New Method for Well Kick Tolerance Calculation

Advances in Petroleum Exploration and Development Vol. 5, No., 013, pp. 69-74 DOI:10.3968/j.aped.1955438013050.1483 ISSN 195-54X [Print] ISSN 195-5438 [Online] www.cscanada.net www.cscanada.or New Method for Well Kick Tolerance Calculation ZHOU Yanjun [a] ; JIA Jianhon [a],* ; WANG Guanlei [a],[b] ; WANG Jinyin [b] [a] Institute of Drillin Technoloy, Shenli Petroleum Enineerin Co., Ltd, Sinopec, Donyin. [b] Collee of Petroleum Enineerin, China University of Petroleum (East China), Qindao, China. * Correspondin author. Received 16 May 013; accepted 6 June 013 Abstract Well kick is an important basic parameter in the well drillin operation, and it directly determines the Casin layers as well as casin depth. At the same time it also directly determines whether the well drillin will be performed continuously or whether the well-killin operation should be carried out in the well drillin process. Based on the current questions about the well kick tolerance values, the influence caused by several factors such as invasion amount of formation fluid, the distribution of formation fluid in the wellbore and the shut-in casin pressure should be taken into consideration. Accordin to the annular multiphase flow theory, the well kick tolerance calculation model is brouht out, besides the relationship between well kick tolerance and formation fluid permeability as well as formation pressure forecastin error is simulated and analyzed. Based on the above analysis it can be seen from the result that when the permeability increases, the well kick tolerance oes up by followin the exponential function module. And when the formation pressure forecastin error increases, well kick tolerance oes up sinificantly. Therefore the simulation result could used to effectively direct the well structure desin for complex deep wells. Key words: Well kick tolerance; Casin depth; Permeability; Formation pressure; Well structure Zhou, Y. J., Jia, J. H., Wan, G. L., & Wan, J. Y. (013). New Method for Well Kick Tolerance Calculation. Advances in Petroleum Exploration and Development, 5(), 69-74. Available from: URL: http://www.cscanada. net/index.php/aped/article/view/j.aped.1955438013050.1483 DOI: http://dx.doi.or/10.3968/j.aped.1955438013050.1483 ILLUSTRATION OF SIGNS ρ, ρ o, ρ m, ρ c Density of as, oil, drillin fluid and drillins, k/m 3 ; E, E o, E m, E c Volume fraction of as, oil, drillin fluid and drillins; v, v o, v m, v c Velocity of as, oil, drillin fluid and drillins, m/s; q, q o Gas production speed and oil production speed in low-deree permeability formation, m 3 /s; R s Producin as-oil ratio; B o Volume coefficient of oil; ρ os Relative density of oil under Standard Condition; ρ s Relative density of as under Standard Condition; A P Cross sectional area inside drillin column, m ; A a Cross sectional area inside annular space, m ; c m Specific heat of drillin fluid, J/k ; K e Coefficient of thermal conductivity of formation, W/m ; m p Mass flow inside drillin column, k/s; m a Mass flow inside annular space, k/s; r p Drillin column radius,m; r a Annular space radius, m; T p Temperature inside drillin column, ; T a Temperature inside annular space, ; T e Temperature of formation or sea water, ; T in Temperature of entrance of drillin column, ; U p Overall heat transfer coefficient inside drillin column, W/m ; v p Velocity of drillin fluid inside the drillin column, m/s; U a Overall heat transfer coefficient inside annular space, W/m ; v a Velocity of drillin fluid inside the annular space, m/s; v s,v so,v sm,v sc Superfacial velocity of as, oil, drillin fluid and drillins, m/s; 69 Copyriht Canadian Research & Development Center of Sciences and Cultures

New Method for Well Kick Tolerance Calculation C, C o, C c Distribution coefficient of as, oil and drillins; v r, v or,v cr Superfacial velocity of as, oil and drillins, m/s; ρ cen Comprehensive density of as core fluid, k/m 3 ; f cen Friction resistance coefficient of as core fluid; T pc Critical temperature of natural as, ; P pc Critical pressure of natural as, MPa; ρas γ ;T Temperature, K; ρair p Pressure,MPa; M Averae molecular weiht of natural as, k/ kmol; ρ Density of natural as under mobility condition, k/m 3 ; T Temperature, ; K Formation permeability, μm ; H Net pay thickness of as layer, m; μ Viscosity of as, mpa s; B Volume coefficient of as; P i Oriinal formation pressure, MPa; P wf (t) Flow pressure at well bottom, MPa. INTRODUCTION The well kick tolerance reflects the rick deree of well kick phenomenon. The value of this parameter is determined by the ability of controllin the well kick in the field. Currently, there are several kinds of definitions and calculation methods for well kick tolerance [1]. In some oversea reports the pit ain (PG), drillin fluid density increment and balanced formation pressure forecastin error are mainly used to represent this parameter. Domestically, well kick tolerance means the allowable value of well kick amount which is enerated because of the error of formation pressure forecastin, which is described by equivalent density. And it s relevant to the formation pressure forecastin error. The value of well kick tolerance is mainly determined accordin to empirical operation. When the equipment technoloy is under ood condition, the value could be set very low while if there is hih risk in the well drillin operation, the value could be set very hih relatively []. Alon with the development towards vertical depth direction of the well drillin operation the drillin formation is complex, the drillin pressure layer system is rich and formation information is uncertain. Under these situation, when the reularly-recommended well kick value is used the hiher error miht be inevitable. In this essay, a series of factors such as permeability of formation, borehole, drill strin size, drillin fluid, well depth, technoloy and operation are taken into comprehensive consideration. Furthermore, the as invasion to formations with different permeability is iven simulation and solution by applyin the annular multiphase flow theory. In the simulation operation, the relationship between well kick tolerance and formation permeability, formation pressure forecastin error is analyzed, which provides enhanced direct to well structure desin for complex deep wells. 1. CALCULATION MODEL OF WELL KICK TOLERANCE Accordin to the characteristics of fluid invasion in formations and by combinin annular fluid mobility form and phase distribution under different situations, the key parameters such as the annulus pressure profile, volume fraction profile and shut-in casin pressure are determined correspondinly. Meanwhile the time factor which is related to formation fluid invasion is taken into consideration, therefore the calculation method of well kick tolerance of formation is enerated. 1.1 Basic Assumption of Annular Multiphase Flow Model [3,4] 1 Continuum theory, which means each phase of fluid is composed of consecutive mass points The fluid in the well is treated based on Black oil model, in other words the phase conversion between oil and as is taken into consideration, however there is no mass transfer between as and drillin fluid (or water) 3 The compressibility of drillin fluid (or water) is not taken into consideration 4 The fluid mobility belons to one-dimension mobility which is followin the well borehole direction 5 It s assumed that there is stable radial heat-transfer between the formation and well borehole, then the fluid inside the well is situated as thermodynamic equilibrium state. 1. Mass Conversion Equation Mass conversion equation of as fraction: Rs ρseo Rs ρseo ( ρe + ) + ( vo + ρev ) q (1) Bo Bo Mass conversion equation of oil fraction: ρos ρos ( Eo) + ( Ev o o) qo () Bo Bo Mass conversion equation of drillin fluid: ( ρmem) + ( ρmev m m) 0 (3) Mass conversion equation of drillin fluid drillins: ( ρcec) + ( ρcev c c) 0 (4) Copyriht Canadian Research & Development Center of Sciences and Cultures 70

ZHOU Yanjun; JIA Jianhon; WANG Guanlei; WANG Jinyin (013). Advances in Petroleum Exploration and Development, 5(), 69-74 1.3 Momentum Conservation Equation ( Eρv+ Eoρovo+ Emρmvm+ ECρCvC) + ( Eρv + AEoρovo + Emρmvm + ECρCvC) P + E ( ρ + Eoρo + Emρm + ECρC)cos α + ( P) + ( ) f 0 (5) 1.4 Enery Equation Because the temperature distribution inside the wellbore could influence the physical parameters of each phase fluid, then it can influence the calculation of well kick tolerance. Therefore it s necessary to do research to the temperature field inside wellbore. There are three staes of recyclin of drillin fluid which are shown as follows. 1 Drillin fluid is pumped into the drillin pipe and moves downward inside the tube pipe; Drillin fluid flows out throuh the drillin bit and enters annular space; 3 Drillin fluid moves inside the annular space and returns back to round surface. Basic assumption [5-6] : 1 The formation heat transfer belons to steady radial heat-transfer; The density of rock, specific heat and thermal conductivity don t chane when the temperature chanes. Besides, specific heat and thermal conductivity are equal in horizontal and vertical directions;3 The heat source, axial forced convection heat transfer and radial forced convection heat transfer inside pipe strin and annular space should be taken into consideration Certain stae of drillin fluid inside the drillin pipe is chosen as the control body and the temperature model of drillin fluid inside the drillin pipe could be received: Temperature field equation inside drillin pipe: Tp Tp Apρmvpcm + mpcm πru p p( Ta Tp) 0 (6) Certain stae of drillin fluid inside the annular space is chosen as the control body and the temperature model of drillin fluid inside the annular space could be received: Temperature field equation inside annular space: Ta Ta Aaρmvacm macm πru a a( Te Ta) + (7) π ru p p( Ta Tp) 0 Heat exchane equation on the interface of annular space and formation: Ta Ua( Te Ta) Ke 0 (8) t r ra 1.5 Phase Volume Fraction Gas phase volume fraction: vs E C ( v + v + v + v ) + v s so sc sm r A (9) Drillins volume fraction: (1 E ) vsc Ec (10) Cc ( vsc + vso + vsm ) + (1 E ) vcr Oil phase volume fraction: (1 E Ec ) vso Eo (11) Co ( vso + vsm ) + (1 E Ec ) vor Drillin fluid volume fraction: E 1 E E E (1) m o c 1.6 Multiphase Flow Friction Pressure Gradient Bubble flow P fmρmulvmul (13) f D f m can be calculated by usin the implicit formula which is brouht out by Colebrook, as follows: 1 ε 1.5 4l 0.69 + (14) f D m ReM fm Slu flow Usually, only the flow friction loss which is enerated in the slu section of the fluid is taken into consideration, therefore the fraction pressure radient calculation formulation could be received as follows: P flρlvl (1 E ) (15) f D The fraction with annular flow mode comes from the hih-speed movement of as core flow, therefore the correspondin as core fraction pressure radient calculation formulation could be described as follows: P f cen ρ cen v (16) f D f cen could be confirmed accordin to the correspondin Wallis formula. 0.079[1 + 75(1 E )] fcen 0.5 (17) R e 1.7 Physical Property Parameters Calculation of Formation Fluid 1 Gas compression factor Gas compression factor represents the ratio of the real volume and ideal volume of as with same quality under certain temperature and pressure condition. The relevant empirical formulas were brouht out by Dranchuk and Abou-Kassem, as follows. 5 Z 1 + c1( Tpr ) ρpr + c( Tpr ) ρpr + c3( Tpr ) ρpr + c4( Tpr, ρpr ) (18) Ppr T P ρ pr 0.7, T pr, Ppr (19) ZT pr Tpc Ppc Density of natural as 71 Copyriht Canadian Research & Development Center of Sciences and Cultures

New Method for Well Kick Tolerance Calculation 3484.4 pγ ρ (0) Z T p 3 Volume fraction of natural as Volume fraction of natural as means the ratio of the volume of natural as with unit volume on formation condition and volume of natural as with unit volume on round surface condition, the relevant formula is shown as follows. V B (1) V sc 4 Viscosity of natural as Viscosity of natural as is the index that could evaluate the mobility of natural as. It could impose important influence to the seepae process of natural as underround and mobility process of natural as in the pipelines. The viscosity of natural as could be calculated accordin to the Lee formula as well as other formulas. y ρ 7 µ C 10 exp x () 1000 1.5 ( 9.4 + 0.0 M ) (1.8 T) C (3) 09 + 19M + 1.8T 5 Solution as oil ratio in formation oil The natural as could be dissolved in formation oil. There are hue difference about the amount of natural as which is dissolved in formation oil due to different types of oil reservoir. And solution as oil ratio is one physical parameter which could evaluate the ability of formation oil to dissolve natural as. And it means the as amount which is dissolved in the formation oil under the temperature and pressure of the reservoir (Standard condition). c 1.076 1 3 Rs Cr 1 p exp[ c3 1 / (3.658 10 T+ 1)] (4) ro 6 Saturated pressure of formation oil The saturated pressure of formation oil means the pressure under which the dissolved natural as in the oil starts to separate from the oil under certain formation condition. The value of saturated pressure is mainly determined by the components of oil and as, as well as the temperature of oil reservoir. And it should be determined by PVT samplin analysis method. However if such analysis material is not existin, it could be determined by the Standin formula [7~8] as follows. 0.83 R s 3 4.073 Pb 4.47[ exp 3.773 10 T ] (5) r ro 7 Volume coefficient of formation oil When the oil is exploited and transferred onto the round surface, the dissolved as in the oil starts to separate from the oil and the volume of previous oil declines because the decrease of temperature and pressure. The volume coefficient of formation oil means the ratio of volume of oil underround and volume of oil after the dissolved natural as separate from the oil on the round surface. It could be determined by the Vazues and Bes empirical formulas [9], as follows. When pressure is equal or lower than saturated pressure, 1.076 ( C + CR 3 s )(0.06486T 1)( 1) ro (6) Bob 1+ CR 1 s + r When pressure is hiher than saturated pressure, Bo Bob exp[ c0 ( Pb P)] (7) Seepae formulation of two-phase mobility which is influenced by different as influx kh qsc [ pi pwf ( t)] 3 8.0853η t (8) µ B.11*10 l( ) rw In the process of as invasion, when the time oes by the as rises and expands in the wellbore which enenders more drillin fluid to flow out. Therefore the pressure at the well bottom will be lower and lower, then pressure drop will increase accordinly. Hence the more as enters the well borehole and overflow becomes more and more severe. And it is very accurate to demonstrate this process by usin this formula. It can be discovered by research that under the certain well structure, the well kick tolerance is mainly influenced by formation pressure forecastin error, formation permeability and formation fluid invasion. To be more specific, the increment of drillin fluid pond represents the as invasion amount into the wellbore, which is relevant to formation permeability and overflow time. Therefore, the main factors what influence the well kick tolerance are formation pressure forecastin error and formation permeability.. THE CALCULATION EXAMPLE OF WELL KICK TOLERANCE Accordin to the eoloical and drillin materials about Northeast-Sichuan reion and by usin the well kick tolerance calculation method which is mentioned in this essay, the chane principle of well kick tolerance alon with the chane of permeability and formation pressure forecastin error is simulated and analyzed..1 The Chane Principle of Well Kick Tolerance Alon with the Chane of Time and Permeability The chane principle of well kick tolerance which is influenced by different as phase permeability is observed (The overflow time is 10 min, 30 min, 60 min and 90 min separately) and the correspondin result is shown in Fiure 1, as follows. Besides the basic data for the well kick tolerance analysis and calculation are shown in Table 1. Copyriht Canadian Research & Development Center of Sciences and Cultures 7

ZHOU Yanjun; JIA Jianhon; WANG Guanlei; WANG Jinyin (013). Advances in Petroleum Exploration and Development, 5(), 69-74 Table 1 Basic Calculation Data Well Depth (m) 3000 Gas Relative Density 0.75 Density of Drillin (/cm 3 ).6 Ground Surface Temperature( ) 0 Ground Temperature Gradient ( /100m).3 Density of Drillin Fluid (/cm 3 ) 1.1 Drillin Fluid Volume (L/s) 30 Plastic Viscosity (mpa s) 30 Yield Value (Pa) 3 Formation pressure Forecastin Error(MPa) 3 Yield Layer Thickness(m) 0 Depth of Casin Shoe Position(m) 500 Drill Strin Size (mm) 17 Open Hole Diameter (mm) 15.9 Drill Strin Lenth (m) 500 Casin Diameter (mm) 0.5 Lenth of Drill Collar (m) 500 Drill Collar Size (mm) 137.3 Fiure 1 Well Kick Tolerance Chane with Permeability Under Different Overflow Time It can be seen from the Fiure 1 that based on the classification standard of formation permeability-namely it belons to super-low permeability formation when the averae permeability is lower than 1.0 10-3 μm, while it belons to very-low permeability formation when the averae permeability is between 1.0 10-3 -10.0 10-3 μm and it belons to low permeability formation when the averae permeability is lower than 50.0 10-3 μm, within the low permeability rane when the overflow time increases the well kick tolerance almost has no chane alon with the increase of permeability. In other words, the averae well kick tolerance almost remains around 0.0335 /cm 3. Furthermore with this rane the well kick tolerance is almost not influenced by time. When the permeability is hiher than 50 10-3 μm, the well kick tolerance beins to show sinificant chane. And when the permeability increases, the well kick tolerance oes up based on the index function trend. To be more specific, when the overflow time is about 90 min and the permeability is around 500 10-3 μm, the well kick tolerance increases up to 0.0745 /cm 3 approximately.. Chane Principle of Well Kick Tolerance Alon with the Chane of Formation Pressure Forecastin Error The principle of influence to well kick tolerance which is caused by different formation pressure forecastin error is researched (The relevant formation permeability is 1 10-3, 10 10-3, 30 10-3, 100 10-3, 500 10-3 μm and 1000 10-3 μm separately) and the result is shown in Fiure, as follows. It can be seen from the Fiure that the formation pressure forecastin error could influence the well kick tolerance apparently. When the formation pressure forecastin error is about.5 MPa, the well kick tolerance is only below 0.0 /cm 3. However when the formation pressure forecastin error increases up to 5MPa the well kick tolerance is hiher than 0.115 /cm 3. At the same time it can be received from the Fiure that the well kick tolerance curves which show the low-deree permeability situation almost overlap toether. It means formation pressure forecastin accuracy is the main factor which influences the well kick tolerance. However when the permeability is relatively hiher, the well kick tolerance increases very fast alon with the increment of formation pressure forecastin error. Hence it means formation pressure forecastin accuracy and permeability are two major factors which affect the well kick tolerance. 73 Copyriht Canadian Research & Development Center of Sciences and Cultures

New Method for Well Kick Tolerance Calculation Well kick tolerance(/cm 3 ) 0.5 0. 0.15 0.1 0.05 Permeability of 1mD Permeability of 10mD Permeability of 30mD Permeability of 100mD Permeability of 500mD Permeability of 1000mD 0.5 3 3.5 4 4.5 5 5.5 Formation pressure forcastin error(mpa) Fiure Well Kick Tolerance Chane with Formation Pressure Forecastin Error Under Different Permeability CONCLUSION (1) Well kick tolerance is an important parameter in drillin enineerin desin, the reasonability of well kick tolerance calculation directly related with the reasonability of well structure and safety of drillin operation for HTHP deep well and super-deep well. () Well kick tolerance is mainly determined by formation pressure forecastin error, formation permeability and formation fluid invasion amount. And increment of drillin fluid pond represents the as invasion amount into the wellbore, which is relevant to formation permeability and overflow time. Hence, well kick tolerance is mainly influenced by formation pressure forecastin error and formation permeability. (3) It can be seen from the simulation result that when the overflow time oes up, the well kick tolerance almost has no chane alon with chane of permeability. However when the permeability is hiher than certain value, well kick tolerance increases based on index function trend alon with the increment of permeability. When the formation pressure forecastin error increases, the well kick tolerance oes up dramatically. REFERENCES [1] Li, K. X. (1990). A Maual Drillin (pp. 94-98). Beijin: Petroleum Industry Press. [] Zhuo, L. B., Ge, Y. H., & Wan, H. G. (009). Early Kick Detection Methods for Deep Water Drillin and Its Future Development. Oil Drillin & Production Technoloy, 31(1), -6. [3] Nicken, H. V. (1985). A Dynamic Computer Model of a Kickin Well: Part II-Model Predictions and Conclusions. SPE Annual Technical Conference and Exhibition, -6 September 1985, Las Veas, Nevada. [4] Bilicki, Z. (1987). Traosition Criteria for Two-Phase Flow Patterns in Vertical Upward Flow. Int. J. of Multiphase FIow, 3(3), 83-94 [5] Kytomaa, H. K., & Brennen, C. E. (1991). Small Amplitude Kinematic Wave Propaation in Two-Component Media. Int. J. of Multiphase Flow, 17(1),13-6. [6] Lammers, J. H., & Biesheuvel, A. (1996). Concentration Waves and the Instability of Bubbly Flows. Journal of Fluid Mechanics, 38, 67-93. [7] Wan, Z. Y., & Sun, B. J. (009). Multiphase Flow Behavior in Annulus with Solid Gas Hydrate Considerin Nature Gas Hydrate Phase Transition. Petroleum Science, 6(1), 57-63. [8] Chen, H., Hills, J. H., & Azzopardi, B. J. (1998). A Study of the Bubble-to-Slu Transition in Vertical Gas-Liquid Flow in Columns of Different Diameter. Int. J. of Multiphase Flow, 4(3), 431-45. [9] Ohnuki, A., & Akimoto, H. (000). Experimental Study on Transition of Flow Pattern and Phase Distribution in Upward Air Water Two-Phase Flow Alon a Lare Vertical Pipe. Int. J. of Multiphase Flow, 6(3), 367-386. Copyriht Canadian Research & Development Center of Sciences and Cultures 74