Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering OMAE2017 June 25-30, 2017, Trondheim, Norway

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1 Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering OMAE2017 June 25-30, 2017, Trondheim, Norway OMAE TEMPERATURE DEPENDENT TORQUE AND DRAG FOR 3-D WELLS: MODEL DESCRIPTION AND FIELD CASE STUDY Ekaterina Wiktorski University of Stavanger Stavanger, Rogaland, Norway Martin Tveiterå University of Stavanger Stavanger, Rogaland, Norway Dan Sui University of Stavanger Stavanger, Rogaland, Norway Bernt S. Aadnoy University of Stavanger Stavanger, Rogaland, Norway ABSTRACT Wellbore friction represents one of the biggest limitations for drilling and completion of long 3-dimensional wells. Traditionally, wellbore friction forces calculation is performed using soft-string torque and drag models, which assume tubular to be in contact with the wellbore at any point along its length. However, precise results are needed for wells with complex geometry and high doglegs. This paper presents a novel way regarding wellbore friction forces calculation, which takes into account both wellbore deviation and wellbore tortuosity. To locate contact points of the string and the wellbore, a Dogleg Severity filter, or DLSfilter is proposed. The DLS-filter is integrated into soft-string torque and drag models by taking into account dogleg, wellbore geometry and depth. Such simple implementation of DLS-filter makes it applicable for any case only if survey data is available. Fundamental understanding of drillstring mechanics and drilling fluids properties is essentially required in planning phase and drilling operations. To enhance the accuracy of torque and drag calculation, thermal effects on buoyancy forces and viscous forces have been studied. Experiments using one oil-based mud (OBM) recipe and one water-based mud (WBM) recipe have been conducted to measure viscosity and density of fluids in different pressure and temperature conditions. Based on the obtained results, viscosity model and density model as functions of pressure and temperature have been developed for better model interpretation of fluids thermal effects in HPHT conditions. Friction factor is a critical parameter to affect wellbore friction, which depends on fluids composition, contact surface, rotary speed, temperature, etc. Conventionally it is set constant for friction forces calculation. Experimental results show that the friction factor is heavily dependent on the temperature. In this study, friction factor was assumed to increase linearly with temperature for torque and drag calculation. The new approach provides more correct values for torque and drag, and gives a better understanding of the downhole environment, as cuttings transport and drillstring dynamics. The study can be further used for the evaluation and recommendation of drilling muds for HPHT wells. Such analysis will aid in the design of appropriate drilling mud in the integrated well planning phase. INTRODUCTION Excessive frictional forces, or torque and drag, are considered one of the major problems when drilling long deviated wells. They occur due to any physical obstructions in the wellbore: cuttings bed, sloughing hole, etc. Torque and drag analysis have been performed by a number of researchers and engineers since the 1980s. The key parameters considered in the models are buoyed string weight, wellbore inclination and friction factor. The latter parameter includes the effect of cuttings bed, fluid rheology, downhole pressure and temperature on modeling of a drillstring in a long deviated well [13]. The friction factor is typically estimated by post-analysing up- and down weights of the string. For torque and drag calculation, it is common to use one constant value in cased hole and another higher constant value in open hole due to the higher surface roughness of open hole. In addition, drilling fluids properties, like density and viscosity have a strong effect on torque and drag. These parameters together with mentioned friction factor are not 1 Copyright 2017 ASME

2 constant along the wellbore length as conventionally assumed, but rather vary with temperatures and pressures. As a part of this study, laboratory experiments were conducted to discover the temperature-pressure-dependency of fluids properties. As a result, three correlations that describe fluid density, viscosity and friction factor as functions of pressure and temperature were included into a soft-string torque and drag model to improve the model accuracy. In our improved torque and drag model, the wellbore is discretized into small sections between the survey points. Friction forces are calculated element by element as in the traditional soft-string models. Density, viscosity and friction factor are updated in each element regarding pressure and temperature of fluids. Finally, a field case from Garshinskoe field (Russia) is used for the method s illustration, where friction forces are calculated in different operations, like tripping, drilling and static operations. Comparisons are provided in terms of the calculations with/without considering thermal effects of drilling fluids. The results show the importance of temperature effect consideration for torque and drag calculation, especially in HPHT wells. NOMENCLATURE α = volumetric expansion coefficient A i = inside pipe area, m 2 A o = outside pipe area, m 2 B = buoyancy, c = compressibility of the fluid, Pa -1 d = drillpipe diameter, m D = wellbore diameter, m DL = dogleg DLS = dogleg severity FEM = finite element method g = gravitational acceleration, m/s -2 HPHT = high pressure high temperature I = wellbore angle MD = measured depth, m OBM = oil-based mud P = pressure, Pa P 0 = reference pressure, Pa PVT = pressure, volume, temperature Re = Reynolds number T = temperature, C T 0 = reference temperature, C U = fluid velocity, m/s WBM = water-based mud Z = true vertical depth, m β = isothermal bulk modulus, Pa µ = fluid viscosity, PaS ρ = fluid density, kg/m 3 ρ 0 = reference fluid density, kg/m 3 ρ o = fluid density in the annulus, kg/m 3 ρ i = fluid density in the drillpipe, kg/m 3 PROBLEM BACKGROUND Torque and drag model Good overview of the studies on this topic can be found in a number of papers, for example [14], [2], and [10]. Mirhaj et al., 2016 [11] made a comprehensive summary of stiff-string models. This section describes the most well-known models for torque and drag calculations and their pros and cons without going into details about models modifications that followed up. Torque and drag is one of the most studied topics in mechanics of drilling, which has started with the works of Johancsik et al., [5]. In 1984, they published a paper to present a mathematical model to calculate torque and drag. This model has been widely used and modified all over the world ever since. In their research, Johancsik et al. consider sliding friction forces caused by contact of the drillstring with the wellbore as the only source of torque and drag, disregarding possible hole instability, cuttings bed, dogleg and tortuosity. Effect of mud lubrication was not taken into account either. Johancsik and colleagues assumed the normal force contributors to be gravity and tension acting through curvatures of the wellbore. Other possible contributors were not considered. This model assumes the string to repeat the shape of the wellbore. The model is user-friendly and is often preferred to models that use stiff string approach because there is no need to determine contact points of the string and the wellbore. However, it gives imprecise values for torque and drag for deep and directional wells. Another approach for solving friction forces is already mentioned stiff-strings models. While it is difficult to say what is the most typical stiff-string model, soft-string models with additional elements characteristic for real behaviour of a string in a wellbore have been developed by a number of authors. A sophisticated method to solve this problem is finite element method for structures (FEM). This method allows to calculate displacements in the drillstring to determine the radial clearance and pipe extension or compression, and shear forces (forces that act in the transverse direction) and bending moments to account for string s bending stiffness. In such models, the string is traditionally described as a structure that consists of 3-dimentional beams connected through the nodes. Each node has six degrees of freedom: three displacements and three rotations in each direction. The boundary conditions for the structure are typically defined at the rotary table and the bit. Good examples of modern studies on this topic are presented, for instance, in Tikhonov 2013 [14], Zhu 2015 [17] and Wu 2011 [16]. In this paper, an analytical 3-dimentional soft-string torque and drag model developed by Aadnoy et al. [1] (see Annex A for the details) is modified to achieve more accuracy in consideration of wellbore geometry, dogleg severity and temperature effect, etc. The wellbore is divided into small cells, where a length of the cells is determined by directional surveys. The torque and drag calculation is performed in each cell according to its shape: straight or curved. The cell s shape is 2 Copyright 2017 ASME

3 determined by the proposed DLS-filter (presented in the next section). DLS-filter Frictional characteristics for straight inclined wellbore sections and curved sections are different. In straight inclined sections, the friction is mainly dependent on the pipe weight. In curved wellbore sections, normal forces, string tension, etc. affect the friction, and the friction is higher than in straight sections. In the following, we propose to use a DLS-filter to discriminate between curved and straight wellbore sections. The DLS-filter is a simple model, which takes into account both planned inclination and wellbore tortuosity. Only few input parameters: dogleg, measured depth, pipe diameter and wellbore diameter are fed to the DLS-filter, which makes it applicable to any case if survey data is available. Figure 1 shows three neighbour survey points: n-1, n and n+1. The distance between them is assumed a circular wellbore segment. In Figure 2, the sinusoidal line represents a wellbore wall and the reference line represents the drillpipe. The height h is a real radial clearance between the drillpipe and the wellbore. Figure 1: Illustration of the DLS-filter The radii (R n-1, R n, R n+1 ) of these three circular sections can be found as following: R!!! =!!!!!!! (1) R! =!!! (2) R!!! =!!!!!!! (3) where L is the wellbore length between two points and DL is the dogleg. Further, the heights x from the drawing can be found using the radii calculated above as: x!!! = R!!! (1 cos!!!! x! = R! (1 cos!! x!!! = R!!! (1 cos!!!! ) (4) ) (5) ) (6) An approximation of the height difference between the reference line and the point x! can be calculated as follows: h =!! x!!! x!!! + x! (7) The radial clearance is given as diameter of the wellbore (D) subtracted diameter of the string (d). Figure 2: A string inside the wellbore Therefore, the conditions for discrimination between straight and curved wellbore section by DLS information are as follows: If h< (D-d) à the wellbore section is considered straight; If h> (D-d) à the wellbore section is considered curved. Temperature model At greater depths, drilling fluid experiences increased pressure and temperature. Pressure and temperature variations affect drilling fluid properties. For instance, fluid is compressed when exposed to high pressure, resulting in increased density. High temperature has the opposite effect: when drilling fluid is heated, it expands, what results in decreased density [6]. This effect is especially pronounced in HPHT wells. The knowledge about fluid properties variation with pressure and temperature is essential to predict the real behaviour of the drilling fluid in the well. The temperature of the circulating fluid is a function of several factors as geothermal gradient and depth, inlet drilling fluid temperature, formation thermal conductivity, earth surface temperature, etc. Heat enters the drillpipe through convection, i.e. circulating fluid acts as the heat transferor between the wellbore and the pipe. Heat is transported from the annulus to the drillpipe through conduction, i.e. heat transfer through the pipe walls caused by temperature differences between the inside and outside of the pipe. Modern equipment gives the possibility to perform direct temperature measurement at a given depth. A solid temperature model is necessary though to simulate the heat transfer from the surrounding environment to the fluid at arbitrary points along the well. A model to simulate the wellbore temperatures used in our study is presented in Apak 2006 [4]. The model s detailed description can be found in Annex B. Density model Density of a drilling fluid circulating in a well depends on pressure and temperature: ρ = ρ(p, T). By taking derivative, we have [8]: p, T = + (8) 3 Copyright 2017 ASME

4 There are a few models to calculate a density of a drilling fluid. In this study, we use a linear model, which is given as follows: ρ = ρ! +!!! p p! ρ! α(t T! ) (9) where the isothermal bulk modulus of a liquid (β) and the volumetric expansion coefficient of a liquid (α) are defined as: β = ρ!! (10) α =!!! ( )! (11) Ρ 0, ρ 0 and T 0 are the reference points for the linearization. The bulk modulus is multiplicative inverse of the fluid s compressibility, c =!. It is a dominating parameter in the! density model as it characterises the pressure variations, which happen more rapidly than the temperature variations [8]. Temperature effect on the fluid density is often neglected because it is not as pronounced as pressure effect. However, for HPHT wells, where the temperature gradient is high, it is important to consider the effect of both parameters. The fluid s compressibility and the volumetric expansion coefficient are related as follows: c = α. Fluid pressure loss in a well Dynamic fluid pressure loss gradient in a well,, is a function of several factors: diameter of the drillpipe, viscosity of the fluid, density of the fluid, velocity of the fluid, roughness of the pipe wall, inclination of the pipe and flow regime type. Fluid pressure loss gradient in a circulating well mainly consists of two terms: frictional pressure gradient and hydrostatic pressure gradient, and can be expressed as follows [8]: = ( )! + ( )! (12) where ( )! = ρgcosi is a hydrostatic pressure gradient and =!!!!! ρu! is a frictional pressure gradient. EXPERIMENTS AND MODELING Fluid density modeling A new method for measuring PVT (pressure, volume, temperature) properties of drilling fluids was applied in this study. A PVT apparatus MPRO 6265 Chandler, Figure 3, was used to determine drilling fluid density under various pressures and temperatures. The experiments were performed for an OBM recipe and a WBM recipe. The recipes are given in Annex C. ` Figure 3: MPRO 6265 Chandler at a laboratory of University of Stavanger A plastic bag filled with mud was placed in the PVT cell, and the latter was then slowly filled with water under standard conditions (1 atm, 24 0 C). The injected volume of water was measured. At the moment first water appeared from the outlet, the inflow was stopped, and pressures in the range of psi and temperatures in the range of 24 0 C 90 0 C were applied. The volume of the mud inside the cell is calculated by subtracting the injected volume from the total volume of the cell. The temperature is raised with small increments, which provides a continuous function, V(T) P, see Figure 4. Mud volume, ml Mud volume, ml psi 1500 psi 3000 psi 4000 psi 5000 psi Temperature, C a) psi 2000 psi 3000 psi 4000 psi 5000 psi Temperature, C b) Figure 4: Thermal expansion of drilling mud under constant pressure, a) OBM sample b) WBM sample. 4 Copyright 2017 ASME

5 Figure 4a) demonstrates that thermal volume expansion for OBM sample is nearly linearly proportional to the temperature. Figure 4b) shows that the expansion gradient increases with the temperature for WBM sample. It means that OBM becomes denser with increasing temperature than WBM. This observation agrees with experiments results presented in [9]. Since the drilling fluid mass is constant, the density is easily back calculated with the known volume. Fluid volume variation with temperature and pressure for OBM sample and WBM sample respectively is presented in the figures below. Picks on the volume curves are the result of the corresponding pressure fluctuations. a) Multiple regression then was applied to determine the bulk modulus and the volumetric expansion coefficient of the drilling fluids used in the experiment, see Table 1. Table 1: Coefficients for the density model The data analysis was applied, and it was determined that the multiple regression is valid. The input parameters one related to pressure and another one related to temperature show significant correlation with the dependent parameter, fluid compressibility (c) for both OBM and WBM samples, as p-values are << 0.05 in both cases. The adjusted R 2 for OBM data analysis is 0.97, and for WBM data analysis is 0.89, which indicates that the variation in the output parameter can be described by the applied model with good precision. The obtained coefficients can now be directly inserted into a density model, equation (9). Fluid viscosity modeling Anton Paar s Modular Compact Rheometer (MCR) 302, Figure 6, was used to measure the viscosity of OBM and WBM samples under various pressures and temperatures. The applied pressures were in the range bars with 40 bars interval, and the temperatures were in the range C with 5 0 first interval and 10 0 the following intervals. Shear rate vs. shear stress for the two fluid samples for the tested pressures can be found in Annex D. The model based on the linear interpolation method was developed to find fluids viscosity at arbitrary pressure and temperature. The model was later integrated into the torque and drag model. Figure 6: Anton Paar s MCR 302 [4] b) Figure 5: Mud volume and density variations with pressure and temperature, a) OBM sample, b) WBM sample. Friction factor modeling As mentioned before, friction factor is typically calculated by post-analysing data from offset drilled wells. In [7], they conducted a series of experiments with tribometer an apparatus to measure friction factor and forces between two surfaces for different fluids. They discovered that friction factor linearly increases with temperature as: (13) 5 Copyright 2017 ASME

6 where µ 0 is constant. The slope depends on the drilling fluid properties and contact surfaces. For instance, steel to steel (cased hole situation) gives lower friction than steel to formation (open hole situation). In [7], overestimated values of µ 0 were chosen to fit the experimental data. Therefore, these values need to be further calibrated regarding each particular case. formation to warm up fluids in the annulus. Once the fluid has reached the temperature of the formation, the annular temperature starts approaching the wellbore temperature of the open hole as well. The temperature in the annulus decreases towards the bottom due to heat transfer from the annulus to the cool drilling fluid. FIELD CASE A field case using data collected from a well drilled in 2015 on Garshinskoe field, Russia illustrates the proposed temperature-dependent torque and drag model. The well was drilled vertically down to 1543m. The total depth was 2524m MD with the maximum inclination 30 0 and azimuth at the bottom of the well. Directional surveys on average were taken every 22 meter. The wellbore was drilled with water down to the point of interest (2476m MD). In our simulations, to show the application of the new model, we analyse two cases: using tested WBM and OBM as drilling fluids for the current well. In the paper, we will mostly provide figures for WBM case. Simulation results for both cases are given in Table 3 and Table 4. Drilling parameters and wellbore configuration are presented in the table below. A table with directional surveys is given in Annex E. Table 2: Drilling parameters and wellbore configuration for the presented field case Bit diameter, in 8.69 Casing OD, in Analysed well depth, MD, m Total well depth, MD, m Flow rate, l/min 37 RPM 40 Fluid density, WBM, kg/m Fluid density, OBM, kg/m Fluid viscosity, WBM, PaS Fluid viscosity, OBM, PaS 20* *10-3 Temperature and Pressure Simulation Torque and drag analysis starts with the calculation of wellbore temperatures and pressures, as the real values for temperatures and pressures at survey points were not available for the analysis. The input parameters for the temperature model are very specific for each geographical and geological area and were unknown. Thus, the average values were assumed and fed to the temperature model described earlier. The temperature profile for the current well using WBM is presented in Figure 7. From the figure, two observations can be done. Firstly, the temperature in the drillstring is lower than that of annulus and formation. It happens due to the cooling effect of the fluid entering at the surface and flowing down through the pipe. Secondly, the annular temperature is very close to the geothermal gradient for the current case. It happens because low flow rate used while drilling allows the hot Figure 7: Temperature distribution for the field case using WBM In this paper, bisection method [15] was used to determine the wellbore pressures in the annulus and the drillpipe. The initial estimates for the annular pressure were the hydrostatic wellbore pressure at the bottom and atmospheric pressure at the outlet. The search interval for the bottomhole pressure was set to 300 bars this value can be changed if required. The pressure was calculated incrementally using analytical equations starting with the bottom and moving upwards along the annulus. The equations are given earlier in the paper. Once we have reached the desired surface pressure, we conclude that the correct bottomhole pressure was found. At the wellbottom, drillpipe pressure is equal to annular pressure. Following this assumption, bisection technique was used to calculate pressures inside the drillpipe for each section, where a section is the distance between two survey points. The calculation results for WBM case are presented in Figure 8. 6 Copyright 2017 ASME

7 Figure 8: Pressure distributions for the filed case using WBM Density and friction factor simulation The density of the drilling fluids was calculated based on the linear model described in the previous section, equation (9). The results are presented in Figure 9. From the figure, we see that the density increases with depth for the analysed WBM. It means that WBM variations with depth are pressure dominated, as density increases with pressure. The density decreases with depth for the OBM sample. It means that variations in density of OBM are temperature dominated, as density decreases with temperature. b) Figure 9: Density profiles for the field case a) WBM, b) OBM Friction factor in the well was calculated as a function of temperature using the model described above. For this case we assumed an open hole friction factor to be 0.25 and cased hole friction factor The slope was set to 1*10-3. Constant friction factor versus friction factor as a function of depth for the WBM case are presented in Figure 10. Figure 10: Constant and varying friction factor for WBM case a) DLS-Filter Simulation One of the main features of the new model is the employment of the DLS-filter to discriminate curved wellbore sections and straight wellbore sections by using DLS data and wellbore geometry. Straight sections are defined as either having zero inclination or constant deviation with zero or 7 Copyright 2017 ASME

8 negligible dogleg. In Figure 11, the 3-D wellbore trajectory of the analysed well is presented along with the DLS-filter. Figure 11: Wellbore trajectory and application of the DLSfiler Torque and Drag Simulation Here, the torque and drag for different operational modes were calculated using the new integrated temperature dependent model. Torque and drag for WBM case are presented in the following figures, and calculation results for both OBM and WBM cases are given in Table 3 and Table 4 together with the results obtained using the original 3-D softstring torque and drag model for easy comparison. From Table 3 and Table 4, we see that the original model underestimates axial force for hoisting operations, and overestimates the same for lowering operations comparing to the axial forces calculated using the new model and WBM and OBM. The static weight calculated by the two models has similar values for WBM and differs slightly for OBM. There are two main reasons for such results, namely, fluid density and friction factor variations with depth. In the static condition, since the string is not moving axially in the well, the friction is negligible, and the dominating parameter affecting the hook load is buoyed weight of the drillstring. The density of the OBM decreases with depth, causing lower buoyancy and higher string weight. The density of the WBM used in the simulations increases with depth. However, since the density variation between well top and the well bottom is very small, it does not affect the final drag. During axial motion, friction factor becomes the dominating parameter to affect the hook load, which acts in the opposite direction to the movement, decreasing slack-off weight and increasing pick-up weight. Since the friction factor increases with depth due to the increased temperature, drag is additionally increased during pick-up and decreased during slack-off for both WBM and OBM case. The new model, unlike the conventional torque and drag models, considers this effect and improves the accuracy of the results. Figure 12: Drag force for the field case, WBM Figure 13: Magnified graph of drag force for the field case, WBM Torque calculated using the original model and the new model is presented in Figure 14. Calculation results show that the old model underestimates torque by around 17% for both WBM and OBM for the presented field case. It means that the thermal effect on the friction forces is significant and should be considered when designing long deviated wells to predict and mitigate the effect of excessive torque and drag on rotating drillstring. 8 Copyright 2017 ASME

9 Figure 14: Torque loss in the well, WBM Table 3: Modeling results for WBM case a) Static drag (DS), pick-up drag (DH) and slack-off drag (DL), b) Static torque (TS), pick-up torque (TH) and slack-off torque (TL). DS, kn DH, kn DL, kn Old model New model a) TS, knm TH, knm TL, knm Old model New model b) Table 4: Modeling results for OBM case a) Static drag (DS), pick-up drag (DH) and slack-off drag (DL), b) Static torque (TS), pick-up torque (TH) and slack-off torque (TL) DS, kn DH, kn DL, kn Old model New model a) TS, knm TH, knm TL, knm Old model New model b) CONCLUSIONS This paper presents experimental and theoretical work to improve an existing soft-string torque and drag model. The following conclusions can be drawn based on the experiments performed with an OBM and a WBM sample: 1. Volumetric thermal expansion gradient is rather constant for the OBM sample and increases with increasing temperature for WBM sample. OBM becomes denser with increasing temperature than WBM; 2. Effect of pressure and temperature on drilling fluids should not be overlooked. PVT tests are especially beneficial to perform on drilling fluids used for HPHT wells. Pressure and temperature dependent friction factor, fluid density and viscosity along with the DLS-filter were incorporated into the 3-D soft-string torque and drag model. The result was an integrated temperature dependent torque and drag model for friction forces calculation under different operational modes: hoisting, lowering and static conditions. The results gave a better understanding how temperature and pressure affect torque and drag in a well. Based on the obtained results, several conclusions can be drawn: 1. Density of tested WBM increases with depth, i.e. WBM s density is pressure dependent; density of tested OBM decreases with depth, i.e. OBM s density is temperature dependent; 2. The original torque and drag model underestimates drag values for pick-up and torque off-bottom and overestimates values for drag under slack-off for tested WBM; the original model underestimates drag values for pick-up, under static conditions and torque off-bottom and overestimates values for drag during slack-off for tested OBM; 3. Friction factor is the crucial parameter for torque and drag calculation in deviated wells. Its effect is more pronounced than the effect of other properties of drilling fluids. In the future research, different drilling mud recipes will be tested for PVT properties using the described method. The friction factor dependence on temperature will be studied by conducting more experiments with tribometer for various surfaces and drilling fluids. The sensitivity analysis of the new model and cuttings transport simulation will be performed to find optimal operational parameters to reduce excessive torque and drag. The proposed model will be used for simulation of friction forces in HPHT wells, and wells with complicated geometry. ACKNOWLEDGMENTS We express our gratitude to Dr. Mahmoud Khalifeh, University of Stavanger (UiS), for providing guidance during experiments with PVT machine and to Jorunn Hamre, UiS, for providing mud samples. We also thank Research network for environmental energy (forskningsnettverket for miljøvennlig energi.) of UiS for their financial support for the master student that contributed to this paper. 9 Copyright 2017 ASME

10 REFERENCES [1] Aadnoy, B.S., Fazaelizadeh, M. and Hareland, G., A 3D analytical model for wellbore friction, Journal of Canadian Petroleum Technology, 49(10), pp [2] Al-basheir Khidir Basheir Al-haj, 2015, Modelling of Torque and Drag in Extended Reach Drilling Using Landmark Software, Bachelor thesis, Sudan University of Science and Technology. [3] Anton Paar, «The Modular Compact Rheometer Series» Retrieved from L=6 [4] Apak, E.C., 2006, A study on heat transfer inside the wellbore during drilling operations, Master thesis, Middle East Technical University. [5] Johancsik, C.A., Friesen, D.B., Dawson, R., 1984, June. Torque and Drag in Directional Wells- Prediction and Measurement, Journal of Petroleum Technology, 36(06), pp [6] Karstad, E., 1999, Time-Dependent Temperature Behavior in Rock and Borehole, PhD thesis, High school in Stavanger, Stavanger. [7] Karstad, E., Aadnoy, B.S. and Fjelde, T., 2009, A study of temperature dependent friction in wellbore fluids, SPE/IADC Drilling Conference and Exhibition. Society of Petroleum Engineers. [8] Kaasa, G.-O., Stamnes, Ø. N., Imsland, L., & Aamo, O. M., 2011, Simplified Hydraulics Model Used for Intelligent Estimation of Downhole Pressure for a Managed-Pressure Drilling Control System, SPE Drilling & Completion, 27(01), pp [9] McMordie Jr, W.C., Bland, R.G. and Hauser, J.M., 1982, Effect of temperature and pressure on the density of drilling fluids,. SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. [10] Mirhaj, S.A., Kaarstad, E. and Aadnoy, B.S., 2011, Improvement of torque-and-drag modeling in long-reach wells, Modern Applied Science, 5(5), pp [11] Mirhaj, S.A., Kaarstad, E. and Aadnoy, B.S., 2016, Torque and Drag Modeling; Soft-string versus Stiff-string Models, SPE/IADC Middle East Drilling Technology Conference and Exhibition. Society of Petroleum Engineers. [12] Mitchell, R.F., 2008, Drillstring Solutions Improve the Torque-Drag Model, IADC/SPE Drilling Conference, Society of Petroleum Engineers. [13] Samuel, R., 2010, "Friction factors: What are they for torque, drag, vibration, bottom hole assembly and transient surge/swab analyses?", Journal of Petroleum Science and Engineering, 73(3,4), pp [14] Tikhonov, V., Valiullin, K., Nurgaliev, A., Ring, L., Gandikota, R., Chaguine, P. and Cheatham, C., 2013, Dynamic Model for Stiff String Torque and Drag, SPE/IADC Drilling Conference. Society of Petroleum Engineers, pp [15] C. Woodford, C. Phillips, 2011, Numerical Methods with Worked Examples: Matlab Edition, Springer Science & Business Media, pp [16] Wu, A., Hareland, G. and Fazaelizadeh, M., 2011, Torque & drag analysis using finite element method, Modern Applied Science, 5(6), pp [17] Zhu, X.H., Li, B., Liu, Q.Y., Chang, X.J., Li, L.C., Zhu, K.L. and Xu, X.F., 2015, New Analysis Theory and Method for Drag and Torque Based on Full-Hole System Dynamics in Highly Deviated Well, Mathematical Problems in Engineering. 10 Copyright 2017 ASME

11 Staight inclined or vertical section: Drag for vertical or straight inclined section, no rotation: F! = F! + β Lw cosα ± μsinα Torque loss for straight inclined section without axial motion: T = μrβw Lsinα Torque loss for vertical section: T=0 Drag for vertical or straight inclined section, combined motion: F! = F! + β Lw cosα ± μsinα sin ψ Torque loss for straight inclined section, combined motion: T = µrβw Lsinαcos ψ Curved section: Drag without rotation: F! = F! e ±!!!!!! + βw L sinα! sinα! α! α! Torque loss without axial motion: T = μrf! θ! θ! Drag, combined motion: F! = F! + F! (e ±!!!!!! 1) sinψ + βw L sinα! sinα! α! α! Torque loss, combined motion: T = µrf! θ! θ! cos ψ ANNEX A TORQUE AND DRAG MODEL USED IN THE PAPER where: α = is wellbore inclination, rad if not trigonometrical function ψ = tan!!!! = tan!! (!! ) angle between tangential and axial velocity, rad!!!!!! F! = drag at the previous segment, N T = torque, Nm L = length of the segment, m β = buoyancy factor, w = weight per meter, N/m, µ = friction factor, r = pipe radius, m, θ = dogleg angle, rad 11 Copyright 2017 ASME

12 ANNEX B TEMPERATURE MODEL Temperature in tubing and annulus in degrees Celsius are calculated respectively as: T! z, t = (C! e!!! + C! e!!! + Gz + T! G A 32)/1.8 T! z, t = 1 A θ!c! e!!! + θ! C! e!!! + G + C! e!!! + C! e!!! + Gz + T! G 32 /1.8 A where: C! = T T! + G A θ 2e θ 2H G θ 1 e θ 1H θ 2 e θ 2H C! = T T! + G A θ 1e θ 1H G θ 1 e θ 1H θ 2 e θ 2H θ! = B + θ! = B B! + 4AB 2 B! + 4AB 2 B = 2πr!! U! k e ρqc (k! + r U! f t! ) A = 2πr U! ρqc T a T t f t! = t! 1 0,3 t!, if 10! t! 1.5; f t! = (0, ,5lnt! 1 +!,!!!, if t! > 1,5 t! = α!t r! 3600 α! = k e ρ e c e The overall coefficient of heat transfer in from annulus to tubing can be found from the following expression: U! = 1/ 1 h! + r k! ln r r + r r 1 h! The overall coefficient of heat transfer in from formation to annulus for an open hole can be simplified to: U! = h! Where the heat transfer of tubing is given as: h! = 0,023!!!! N #!,! N!!!,! ; 12 Copyright 2017 ASME

13 And the heat transfer of annulus is given as: h! = 0,023!!!! N #!,! (N )!,!. In these two equations, Prandtl number is given as N =!!!!, and Reynold s number for pipe is given as N! = ρq2! μa. Parameters used in this model, their units and values used for our simulations are summarized in the table below: Symbol: Definition: Unit: Value: c e Specific heat of earth Btu/(lb-F) 0.2 c fl Specific heat of fluid Btu/(lb-F) 0.4 k e Thermal conductivity of earth Btu/(ft-F-hr) 1.3 k t Thermal conductivity of tubing Btu/(ft-F-hr) 20 r ci Inner radius of casing inch r ti Inner radius of tubing inch 2.5 r to Outer radius of tubing inch r ω Well radius inch ρ e Density of the earth lb/ft G Geothermal gradient F/ft g Gravitational acceleration m/s H Total TVD ft k f Thermal conductivity of fluid Btu/(ft-F-hr) 1 Q Fluid s flow rate gal/hr t Circulation time hr t D Dimensionless time N/A N/A T i Inlet temperature F 68 T s Temperature of surface F 68 z True vertical depth ft N/A μ Dynamic fluid viscosity lb/ft/hr ρ Fluid s density lb/gal Copyright 2017 ASME

14 Water-based mud recipe: 1. Water, 10 liters 2. NaCl, 50 g 3. CaCl 2 x 2H 2 O, 50 g 4. Bentonite, 600 g 5. Barite, 1000 g 6. Sifted sand (0-100 µm), 80 g Oil-based mud recipe: 1. Mineral oil (EDC95/11), 206 ml 2. CaCl 2 solution, 60 ml 3. Emulgator (One-Mul), 10 ml 4. Ca(OH) 2, 8.5 g 5. Organic clay (Versa Vert Vis), 5.5 g 6. Versatrol, 6 g 7. Barite, 115 g ANNEX C RECIPES FOR MUD SAMPLES USED IN THE EXPERIMENTAL WORK 14 Copyright 2017 ASME

15 Shear rate vs. shear stress for OBM sample: ANNEX D 40 bar 80 bar Shear stress, Pa Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa 120 bar Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa 160 bar Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C 15 Copyright 2017 ASME

16 Shear rate vs. shear stress for WBM sample: 40 bar 80 bar Shear stress, Pa Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa 120 bar Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C Shear stress, Pa 160 bar Shear rate, 1/s 25 deg C 40 deg C 50 deg C 60 deg C 70 deg C 80 deg C 16 Copyright 2017 ASME

17 ANNEX E DIRECTIONAL SURVEYS FOR THE PRESENTED FIELD CASE Inclination, deg Azimuth, deg MD,m TVD,m Inclination, deg Azimuth, deg MD,m TVD,m 0,39 188, , ,3 29,04 95, , ,1 0,64 144, , ,7 29,73 95, , ,1 1,68 123, , ,1 30,04 95, , ,4 2,71 111, , ,1 30,02 96, , ,7 4,34 104, , ,4 30,02 98, , ,7 5,72 98, , ,8 30,17 99, , ,0 7,23 95, , ,0 30,22 100, , ,9 8,20 96, , ,2 29,89 100, , ,7 9,23 95, , ,3 10,23 95, , ,2 11,49 97, , ,1 12,34 96, , ,9 13,72 96, , ,6 15,07 96, , ,1 15,92 96, , ,6 17,01 97, , ,8 18,71 97, , ,0 20,13 97, , ,0 22,11 97, , ,7 23,32 97, , ,1 24,00 96, , ,4 24,72 97, , ,5 25,66 97, , ,5 27,20 96, , ,3 28,50 97, , ,9 29,58 96, , ,1 30,77 96, , ,0 30,74 96, , ,2 29,05 95, , ,8 29,30 95, , ,1 29,20 95, , ,3 29,38 95, , ,5 28,93 95, , ,7 17 Copyright 2017 ASME

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