier et al. (22a) compared their numerical results with previous publications to predict the velocity profile of a non-newtonian fluid in annuli. They separated the analysis of axial and tangential velocity to address the effect of pipe rotation on velocity pattern. The numerical investigation of Escudier et al. (2) predicts that if the inner pipe is highly acentered it creates two local regions of maximum axial velocity for the radius ratio (κ) of.5 and.8. They also reported an unexpected result for high values of eccentricity (ε >.9) where the friction factor increases rather than decreases. It is stated that the detailed flow behavior of various radius ratio are significantly different. Ooms et al. (1999) followed similar technique of numerical simulation as explained in detail by Escudier et al. (2) to investigate the influence of drillpipe rotation on pressure losses during drilling. They used measured standpipe pressure of a development well in North Sea to correlate with the numerical predictions. The measurements show that due to pipe rotation the frictional pressure drop decreases which is signified with an increased standpipe pressure. It is stated that at high flow rates, due to turbulent flow regime, the pressure drop is independent of pipe rotation which is confirmed both by measured values and their numerical simulation. To properly analyze the secondary flow induced by pipe rotation, Escudier et al. (22b) introduced a velocity ratio parameter (ζ) which separates the resulting flow into three types: axial dominated, rotational dominated and mixed flow regime. The velocity ratio is defined as follows: ζ (1) where ω is the angular velocity of the inner pipe (rad/s), R i is the inner pipe (i.e. outer diameter of the casing), and U is the average axial velocity (m/s). This parameter is used to indicate the secondary flow induced by pipe rotation. If ζ <1 the flow is axial dominated. As a result, the shear thinning occurs mainly in the vicinity of the inner and outer cylinders. If ζ >1 the rotational flow is dominated. In the case of 1< ζ <1 the resulting flow called mixed (Escudier et al. 22b). Ozbayoglu and Omurlu (26) presented a numerical simulation of the flow of non-newtonian fluid through annulus using commercial CFD software. The geometry consideration in their study corresponds with the common sizes encountered in Coil Tubing application. Comparing their experimental data set which includes Newtonian fluid and Power Law fluids with the numerical results gives a reasonable match. Considering, 5 and 1% eccentricity, they confirmed that the frictional pressure losses decrease with the increase of eccentricity. Diaz et al. (24) evaluated three modeling approaches in order to estimate ECD in Casing Drilling operations; hook load measurement, an extension of Narrow Slot approximation, and using surface pump pressure measurements. It is reported that the difference between evaluated pressure drop and measurement could be up to ±6%. Comparing the above mentioned approaches, it is found that hook load method (including modeling and measurement) correlate well with the flowing bottom hole pressure. Hemphill and Ravi (25) proposed an engineering approach to combine the axial and rotational velocities through manipulation of the point velocities across the annular gap using Herschel-Bulkley rheological model. Initially they obtained the axial velocity and rotational velocity in an uncoupled scenario and then they combined the results to get the velocity magnitude. Their results show that inner pipe rotation reduces the pressure gradient up to 6%. They recognized that minimum pressure drop correlate with the flow rate and it occurs in rotation speeds of 1-15 rpm. Afterwards, the pressure drop increases linearly as a function of pipe rotation. Pereira et al. (27) studied the effect of pipe rotation in their CFD numerical scheme where they used a Cross rheological model. Their numerical results show that the pressure losses decreases with the increase of pipe rotation. It is also reported that in most of the cases increasing the eccentricity favorably reduces the frictional pressure losses. The velocity profile for the case of eccentric pipe rotation indicates the presence of some stagnation region in the narrow annular space as well as deflection of the maximum axial velocity. Essa (29) studied the flow of non-newtonian fluids in pipes using CFD. He compared the velocity profile obtained by CFD with the theoretical velocity profile for three fluids of each of the Newtonian, Power-Law, Bingham plastic and Herschel- Bulkley models. He reported that the CFD prediction of velocity profile was accurate for shear-thinning Power-law fluids, whereas CFD seems to underestimate the velocity profile of the more complex fluids (such as Herschel-Bulkley model) in the plug region. This underestimation is more pronounced with the increase of the yield stress. Karimi Vajargah et al. (213) investigated the effect of tool joints on pressure drop using CFD modeling. Oguggue (29) investigated the effect of eccentricity on frictional pressure losses using CFD modeling in the case of Power- Law fluid. It is reported that the highest shear exists in the narrow sector of an eccentric annulus which lead into a considerable reduction in viscosity. At a constant flow rate, it is shown that frictional pressure losses reduce with increasing eccentricity. Comparing experimental correlation proposed by Haciislamoglu and CFD results reveals that CFD tends to overestimate the frictional pressure loss with increasing eccentricity and flow behavior index. Mokhtari et al. (212) followed computational fluid dynamic (CFD) technique to solve the fluid flow in eccentric annulus at
4 SPE 16613 various radius ratio specially those of Casing Drilling geometry. It is reported that with the increase of radius ratio (κ) the pressure loss increases. The numerical results imply that the maximum velocity occurs not at full eccentric case rather at ε=.5. However, a significant increase in pressure losses can be seen for the case of κ >.8. It is also shown that the eccentricity effect is more pronounced at higher power-law indices and higher radius ratios. Moreover, the use of CFD in drilling engineering is not limited to understand the single phase fluid dynamics. For example, Sorgun et al. (211) and (213) simulated gas-liquid flow inside narrow horizontal eccentric annulus using computational fluid dynamics (CFD) model and compared results by experimental data. Fu et al. (213) simulated the interactions between cuttings and drilling fluid in horizontal eccentric annulus. The effect of fluid flow rate and the impact of the rate of penetration (ROP) on flow patterns, cuttings concentration and pressure losses were investigated and validated using experimental data. Altogether, few works have been published for simulating the Yield Power-Law fluid flow through annular spacing with both pipe rotation and eccentricity. The purpose of this study is to establish a framework to evaluate frictional pressure losses in the annulus space of casing while drilling operation. It is intended to perform CFD simulation for selected geometries and fluid properties in order to investigate the effect of geometrical parameters as well as rheological parameters on pressure drop. In fact, successful Casing Drilling operations were reported at radius ratio of κ~.8 (Karimi et al. 211). Comparison with the evaluated field data is conducted to investigate the role of pipe rotation and eccentricity on pressure losses. Having an appropriate prediction of pressure losses through Casing Drilling operation will help to optimize drilling activities. For example one can evaluate the proper pump pressure requirements for each section of the wellbore profile and also the required mud weight in order to perform drilling. Approach The road map to achieve our designated objectives includes several stages; initially we shall construct the geometry of the Casing Drilling for a given wellbore condition. Accordingly, the domain should be discretized in a manner that the result will not be grid dependent. Comparing with the available analytical solution will validate our discretization scheme. To achieve that, we designed a series of cases to be investigated. Then, we proceed with the simulation of non-newtonian fluid model (Yield Power-Law model). Consequently, we made an effort to analyze the effect of eccentricity as well as pipe rotation in the case of Yield Power-Law fluid. Assumptions In order to simplify the simulation, few assumptions could be envisioned. In drilling operation due to the continuous fluid circulation through the annulus, steady state flow condition prevails. In top hole section, where the well is not deep the fluid can be treated as incompressible fluid. The laminar flow regime is considered in our simulation to verify the CFD results with the analytical solution. It is assumed that a single phase fluid flows through the annulus and the pipe geometry is uniform along the test section as well as concentric annulus. In most of the applications earth thermal gradient is considered to be around 1ºF per 7 feet. Thus the test section (1 m) could be considered in constant temperature conditions. For the sake of simplicity, the effect of drill cuttings in our simulation is neglected in order to be able to validate the CFD results with the analytical solution. Initially we treated the casing to be stationary (no pipe rotation) and there is no slip condition at the walls (both inner pipe and wellbore wall). The pipe and the wellbore are assumed to be smooth. We also assume that the geometry remains uniform along the pipe which means that for the time being we neglect the effect of tool joint on pressure losses. The pipe section is considered to be either 5 or 1 meter long. Methodology Analytical Solutions Analytical solutions have been used in petroleum industry for different purposes, including the prediction of flow and pressure behavior of traditional vertical wells (Van Everdingen and Hurst, 1949) and more-complex multi-fractured horizontal wells (Shojaei and Tajer, 213). Analytical solutions are faster and more convenient as compared to numerical techniques, but lack generality in most cases. To verify the accuracy of a given numerical technique, its results can be compared with the corresponding analytical solution for the cases where an analytical solution is available. In order to make sure that the velocity profile has been fully developed, it is best to estimate the required entry length of the pipe test section. Entry length is defined as the pipe length at which the center line velocity is 99% of the fully developed center-line velocity. The entrance length could be expressed with the dimensionless entrance length number as: Where L e is the length of fully developed velocity profile (m) and d is the pipe cross section diameter (m). For laminar flow of Newtonian fluid, the entrance length is correlated with the Reynolds number:.6 (3) For laminar flow of Non-Newtonian fluid, we used the criterion proposed by Mehrotra et al. (199). It is suggested that the dimensionless entrance length to be: (2)
SPE 16613 5.556 For example for the case of Newtonian fluid with a viscosity of.1 cp and an average velocity of.1m/s in narrow slot of.52m, it is estimated that after 3.1 m the velocity profile should have been fully developed. Accordingly, the pipe length should be selected such that to ensure the fully developed flow. Non-Newtonian Fluid Flow in Narrow Slot Rheology of Yield Power-Law Fluid is represented with three parameters. The shear stress in the fluid domain is expressed in terms of yield stress, power-law index and consistency index. It should be noticed that the exact solution for flow of Yield Power-Law fluid is not available in cylindrical geometry. If ratio of inner pipe to outer wall diameter is greater than.3 one can obtain the analytical solution using Narrow Slot approximation (Bourgoyne et al. 1986). The geometry representation of Narrow Slot is illustrated in Figure 2. In that illustration h is the height of channel ( ) and the channel width is to be consistent with the corresponding cylindrical geometry. considered as Derivation of the governing equations is based on momentum balance equation and it can be found in Aadnoy et al. (29). To be concise, the average velocity across the pipe is given as: 2 12 1 (5) where K is the consistency index (kg/m-s), m is the power-law index, and is the fluid yield stress (Pa) as they are included in Herschel-Bulkley viscous model. In the above equation, is shear stress at the wall which is designated as: 2 (6) In this approach, velocity is expressed with two distinctive equations (i.e. in the plug region and periphery region). Accordingly: 2 1 where V p is velocity in the plug region. The velocity magnitude in the surrounding region between plug zone and wall is expressed as: 2 1 2 (8) (4) (7) W 2πR i kr i R h Figure 2: Geometrical parameters of cylindrical (left) and Narrow Slot configurations (right) for a concentric pipe within the Wellbore Computational Domain In this paper, the geometry consists of two concentric (or eccentric) long pipes with four surface boundaries: inlet, outlet, inner pipe (Casing), and wellbore wall. The pipe length was selected long enough to ensure a fully developed flow throughout the domain. Consequently, five geometries were generated in order to investigate the effect of radius ratios encountered in Casing Drilling on pressure losses (Table 1). It should be noticed that the outer diameter (wellbore wall) was kept constant as 17.5 in. The corresponding values of the Narrow slot configuration were also provided in Table 1. Computational Mesh The accuracy of the steady state numerical solution is crucial since this solution constitutes a base case for other complicated geometries where there is no analytical solution available. Validation of the numerical method was carried out by comparing CFD results; i.e., the pressure gradient and the velocity field, with that of narrow-slot analytical solution. 2πR
6 SPE 16613 All five geometries were meshed and the meshing for two geometries; i.e, κ =.7 and κ =.9, are illustrated in Figure 3. The annular gap between the inner pipe and the wellbore wall has been configured in two arrangements, the first one is the concentric geometry, and the other one is the eccentric layout. To further analyze the effect of eccentricity on pressure loss, we consider five cases which will be explained in the following sections. Initially, an optimization process was performed to find the best meshing size with the lowest error. The procedure was to perform a number of simulations with different mesh size and the results were compared with the Narrow Slot analytical solution of a Non-Newtonian fluid. In order to capture the velocity field in the region of high shear rate (i.e. close to the wall) two inflation layers were defined within the cross sectional area of the pipe. Discretization of the domain along the tangential direction was selected in the range of 2 to 3 divisions (Escudier et al. 22). It is also confirmed that the numerical results are consistent for both 5 and 1m pipe length. Figure 3: Illustration of Meshing along Annulus in Cylindrical Geometry, κ=.7 (left) and κ =.9 (right) Table 1: Geometrical Parameters used in CFD simulation and corresponding values of Narrow Slot geometry Case κ =D i /D o D i (in) h (in) w (in) 1.7 12.25 2.625 46.731 2.76 13.375 2.65 48.491 3.8 14 1.75 49.48 4.85 14.875 1.3125 5.854 5.9 15.75.875 52.229 Boundary Conditions and Fluid Properties To simplify the sensitivity analysis, it is assumed that the fluid flows under isothermal and laminar conditions. At the inlet a constant fluid velocity equal to the bulk fluid velocity along the pipe was specified and the boundary condition at the outlet was taken a zero static pressure. To initialize the CFD analysis, the fluid properties of a Yield Power-Law fluid were assumed as given in Table 2. Verification of CFD Results There is no analytical solution available for flow of Yield Power-Law fluid in the annulus section. Therefore we used CFD simulation to generate the results in the cylindrical geometries. The results of the CFD solution can be verified by comparing them versus the narrow slot approximate solution for Yield Power-Law fluid. To achieve that, we performed a sensitivity study of CFD simulation by selecting different rheological values in order to examine the accuracy of our computation as well as meshing properness. Initially we chose the values of yield stress as.833, 1.183, 1.533, to quantify the error magnitude of CFD calculations. The simulation was performed for each configuration (concentric geometry) and the results were compared with the analytical solution of Narrow Slot approximation. Figure 4 shows the comparison of frictional pressure losses calculated by CFD and that of analytical solution as a function of radius ratio. It is realized that the value of error for all cases are reasonable and the largest error was less than 3%. The figure also illustrates the dependency of the pressure losses to the value of yield stress. It is noticed that the frictional pressure drop curves show a similar pattern for various values of yield stress. With the increase of the yield stress, the frictional pressure drop increases. It is also evident that the meshing scheme is almost insensitive to the values of the yield stress where a good match between CFD result and analytical solution is manifested. As it is depicted in
SPE 16613 7 Figure 4, smaller annular gap yields higher frictional pressure drop. The illustration reveals a similar pattern in pressure drop for the three selected values of yield stresses. This growth trend of pressure loss as a function of radius ratio is also observed in previous publication by Mokhtari et al. (212) where they considered Power-Law fluids. To further verify the results of the numerical method, we also examined the effect of consistency index of the Yield Power- Law fluid on frictional pressure losses. Figure 5 shows the comparison of the pressure losses obtained from CFD results with Narrow slot approximate solution for three selected values of consistency index as a function of radius ratio. It is noticed also that the annular pressure drop increases remarkably at radius ratios above.8. As the consistency index of the fluid increases, it is expected to observe higher shear stress which is clearly verified by the approximate analytical solution. A comparison between CFD results and analytical solution as a function of radius ratios for three selected values of power-law index is illustrated in Figure 6. As the fluid becomes more shear thinning the growth rate of pressure drop as a function of annulus gap decreases. As the Fluid Behavior Index increases toward unity, the pressure drop increases which is the outcome of effective viscosity increase. Accordingly, higher frictional pressure losses occur. It should be emphasized that there is no cross over point for various degrees of Fluid Behavior Index as it may occur for Power-Law fluids (Mokhtari et al. 212). This can be explained by the fact that the yield stress affects the frictional pressure loss significantly even at wider annular gap (low κ values) and compensates the opposite response due to the growth of effective viscosity growth (increase of Power-Law index). Such a response does not appear in Power-Law fluids. The effect of Fluid Behavior Index can also be shown in the velocity profile in the annular gap. Figure 8 shows a comparison of the velocity profile prediction of the approximate solution for a concentric configuration in which κ=.8. As the Fluid Behavior Index of the drilling fluid decreases (i.e. the shear thinning behavior amplifies), the plug flow region expands. It is reported by Essa (29) that CFD is underestimating the velocity profile in the case of Yield Power-Law fluids. This phenomenon is probably due to the special treatment of yield stress in CFD scheme by using a critical shear stress. 5 Table 2: Fluid Properties for Sensitivity Analysis Parameters Value Average Velocity, (m/s).1 Density, (kg/m 3 ) 998.2 Viscosity Model Herschel-Bulkley Yield Stress, (Pa) 1.5327 Consistency Index, (kg/m-s).3745 Fluid Behavior Index, m.5989 Pressure loss gradient (Pa/m) 4 3 2 1.5.6.7.8.9 1 Radius ratio, κ Analytical τy=1.5327 Numerical τy=1.5327 Analytical τy=1.1827 Numerical τy=1.1827 Analytical τy=.8327 Numerical τy=.8327 Figure 4: The effect of radius ratio on pressure drop for selected values of yield stress using CFD and analytical approximate solution
8 SPE 16613 6 Pressure loss gradient (Pa/m) 5 4 3 2 1.5.6.7.8.9 1 Analytical k=.27 Analytical k=.37 Analytical k=.47 Radius ratio, κ Numerical k=.27 Numerical k=.37 Numerical k=.47 Figure 5: The effect of radius ratio on pressure drop for selected values of consistency index using CFD and approximate solution 8 7 Pressure loss gradient (Pa/m) 6 5 4 3 2 1.5.6.7.8.9 1 Radius ratio, κ Analytical m=.4 Numerical m=.4 Analytical m=.6 Numerical m=.6 Analytical m=.8 Numerical m=.8 Figure 6: The effect of radius ratio on pressure drop for selected values of Fluid Behavior Index using CFD and approximate solution
SPE 16613 9.14.12 Velocity (m/s).1.8.6.4.2.1.2.3.4.5 Radial Position (m) n=.4 n=.6 n=.8 Figure 7: The effect of Fluid Behavior Index on velocity profile for the radius ratio of.8 The Effect of Eccentricity on Pressure Loss The governing equations become complicated as the inner pipe (Casing) becomes offset to an unknown value. It is therefore important to evaluate the effect of eccentricity on frictional pressure losses. The eccentricity describes how off-center a pipe is within another pipe or the open-hole. A pipe would be said to be concentric (% eccentric) if it were perfectly centered in the outer pipe or hole. In general, eccentricity is defined as: ε (9) where is the difference between the center position of inner pipe and wellbore, R o is the wellbore radius and R i is the inner pipe diameter. Accordingly, we attempted to increase the eccentricity of the inner pipe and investigate its effect on frictional pressure losses. Here, we considered five eccentric cases for each geometry, namely e =.1,.3,.5,.7 and.9. It should be noticed that the meshing scheme of the eccentric pipe should be repeated accordingly in order to discretize the wider gap region properly. The meshing configurations for radius ratio of.76 using eccentric values of.1,.5, and.9 are illustrated in Figure 8. A ------------------------------A` A ---------------------------A` A ------------------------A` Figure 8: Meshing configurations for radius ratio of.76 using eccentricity of.1 (left),.5 (center) and.9 (right) Monitoring the velocity profile in the horizontal cross section (A-A`) reveals that the velocity is higher in the wider gap whereas the fluid flows slower in the narrow region. As a result of geometrical configuration, the overall effect of the wall friction on fluid domain is reduces. Therefore it is expected that the increase of eccentricity reduces pressure drop. The resultant frictional pressure gradients corresponding to each eccentricity for selected radius ratios are depicted in Figure 9. It can be seen that the effect of eccentricity on pressure loss is more dominant in the range of ε =.2 and ε =.8. In other words eccentricity starts to affect the frictional pressure loss if ε >.1 and it will be declined after ε >.8. This is also remarked by previous published results such as Cartalos and Dupuis (1993), Escudier et al. (2), Mokhtari et al. (212). In general, it is concluded that as eccentricity increases the pressure drop along the casing annulus decreases. Further analysis of the numerical results can be performed by using the ratio of pressure drop in eccentric annulus to the concentric annulus (M) as suggested by Haciislamolu and Langlinais (1994). This ratio is plotted for all geometrical configurations considered in this study in Figure 1. It turns out that all curves overlay each other. This implies that a general pattern can be recognized in terms of growth of eccentricity. Alternatively, empirical correlations could be developed to express the pressure loss of an eccentric pipe as a function concentric pipe pressure loss. The small discrepancy between some cases can be attributed to the numerical error introduced by the non-uniform mesh size.
1 SPE 16613 The Effect of Pipe Rotation on Pressure Loss We also attempted to evaluate the effect of pipe rotation on frictional pressure losses (i.e. Casing Drilling). The inner pipe rotates with 2, 3, 4, 5 and 6 rpm which can be done by selecting the inner pipe boundary condition as a moving wall. We also specified the rotation speed in the center of the pipe that it rotates around its axial axis. As we discussed in the introduction, we can define a velocity ratio (ζ) parameter in order to specify the flow regimes in the annular space. It is found that the velocity ratio in the geometries considered in this study is between 1 and 1. That range specifies a mixed flow regime (i.e. between axial dominated and rotational dominated flow). Figure 11 shows a comparative analysis of the effect of pipe rotation on frictional pressure drop for all given geometries. Similar pattern of pressure drop as a function of radius ratio can be recognized. It is obvious that pipe rotation promotes shear thinning response to reduce the apparent viscosity exerted by Yield Power-Law fluid. The effect of pipe rotation on frictional pressure loss can be explained by looking into the velocity profile across the annular gap (Figure 11). For example, for the first configuration (κ=.7), the effect of pipe rotation distributed almost along the radial direction. The plug zone disappears by the increase of pipe rotation. This can be justified by the nature of shear thinning properties of Yield Power-Law fluid. We also illustrated the velocity profile inside annulus as depicted in Figure 12. As the rotation speed is increased the fluid behaves as less viscous. It is realized that by increasing inner pipe rotation the pressure loss will be lower which is reported also by Hemphill and Ravi (25). Pressure Gradient (Pa/m) 5 45 4 35 3 25 2 15 1 5.5.6.7.8.9 1 Radius ratio, κ ε = ε =.1 ε =.3 ε =.5 ε =.7 ε =.9 Figure 9: The effect of radius ratio on pressure drop for selected eccentricity values 1.2 Pressure Drop Ratio, M (dimensionless) 1.8.6.4.2.2.4.6.8 1 Eccentricity κ =.7 κ =.764 κ =.8 κ =.85 κ =.9 Figure 1: Effect of eccentricity on pressure drop ratios for selected radius ratios
SPE 16613 11 Pressure Gradient (Pa/m) 5 45 4 35 3 25 2 15 1 5 2 4 6 8 Pipe rotation (rpm) κ =.7 κ =.764 κ =.8 κ =.85 κ =.9 Figure 11: Velocity profile of Yield Power-Law in Concentric Annulus.6.5 Velocity (m/s).4.3.2.1.2.4.6.8 Position (m) Velocity Magnitude Tangential Velocity Axial Velocity Figure 12: Magnitude of velocity components in radial direction using 3 RPM for the radius ratio of.764 It is also a general practice to represent the results in terms of non-dimensional variables; i.e., friction factor in order to compare them the effect of no pipe rotation for the given geometry. The evaluated pressure drop for the case of no pipe rotation can be selected as a reference and then normalize all other values to obtain a ratio of friction factors. In another words, f/f means the ratio of friction factor with pipe rotation to that of without pipe rotation. The results are depicted in Figure 13. As can be seen the effect of pipe rotation is almost repeated for all given geometries, meaning that the pipe rotation lower the pressure drop in a similar manner. Using CFD to Simulate Field Data The geometry of the Casing Drilling operation corresponds to the second case with the radius ratio of.764 that was meshed and verified. The Fann viscometer dial reading data were converted to the corresponding shear rate and shear stress values using appropriate conversion factor. The results were then recognized as the rheological properties of Yield Power-Law fluid where the values of fluid properties are provided in Table 3.
12 SPE 16613 1.2 Pressure Drop Ratio, M (dimensionless) 1.8.6.4.2 κ =.7 κ =.764 κ =.8 κ =.85 κ =.9 2 4 6 8 Pipe rotation (rpm) Figure 13: The effect of pipe rotation on friction factor for the given geometries Table 3: Fluid Properties of Field Data Parameters Value Average Velocity, (m/s).89 Density, (kg/m 3 ) 124 Viscosity Model Herschel-Bulkley Yield Stress, (Pa).846 Consistency Index, (kg/m-s).416 Power-Law Index, n.591 Using the given fluid properties, we tried to match the CFD prediction with that of field data. The frictional pressure drop for field data was reported to be 135 Pa/m which could be obtained from Equivalent Circulating Density (ECD) data. Initially, we tried to obtain the pressure drop of the concentric geometry without pipe rotation. The CFD yields the pressure drop for the given geometry to be 33 Pa/m. The predicted value of pressure loss differs significantly from that of reported field data. The next step is to implement the effect of pipe rotation. Accordingly, the pressure drop evaluated to be around 178Pa/m. In order to match the real data, we can postulate that the casing may rotate off center. Therefore an attempt was made to realize the geometries with some guessed eccentricity values. Therefore, the closest prediction of pressure drop to that of field data yields the possible value of eccentricity. Increasing the eccentricity of the casing to the value of.9 reduced the pressure drop to for the given geometry. As a result, a combination of pipe rotation and eccentricity can give a lower pressure drop, here evaluated to be 151 Pa/m. The final velocity distribution is shown in Figure 13. The discrepancy between simulation and field data may be attributed due to neglecting the following constraints: the tool joints were not included in the geometry, and the walls were treated to be smooth surface. The effect of drill cuttings on flow regime drop was ignored. It is also interesting to note that the wellbore shape might not be circular as it is envisioned in our model. In addition to these reasons, assumption of no slip condition may not be appropriate for real application. Thermal effect as well as compressibility of the fluid may all contribute to overestimation of pressure losses. Case Table 4: Field Data Analysis Pressure gradient (Pa/m) Narrow Slot approximation 33 RPM = 7 and concentric 178 RPM = 7 and ε =.9 151 Field Data 135
SPE 16613 13 Figure 14: Velocity magnitude distribution across annular space using CFD to meet the reported pressure drop of the field Concluding Remarks Result of CFD simulation is verified by comparing with the Narrow Slot approximate solution. Comparing pressure loss and velocity profile prediction obtained from numerical and approximate solution were considered as a criterion to verify the accuracy of the simulation. In addition, the results of sensitivity analysis support the accuracy of our CFD scheme. The outcome of sensitivity analysis revealed that at radius ratios above.8 the frictional pressure gradient increases remarkably. It should be noticed that decreasing fluid behavior index reduces the growth of pressure losses. Implementing eccentricity in our simulation indicate that a general pattern can be recognized as a function of pipe eccentricity for Yield Power-Law fluids. CFD modeling predicts that the effect of eccentricity on pressure loss is more dominant in the range of ε =.2 and ε =.8 for the given geometries. The effect of pipe rotation is also incorporated in CFD simulation. It is also concluded that increasing pipe rotation helps to reduce the frictional pressure loss in annulus. This phenomenon is attributed to shear thinning properties of Yield Power-Law fluid. Thus pipe rotation tends to decrease frictional pressure loss by changing rheological status of the fluid inside the annulus. Comparing the results of CFD simulation with field data in a step-wise manner yields that Casing may have been offcentered in the wellbore. It is suggested to consider the effect of wall roughness at least for the wellbore wall to have more realistic estimation of the frictional pressure loss. In addition, it can be recommended to try to include several pipe joints along test section and study the effect of tool joints on pressure losses. Nomenclature CFD Computational Fluid Dynamics NPT Non Productive Time YPL Yield Power-Law fluid Frictional pressure losses E Dimensionless entrance length h Height of channel L e Entrance length m Power-law index w Channel width Re Reynolds Number V p Velocity in the plug region V y Velocity profile in the region surrounding plug κ Radius ratio of inner pipe and wellbore Difference between the center position of inner pipe and wellbore ε Eccentricity factor µ Fluid viscosity (Newtonian) ζ Velocity ratio Yield stress Shear stress at the wall
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