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Numerical Simulation of Wellhead Back Pressure in Under-balanced Drilling
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 107 (2017) 150 – 156
3rd International Conference on Energy and Environment Research, ICEER 2016, 7-11 September 2016, Barcelona, Spain
Numerical Simulation of Wellhead Back Pressure in Underbalanced Drilling Jie Zhanga*, Junwu Zoua, Kuang Nieb, Yuesheng Shaoc, Yuanchang Zhaoa, Wenlong Zhanga a
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation͌Southwest Petroleum University, Chengdu, Sichuan,China b Missouri University of Science and Technology, petroleum engineering, Rolla, Missouri,USA c Daqing Oilfield Company the second Drilling Company, Daqing, Heilongjiang, China
Abstract Based on the application of liquid-phase under-balanced drilling in a vertical well, this paper studies the wellhead back pressure (WBP) on annular gas-liquid two-phase flow characteristics and its impact on the law of gas cut speed. Annular gas-liquid twophase flow transient calculation model and a model of gas cut during drilling are established in this study. And used to calculate the changing law of WBP under constant and variable bottom hole underbalanced. Results show that a risk of excessive gas cut or WBP exists when uncovering gas reservoir under constant underbalanced. The WBP needed for using variable negative pressure to keep gas cut speed unchanged remains stable after a period of growth. And is mainly affected by gas cut speed, formation permeability, time to apply WBP, and other factors. The simulation result is compared with the WBP value collected on site in real time, show that the changing trend is roughly the same. © 2017 2016 The TheAuthors. Authors.Published PublishedbybyElsevier Elsevier Ltd. © Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific (http://creativecommons.org/licenses/by-nc-nd/4.0/).committee of the 3rd International Conference on Energy and Environment Research. under responsibility of the scientific committee of the 3rd International Conference on Energy and Environment Research. Peer-review Keywords: Bottom hole underbalanced; Gas cut speed; Two-phase flow instantaneous model; Under-balanced drilling;Wellhead back pressure.
* Corresponding author. Tel.: 028-83037036. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd International Conference on Energy and Environment Research. doi:10.1016/j.egypro.2016.12.155
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Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
1. Introduction Whether or not control of bottom hole underbalanced differential is reasonable is the key to the application of under-balanced drilling. To ensure that bottom hole underbalanced in gas cut remains constant while drilling, realtime data must be obtained to regulate throttle valve [1] and control wellhead back pressure, thus controlling bottom hole underbalanced to be in a reasonable range [2]. The bottom hole underbalanced values of under-balanced drilling can be divided into two types, namely, constant negative value and variable negative value[3]. The control of bottom hole underbalanced value mainly refers to wellhead back pressure and pump pressure. The control action of wellhead back pressure on the bottom hole pressure is intuitive. Therefore, the gas–liquid two-phase flow of wellbore annulus in gas cut while drilling should be studied [4,5]. This paper aims to establish a gas cut model and an annulus gas–liquid two-phase flow model, as well as change the physical model problems into mathematical problems by using the four-point difference method [6,7]. This study calculates and analyzes the wellhead back pressure needed to control bottom hole underbalanced and its influencing factors, as well as comparatively analyzes site data, for conducting the wellhead back pressure simulation. 2. Establishment of a model of under-balanced gas cut while drilling 2.1. Establishment of the model of under-balanced gas cut while drilling Under the underpressured condition of the bottom hole, the model expression in Eq.(1) can be obtained according to the calculation model of unstable seepage gas invasion Q sc =
where, A =
− A + A 2 + 4 B[ Pe2 − Pwf2 (t )] 2B
1.27 × 10 −6 T μ Z K
v rop t
(1)
2.282 × 10 −21 βγ g μ Z ª 1 1 º º ª 0.472 re + S» , B = «ln « − ». rw R ¼ ¬ ¬ rw re ¼
After gas cutting time t is obtained based on the integral formula. The reservoir uncovering process can be ignored to calculate the gas cut volume while drilling a thin gas reservoir. The gas cut volume calculation model is expressed as Eq.(2) Qsc =
− A + A 2 + 4 B[ Pe2 − Pwf2 (t )] 2B
hb
(2)
where K is the permeability (mD), h is the thickness of the uncovered reservoir (m), hb is the constant thickness of the thin gas reservoir (m), and vrop is the penetration rate (m/h), rw is the bottom radius (m), ȕ is the inertial resistance coefficient caused by turbulent current, Qsc is the standard gas production rate in unit time (m3/d), Qt is the total gas cutting volume under standard conditions (m3), S is the skin factor, Z is the mean gas compressibility factor, μ is the mean gas viscosity (mPa·s), Pwf is the bottom hole flowing pressure (MPa), and t is time (s). 3. Establishment of annular gas–liquid two-phase flow transient model 3.1. Governing equations In the process of under-balanced drilling to uncover a reservoir, the gas–liquid two-phase flow in the annulus shows transient characteristics, namely, time varying pressure field and velocity field in the annulus. Therefore, a transient gas–liquid two-phase flow model should be established, and governing equations are established based on the gas–liquid two-phase flow equations (Eq.(3)) [8-11].
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Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
∂ ( ρg vg Hg A) ∂ ( ρg Hg A) ° + =C ∂z ∂t ° ° ∂ ª ρ v 1− H Aº ∂ ªρ 1− H Aº (3) g) ¼ l( g) ¼ ° ¬ l l( + ¬ =0 ® ∂z ∂t ° °∂ ∂ ( ρg Hg vg2 + ρl Hl vl2 ) ∂P § ∂P · ° ( ρmvm ) + + + ¨ ¸ + ρm g = 0 ∂z ∂z © ∂z ¹ fr ° ∂t ¯ where, before drilling the producing formation or when the gas cut volume reaches the steady state while drilling, C=0; the changing process of the gas cut volume while drilling, C=qg.
3.2. Establishment of definite conditions According to the variation of overflow and bottom hole pressure in no back pressure gas cut, annulus flow parameters at the moment when the wellhead back pressure is initially applied are used as the initial conditions of wellhead drilling under pressure. Then, the parameters at the next node are solved by using continuous equation/auxiliary equation and momentum equation. When H = 0, the wellhead pressure calculated at the moment is the needed back pressure. Constant gas cut speed is based on design negative pressure. Eq.(1) are used to derive boundary conditions of the bottom hole flow pressure Pwf (t ) = Pe2 −
2 BQsc + Av rop t − A 2 v rop t 4 Bv rop t
° P(t , H ) = Pwf (t ) ® °¯Qsc = the setting value
(4)
(5)
where Pwf(t) is the bottom hole flow pressure at t (MPa), and Qsc refers to the speed of gas cut while drilling (the volume under standard conditions) (m3/d). 3.3. Solving process Solving the above transient two-phase flow model is complicated. In this paper, the four-point difference method is used to scatter the annulus to the rectangular grid and then establish the time and space grid. The solution of the transient model in the definite solution domain is changed to a discrete solution on the grid node in the definite solution domain. The solutions of all nodes in the space domain are gradually obtained until they cover the entire time and space domain. Thus, the corresponding solution can be obtained [12,13]. First, the initial conditions are determined. After gas cut occurs, the bottom hole pressure is estimated. To solve the corresponding gas cut speed, the pressure must be estimated at the next moment. Then, the density and viscosity of gas and other basic parameters are determined. Continuous equation is used to calculate the speed of all phases. The gas–liquid two-phase flow model is used to calculate gas fraction. If the conditions are met, further calculation is carried out; otherwise, the above parameters are re-estimated. Thus, the parameters of all nodes in the space can be obtained. In addition, the wellhead pressure needed for the remaining constant gas cut speed at a certain moment is the back pressure to be obtained. 4. Analysis of calculation result Based on the established calculation model of the gas cut volume while drilling, this paper analyzes the variation in bottom hole pressure and overflow amount during gas cut.
Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
4.1. Drilling under constant bottom hole underbalanced The initial negative pressure is set to 1 MPa. Gas cut occurs while drilling a reservoir for 10 min. Wellhead back pressure is applied to keep the bottom hole underbalanced constant.. Wellhead back pressure equation is used for calculation [14]. After gas cut has occurred for 10 min, the bottom hole underbalanced is stabilized to the wellhead back pressure required for the design negative pressure value, as shown in Fig.1. Fig. 1 shows that the wellhead back pressure changes slightly at the beginning. With time, the annulus gas–liquid mixed-phase liquid column pressure rapidly decreases. After the gas is up to the wellhead completely, the variation in wellhead back pressure declines. Afterward, the gas cut speed and the back pressure increase. In the gas reservoir with a high gas production, the wellhead back pressure rapidly exceeds the wellhead equipment bearing pressure. Therefore, using the constant negative pressure method from the angle of processing capacity of equipment is undesirable.
Fig. 1. Wellhead back pressure required during uncovering producing formation under constant negative pressure.
Fig. 2. Variation in wellhead back pressure required to maintain constant gas cut speed after gas up to wellhead.
4.2. Calculation of wellhead back pressure under variable negative pressure The control principle of uncovering producing formation under variable negative pressure is to maintain a constant gas cut speed while uncovering the reservoir. Then, the simulation calculation is conducted for constant gas cut speed while uncovering the reservoir under variable negative pressure to simulate and analyze the process of applying back pressure before and after wellhead producing gas. 4.2.1. applying back pressure after wellhead producing gas Fig. 2 shows that the back pressure needed for the wellhead while uncovering the reservoir is higher when the bottom hole gas cut speed is smaller. In addition, the wellhead back pressure must be rapidly applied to avoid gas cut amount beyond the set gas cut speed. If the gas cut speed is slower, the time required to stabilize the wellhead back pressure is shorter. When the constant gas cut speed of 120 m3/h is set as the boundary condition, the calculation result is shown as Fig. 3. For higher formation permeability, the bottom hole underbalanced required to maintain the same gas cut speed is smaller, and the back pressure applied to the wellhead is relatively higher. To ensure lower reservoir permeability, the bottom hole gas cut speed slowly increases, and the time to apply back pressure lags behind.
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Fig. 3. Variation in wellhead back pressure under different permeabilities
Fig. 4. Effect of permeability on wellhead back pressure.
4.2.2. applying back pressure before gas up to wellhead The situation after drilling the reservoir for 15 min is used as the initial simulation condition and the bottom hole gas cut speed while drilling is controlled to 100 m3/h for the boundary condition of the simulation calculation. The simulation result in Fig. 4 shows that, combined with higher formation permeability, the required wellhead back pressure will be high while the reservoir is uncovered through under-balanced drilling under variable bottom hole underbalanced to control lower gas cut speed. Moreover, it may be beyond the wellhead pressure bearing capacity of the reservoir. A comparative analysis of the calculation results of the two models shows that the calculation of the variation of bottom hole pressure based on gas cut situation of variable thickness of producing formation is in accordance with the actual working conditions of under-balanced drilling. 5. Example A certain well in Middle Taklimakan Desert Oil Field is drilled to a depth of 5355 m. A drill with a diameter of 168.3 mm is used to make a third opening. Under-balanced drilling is used for the section of 4248 m to 5355 m. The density of the drilling liquid is 1.16 g/cm3, the displacement is 15 L/s, and the pump pressure is 20 MPa. Gas is produced in the wellhead when the drilling depth is 4262.69 m. The wellhead pressure is 0.21 Mpa, and the gas cut speed while drilling is 96 m3/h. To guarantee controlled annulus intake, the wellhead back pressure is gradually increased as the reservoir is uncovered. In Fig. 5, the wellhead back pressure is stabilized to 2 MPa when drilling is 4267.23 m deep. Throughout the drilling process at a constant gas cut speed, the flame is 5 m high, and the gas cut amount while drilling indicated in a ground flow meter is 150 m3/h. The level of drilling liquid is unchanged after the height of flame is stabilized. The definite conditions for model calculation are shown in Table 1. Table 1. Initial conditions of the simulation calculation Depth (m)
Gas ascent speed(m/s)
Gas density (g/cm3)
Liquid ascent speed (m/s)
Wellhead back pressure (MPa)
Bottom hole flow pressure (MPa)
Reservoir pressure (MPa)
Rate of penetrati on (m/h)
Gas cut speed while drilling (m3/h)
Permeability (mD)
4262.69
5.6
0.05
3.5
1.5
46.7
48
15
138
50
Fig. 6 shows a comparative diagram of the calculated result and site data. The comparative result shows that the variations in wellhead back pressure are generally consistent, particularly when the wellhead back pressure is stable. The calculated value is close to the measured value on site with a small error; when the applied back pressure at the wellhead and the back pressure are consistent, the calculated and the measured values on site have a certain
Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
difference. This difference is due to the unstable actual annulus gas–liquid two-phase flow that causes all parameters to fluctuate.
Fig. 5. Discharge of drilling fluid at outlet and inlet before and after flame is stable.
Fig. 6. Comparative diagram of the simulation calculation of the variation in wellhead back pressure and the measured data on site.
6. Conclusion Using a constant negative pressure for drilling while uncovering a thicker gas reservoir through under-balanced drilling is inappropriate. Variable negative pressure drilling should be used to maintain constant gas cut speed and to prevent the gas cut amount in the annulus and wellhead pressure from being out of control as the reservoir is gradually uncovered. After drilling the gas producing formation, the variation in bottom hole pressure is calculated in gas cut status under variable thicknesses of producing formation. The result is in accordance with the actual working conditions of under-balanced drilling. When uncovering the reservoir under variable negative pressures, the required wellhead back pressure is higher if the gas cut speed is slower. The wellhead back pressure required to maintain a constant gas cut speed is higher if the permeability rate is higher. For gas reservoirs with higher permeability, controlling gas cut speed is difficult. Otherwise, it will cause higher wellhead back pressure. Moreover, higher penetration rate causes the wellhead back pressure to stabilize within a short time. However, it does not significantly influence the final steady-state value of wellhead back pressure. Acknowledgements Financial support from Natural Science Foundation of China (NSFC) is gratefully acknowledged (No. 51274168), and National Key Basic Research and Development Program (973 Program) (NO. 2013CB228003). References [1] Fredericks PD, Reitsma D, Runggai T, Hudson JN, Zaeper R, Backhaus O, Hernandez M. Successful implementation of first closed loop, multiservice control system for automated pressure management in a shallow gas well offshore Myanmar. In: IADC/SPE Drilling Conference, Orlando, Florida, March 4-6, 2008. [2] Santos, Helio, Christian Leuchtenberg, and Sara Shayegi. Micro-flux control: the next generation in drilling process for ultra-deepwater, In: Offshore Technology Conference, Houston, Texas May 5-8, 2003. [3] Rasoul I, Nasimi R. Application of artificial bee colony-based neural network in bottom hole pressure prediction in underbalanced drilling. Journal of Petroleum Science and Engineering 2011;78(1): 6-12. [4] Nunes JOL, Bannwart AC, Ribeiro PR. Mathematical modelling of gas kicks in deep water scenario. In:IADC/SPE Asia Pacific Drilling Technology, Jakarta, Indonesia, September 8-11, 2002. [5] Nickens HV. A dynamic computer model of a kicking well. SPE Drilling engineering 1987;2(2):159-173. [6] Yue J, Luo L, Gonthier Y, Chen G, Yuan Q. An experimental investigation of gas–liquid two-phase flow in single microchannel contactors. Chemical Engineering Science 2008;63(16):4189-4202. [7] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. AIChE Journal 1976; 22(1):47-55.
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Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156 [8] Caetano EF, Shoham O, Brill JP. Upward vertical two-phase flow through an annulus-Part II: Modelling bubble, slug, and annular flow. Journal of Energy Resources Technology 1992;114(1):14-30. [9] Zhou L, Ahmed RM, Miska S, Takash N, Yu M, Pickell MB. Experimental study of aerated mud flows under horizontal borehole conditions. presented at the SPE/ICoTA Coiled Tubing Conference and Exhibition, Houston, March 23-24, 2004. [10] Salehi S, Hareland G, Nygaard R. Numerical simulations of wellbore stability in under-balanced-drilling wells. Journal of Petroleum Science and Engineering 2010;72(3):229-235. [11] Zhou L, Ahmed RM, Miska SZ, Takach NE, Yu M, Saasen A. Hydraulics of drilling with aerated muds under simulated borehole conditions. In: SPE/IADC Drilling Conference, Amsterdam, Netherlands, February 23-25, 2005. [12] Yongming, C. Design and control of negative differential pressure in flow drilling. Drilling & Production Technology 2000;23(2):11-13. [13] Xiangqi Z, Xiangfang L, Tao G, Xiuxiang, S, Engao T. Theory of controlling wellhead back pressure in UBD. Petroleum Drilling Techniques 2002;30(6):12-14. [14] Jiang Zhibo Z, Wei L, Qian W. Automatic control of bottom hole pressure during precisely managed pressured drilling. Natural Gas Industry 2012;32(7):48-51.
ScienceDirect Energy Procedia 107 (2017) 150 – 156
3rd International Conference on Energy and Environment Research, ICEER 2016, 7-11 September 2016, Barcelona, Spain
Numerical Simulation of Wellhead Back Pressure in Underbalanced Drilling Jie Zhanga*, Junwu Zoua, Kuang Nieb, Yuesheng Shaoc, Yuanchang Zhaoa, Wenlong Zhanga a
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation͌Southwest Petroleum University, Chengdu, Sichuan,China b Missouri University of Science and Technology, petroleum engineering, Rolla, Missouri,USA c Daqing Oilfield Company the second Drilling Company, Daqing, Heilongjiang, China
Abstract Based on the application of liquid-phase under-balanced drilling in a vertical well, this paper studies the wellhead back pressure (WBP) on annular gas-liquid two-phase flow characteristics and its impact on the law of gas cut speed. Annular gas-liquid twophase flow transient calculation model and a model of gas cut during drilling are established in this study. And used to calculate the changing law of WBP under constant and variable bottom hole underbalanced. Results show that a risk of excessive gas cut or WBP exists when uncovering gas reservoir under constant underbalanced. The WBP needed for using variable negative pressure to keep gas cut speed unchanged remains stable after a period of growth. And is mainly affected by gas cut speed, formation permeability, time to apply WBP, and other factors. The simulation result is compared with the WBP value collected on site in real time, show that the changing trend is roughly the same. © 2017 2016 The TheAuthors. Authors.Published PublishedbybyElsevier Elsevier Ltd. © Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the scientific (http://creativecommons.org/licenses/by-nc-nd/4.0/).committee of the 3rd International Conference on Energy and Environment Research. under responsibility of the scientific committee of the 3rd International Conference on Energy and Environment Research. Peer-review Keywords: Bottom hole underbalanced; Gas cut speed; Two-phase flow instantaneous model; Under-balanced drilling;Wellhead back pressure.
* Corresponding author. Tel.: 028-83037036. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 3rd International Conference on Energy and Environment Research. doi:10.1016/j.egypro.2016.12.155
151
Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
1. Introduction Whether or not control of bottom hole underbalanced differential is reasonable is the key to the application of under-balanced drilling. To ensure that bottom hole underbalanced in gas cut remains constant while drilling, realtime data must be obtained to regulate throttle valve [1] and control wellhead back pressure, thus controlling bottom hole underbalanced to be in a reasonable range [2]. The bottom hole underbalanced values of under-balanced drilling can be divided into two types, namely, constant negative value and variable negative value[3]. The control of bottom hole underbalanced value mainly refers to wellhead back pressure and pump pressure. The control action of wellhead back pressure on the bottom hole pressure is intuitive. Therefore, the gas–liquid two-phase flow of wellbore annulus in gas cut while drilling should be studied [4,5]. This paper aims to establish a gas cut model and an annulus gas–liquid two-phase flow model, as well as change the physical model problems into mathematical problems by using the four-point difference method [6,7]. This study calculates and analyzes the wellhead back pressure needed to control bottom hole underbalanced and its influencing factors, as well as comparatively analyzes site data, for conducting the wellhead back pressure simulation. 2. Establishment of a model of under-balanced gas cut while drilling 2.1. Establishment of the model of under-balanced gas cut while drilling Under the underpressured condition of the bottom hole, the model expression in Eq.(1) can be obtained according to the calculation model of unstable seepage gas invasion Q sc =
where, A =
− A + A 2 + 4 B[ Pe2 − Pwf2 (t )] 2B
1.27 × 10 −6 T μ Z K
v rop t
(1)
2.282 × 10 −21 βγ g μ Z ª 1 1 º º ª 0.472 re + S» , B = «ln « − ». rw R ¼ ¬ ¬ rw re ¼
After gas cutting time t is obtained based on the integral formula. The reservoir uncovering process can be ignored to calculate the gas cut volume while drilling a thin gas reservoir. The gas cut volume calculation model is expressed as Eq.(2) Qsc =
− A + A 2 + 4 B[ Pe2 − Pwf2 (t )] 2B
hb
(2)
where K is the permeability (mD), h is the thickness of the uncovered reservoir (m), hb is the constant thickness of the thin gas reservoir (m), and vrop is the penetration rate (m/h), rw is the bottom radius (m), ȕ is the inertial resistance coefficient caused by turbulent current, Qsc is the standard gas production rate in unit time (m3/d), Qt is the total gas cutting volume under standard conditions (m3), S is the skin factor, Z is the mean gas compressibility factor, μ is the mean gas viscosity (mPa·s), Pwf is the bottom hole flowing pressure (MPa), and t is time (s). 3. Establishment of annular gas–liquid two-phase flow transient model 3.1. Governing equations In the process of under-balanced drilling to uncover a reservoir, the gas–liquid two-phase flow in the annulus shows transient characteristics, namely, time varying pressure field and velocity field in the annulus. Therefore, a transient gas–liquid two-phase flow model should be established, and governing equations are established based on the gas–liquid two-phase flow equations (Eq.(3)) [8-11].
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Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
∂ ( ρg vg Hg A) ∂ ( ρg Hg A) ° + =C ∂z ∂t ° ° ∂ ª ρ v 1− H Aº ∂ ªρ 1− H Aº (3) g) ¼ l( g) ¼ ° ¬ l l( + ¬ =0 ® ∂z ∂t ° °∂ ∂ ( ρg Hg vg2 + ρl Hl vl2 ) ∂P § ∂P · ° ( ρmvm ) + + + ¨ ¸ + ρm g = 0 ∂z ∂z © ∂z ¹ fr ° ∂t ¯ where, before drilling the producing formation or when the gas cut volume reaches the steady state while drilling, C=0; the changing process of the gas cut volume while drilling, C=qg.
3.2. Establishment of definite conditions According to the variation of overflow and bottom hole pressure in no back pressure gas cut, annulus flow parameters at the moment when the wellhead back pressure is initially applied are used as the initial conditions of wellhead drilling under pressure. Then, the parameters at the next node are solved by using continuous equation/auxiliary equation and momentum equation. When H = 0, the wellhead pressure calculated at the moment is the needed back pressure. Constant gas cut speed is based on design negative pressure. Eq.(1) are used to derive boundary conditions of the bottom hole flow pressure Pwf (t ) = Pe2 −
2 BQsc + Av rop t − A 2 v rop t 4 Bv rop t
° P(t , H ) = Pwf (t ) ® °¯Qsc = the setting value
(4)
(5)
where Pwf(t) is the bottom hole flow pressure at t (MPa), and Qsc refers to the speed of gas cut while drilling (the volume under standard conditions) (m3/d). 3.3. Solving process Solving the above transient two-phase flow model is complicated. In this paper, the four-point difference method is used to scatter the annulus to the rectangular grid and then establish the time and space grid. The solution of the transient model in the definite solution domain is changed to a discrete solution on the grid node in the definite solution domain. The solutions of all nodes in the space domain are gradually obtained until they cover the entire time and space domain. Thus, the corresponding solution can be obtained [12,13]. First, the initial conditions are determined. After gas cut occurs, the bottom hole pressure is estimated. To solve the corresponding gas cut speed, the pressure must be estimated at the next moment. Then, the density and viscosity of gas and other basic parameters are determined. Continuous equation is used to calculate the speed of all phases. The gas–liquid two-phase flow model is used to calculate gas fraction. If the conditions are met, further calculation is carried out; otherwise, the above parameters are re-estimated. Thus, the parameters of all nodes in the space can be obtained. In addition, the wellhead pressure needed for the remaining constant gas cut speed at a certain moment is the back pressure to be obtained. 4. Analysis of calculation result Based on the established calculation model of the gas cut volume while drilling, this paper analyzes the variation in bottom hole pressure and overflow amount during gas cut.
Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
4.1. Drilling under constant bottom hole underbalanced The initial negative pressure is set to 1 MPa. Gas cut occurs while drilling a reservoir for 10 min. Wellhead back pressure is applied to keep the bottom hole underbalanced constant.. Wellhead back pressure equation is used for calculation [14]. After gas cut has occurred for 10 min, the bottom hole underbalanced is stabilized to the wellhead back pressure required for the design negative pressure value, as shown in Fig.1. Fig. 1 shows that the wellhead back pressure changes slightly at the beginning. With time, the annulus gas–liquid mixed-phase liquid column pressure rapidly decreases. After the gas is up to the wellhead completely, the variation in wellhead back pressure declines. Afterward, the gas cut speed and the back pressure increase. In the gas reservoir with a high gas production, the wellhead back pressure rapidly exceeds the wellhead equipment bearing pressure. Therefore, using the constant negative pressure method from the angle of processing capacity of equipment is undesirable.
Fig. 1. Wellhead back pressure required during uncovering producing formation under constant negative pressure.
Fig. 2. Variation in wellhead back pressure required to maintain constant gas cut speed after gas up to wellhead.
4.2. Calculation of wellhead back pressure under variable negative pressure The control principle of uncovering producing formation under variable negative pressure is to maintain a constant gas cut speed while uncovering the reservoir. Then, the simulation calculation is conducted for constant gas cut speed while uncovering the reservoir under variable negative pressure to simulate and analyze the process of applying back pressure before and after wellhead producing gas. 4.2.1. applying back pressure after wellhead producing gas Fig. 2 shows that the back pressure needed for the wellhead while uncovering the reservoir is higher when the bottom hole gas cut speed is smaller. In addition, the wellhead back pressure must be rapidly applied to avoid gas cut amount beyond the set gas cut speed. If the gas cut speed is slower, the time required to stabilize the wellhead back pressure is shorter. When the constant gas cut speed of 120 m3/h is set as the boundary condition, the calculation result is shown as Fig. 3. For higher formation permeability, the bottom hole underbalanced required to maintain the same gas cut speed is smaller, and the back pressure applied to the wellhead is relatively higher. To ensure lower reservoir permeability, the bottom hole gas cut speed slowly increases, and the time to apply back pressure lags behind.
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Fig. 3. Variation in wellhead back pressure under different permeabilities
Fig. 4. Effect of permeability on wellhead back pressure.
4.2.2. applying back pressure before gas up to wellhead The situation after drilling the reservoir for 15 min is used as the initial simulation condition and the bottom hole gas cut speed while drilling is controlled to 100 m3/h for the boundary condition of the simulation calculation. The simulation result in Fig. 4 shows that, combined with higher formation permeability, the required wellhead back pressure will be high while the reservoir is uncovered through under-balanced drilling under variable bottom hole underbalanced to control lower gas cut speed. Moreover, it may be beyond the wellhead pressure bearing capacity of the reservoir. A comparative analysis of the calculation results of the two models shows that the calculation of the variation of bottom hole pressure based on gas cut situation of variable thickness of producing formation is in accordance with the actual working conditions of under-balanced drilling. 5. Example A certain well in Middle Taklimakan Desert Oil Field is drilled to a depth of 5355 m. A drill with a diameter of 168.3 mm is used to make a third opening. Under-balanced drilling is used for the section of 4248 m to 5355 m. The density of the drilling liquid is 1.16 g/cm3, the displacement is 15 L/s, and the pump pressure is 20 MPa. Gas is produced in the wellhead when the drilling depth is 4262.69 m. The wellhead pressure is 0.21 Mpa, and the gas cut speed while drilling is 96 m3/h. To guarantee controlled annulus intake, the wellhead back pressure is gradually increased as the reservoir is uncovered. In Fig. 5, the wellhead back pressure is stabilized to 2 MPa when drilling is 4267.23 m deep. Throughout the drilling process at a constant gas cut speed, the flame is 5 m high, and the gas cut amount while drilling indicated in a ground flow meter is 150 m3/h. The level of drilling liquid is unchanged after the height of flame is stabilized. The definite conditions for model calculation are shown in Table 1. Table 1. Initial conditions of the simulation calculation Depth (m)
Gas ascent speed(m/s)
Gas density (g/cm3)
Liquid ascent speed (m/s)
Wellhead back pressure (MPa)
Bottom hole flow pressure (MPa)
Reservoir pressure (MPa)
Rate of penetrati on (m/h)
Gas cut speed while drilling (m3/h)
Permeability (mD)
4262.69
5.6
0.05
3.5
1.5
46.7
48
15
138
50
Fig. 6 shows a comparative diagram of the calculated result and site data. The comparative result shows that the variations in wellhead back pressure are generally consistent, particularly when the wellhead back pressure is stable. The calculated value is close to the measured value on site with a small error; when the applied back pressure at the wellhead and the back pressure are consistent, the calculated and the measured values on site have a certain
Jie Zhang et al. / Energy Procedia 107 (2017) 150 – 156
difference. This difference is due to the unstable actual annulus gas–liquid two-phase flow that causes all parameters to fluctuate.
Fig. 5. Discharge of drilling fluid at outlet and inlet before and after flame is stable.
Fig. 6. Comparative diagram of the simulation calculation of the variation in wellhead back pressure and the measured data on site.
6. Conclusion Using a constant negative pressure for drilling while uncovering a thicker gas reservoir through under-balanced drilling is inappropriate. Variable negative pressure drilling should be used to maintain constant gas cut speed and to prevent the gas cut amount in the annulus and wellhead pressure from being out of control as the reservoir is gradually uncovered. After drilling the gas producing formation, the variation in bottom hole pressure is calculated in gas cut status under variable thicknesses of producing formation. The result is in accordance with the actual working conditions of under-balanced drilling. When uncovering the reservoir under variable negative pressures, the required wellhead back pressure is higher if the gas cut speed is slower. The wellhead back pressure required to maintain a constant gas cut speed is higher if the permeability rate is higher. For gas reservoirs with higher permeability, controlling gas cut speed is difficult. Otherwise, it will cause higher wellhead back pressure. Moreover, higher penetration rate causes the wellhead back pressure to stabilize within a short time. However, it does not significantly influence the final steady-state value of wellhead back pressure. Acknowledgements Financial support from Natural Science Foundation of China (NSFC) is gratefully acknowledged (No. 51274168), and National Key Basic Research and Development Program (973 Program) (NO. 2013CB228003). References [1] Fredericks PD, Reitsma D, Runggai T, Hudson JN, Zaeper R, Backhaus O, Hernandez M. Successful implementation of first closed loop, multiservice control system for automated pressure management in a shallow gas well offshore Myanmar. In: IADC/SPE Drilling Conference, Orlando, Florida, March 4-6, 2008. [2] Santos, Helio, Christian Leuchtenberg, and Sara Shayegi. Micro-flux control: the next generation in drilling process for ultra-deepwater, In: Offshore Technology Conference, Houston, Texas May 5-8, 2003. [3] Rasoul I, Nasimi R. Application of artificial bee colony-based neural network in bottom hole pressure prediction in underbalanced drilling. Journal of Petroleum Science and Engineering 2011;78(1): 6-12. [4] Nunes JOL, Bannwart AC, Ribeiro PR. Mathematical modelling of gas kicks in deep water scenario. In:IADC/SPE Asia Pacific Drilling Technology, Jakarta, Indonesia, September 8-11, 2002. [5] Nickens HV. A dynamic computer model of a kicking well. SPE Drilling engineering 1987;2(2):159-173. [6] Yue J, Luo L, Gonthier Y, Chen G, Yuan Q. An experimental investigation of gas–liquid two-phase flow in single microchannel contactors. Chemical Engineering Science 2008;63(16):4189-4202. [7] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. AIChE Journal 1976; 22(1):47-55.
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