Multiphase flow behavior for acid-gas mixture and drilling fluid flow in vertical wellbore

Accepted Manuscript Multiphase flow behavior for acid-gas mixture and drilling fluid flow in vertical wellbore Baojiang Sun, Yanli Guo, Wenchao Sun, Yonghai Gao, Hao Li, Zhiyuan Wang, Hongkun Zhang PII:

S0920-4105(16)31252-9

DOI:

10.1016/j.petrol.2018.02.016

Reference:

PETROL 4686

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 7 December 2016 Revised Date:

16 December 2017

Accepted Date: 7 February 2018

Please cite this article as: Sun, B., Guo, Y., Sun, W., Gao, Y., Li, H., Wang, Z., Zhang, H., Multiphase flow behavior for acid-gas mixture and drilling fluid flow in vertical wellbore, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/j.petrol.2018.02.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

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Multiphase flow behavior for acid-gas mixture and

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drilling fluid flow in vertical wellbore

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Baojiang Sun *, Yanli Guo, Wenchao Sun, Yonghai Gao, Hao Li, Zhiyuan Wang, Hongkun Zhang

School of Petroleum Engineering, China University of Petroleum (East China),

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Qingdao, 266580, China.

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* Corresponding Author:

Mailing address: School of Petroleum Engineering, China University of Petroleum

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(East China), No. 66 Changjiang West Road, Huangdao, Qingdao, 266580, China

Tel.: 86-532-86981707; fax: 86-532-86981928

E-mail address: [email protected]

ACCEPTED MANUSCRIPT Abstract The transition laws of multiphase flow in a wellbore during acid-gas mixture influx are important for the hydraulic parameters design and wellbore pressure control

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in acid gasfield drillings. Herein, the phase change of acid-gas mixture in a wellbore was investigated by the experimental analysis. The results indicate that the acid-gas mixture in the supercritical phase exists under conditions of certain wellbore

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temperature and pressure, which makes its physical properties change abruptly near

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the critical point. Moreover, considering the phase change and dissolution of acid-gas mixture in drilling fluids, the multiphase flow may go through in turn the single phase flow, supercritical-liquid two phase flow, liquid-liquid two phase flow and gas-liquid two phase flow (including bubbly flow, slug flow, churn flow and annular flow) with

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the mixed fluids rising from bottom hole to wellhead. Meanwhile, the flow transition criteria, drift flux models and friction factor calculating methods for this type of multiphase flow were proposed. Finally, the multiphase flow characteristics in a

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wellbore during acid-gas mixture influx were analyzed using the new method with an

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example. The results suggest that during the acid-gas mixture rising up along the wellbore, the flow pattern transforming from the supercritical-liquid two phase flow or the liquid-liquid two phase flow into gas-liquid two phase flow can cause a large volume expansion, increasing the blowout risk. Keywords: Multiphase flow; Acid-gas mixture; Supercritical phase; Phase change; Dissolution; Vertical wellbore

ACCEPTED MANUSCRIPT 1. Introduction The underbalanced drilling technology has gradually reached maturity for speeding up drilling and reducing formation pollution in drilling engineering

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(Bennion et al., 1998; Guo, 2000; Zhou and Zhou, 2001; Shirkavand et al., 2010). The formation fluids are allowed to flow into the borehole during the underbalanced drilling processes, so there are inevitable multiphase flows in wellbores, including

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formation oil, gas, water and drilling fluid, which has a significant influence on the

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drilling hydraulic parameters design and wellbore pressure control. The transition laws for multiphase flow patterns have attracted the attentions of more and more international scholars. The bubble coalescence is one of the earliest flow pattern transition mechanisms (Kirkpatrick and Lockett, 1974; Otake et al., 1977; Bilichi and

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Kestin, 1987; Taitel, 1980). However, Matuszkiewicz et al. (1987), Batchelor (1988), Van Wijngaarden and Kapteyn (1990) and Cheng (1998) hold that flow pattern

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transition is not due to the bubble coalescence but to the instability of void fraction wave. Some scholars experimentally studied the gas-liquid two phase flow laws in a

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vertical annular tube and divided their flow patterns, respectively. It was widely considered that their flow patterns are similar with that in a vertical circular tube, as shown in Table 1. However, the most widely used one for drilling wells among them is the four flow patterns of bubbly, slug, churn and annular flow (Raghavan, 1989; Aggour et al., 1996; Osman, 2004; Sun et al., 2011).

ACCEPTED MANUSCRIPT Table 1. The various gas-liquid two phase flow patterns in a vertical tube.

Oshinowo and Charles (1974)

bubbly, slug, churn and annular flow bubbly, slug and annular flow bubbly, slug, frothy, annular and mist flow bubbly, slug, churn, wire-annular, annular flow bubbly, dispersed bubbly, slug, frothy and annular flow

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Weisman et al. (1979), Taitel (1980), Vince and Lahey (1982) Sadatomi et al. (1982) Bilicki and Kestin (1987) Annunziato (1988) Kelessidis and Dukler (1989), Caetano et al. (1992)

Flow Patterns bubbly, slug, froth, ripple, film and mist flow bubbly, quiet-slug, dispersed-slug, frothy-slug, frothy and annular flow

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Scholars Govier et al. (1961)

In recent years, with the increase of gas reservoirs containing rich CO2 or H2S

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being drilled in the oil and gas exploration (Moroni et al., 2008; Lécolier et al., 2010; Awad and Macwan, 2012), these invaded acid-gas mixture in bottom hole may appear supercritical state, which is different from the air or CH4 gases. For instance,

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Chongqing “12.23” gas blowout in China in 2003 caused scholars’ concern about the supercritical CO2 and H2S in well drilling. However, no other researches have been found showing the effects of supercritical fluids on the multiphase flow pattern

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transition in a vertical wellbore. The typical method is just based on the gas-liquid

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two phase flow for the wellbore multiphase flow simulation, which may lead to high data error for the acid-gas mixture and drilling fluid flow in wellbore. Hence, the multiphase flow behavior of the acid-gas mixture and drilling fluid flow in a vertical wellbore are very significant for the hydraulic parameters design and wellbore pressure control in acid gasfield drillings. Herein, firstly the phase change of the acid-gas mixture was investigated for revealing its variation under certain temperature and pressure conditions of wellbores, then the multiphase flow behavior in wellbore were discussed and their transition criteria and the friction factor calculating methods

ACCEPTED MANUSCRIPT were proposed. Finally, the multiphase flow characteristics in a wellbore during acid-gas mixture influx were analyzed using the new proposed method. 2. Phase change for acid-gas mixture in wellbore

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Due to the high bottom hole pressure (BHP) for well drilling, the acid-gas mixture, invading into the bottom hole, can be dissolved thoroughly in drilling fluids.

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Herein, the dissolution and precipitation of acid-gas mixture in drilling fluids is only considered as the effect on the phase change of acid-gas mixture.

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The temperature-pressure phase diagrams of air (mainly N2 and O2), CO2 and CH4 mixtures were calculated by PVTsim software, as shown in Fig. 1. It can be seen that the phase envelopes of CO2 and CH4 mixtures are between that of CO2 and CH4. The ranges of their phase envelope are also different due to the different volume

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fraction. The dew point and bubble point line, enclosing the phase envelope, intersect at the critical point. The mixture will be in the supercritical state when both its

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temperature and pressure are higher than that of its critical point. The temperature in a wellbore generally changes in the range of 0~100 ℃. Due to the critical temperature

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of CH4 or airless than that of wellbore, they usually are treated as gaseous even when they are in the supercritical state during the drilling process. However, the acid-gas mixture cannot be treated like this since their critical temperature is close to that of wellbore. So we performed an experiment to further study the phase change of acid-gas mixture in a vertical wellbore.

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Fig. 1. The pressure-temperature phase diagrams for various gas mixtures. 2.1. Experimental setup and procedures

Fig. 2 shows a schematic for the experimental setup. A reactor was designed with a length of 0.5 m and an inner diameter of 0.15 m, and its maximum working

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pressure is 40 MPa. A pump was used to pump the prepared gases from the high pressure gas cylinder into the reactor. A piston was located at the bottom of the

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reactor to control the pressure of this system, and an oil bath circle passage was set around the reactor to control the temperature of this system. A mixer in the reactor

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was used to mix the fluids thoroughly. A temperature and pressure sensor was installed on the reactor to record the temperature and pressure of the fluids. A transparent observation window, with a length of 0.10 m and a width of 0.02 m, was set on the reactor for a high-speed camera used to measure the gas phase behavior. The maximum resolution of the high-speed camera (Olympus I-speed TR) is 1280 × 1024 at a speed of 2000 fps. The accuracy of temperature sensor (Pt 100) is 0.1 ◦C. The accuracy of the pressure sensor (Baissde 701) is 0.075 MPa.

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Fig. 2. The schematic diagram for the experimental setup.

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Because the H2S gas is deadly toxic, the prepared acid-gas mixture in the experiment just consist of 95.6 % (molar fraction) CO2 and 4.4 % CH4 based on the example of well-1 in Fig. 1. The experimental procedures are as follows: (1) Inject certain amount of water into the reactor.

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(2) Circulate the oil in the oil bath circle passage at a given temperature. (3) Pump the prepared gases into the reactor until the system pressure reaches a

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given value.

(4) Turn on the mixer to mix the fluids thoroughly, control the piston to maintain

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a stable pressure for the system during the experiment. (5) Use the high-speed camera to record the gases phase behavior. Herein, the purpose of the step (1) ~ (3) is to provide a wellbore environment for

the gases phase change. It can be seen from Fig. 3 that the phases of the mixture rising in the wellbore can change, followed by supercritical phase, liquid phase, gas-liquid phase and gas phase.

ACCEPTED MANUSCRIPT During the experiment, the five representative temperature-pressure points were adopted from the Well-1 temperature profile in the following Fig. 3, and their distribution on Well-1 temperature profile was shown by point ① ~ ⑤.

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2.2. Phase changes Fig. 3 shows the phase changes of the acid-gas mixture (95.6% (molar fraction) CO2 and 4.4% CH4) in a wellbore. It can be seen that the wellbore temperature goes

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across the phase envelope of the CO2-rich natural gas. Furthermore, this mixture will

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be in the supercritical phase when both its temperature and pressure are higher than that of its critical point. Then, due to the decrease of wellbore temperature with the decrease of well depth, the phases of this mixture rising in the wellbore can change,

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followed by liquid phase, gas-liquid phase and gas phase.

Fig. 3. The phase changes of acid-gas mixture rising in wellbore. The phenomena of their phase changes under the corresponding conditions of points ① ~ ⑤ (shown in Fig. 3) were obtained using the high-speed camera, as shown in Fig. 4. Fig. 4 (a) indicates that the gas mixtures are being in the supercritical

ACCEPTED MANUSCRIPT state at point ①. There is an obviously bending interface between the gas mixtures and water due to their interfacial tension, which indicates that their physical properties are more close to that of gases. Fig. 4 (b) also shows that the gas mixtures are being in

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the supercritical state at point ②, but they are in the vicinity of their critical point. Hereby, the abrupt changes of their density, viscosity and surface tension in this state lead to an essential difference with that in the gaseous or liquid state. Xue et al. (2004)

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proved that gas fluids may abruptly change in the vicinity of the critical point, which

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means slight changes of pressure and temperature can significantly change their physical properties. Therefore, these properties in the supercritical state should be calculated separately. Fig. 4 (c) shows that the gas mixtures are in the liquid state at point ③. The horizontal interface between the gas mixtures and water suggests that

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their physical properties are more close to that of liquids. The vapor begins to appear in the gas mixtures, because their pressure is less than their bubble-point pressure at point ④ (shown in Fig. 4 (d)); then all the mixtures can be transformed into vapor

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with the further decrease of their pressure at point ⑤ (shown in Fig. 4 (e)). The

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whole system keeps being in the gas-liquid two phase state during this process, so their physical properties can be calculated using the traditional methods of the gas-liquid two phase flow.

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Fig. 4. The phenomenon diagram for phase changes of the CO2-rich natural gas under conditions of certain wellbore temperature and pressure. It was proved that the phases of the mixture rising in a wellbore may change, followed by supercritical phase, liquid phase, gas-liquid phase and gas phase. Hence,

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the traditional gas-liquid two phase flow cannot be applicable completely for a well with H2S/CO2-rich natural gas, and the effect of phase change of acid-gas mixture on

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the flow pattern transition in wellbores must be considered. 3. Multiphase flow type for acid-gas mixture and drilling fluid flow in wellbore

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3.1. Multiphase flow type

Fig. 5 shows the multiphase flow types of the acid-gas mixture and drilling fluid

flow in a vertical wellbore. Hasan and Kabir (1988) suggests that gases invading into the bottom hole may be dissolved in the drilling fluid in whole, so only one single phase flow exists in the wellbore. Moreover, its pressure will gradually decrease with the fluids rising up along the wellbore, which result in the gas releasing from the fluids. So the one single phase flow transformed into gas-liquid two phase flow. For this type of multiphase flow, the flow pattern firstly transformed into a bubbly flow,

ACCEPTED MANUSCRIPT and then as its pressure further decreasing, the flow pattern may continue to change, followed by slug flow, churn flow and annular flow. However, based on the above analysis, the wellbore temperature and pressure profiles will cross through the vicinity of the critical point for the acid-gas mixture.

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Therefore, the supercritical-liquid or the liquid-liquid two phase flow may come out during the mixed fluids rising upward in wellbore under the low fluids velocity condition. If the invaded fluids dissolve in the drilling fluid in whole, the multiphase

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flow type of the mixed fluids will change from the bottom hole to the wellhead, followed by single phase flow, supercritical-liquid two phase flow, liquid-liquid two

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phase flow and gas-liquid two phase flow (including bubbly flow, slug flow, churn flow and annular flow), as shown schematically in Fig. 5 (a). However, if the invaded fluids dissolve in the drilling fluids in part, its flow type will change followed by supercritical-liquid two phase flow, liquid-liquid two phase flow and gas-liquid two

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phase flow, as shown schematically in Fig. 5 (b). A final note about the gas-liquid two phase flow is that both the liquid status of drilling fluid and acid-gas mixture are

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treated as one liquid phase.

ACCEPTED MANUSCRIPT Fig. 5. The multiphase flow types in a vertical wellbore during the acid-gas mixture influx. 3.2. Multiphase flow transition criteria

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(1) Single phase flow. The solubility of acid-gas mixture must be calculated for identifying whether there is the single phase flow. If the acid-gas mixture invading into a wellbore are

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dissolved in drilling fluids in whole, the flow state in the wellbore can be treated as a

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single phase flow. The solubility of acid-gas mixture in liquids is calculated using the following equations (Sun et al., 2013).

xi = Pyiϕiv

( Pϕ ) l i

(4a)

(4b)

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  ln ϕi = bi ( Z − 1) b − ln ( Z − b ) − a ( 2.818b )  2 a ∑ x j aij − bi b  ⋅ j   ln ( Z + 2.414b ) ( Z + 16.971b ) 

where, f i v , fi l are the fugacity of acid-gas mixture in the mixed fluids; yi , xi are the molar fraction of acid-gas mixture in the mixed fluids; ϕiv , ϕil are the fugacity

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coefficients of acid-gas mixture in the mixed fluids; a, b are the coefficients; Z is

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compressibility factor.

(2) Supercritical-liquid two phase flow.

If the acid-gas mixture invading into a wellbore are dissolved in the drilling fluid

in part, the flow state in the wellbore can be treated as a two phase flow. In addition, the acid-gas mixture may release from the drilling fluid with the pressure decrease during they rising up along a wellbore, so a single phase flow in the wellbore can transform into a two phase flow.

ACCEPTED MANUSCRIPT When the acid-gas mixture is in the supercritical state (namely, both its temperature and pressure in wellbores are higher than that of their critical point), there will be the supercritical-liquid two phase flow in wellbores. P ≥ Pc , T ≥ Tc

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(5a)

where, P is the pressure of mixed fluids in wellbore, Pa; T is the temperature of

critical temperature of the acid-gas mixture, ℃.

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(3) liquid-liquid two phase flow.

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mixed fluids, ℃; Pc is the critical pressure of the acid-gas mixture, Pa; Tc is the

When the acid-gas mixture is in the liquid state (namely, their pressure in the wellbore is less than their critical-point pressure and their temperature is higher than their bubble-point temperature), there will be the liquid-liquid two phase flow in

P < Pc , T ≥ Tb

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wellbore. (6a)

pressure, ℃.

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where, Tb is the bubble-point temperature of the acid-gas mixture at a given

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(4) gas-liquid two phase flow. When the acid-gas mixture are in the gas-liquid or gas state (namely, their

pressure in the wellbore is higher than their critical-point pressure and their temperature is less than their critical-point temperature, or, their pressure in the wellbore is less than their critical point pressure and their temperature is less than their bubble-point temperature), there will be the gas-liquid two phase flow in wellbore.

ACCEPTED MANUSCRIPT P ≥ Pc , T < Tc or P < Pc , T < Tb

(7)

Transition criteria (Hasan and Kabir, 1988) were improved to predict the flow patterns of gas-liquid two phase flow in this work, as follows.

u sg < k1 ( 0.429u sl + 0.357u gr )

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Bubbly flow: (8a)

Slug flow: usg ≥ k1 (0.429usl + 0.357u gr )

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(9a)

Churn flow:

Annular flow:

(10b)

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 ρ g usg2 > 25.41log ( ρl usl2 ) − 38.9 for ρl usl2 > 74.4   2 2 1.7 2  ρ g usg > 0.0051( ρl usl ) for ρl usl ≤ 74.4

(11a)

0.25

(11b)

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0.333 usg ≥ k2  gσ ( ρl − ρ g ) ρ g2   

(10a)

0.25

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0.333 usg < k2  gσ ( ρl − ρ g ) ρ g2   

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 ρ g usg2 > 25.41log ( ρl usl2 ) − 38.9 for ρl usl2 > 74.4   2 2 1.7 2  ρ g usg > 0.0051( ρl usl ) for ρl usl ≤ 74.4

where, usl , u sg , u gr are the apparent velocity of liquid, gas and gas drift velocity, respectively, m/s; ρl , ρ g are the density of liquid and gas, respectively, kg/m3; σ is the surface tension, N/m; g is the local gravitational acceleration, m/s2; k1 and

k2 are the correction factors. 4. Multiphase flow model and its application 4.1 Governing equations for mass, momentum and energy balance

ACCEPTED MANUSCRIPT The multiphase flow model for the acid-gas mixture and drilling fluid flow in wellbores consists of two continuity equations, one momentum equation and one energy balance equation. The acid-gas mixture and drilling fluid flow in a control unit

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is presented schematically in Fig. 6.

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Fig. 6. The acid-gas mixture and drilling fluid flow in a control unit. (1) Continuity equations.

The assumptions are made that the acid-gas mixture and drill fluid flow in a

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vertical wellbore is regarded as one-dimensional and the difference between the

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acid-gas mixture released from the drilling fluids and that produced from the reservoirs is to be neglected. Hereby, the continuity equation for acid-gas mixture can be defined as:

Inflow + Produced + Released – Outflow = Total variation.

That is, the continuity equation of acid-gas mixture is shown as follows:

 v E A ∂ ∂ ( ρ x Ex A) +  ρ x vx Ex A + m m Rms ρ xs  = qx ∂t ∂s  Bm 

(12)

where, when P ≥ Pc , T ≥ Tc , the subscript x represents the acid-gas mixture in

ACCEPTED MANUSCRIPT supercritical state; when P < Pc , T ≥ Tb , the subscript x represents the acid-gas mixture in liquid state; when P ≥ Pc , T < Tc or P < Pc , T < Tb , the subscript x represents the acid-gas mixture in gas state.

 v E A ∂ ∂ ( ρm Em A) +  ρmvm Em A − m m Rms ρ gs  = 0 Bm ∂t ∂s  

(13)

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(2) Momentum equation.

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Similarly, the continuity equation of drilling fluid can be obtained:

The momentum equation (Eq. (14)) describes the pressure drop due to fluid

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weight, fluid acceleration, viscous friction between the fluid and wellbore wall, and momentum exchange between the acid-gas mixture and drilling fluid.

(14)

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∂ ∂ ( ρm vm Em A + ρ x vx Ex A) + ( ρmvm2 Em A + ρ x vx2 Ex A) ∂t ∂l d ( Ap ) d ( AFr ) + Ag ( ρ m Em + ρ x Ex ) + + =0 ds ds (3) Energy balance equation.

The energy balance equation (Eq. (15)) describes the temperature drop due to

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heat transfer between the acid-gas mixture, drilling fluid and surrounding formation

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through wellbore wall.

∂ ∂ ρm EmC pmTA + ρ x Ex C pxTA ) + ( ρm vm Em AC pmT + ρ x vx Ex AC pxT ) ( ∂t ∂s ∂ ( ρ m Em Rms ) qFm − qtam qFx − qtax − = + ∂t ds ds

(15)

where, E is the volume fraction; ρ is the density, kg/m3; v is the velocity, m/s; 2 A is the cross-sectional area, m ; Rms is the local solution gas-drilling fluid ratio;

Bm is the local volume coefficient of the drilling fluids; ρ xs is the gas density under

the standard condition, kg/m3; q x is the mass flow rate per unit length, kg/(s·m); C p

ACCEPTED MANUSCRIPT is specific heat capacity, J/(kg·K); qF is the heat exchange amount between the annular fluids and external, J; qta is the heat exchange amount between the annular fluids and drill string, J; T is the annular temperature, K; p is the annular pressure,

the drilling fluid and the acid-gas mixture, respectively.

4.2 Pressure drop calculation due to viscous friction

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Pa; g is the local gravity acceleration, m/s2 ; the subscripts m and x represent

(1) Single phase flow.

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different under the various flow types for Eq. (14).

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The pressure drop calculation due to viscous friction and friction factor are

The friction factor of the power-law fluid is used for the liquid-liquid two phase flow (Sun et al., 2013). (6a)

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2 Fr = 2 f uam ρ am De

(6b)

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n  8k  8uam 3n + 1  f = ⋅  , for Re ≤ 2000 2  ρamuam 4n    De    f 1− n / 2  0.2 2.0k  1  − 1.2 , for Re > 2000  f = n0.75 log  Re  4      n 

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where, Fr is the viscous friction head; ρ am is the mean density of the mixed fluids, kg/m3; u am is the mean velocity of the mixed fluids, m/s; De is the equivalent diameter, m; n is the flow index of the mixed fluids; k is the correction factor; Re is the mean Reynolds number of the mixed fluids, which can refer to the reference proposed by Gao (2007).

(2) Liquid-liquid two phase flow and supercritical-liquid two phase flow. The following equation was established for the friction factor of SC-CO2 by

ACCEPTED MANUSCRIPT Wang et al. (2014) 2 Fr = 2 f uam ρ am De

(5a)

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64   f = Re , for Re < 2300    Re − 3516  2    f = 0.06539 exp  −    , for 2300 ≤ Re ≤ 3400    1248    0.95 1.108     ε  ε  1 9.26 18.35    e e  , = −2.34 log  − log   +   f 1.72 De Re  Re     29.36 De      for 3400 < Re < 2 × 106

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(5b)

roughness, m.

(3) gas-liquid two phase flow. Bubbly flow: 2 Fr = 2 f uam ρ am De

(8a)

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where, f is the friction coefficient of SC-CO2; εe is the equivalent absolute

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1 f = −4log ( ε e 3.71De − 5.05log A Re )  1.110 0.898  A = ( ε e 2.549 De ) + ( 7.149 Re )

(8b)

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Slug flow and churn flow:

2 Fr = 2 f (1 − E g ) u am ρ am De

(9)

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f is same as Eq. (8b). Annular flow:

Fr = 2 f u sg2 ρ am

(D E ) e

2 g

(11a)

f = 0.079 1 + 75 (1 − Eg ) ( Re g 0.25 ) 

(11b)

4.3 Drift flux model The calculating methods of the drift velocity and void fraction are also different under the various flow types. Herein, we suppose that the interphase slip is neglected

ACCEPTED MANUSCRIPT for supercritical-liquid and liquid-liquid two phase flow. Therefore, the drift velocity and void fraction calculating methods for the gas-liquid two phase flow are proposed as follows (Hasan and Kabir, 1988, 2002).

 E g = u sg ( c0uam + u gr )   0.25 2 u gr = 1.53  gσ ( ρl − ρ g ) ρ l 

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Bubbly flow:

(8b)

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Slug flow and churn flow:

(9b)

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 E g = usg ( c0uam + u gr )   0.5 u gr = ( 0.3 + 0.22 Ddr D p )  g ( Ddr − D p )( ρl − ρ g ) ρl 

Annular flow:

(11b)

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E = (1 + Y 0.8 )−0.378  g 0.5 0.1 0.9  Y = (1 − X ) X  ( ρg ρl ) ( µl µg )  0.25 ugr = 1.53  gσ ( ρl − ρ g ) ρl2    

where, u gr is the gas drift velocity, m/s; c0 is the velocity distribution factor; Ddr

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is the inside diameter of wellbore, m; D p is the outside diameter of drill string, m;

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Y is the porosity factor; X is the gas flow factor. 4.4 Other auxiliary equations To enclose the above equations, the auxiliary equations must be established. The

most important auxiliary equations are the flow transition criteria, the friction factor equations and the drift velocity equations proposed above, and the other auxiliary equations refer to the reference proposed by Gao (2007).

4.5 Case study

ACCEPTED MANUSCRIPT Herein, the multiphase flow in a wellbore during the acid-gas mixture influx was calculated by using the above model based on an exploration well in Xibei Oilfield of China. Fig. 7 shows its well structure. The data of this vertical well are as follows: the

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well depth is 6651 m; the discharge, density and viscosity of drilling fluid are 22 L/s, 1.85 g/cm3 and 42 mPa·s, respectively; the geothermal gradient is 2.56 ℃/100 m; the

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5.1 % CO2, 82.6 % H2S and 12.3 % CH4.

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formation pressure coefficient is 1.254. The invaded gases for simulation consist of

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Fig. 7. The schematic diagram for the well structure. The results comparison between this work with OLGA (a commercial software

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for multiphase flow simulation) was obtained based on the above case (shown in Table 2). The simulation included three kinds of conditions: no gas influx, CH4 gas influx and CO2 gas influx, and the simulating time is 60 min. It indicates that the relative error of WT (wellhead temperature) is less than 10% under the three conditions, while the relative error of BHP (bottom hole pressure) is also less than 10% under the conditions of no gas influx and CH4 gas influx. However, the relative error of BHP exceeds 10% under the condition of CO2 gas influx. This is because the

ACCEPTED MANUSCRIPT models in OLGA did not consider the liquid-liquid and the supercritical-liquid two phase flow, while this word did is.

Table 2. The results comparison between this work with OLGA.

OLGA This work

CH4 gas influx 46.8 107.8 44.3 116.7 -5.3 8.3

CO2 gas influx 47.1 109.6 44.5 121.4 -5.5 10.8

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Relative error

WT/℃ BHP/MPa WT/℃ BHP/MPa WT/% BHP/%

No gas influx 44.7 131.3 43.2 127.5 -3.4 -2.9

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Type

Fig. 8 shows the temperature-pressure field and volume fraction distribution in

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the wellbore at different time during the gas influx. Fig. 8 (b) indicates that the volume fraction of acid-gas mixture increases with the increase of time, and its peak is much larger near the wellhead than that near the bottom hole. It can be explained by

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that the flow types of the mixed fluids will transform from the supercritical-liquid or liquid-liquid two phase flow to the gas-liquid two phase flow, due to the change of the temperature and pressure during their rising up along the wellbore (shown in Fig. 8

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(a)). The density of the acid-gas mixture is close to the liquid density when it is in the

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supercritical state, so it has small volume and is not monitored easily at the bottom hole. However, the gas will be released largely from the mixed fluids and expand abruptly when rising up to the wellhead, which lead to the volume fraction increasing rapidly near the wellhead. Thus, the acid-gas mixture influx during drilling has the “hidden” and “sudden” characteristics. It follows that the supercritical-liquid two phase flow and the liquid-liquid two phase flow is very important, and the results can guide the hydraulic parameters design during drilling the acid reservoirs.

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(a) The temperature-pressure field distribution

(b) The volume fraction distribution

Fig. 8. The temperature-pressure field and volume fraction distribution in the wellbore at different time during the gas influx.

5 Conclusions The phase change of acid-gas mixture in a wellbore was investigated by the experimental analysis. The acid-gas mixture in the supercritical phase exists under

ACCEPTED MANUSCRIPT conditions of certain wellbore temperature and pressure. Hence, the effects of their phase changing on the multiphase flow in wellbore cannot be neglected. Based on the phase change and dissolution of acid-gas mixture in drilling fluids, the mixed fluids

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rising from bottom hole to wellhead may go through in turn the single phase flow, supercritical-liquid two phase flow, liquid-liquid two phase flow, gas-liquid two phase flow (bubbly flow, slug flow, churn flow and annular flow). Meanwhile, the flow

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the various flow types were proposed.

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transition criteria, drift flux models and the friction factor calculating methods under

While the acid-gas mixture invades into the vertical wellbore and rises up, the flow types transforming from the supercritical-liquid flow (or the liquid-liquid flow) into gas-liquid flow may cause a large volume expansion, increasing the blowout risk.

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The proposed flow types in wellbore, including the supercritical-liquid flow and the liquid-liquid flow, reveal the “hidden” and “sudden” characteristics of the acid-gas mixture influx. The results can guide the hydrostatic parameters design during drilling

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the acid reservoirs.

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Acknowledgments

This work was supported by the National Key Basic Research Program of China

(973 Program, 2015CB251200), the National Science and Technology Major Project of China (2016ZX05020-006), the National Natural Science Foundation for Outstanding Youth of China (51622405), and the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_14R58).

References

ACCEPTED MANUSCRIPT Aggour, M., Alyousef, H., Almuraikhi, A., 1996. Vertical multiphase flow correlations for high production rates and large tubulars. SPE Production & Facilities 11 (1), 41-48.

RI PT

Annunziato, M., 1988. Measuring system for two-phase flow pattern recognition using statistical analysis. Fluids Engineering Division 73 (2), 15-21.

Awad, M., Macwan, N., 2012. H2S risk management. Society of Petroleum Engineers,

SC

Doi:10.2118/162613-MS.

M AN U

Batchelor, G.K., 1988. A new theory of the instability of a uniform fluidized bed. Journal of Fluid Mechanics 193, 75-110.

Bennion, D.B., Thomas, F.B., Bietz, R.F., Bennion, D.W., 1998. Underbalanced drilling: praises and perils. SPE Drilling & Completion 13 (4), 214-222.

TE D

Bilicki, Z., Kestin, J., 1987. Transition criteria for two-phase flow patterns in vertical upward flow. International Journal of Multiphase Flow 13 (3), 283-294. Caetano, E.F., Shoham, O., Brill, J.P., 1992. Upward vertical two-phase flow through

EP

an annulus part i: single-phase friction factor, Taylor bubble rise velocity, and

AC C

flow pattern prediction. Journal of Energy Resources Technology 114 (1), 1-13. Cheng, H., Hills, J.H., Azzorpardi, B.J., 1998. A study of the bubble-to-slug transition in vertical gas-liquid flow in columns of different diameter. International Journal of Multiphase Flow 24 (3), 431-452.

Gao Yonghai, 2007. Study on Multi-phase flow in wellbore and well control in deep water drilling. Doctoral dissertation: China University of Petroleum, 47-64. Guo, Y., 2000. Improvement on the procedure in exploration well by unbalanced

ACCEPTED MANUSCRIPT drilling: a case history in BS7 well in People’s Republic of China. Society of Petroleum Engineers, Doi: 10.2118/59263-MS. Govier, G.W., Sullivan, G.A., Wood, R.K., 1961. The upward vertical flow of

RI PT

oil-water mixtures. Canadian Journal of Chemical Engineering 39 (2), 67-75. Hasan, A.R., Kabir, C.S., 1988. A study of multiphase flow behavior in vertical wells. SPE Production Engineering 3 (2), 263-272.

SC

Hasan, A.R., Kabir, C.S., 2002. Fluid flow and heat transfer in wellbores. Society of

M AN U

Petroleum Engineers.

Lécolier, E., Rivereau, A., Ferrer, N., Audibert, A., Longaygue, X., 2010. Durability of oil well cement formulations aged in H2S-containing fluids. SPE Drilling & Completion 25 (1), 90-95.

TE D

Matuszkiewicz, A., Flamand, J.C., Bouré, J.A., 1987. The bubble-slug flow pattern transition and instabilities of void fraction waves. International Journal of Multiphase Flow 13 (2), 199-217.

EP

Moroni, N., Repetto, C., Ravi, K., 2008. Zonal Isolation in Kashagan Field: Reservoir CO2

and

H2S.

Society

of

Petroleum

Engineers,

AC C

Containing

Doi:10.2118/112703-MS.

Kelessidis, V.C., Dukler A.F., 1989. Modeling flow pattern transition for upward gas-liquid in vertical concentric and eccentric annuli. International Journal of Multiphase Flow 15 (2), 173-191. Kirkpatrick, R.D., Lockett, M.J., 1974. The influence of approach velocity on bubble coalescence. Chemical Engineering Science 29 (12), 2363-2373.

ACCEPTED MANUSCRIPT Otake, T., Tone, S., Nakao, K., Mitsuhashi, Y., 1977. Coalescence and breakup of bubbles in liquids. Chemical Engineering Science 32 (4), 377-383. Oshinowo, T., Charles, M.E., 1974. Vertical two-phase flow part i: flow pattern

RI PT

correlations. Canadian Journal of Chemical Engineering 52 (52), 25-35. Osman, E.S.A., 2004. Artificial neural network models for identifying flow regimes and predicting liquid holdup in horizontal multiphase flow. SPE Production &

SC

Facilities 19 (1), 33-40.

Evaluation 4 (4), 585-594.

M AN U

Raghavan, R., 1989. Well-test analysis for multiphase flow. SPE Formation

Sadatomi, M., Sato, Y., Saruwatari, S., 1982. Two-phase flow in vertical noncircular channels. International Journal of Multiphase Flow 8 (6), 641-655.

TE D

Shirkavand, F., Hareland, G., Olson, W., 2010. The design and development of a drilling simulator for planning and optimizing under-balanced drilling operations. Journal of Canadian Petroleum Technology 49 (6), 68-73.

EP

Sun B., Wang Z., Gong P., Song R., 2011. Application of a seven-component

AC C

multiphase flow model to deepwater well control. Acta Petrolei Sinica 32 (6), 1042-1049.

Sun Baojiang, Gong Peibin, Wang Zhiyuan., 2013. Simulation of gas kick with high H2S content in deep well. Journal of Hydrodynamics 25 (2), 264-273.

Taitel, Y., Bornea, D., Dukler, A.E., 1980. Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AIChE Journal 26 (3), 345-354. Van Wijngaarden L., Kapteyn C, 1990. Concentration waves in dilute bubble/liquid

ACCEPTED MANUSCRIPT mixtures. Journal of Fluid Mechanics 212, 111-137. Vince, M.A., Lahey, R.T., 1982. On the development of an objective flow regime indicator. International Journal of Multiphase Flow 8 (2), 93-124.

RI PT

Wang Zhiyuan, Sun Baojiang, Wang Jintang, Hou Lei., 2014. Experimental study on the friction coefficient of supercritical carbondioxide in pipes. International Journal of greenhouse gas control 25 (6), 151-161.

SC

Weisman, J., Duncan, D., Gibson, J., Crawford, T., 1979. Effects of fluid properties

M AN U

and pipe diameter on two-phase flow patterns in horizontal lines. International Journal of Multiphase Flow 5 (6), 437-462.

Xue Weidong, Zhu Zhenghe, Zou Lexi, Zhang Guangfeng, 2004. Theoretic calculation on thermodynamic character for SCF CO2. Journal of Atomic and

TE D

Molecular Physics 21 (2), 295-300.

Zhou, L., Zhou, K., 2001. Application and design of unbalanced-drilling with formation

fluid

AC C

EP

10.2118/68497-MS.

injection.

Society

of

Petroleum

Engineers,

Doi:

ACCEPTED MANUSCRIPT 1. Phase change of acid-gas mixture in a vertical wellbore was investigated. 2. The supercritical-liquid flow and liquid-liquid flow were found in wellbores. 3. Transition criteria and models for the multiphase flow were improved.

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4. The multiphase flow characteristics depend on the multiphase flow transition.