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Non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation of marine gas hydrate reservoirs
Available online at www.sciencedirect.com
ScienceDirect Natural Gas Industry B 6 (2019) 282e292 www.elsevier.com/locate/ngib
Research Article
Non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation of marine gas hydrate reservoirs*,** Wei Na a,*, Zhao Jinzhou a, Sun Wantong a, Zhou Shouwei a, Zhang Liehui a, Li Qingping b, Fu Qiang a,b, Lu¨ Xin b & Zheng Lijun b a
State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan, 610500, China b CNOOC Research Institute Co., Ltd., Beijing, 100027, China Received 15 July 2018; accepted 25 October 2018 Available online 30 May 2019
Abstract In the core process of fractured marine gas hydrate (hereinafter referred to as hydrate) particles being transported up to the surface platform by airtight pipeline in the solid fluidization exploitation of marine gas hydrate reservoirs, influenced by the rising temperature and the dropping pressure, the solid hydrates will decompose and produce a large amount of gas at a certain critical point, causing the liquidesolid two-phase flow in the wellbore to change into complicated gaseliquidesolid multiphase non-equilibrium flow, which further aggravate well control, solid phase transportation and other safety risks. In view of this, the dynamic hydrate decomposition law in the above process was studied in this paper by establishing multiphase wellbore flow mathematical models of wellbore temperature and pressure field, hydrate phase equilibrium, hydrate dynamic decomposition in multiphase riser pipe flow, wellbore multiphase flow coupled hydrate dynamic decomposition, and a numerical calculation method was proposed and verified. The following results were obtained. First, by numerical model analysis, the effects of liquid phase displacement, solid throughput (daily gas production rate) and wellhead back pressure under different construction parameters on multiphase non-equilibrium pipe flow were obtained. In addition, the field construction guidance measures were put forward based on multiphase nonequilibrium pipe flow characteristics as follows: to properly increase the solid throughput so as to increase the natural gas production, to appropriately increase the liquid-phase displacement and the wellhead back pressure so as to ensure well control safety. This study provides not only a theoretical basis for the prediction of multiphase non-equilibrium pipe flow in the solid fluidization exploitation, but a technical support for the field construction parameter optimization and well control safety. © 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Natural gas hydrate; Solid fluidization exploitation; Non-equilibrium multiphase wellbore flow; Decomposition; Well control risks; Construction parameter; Prediction methods
* Project supported by the National Key R&D Program “New Technology for Marine Hydrate Solid Fluidization Testing” (No.: 2016YFC0304008), Strategic Research Project for Medium- and Long-Term Development Strategy Research in China's Engineering Science and Technology “Research on Deep Sea Gas Hydrate Development Strategy for 2035” (No.: 2017- ZCQ-5), Key Project of National Natural Science Foundation of China, and “Measurement and Control Theory and Key Issues of Managed Pressure Drilling” (No.: 51334003). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2018.10.013. * Corresponding author. E-mail address: [email protected] (Wei N.). Peer review under responsibility of Sichuan Petroleum Administration.
0. Introduction For safe and efficient development of natural gas hydrate (hereinafter referred to as hydrate) reservoirs, the authors proposed an innovative technical idea: solid fluidization exploitation of marine gas hydrate reservoirs [1e7]. However, the research on solid fluidization exploitation of marine gas hydrate reservoirs is still in its early stage and some theoretical issues need to be further studied. Particularly, in the process of transporting hydrate solid particles up to the surface platform in airtight pipeline, influenced by the rising
https://doi.org/10.1016/j.ngib.2018.10.008 2352-8540/© 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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temperature and the dropping pressure in the pipeline (wellbore), the hydrates will decompose and produce a large amount of gas, causing the liquidesolid two-phase flow in the wellbore to change into complicated gaseliquidesolid nonequilibrium multiphase flow. The complicated multiphase flow will further affect the dynamic decomposition of hydrate particles. In this process, the wellbore flow is a multi-phase non-equilibrium wellbore flow with complicated characteristic parameters, which further aggravates well control, solidphase particle transportation and other safety risks. Many scholars have worked a lot on the characteristics of multiphase wellbore flow, mainly focusing on the flow pattern division and prediction [8e11] and wellbore pressure calculation and measurement [12e14]. There are no studies about the wellbore multiphase flow characteristics of coupling hydrate decomposition. Moreover, the research on hydrate decomposition mainly focuses on the decomposition temperature and pressure conditions [15e19] and the decomposition rate model and prediction [20e23]. The dynamic decomposition law of hydrate particles in the process of temperature increasing and pressure decreasing under the condition of multiphase wellbore flow rising has not been reported. In this paper, the law of multiphase non-equilibrium wellbore flow in the solid fluidization exploitation of marine gas hydrate reservoirs was studied using the mathematical models of wellbore temperature and pressure field, mathematical model of hydrate dynamic decomposition in multiphase riser pipe flow and mathematical model of wellbore multiphase flow in coupled hydrate dynamic decomposition, and thus a numerical calculation method was proposed. 1. Mathematical model of non-equilibrium multiphase wellbore flow 1.1. Wellbore temperature model Based on the law of energy conservation and the basic equation of heat conduction, considering the process of solid fluidization exploitation of marine gas hydrate reservoirs, a temperature distribution model of mixed fluid in wellbore is established: rm vm cm
pD2pi dTm ¼ qw þ qf þ qh 4 dz
ð1Þ
where, rm is the density of mixed fluid in the wellbore, kg/m3; similarly, vm: the velocity of mixed fluid in the wellbore, m/s; cm: the specific heat capacity of mixed fluid in the wellbore, J/ (kg$K); Dpi: the inner diameter of the wellbore, m; Tm: the temperature of mixed fluid in the wellbore, K; z: the well depth, m; qw: the heat exchange between seawater and wellbore, W/m; qf: the heat generated by the frictional flow of mixed fluid in the wellbore, W/m; qh: the phase change heat during the decomposition of hydrate particles in the rising process, W/m. For the solution of qw, qf and qh, refer to Refs. [24e26].
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1.2. Wellbore pressure model Based on the process of solid fluidization exploitation of marine gas hydrate reservoirs, a wellbore pressure model in the process of mixed fluid flow is established: dpm ¼ pG þ pF þ pA ð2Þ dz where, pm is wellbore pressure, MPa; pG, pF and pA are respectively the pressure drop due to gravity, friction and fluid velocity change, MPa/m. For the solution of pG, pF and pA, refer to Refs. [27e29]. 1.3. Hydrate phase equilibrium model In order to judge whether the hydrate solid phase particles decompose under a certain temperature and pressure during the rising process, it is necessary to establish a hydrate phase equilibrium model. For purpose of simplified calculation, the hydrate phase equilibrium model established by Dzyuba and Zektser [30] after experiment is used: Tm ¼ 9:6339 ln peq þ 264:9661
ð3Þ
where, peq represents the equilibrium pressure of the hydrate phase at a certain temperature, MPa. 1.4. Hydrate dynamic decomposition model in multiphase riser pipe flow In the riser pipe flow, according to the hydrate phase equilibrium model, before the hydrate solid phase particles rise to a critical position of decomposition, they do not decompose and the decomposition rate is zero; after the hydrate solid phase particles rise to a critical position of decomposition, they decompose. In order to calculate the hydrate decomposition, the gas hydrate was assumed to be a methane hydrate. Based on the Kim model [20], a hydrate dynamic decomposition model in multiphase riser pipe flow is established: dnhyd ¼ khyd Shyd feq jðTm ;peq Þ fm jðTm ;pm Þ ð4Þ dthyd where, nhyd is the amount of hydrated matter in the hydrate solid phase particles, mol; similarly, thyd: the hydrate decomposition time, s; khyd: the hydrate decomposition rate constant, mol/(s$m2$MPa); Shyd: the surface area of hydrate solid phase particle decomposition, m2; feq and fm: respectively the fugacity of methane gas at Tm and peq, pm. The solution of each parameter is as follows: 1.4.1. Hydrate decomposition rate constant The hydrate decomposition rate constant is expressed as follows: 1 khyd
¼
1 khydc
þ
1 khydf
ð5Þ
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where, khydc represents the decomposition rate of hydrate itself, mol/(s$m2$MPa); khydf represents the mass transfer rate of methane gas at Tm and pm, mol/(s$m2$MPa). According to the Arrhenius equation, the decomposition rate of hydrate itself is calculated as follows: khydc ¼ k0hydc e½Eact =ðRTm Þ
ð6Þ
where, k0hydc represents the intrinsic decomposition rate constant of hydrate, mol/(s$m2$MPa); Eact represents the activation energy of hydrate decomposition reaction, J/mol; R represents the general gas constant, 8.314 J/(mol$K). Assuming that the hydrate solid particles are homogeneous spheres during the decomposition process, according to the empirical formula [31], the mass transfer of the particle spheres to the fluid is expressed as follows: nsh ¼ 0:347Re
0:62
nsc
1 3
ð7Þ
According to the theory of mass transfer, the following equation can be obtained: 8 > d k0 > > nsh ¼ s hydf > > > DAB > > < ds v m rm ð8Þ Re ¼ > mm > > > > > mm > > : nsc ¼ rm DAB Then the mass transfer rate of methane gas at Tm and pm is obtained as follows: khydf ¼
k0hydf
0:62 0:67 6 106 pm 0:347r0:29 m vm DAB 10 pm ¼ 0:38 Zg RTm Zg RTm m0:29 m ds
ð9Þ
where, nsh represents the Sherwood number; similarly, Re: the Reynolds number; nsc: the Schmidt number; ds: the hydrate solid phase particle diameter, m; k0hydf: the mass transfer coefficient, m/s; vm: the velocity of mixed fluid in the wellbore, m/s; rm: the density of mixed fluid in the wellbore, kg/m3; pm: the wellbore pressure, MPa; Tm: the temperature of mixed fluid in the wellbore, K; DAB: the diffusion coefficient of methane gas in the wellbore flow, m2/s; mm: the viscosity of mixed fluid in the wellbore, Pa$s; Zg: the natural gas compression factor, dimensionless. 1.4.2. Surface area of hydrate solid phase particle decomposition It is assumed that hydrate solid phase particle decomposition occurs at the interface [32], which is assumed to be a homogeneous sphere according to the foregoing. Therefore, the decomposition surface area is as follows: 2 2 p 6Vhyd 3 1 1 6nhyd Mhyd 3 3 Shyd ¼ ¼ p 4 4 p rhyd
ð10Þ
pd3
here, Vhyd ¼ Ehyd Vs ¼ Ehyd 6 s .where, 4 represents sphericity, dimensionless; similarly, Vhyd: the volume of hydrate in solid phase particles, m3; Mhyd: the molar mass of hydrate, kg/mol; rhyd: hydrate density, kg/m3; Ehyd: the abundance of hydrate in solid phase particles; Vs: the volume of solid phase particles, m3. 1.4.3. Fugacity of methane gas According to the definition of gas fugacity, the following equation can be obtained [33]: 0 1 Zpx B C ð11Þ Ratm Tx ln fx jðTx ;px Þ ¼ lim @ Vx dpx þ Ratm Tx lnp* A p*/0
p*
where, Ratm represents the general gas constant expressed in standard atmospheric pressure, which is 0.082 06 atm$L/ (mol$K) (1 atm ¼ 101.325 kPa); similarly, Tx: the ambient temperature, K; px: the ambient pressure, atm; p*: the reference state pressure, atm; fx: the fugacity of methane gas at standard atmospheric pressure at Tx and px, atm; Vx: the molar volume of methane gas at Tx and px, L/mol. Since the ReK equation of state is simple to calculate and generally has a high accuracy, it is assumed that the methane gas state obeys the ReK equation of state and then the following equation can be obtained: px ¼
Ratm Tx a 0:5 Vx b Tx Vx ðVx þ bÞ
ð12Þ
where, a and b represent the ReK constant, a provides a measure of the attraction between molecules, and b provides a measure of the size of the molecule. Therefore, the formula for calculating the fugacity of methane gas is derived as follows: ! a ln VxVþb þ Vxaþb Ratm Tx b b x fx jðTx ;px Þ ¼ exp ln þ ð13Þ Vx b Vx b Ratm T 1:5 x
1.5. Wellbore multiphase flow model of coupled hydrate dynamic decomposition The gas and liquid phase mass conservation equations are expressed as follows: ! ! 8 2 2 > v pDpi v pDpi > > r Eg þ r Eg vg ¼ mhydg > > vz 4 g 4 g < vt ð14Þ ! ! 2 2 > > pD pD v v > pi pi > > r El þ r El vl ¼ mhydl : vt vz 4 l 4 l The gaseliquidesolid phase mixed momentum equation in the wellbore is expressed as follows:
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v 6 v rl El v l þ r g Eg v g þ r s Es v s þ 10 pm þ rl El v2l þ rg Eg v2g vt vz 2f rm v2m þ rs Es v2s þ rm g sin q þ Dpi ¼0
285
as an example (Fig. 1). In Fig. 1, a, b and g are the calculation error precision. 2.3. Numerical calculation verification
The mixing temperature in the wellbore of the horizontal subsea section is equal to the external seabed temperature, which is expressed as follows:
In order to verify the accuracy of numerical calculation of non-equilibrium multiphase wellbore flow in solid fluidization exploitation of marine gas hydrate reservoirs, we used the established numerical calculation method for non-equilibrium multiphase wellbore flow to obtain the wellbore temperature, pressure, gas holdup, solid phase content, and gaseliquidesolid phase velocity curve, as shown in Fig. 2. The numerical calculation results are compared with the data from the scale physical simulation experiment of solid fluidization exploitation of marine gas hydrate made by Zhou Shouwei et al. [5,34,35]. According to the experimental basic data in the literature, the seawater depth is 1315 m, the well depth is 1500 m, the wellbore diameter of the experimental pipe section is 0.076 m, the simulated sea surface temperature is 308 K, the abundance of hydrate in the solid phase particles is 70%, the simulated construction displacement is 0.008 m3/s, the liquid phase density is 1030 kg/m3, and the solid phase throughput is 0.54 m3/h. It can be seen from Fig. 2 that the obtained numerical calculation value has little error compared with the experimental value in the literature, and the change trend is consistent. In order to further quantitatively analyze the error between the numerical calculation value and the experimental value in the literature, the following error definition equation is used:
Tm ðzH ; tÞ ¼ Tw ðzH Þ
s ¼ xs xr
ð15Þ where, Dpi represents the inner diameter of the wellbore, m; similarly, rg, rl and rs: respectively the gas, liquid and solid phase density in the wellbore, kg/m3; vg, vl and vs: respectively the gas, liquid and solid phase velocities in the wellbore, m/s; Eg, El and Es: respectively the gas holdup, liquid holdup and solid phase content, dimensionless; mhydg and mhydl: respectively the mass change rate of gas and liquid phase per unit length, kg/(s$m). 2. Numerical calculation method 2.1. Boundary and initial conditions In order to simplify the model, it is assumed that the solid phase particles of hydrate can be safely migrated in the horizontal section, and the migration velocity is equal to the liquid phase velocity, which is expressed as follows: vs ðzHo ; tÞ ¼ vl ðzHo ; tÞ
ð16Þ
ð17Þ
The wellhead pressure is equal to the wellhead back pressure, which is expressed as follows: pm ð0; tÞ ¼ pb
ð18Þ
where, zHo represents the well depth of the horizontal subsea section, m; similarly, vs(zHo, t) and vl (zHo, t): respectively the solid and liquid phase velocity in the subsea horizontal wellbore, m/s; zH: the vertical depth of the subsea horizontal section, m; Tm(zH, t) and Tw(zH): respectively the temperature of mixed fluid in the subsea horizontal wellbore and the temperature of outside seawater, K; pm(0,t) and pb: respectively the wellhead pressure and wellhead back pressure, MPa. 2.2. Numerical calculation method In order to study the non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation of marine gas hydrate reservoirs, we used the finite difference numerical calculation method. The space domain is the wellbore, and the time domain is the hydrate solid phase particles being transported from the bottom of the well to the wellhead. Assuming that at time n, the parameters of any two nodes i and i þ 1 in the wellbore are known, the numerical calculation process is illustrated by taking node i and i þ 1 from the time n to n þ 1
ð19Þ
where, s represents the error, dimensionless; similarly, xs: the numerical calculation value; xr: the experimental value in the literature. The average wellbore temperature error is calculated to be 0.022 C, the average wellbore pressure error is 0.023 MPa, the average gas holdup error is 0.010%, the average solid phase content error is 0.004%, and the average gas phase velocity error is 0.005 m/s, the average liquid phase velocity error is 0.003 m/s and the average solid phase velocity error is 0.004 m/s. It can be seen that the numerical model and calculation method proposed in this study have a high accuracy, which lays a foundation for the analysis of nonequilibrium multiphase wellbore flow characteristics. 3. Non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation The solid fluidization exploitation of marine gas hydrate reservoir is shown in Fig. 3. The well depth is 1400 m, the vertical depth is 1000 m, the vertical well depth is 0e830 m, the depth of deviated section is 830e1100 m and the horizontal well depth is 1100e1400 m; the outer diameter of the wellbore is 0.508 m, the inner diameter of the wellbore is 0.476 m and the density of the liquid phase of the pipe is
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Fig. 1. Flow chart of numerical calculation of non-equilibrium multiphase wellbore flow in solid fluidization exploitation.
1030 kg/m3. Gas hydrate reservoir characteristics in the South China Sea: the depth of seawater is 1000 m; the sea surface temperature is 293 K; the abundance of hydrate in solid phase particles is 70%. In order to obtain the non-equilibrium multiphase wellbore flow characteristics in the process of gas hydrate solid phase
particles being transported up to the surface platform in airtight pipeline, the established mathematical model and numerical calculation method are used to analyze the non-equilibrium multiphase wellbore flow characteristics of solid fluidization exploitation under different liquid phase displacement, solid throughput and wellhead back pressure conditions.
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Fig. 2. Comparison of numerical calculation values (xs) with experimental values in the literatures (xr).
3.1. Wellbore flow characteristics under different liquid phase displacements As to the numerical calculation parameters, the liquid phase displacement is 0.03 m3/s, 0.05 m3/s and 0.07 m3/s, respectively, the solid throughput is 1.5 m3/h (corresponding to the daily gas production of about 4133 m3), and the wellhead back pressure is 0.1 MPa. Through numerical calculation, the
Fig. 3. Schematic diagram of non-equilibrium multiphase wellbore flow in solid fluidization exploitation of marine gas hydrate reservoirs.
287
wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different liquid phase displacements in the solid fluidization exploitation of marine gas hydrate reservoirs were obtained, as shown in Fig. 4. It can be seen from Fig. 4a and b that, when the hydrate solid phase particles are transported upwards to the sea surface platform, the wellbore temperature is equal to the external seawater temperature in the horizontal subsea section from 1400 to 1100 m. In the deviated section and the vertical section of 1100 to 0 m, the wellbore temperature rises with the increase of external seawater temperature. With the increase of liquid phase displacement, the heat exchange time between the mixed fluid in the wellbore and the seawater is shortened and the heat transfer amount of seawater to the wellbore decreases, so the wellbore temperature drops and then the phase equilibrium pressure calculated by the hydrate phase equilibrium model decreases (Fig. 4b). With the increase of liquid phase displacement, the solid phase content (Es) in the wellbore decreases under the same solid throughput (Fig. 4i), resulting in a decrease in the density of mixed fluid in the wellbore, which in turn reduces the wellbore pressure. However, the increase of the velocity of each phase in the wellbore (Fig. 4def) will increase the frictional pressure drop and increase the wellbore pressure. Therefore, the wellbore pressure does not change significantly (Fig. 4b). In Fig. 4b, the intersection of the wellbore pressure curve and the phase equilibrium pressure curve under any determined liquid phase displacement condition is the critical position at which the hydrate solid phase particles decompose when they are transported upward with seawater. Later, as the hydrate solid particles rise in the wellbore, the amount of substance continues to decrease (Fig. 4c) and the hydrate is completely decomposed at the position where the amount of substance is 0. From the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the critical position of hydrate decomposition moves upward and the complete decomposition position moves up. It can be seen from Fig. 4def that in the horizontal subsea section from 1400 to 1100 m, according to the previous assumption, the hydrate solid phase particle velocity of the horizontal section is equal to the liquid phase velocity; the gas phase is not contained in the wellbore, and the gas phase velocity is 0. In the deviated section of 1100 to 830 m, since the cross-sectional area of the flow passage in the wellbore is constant (the inner diameter of the wellbore is constant), the liquid phase velocity is constant and the solid phase velocity gradually decreases. In the vertical section of 830 to 0 m, based on the critical position of hydrate decomposition in Fig. 4b and c, when the hydrate does not decompose, the gas phase velocity is still 0, and the liquid phase velocity and solid phase velocity remain stable. When the hydrate solid phase particles are transported upward to the decomposition critical position, the hydrate in the solid phase particles is decomposed into gas and water. Therefore, the liquidesolid two-phase flow
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Fig. 4. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different liquid phase displacements (0.03, 0.05 and 0.07 m3/s).
in the wellbore changes into the complex gaseliquidesolid multiphase flow. As the multi-phase flow continues to rise, the well depth decreases, the gas expands and the volume becomes larger, the gas phase velocity increases, and the carrier action causes the liquid phase velocity to increase. However, due to the decrease in the density of the mixed fluid in the wellbore, the carrying capacity is decreased. Therefore, the solid phase velocity decreases as the well depth decreases. At the same time, from the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the gas, liquid and solid phase velocities in the wellbore increase. In Fig. 4gei, combined with Fig. 4def, it can be seen that in the horizontal subsea section from 1400 to 1100 m, the gas holdup is 0 and the liquid holdup and solid phase content remain stable. In the deviated section of 1100 to 830 m, the solid phase velocity gradually decreases, causing the solid phase content to gradually increase, and the liquid holdup in the corresponding wellbore decreases. In the vertical section of 830 to 0 m, according to Fig. 4c, when the hydrate does not decompose, the gas holdup is 0 and the liquid holdup and solid phase content remain stable. When the hydrate solid phase particles are transported upward to
the decomposition critical position with seawater, the hydrate in the solid phase particles is decomposed into gas and water. Therefore, during the decomposition of hydrate, the gas holdup increases, the liquid holdup increases and the solid phase content decreases. When the hydrate solid phase particles are transported up to the position of complete decomposition with seawater, the liquid holdup no longer increases and the solid phase content no longer decreases. Meanwhile, as the well depth decreases, the gas expansion volume becomes larger and the gas holdup increases, resulting in a decrease in the density of mixed fluid in the wellbore, which in turn causes a decrease in the carrying capacity. Therefore, the solid phase content increases and the corresponding liquid holdup decreases. At the same time, from the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the gas holdup in the wellbore decreases, the liquid holdup increases and the solid phase content decreases. When the liquid phase displacement is at least 0.03 m3/s, the solid phase velocity rises abruptly (Fig. 4f) and the solid phase content suddenly decreases (Fig. 4i) near the wellhead (well depth is close to 0). It shows if other conditions are certain and the displacement is
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289
Fig. 5. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different solid throughputs (1.5, 3.0, and 4.5 m3/h).
small, the multi-phase flow pattern changes due to the high gas holdup at the wellhead, which leads to the transformation of the mixed fluid carrying capacity. At the same time, the flow pattern change poses a high challenge to well control safety. As can be seen from Fig. 4, in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, in order to prevent well control safety problems and improve the hydrate solid-phase particle transport capacity, it is necessary to appropriately increase the liquid phase displacement. 3.2. Characteristics of pipe flow under different solid throughputs As to the numerical calculation parameters, the solid throughput is 1.5 m3/h, 3.0 m3/h and 4.5 m3/h (corresponding to gas production of approximately 4133 m3/d, 8266 m3/d and 12399 m3/d), respectively, the liquid phase displacement is 0.03 m3/s and the wellhead back pressure is 0.1 MPa. Through numerical calculation, the wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different solid throughputs were obtained, as shown in Fig. 5.
In Fig. 5a and b, as the solid throughput increases, the amount of heat transfer from the seawater to the wellbore does not change much. Therefore, the wellbore temperature and the calculated phase equilibrium pressure do not change much. In Fig. 5b, a higher solid throughput will result in more solid phase entering the wellbore per unit time, which will increase the density of mixed fluid in the wellbore. In the well section where the hydrate does not decompose (the lower part of the wellbore), the flow in the wellbore is a liquidesolid two-phase flow, so the density of the mixed fluid in the wellbore increases, the gravity pressure drop increases and the wellbore pressure rises in the lower well section; In the well section after the decomposition of hydrate (the upper part of the wellbore), the gas is decomposed from the hydrate and the flow in the wellbore becomes a gaseliquidesolid multiphase flow. The gas phase has a tendency to reduce the density of mixed fluid in the wellbore, and the influence of the solid phase content is also considered. Therefore, the wellbore pressure does not change significantly with the increase of the solid throughput in the upper well section. At the same time, the critical position for the decomposition of hydrate solid phase particles rising upward with seawater does not change significantly with the increase of solid throughput and the
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Fig. 6. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different wellhead back pressures (0.1, 1.0, 2.0 MPa).
complete decomposition position also does not change significantly (Fig. 5c). In Fig. 5dei, the higher the solid throughput, the higher the solid phase content (Fig. 5i). When the hydrate solid phase particles are transported upward to the decomposition critical position with seawater, the more gas generated by the decomposition of the hydrate, the higher the gas holdup (Fig. 5g), the lower the corresponding liquid holdup (Fig. 5h). As the well depth decreases, the larger the solid throughput, the larger the gas volume after expansion, the higher the gas phase velocity (Fig. 5d), and the higher the liquid phase velocity due to its carrying capacity (Fig. 5e). At the same time, under the condition of high solid throughput, the gas holdup at the wellhead is higher, resulting in more intense multi-phase flow pattern transformation, which leads to greater transformation of the carrying capacity. Therefore, the more the solid phase velocity at the wellhead rises (Fig. 5f), the more the solid phase content decreases (Fig. 5i). At the same time, it poses a greater challenge to well control safety. As can be seen from Fig. 5, in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, the increase of solid throughput can result in the increase of the amount of hydrate delivered to the surface platform per unit time, thereby increasing gas production. However, the well
control safety problems will be more serious. Therefore, solid throughput should be increased on the premise of well control safety. 3.3. Wellbore flow characteristics under different wellhead back pressures As to the numerical calculation parameters, the wellhead back pressure is 0.1 MPa, 1.0 MPa and 2.0 MPa, respectively; the liquid phase displacement is 0.03 m3/s and the solid phase transport is 1.5 m3/h (corresponding gas production is about 4133 m3/d). Through numerical calculation, the wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different liquid phase displacements were obtained, as shown in Fig. 6. In Fig. 6aec, as the wellhead back pressure increases, the amount of heat transfer from the seawater to the wellbore does not change much. Therefore, the wellbore temperature and the phase equilibrium pressure do not change much. The pressure in the wellbore obviously increases. The critical position of decomposition and the complete decomposition position of hydrate both move up.
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In Fig. 6dei, before hydrate solid phase particles are transported upwards to the critical position of decomposition, the flow in the wellbore is liquidesolid two-phase flow. As the back pressure of the wellhead increases, the velocity of each phase and the content of each phase remain unchanged. After the hydrate solid phase particles are transported upwards to the critical position of decomposition, the hydrate decomposes to generate gas. The higher the wellhead back pressure, the smaller the gas expansion, the lower the gas phase velocity and gas holdup (Fig. 6d and g), the lower the liquid phase velocity (Fig. 6e), and the higher the liquid holdup (Fig. 6h). Moreover, the higher the density of mixed fluid in the wellbore, the higher the carrying capacity, the higher the solid phase velocity (Fig. 6f), and the lower the solid phase content (Fig. 6i). At the same time, under a high wellhead back pressure, the smaller the change of solid phase velocity and solid phase content (Fig. 6f and i) at the wellhead, the more helpful it is to ensure well control safety. It can be seen from Fig. 6 that increasing wellhead back pressure can significantly increase wellbore pressure and reduce well control safety risks caused by gas expansion at the wellhead. Therefore, the wellhead back pressure should be properly applied in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs. 4. Conclusions 1) Increase of liquid phase displacement can result in a significant reduction of wellbore temperature and hydrate phase equilibrium pressure to shift up the critical position of hydrate decomposition; and can result in a significant increase of gas, liquid and solid phase velocities, thus decreasing gas holdup and solid phase content. 2) With the increase of solid throughput, the wellbore temperature and hydrate phase equilibrium pressure do not change, the wellbore pressure rises in the lower well section and does not change significantly in the upper well section, the critical position of hydrate decomposition does not change, the solid phase content increases significantly, the gas holdup at the wellhead increases significantly, the liquid holdup decreases significantly, and the gaseliquidesolid phase velocity increases. 3) Increase of the wellhead back pressure can result in a significant increase of the wellbore pressure and the critical position of hydrate decomposition moving up; it can also result in a significant reduction of the gas holdup after hydrate decomposition, the decrease of gas and liquid phase velocity, the increase of the solid phase velocity, the decrease of the solid phase content and the increase of the liquid holding rate. 4) In the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, proper increase of solid throughput can increase gas production, but problems such as well control risks will be intensified. In order to prevent the wellbore flow safety
291
problems such as well control risks and improve the hydrate solid phase particle transport capacity, it is necessary to appropriately increase the liquid phase displacement and the wellhead back pressure.
Conflict of interest The authors declare that there is no conflicts of interest. References [1] Kvenvolden KA, Ginsburg GD & Soloviev VA. Worldwide distribution of subaquatic gas hydrates. Geo Mar Lett 1993;13(1):32e40. [2] Boswell R & Collett TS. Current perspectives on gas hydrate resources. Energy Environ Sci 2011;4(4):1206e15. [3] Zhou Shouwei, Chen Wei & Li Qingping. The green solid fluidization development principle of natural gas hydrate stored in shallow layers of deep water. China Offshore Oil Gas 2014;26(5):1e7. [4] Zhou Shouwei, Chen Wei, Li Qingping, Zhou Jianliang & Shi Hesheng. Research on the solid fluidization well testing and production for shallow non-diagenetic natural gas hydrate in deep water area. China Offshore Oil Gas 2017;29(4):1e8. [5] Zhou Shouwei, Zhao Jinzhou, Li Qingping, Chen Wei, Zhou Jianliang, Wei Na, et al. Optimal design of the engineering parameters for the first global trial production of marine natural gas hydrates through solid fluidization. Nat Gas Ind 2017;37(9):1e14. [6] Zhou Shouwei, Li Qingping, Chen Wei, Zhou Jianliang, Huang Xin, Fu Qiang, et al. 201310595204. Green mining system of natural gas hydrate from non-lithified stratums of deep-sea seabed superficial layers: China, vol. X; 2016-3-2 [2018-6-15], http://www.wanfangdata.com.cn/ details/detail.do?_type¼patent&id¼ CN201310595204.X. [7] Zhou Shouwei & Li Qingping. 201310596104. Method for green mining of natural gas hydrate of shallow non-diagenesis stratum of deep sea-bed: China, vol. 9; 2014-3-12 [2018-6-15], http://www.wanfangdata.com.cn/ details/detail.do?_type¼patent&id¼ CN201310596104.9. [8] Ozerov AY. Cluster regime-the new regime of flowing of gaseliquid mixture in vertical columns (based on experimental data). AIP Conf Proc 2010;1207(348):348e54. [9] Lawson JD & Brill JP. A statistical evaluation of methods used to predict pressure losses for multiphase flow in vertical oilwell tubing. J Pet Technol 1974;26(8):903e14. [10] Sadatomi M, Sato Y & Saruwatari S. Two-phase flow in vertical noncircular channels. Int J Multiph Flow 1982;8(6):641e55. [11] Ansari AM. A comprehensive mechanistic model for upward two-phase flow in wellbores. SPE Prod Facil 1994;9(2):143e51. [12] Wang Zhiming, Zhang Quan, Zeng Quanshu & Wei J. A unified model of oil/water two-phase flow in the horizontal wellbore. SPE J 2017;22(1):353e64. [13] Wei Na, Meng Yingfeng, Li Gao, Li Yongjie, Wan Liping, Li Hongtao, et al. Transient flow in continuous gas invasion wellbore under condition of circulation cease in liquid-based whole process underbalance drilling. J China Univ Petrol Ed Nat Sci 2012;36(6):74e8. [14] Wei Na, Meng Yingfeng, Li Gao, Li Yongjie, Xu Chaoyang & Li Hongtao. Transient flow characteristics of gas lift in underbalanced drilling. Acta Pet Sin 2014;35(1):166e71. [15] Michalis VK, Costandy J, Tsimpanogiannis IN, Stubos AK & Economou IG. Prediction of the phase equilibria of methane hydrates using the direct phase coexistence methodology. J Chem Phys 2015;142(4):044501. [16] Clarke MA, Poolladi-Darbish M & Bishnoi PR. A method to predict equilibrium conditions of gas hydrate formation in porous media. Ind Eng Chem Res 1999;38(6):2485e90. [17] Østergaard KK, Anderson R, Llamedo M & Tohidi B. Hydrate phase equilibria in porous media: effect of pore size and salinity. Terra Nova 2002;14(5):307e12.
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[18] Zhang W, Wilder JW & Smith DH. Interpretation of ethane hydrate equilibrium data for porous media involving hydrateeice equilibria. AIChE J 2002;48(10):2324e31. [19] Klauda JB & Sandler SI. Predictions of gas hydrate phase equilibria and amounts in natural sediment porous media. Mar Petrol Geol 2003;20(5):459e70. [20] Kim HC, Bishnoi PR, Heidemann RA & Rizvi S. Kinetics of methane hydrate decomposition. Chem Eng Sci 1987;42(7):1645e53. [21] Kamath VA, Holder GD & Angert PF. Three phase interfacial heat transfer during the dissociation of propane hydrates. Chem Eng Sci 1984;10(39):1435e42. [22] Clarke M & Bishnoi PR. Determination of the intrinsic rate of ethane gas hydrate decomposition. Chem Eng Sci 2000;55(21):4869e83. [23] Goel N, Wiggins M & Shah S. Analytical modeling of gas recovery from in situ hydrates dissociation. J Pet Sci Eng 2001;29(2):115e27. [24] Wei Na, Sun Wantong, Meng Yingfeng, Zhou Shouwei, Gao Li, Guo Ping, et al. Sensitivity analysis of multiphase flow in annulus during drilling of Marine natural gas hydrate reservoirs. J Nat Gas Sci Eng 2016;36(A):692e707. [25] Wei Na, Sun Wantong, Meng Yingfeng, Zhou Shouwei, Fu Qiang, Guo Ping, et al. Annular phase behavior analysis during Marine natural gas hydrate reservoir drilling. Acta Pet Sin 2017;38(6):710e20. [26] Sun Wantong, Meng Yingfeng, Wei Na, Li Yongjie, Li Gao & Chen Guangling. Sensitivity of wellbore temperature in offshore drilling. Nat Gas Technol Econ 2016;10(4):36e40. [27] Wei Na, Meng Yingfeng, Gao Li, Guo Ping, Liu Anqi, Tian Xu, et al. Foam drilling in natural gas hydrate. Therm Sci 2015;19(4):1403e5.
[28] Wei Na, Meng Yingfeng, Gao Li, Li Yongiie, Liu Anqi, Long Junxi, et al. Cuttings-carried theories and erosive rule in gas drilling horizontal well. Therm Sci 2014;18(5):1695e8. [29] Wei Na, Meng Yingfeng, Wu Pengcheng, Li Gao, Fang Qiang, Li Pengjie, et al. A mathematical model for gaseliquid transient flow in wellbore during empty well killing in gas drilling. Nat Gas Ind 2017;37(6):64e71. [30] Dzyuba AV & Zektser IS. Variations in submarine groundwater runoff as a possible cause of decomposition of marine methane-hydrates in the Arctic. Water Resour 2013;40(1):74e83. [31] Hamaguchi R, Nishimura Y, Inoue G, Matsukuma Y & Minemoto M. Gas hydrate decomposition rate in flowing water. J Energy Resour Technol 2006;129(2):102e6. [32] Baghel VS, Kumar R & Roy S. Heat transfer calculations for decomposition of structure I methane hydrates by molecular dynamics simulation. J Phys Chem C 2013;117(23):12172e82. [33] Wang Yongzhen. Advanced thermodynamics. Beijing: Tsinghua University Press; 2013. p. 171e3. [34] Zhao Jinzhou, Zhou Shouwei, Zhang Liehui, Wu Kaisong, Guo Ping, Li Qingping, et al. The first global physical simulation experimental systems for the exploitation of marine natural gas hydrates through solid fluidization. Nat Gas Ind 2017;37(9):15e22. [35] Wei Na, Meng Yingfeng, Zhou Shouwei, Guo Ping, Li Qingping, Zhang Mi, et al. 201510659180. Experimental simulation device for solid-state fluidized exploiting of ocean natural gas hydrate: China, vol. 9; 2017-3-29 [2018-6-15], http://www.wanfangdata.com.cn/details/ detail.do?_type¼patent&id¼ CN201510659180.9.
ScienceDirect Natural Gas Industry B 6 (2019) 282e292 www.elsevier.com/locate/ngib
Research Article
Non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation of marine gas hydrate reservoirs*,** Wei Na a,*, Zhao Jinzhou a, Sun Wantong a, Zhou Shouwei a, Zhang Liehui a, Li Qingping b, Fu Qiang a,b, Lu¨ Xin b & Zheng Lijun b a
State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan, 610500, China b CNOOC Research Institute Co., Ltd., Beijing, 100027, China Received 15 July 2018; accepted 25 October 2018 Available online 30 May 2019
Abstract In the core process of fractured marine gas hydrate (hereinafter referred to as hydrate) particles being transported up to the surface platform by airtight pipeline in the solid fluidization exploitation of marine gas hydrate reservoirs, influenced by the rising temperature and the dropping pressure, the solid hydrates will decompose and produce a large amount of gas at a certain critical point, causing the liquidesolid two-phase flow in the wellbore to change into complicated gaseliquidesolid multiphase non-equilibrium flow, which further aggravate well control, solid phase transportation and other safety risks. In view of this, the dynamic hydrate decomposition law in the above process was studied in this paper by establishing multiphase wellbore flow mathematical models of wellbore temperature and pressure field, hydrate phase equilibrium, hydrate dynamic decomposition in multiphase riser pipe flow, wellbore multiphase flow coupled hydrate dynamic decomposition, and a numerical calculation method was proposed and verified. The following results were obtained. First, by numerical model analysis, the effects of liquid phase displacement, solid throughput (daily gas production rate) and wellhead back pressure under different construction parameters on multiphase non-equilibrium pipe flow were obtained. In addition, the field construction guidance measures were put forward based on multiphase nonequilibrium pipe flow characteristics as follows: to properly increase the solid throughput so as to increase the natural gas production, to appropriately increase the liquid-phase displacement and the wellhead back pressure so as to ensure well control safety. This study provides not only a theoretical basis for the prediction of multiphase non-equilibrium pipe flow in the solid fluidization exploitation, but a technical support for the field construction parameter optimization and well control safety. © 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Natural gas hydrate; Solid fluidization exploitation; Non-equilibrium multiphase wellbore flow; Decomposition; Well control risks; Construction parameter; Prediction methods
* Project supported by the National Key R&D Program “New Technology for Marine Hydrate Solid Fluidization Testing” (No.: 2016YFC0304008), Strategic Research Project for Medium- and Long-Term Development Strategy Research in China's Engineering Science and Technology “Research on Deep Sea Gas Hydrate Development Strategy for 2035” (No.: 2017- ZCQ-5), Key Project of National Natural Science Foundation of China, and “Measurement and Control Theory and Key Issues of Managed Pressure Drilling” (No.: 51334003). ** This is the English version of the originally published article in Natural Gas Industry (in Chinese), which can be found at https://doi.org/10.3787/j.issn. 1000-0976.2018.10.013. * Corresponding author. E-mail address: [email protected] (Wei N.). Peer review under responsibility of Sichuan Petroleum Administration.
0. Introduction For safe and efficient development of natural gas hydrate (hereinafter referred to as hydrate) reservoirs, the authors proposed an innovative technical idea: solid fluidization exploitation of marine gas hydrate reservoirs [1e7]. However, the research on solid fluidization exploitation of marine gas hydrate reservoirs is still in its early stage and some theoretical issues need to be further studied. Particularly, in the process of transporting hydrate solid particles up to the surface platform in airtight pipeline, influenced by the rising
https://doi.org/10.1016/j.ngib.2018.10.008 2352-8540/© 2019 Sichuan Petroleum Administration. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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temperature and the dropping pressure in the pipeline (wellbore), the hydrates will decompose and produce a large amount of gas, causing the liquidesolid two-phase flow in the wellbore to change into complicated gaseliquidesolid nonequilibrium multiphase flow. The complicated multiphase flow will further affect the dynamic decomposition of hydrate particles. In this process, the wellbore flow is a multi-phase non-equilibrium wellbore flow with complicated characteristic parameters, which further aggravates well control, solidphase particle transportation and other safety risks. Many scholars have worked a lot on the characteristics of multiphase wellbore flow, mainly focusing on the flow pattern division and prediction [8e11] and wellbore pressure calculation and measurement [12e14]. There are no studies about the wellbore multiphase flow characteristics of coupling hydrate decomposition. Moreover, the research on hydrate decomposition mainly focuses on the decomposition temperature and pressure conditions [15e19] and the decomposition rate model and prediction [20e23]. The dynamic decomposition law of hydrate particles in the process of temperature increasing and pressure decreasing under the condition of multiphase wellbore flow rising has not been reported. In this paper, the law of multiphase non-equilibrium wellbore flow in the solid fluidization exploitation of marine gas hydrate reservoirs was studied using the mathematical models of wellbore temperature and pressure field, mathematical model of hydrate dynamic decomposition in multiphase riser pipe flow and mathematical model of wellbore multiphase flow in coupled hydrate dynamic decomposition, and thus a numerical calculation method was proposed. 1. Mathematical model of non-equilibrium multiphase wellbore flow 1.1. Wellbore temperature model Based on the law of energy conservation and the basic equation of heat conduction, considering the process of solid fluidization exploitation of marine gas hydrate reservoirs, a temperature distribution model of mixed fluid in wellbore is established: rm vm cm
pD2pi dTm ¼ qw þ qf þ qh 4 dz
ð1Þ
where, rm is the density of mixed fluid in the wellbore, kg/m3; similarly, vm: the velocity of mixed fluid in the wellbore, m/s; cm: the specific heat capacity of mixed fluid in the wellbore, J/ (kg$K); Dpi: the inner diameter of the wellbore, m; Tm: the temperature of mixed fluid in the wellbore, K; z: the well depth, m; qw: the heat exchange between seawater and wellbore, W/m; qf: the heat generated by the frictional flow of mixed fluid in the wellbore, W/m; qh: the phase change heat during the decomposition of hydrate particles in the rising process, W/m. For the solution of qw, qf and qh, refer to Refs. [24e26].
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1.2. Wellbore pressure model Based on the process of solid fluidization exploitation of marine gas hydrate reservoirs, a wellbore pressure model in the process of mixed fluid flow is established: dpm ¼ pG þ pF þ pA ð2Þ dz where, pm is wellbore pressure, MPa; pG, pF and pA are respectively the pressure drop due to gravity, friction and fluid velocity change, MPa/m. For the solution of pG, pF and pA, refer to Refs. [27e29]. 1.3. Hydrate phase equilibrium model In order to judge whether the hydrate solid phase particles decompose under a certain temperature and pressure during the rising process, it is necessary to establish a hydrate phase equilibrium model. For purpose of simplified calculation, the hydrate phase equilibrium model established by Dzyuba and Zektser [30] after experiment is used: Tm ¼ 9:6339 ln peq þ 264:9661
ð3Þ
where, peq represents the equilibrium pressure of the hydrate phase at a certain temperature, MPa. 1.4. Hydrate dynamic decomposition model in multiphase riser pipe flow In the riser pipe flow, according to the hydrate phase equilibrium model, before the hydrate solid phase particles rise to a critical position of decomposition, they do not decompose and the decomposition rate is zero; after the hydrate solid phase particles rise to a critical position of decomposition, they decompose. In order to calculate the hydrate decomposition, the gas hydrate was assumed to be a methane hydrate. Based on the Kim model [20], a hydrate dynamic decomposition model in multiphase riser pipe flow is established: dnhyd ¼ khyd Shyd feq jðTm ;peq Þ fm jðTm ;pm Þ ð4Þ dthyd where, nhyd is the amount of hydrated matter in the hydrate solid phase particles, mol; similarly, thyd: the hydrate decomposition time, s; khyd: the hydrate decomposition rate constant, mol/(s$m2$MPa); Shyd: the surface area of hydrate solid phase particle decomposition, m2; feq and fm: respectively the fugacity of methane gas at Tm and peq, pm. The solution of each parameter is as follows: 1.4.1. Hydrate decomposition rate constant The hydrate decomposition rate constant is expressed as follows: 1 khyd
¼
1 khydc
þ
1 khydf
ð5Þ
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where, khydc represents the decomposition rate of hydrate itself, mol/(s$m2$MPa); khydf represents the mass transfer rate of methane gas at Tm and pm, mol/(s$m2$MPa). According to the Arrhenius equation, the decomposition rate of hydrate itself is calculated as follows: khydc ¼ k0hydc e½Eact =ðRTm Þ
ð6Þ
where, k0hydc represents the intrinsic decomposition rate constant of hydrate, mol/(s$m2$MPa); Eact represents the activation energy of hydrate decomposition reaction, J/mol; R represents the general gas constant, 8.314 J/(mol$K). Assuming that the hydrate solid particles are homogeneous spheres during the decomposition process, according to the empirical formula [31], the mass transfer of the particle spheres to the fluid is expressed as follows: nsh ¼ 0:347Re
0:62
nsc
1 3
ð7Þ
According to the theory of mass transfer, the following equation can be obtained: 8 > d k0 > > nsh ¼ s hydf > > > DAB > > < ds v m rm ð8Þ Re ¼ > mm > > > > > mm > > : nsc ¼ rm DAB Then the mass transfer rate of methane gas at Tm and pm is obtained as follows: khydf ¼
k0hydf
0:62 0:67 6 106 pm 0:347r0:29 m vm DAB 10 pm ¼ 0:38 Zg RTm Zg RTm m0:29 m ds
ð9Þ
where, nsh represents the Sherwood number; similarly, Re: the Reynolds number; nsc: the Schmidt number; ds: the hydrate solid phase particle diameter, m; k0hydf: the mass transfer coefficient, m/s; vm: the velocity of mixed fluid in the wellbore, m/s; rm: the density of mixed fluid in the wellbore, kg/m3; pm: the wellbore pressure, MPa; Tm: the temperature of mixed fluid in the wellbore, K; DAB: the diffusion coefficient of methane gas in the wellbore flow, m2/s; mm: the viscosity of mixed fluid in the wellbore, Pa$s; Zg: the natural gas compression factor, dimensionless. 1.4.2. Surface area of hydrate solid phase particle decomposition It is assumed that hydrate solid phase particle decomposition occurs at the interface [32], which is assumed to be a homogeneous sphere according to the foregoing. Therefore, the decomposition surface area is as follows: 2 2 p 6Vhyd 3 1 1 6nhyd Mhyd 3 3 Shyd ¼ ¼ p 4 4 p rhyd
ð10Þ
pd3
here, Vhyd ¼ Ehyd Vs ¼ Ehyd 6 s .where, 4 represents sphericity, dimensionless; similarly, Vhyd: the volume of hydrate in solid phase particles, m3; Mhyd: the molar mass of hydrate, kg/mol; rhyd: hydrate density, kg/m3; Ehyd: the abundance of hydrate in solid phase particles; Vs: the volume of solid phase particles, m3. 1.4.3. Fugacity of methane gas According to the definition of gas fugacity, the following equation can be obtained [33]: 0 1 Zpx B C ð11Þ Ratm Tx ln fx jðTx ;px Þ ¼ lim @ Vx dpx þ Ratm Tx lnp* A p*/0
p*
where, Ratm represents the general gas constant expressed in standard atmospheric pressure, which is 0.082 06 atm$L/ (mol$K) (1 atm ¼ 101.325 kPa); similarly, Tx: the ambient temperature, K; px: the ambient pressure, atm; p*: the reference state pressure, atm; fx: the fugacity of methane gas at standard atmospheric pressure at Tx and px, atm; Vx: the molar volume of methane gas at Tx and px, L/mol. Since the ReK equation of state is simple to calculate and generally has a high accuracy, it is assumed that the methane gas state obeys the ReK equation of state and then the following equation can be obtained: px ¼
Ratm Tx a 0:5 Vx b Tx Vx ðVx þ bÞ
ð12Þ
where, a and b represent the ReK constant, a provides a measure of the attraction between molecules, and b provides a measure of the size of the molecule. Therefore, the formula for calculating the fugacity of methane gas is derived as follows: ! a ln VxVþb þ Vxaþb Ratm Tx b b x fx jðTx ;px Þ ¼ exp ln þ ð13Þ Vx b Vx b Ratm T 1:5 x
1.5. Wellbore multiphase flow model of coupled hydrate dynamic decomposition The gas and liquid phase mass conservation equations are expressed as follows: ! ! 8 2 2 > v pDpi v pDpi > > r Eg þ r Eg vg ¼ mhydg > > vz 4 g 4 g < vt ð14Þ ! ! 2 2 > > pD pD v v > pi pi > > r El þ r El vl ¼ mhydl : vt vz 4 l 4 l The gaseliquidesolid phase mixed momentum equation in the wellbore is expressed as follows:
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v 6 v rl El v l þ r g Eg v g þ r s Es v s þ 10 pm þ rl El v2l þ rg Eg v2g vt vz 2f rm v2m þ rs Es v2s þ rm g sin q þ Dpi ¼0
285
as an example (Fig. 1). In Fig. 1, a, b and g are the calculation error precision. 2.3. Numerical calculation verification
The mixing temperature in the wellbore of the horizontal subsea section is equal to the external seabed temperature, which is expressed as follows:
In order to verify the accuracy of numerical calculation of non-equilibrium multiphase wellbore flow in solid fluidization exploitation of marine gas hydrate reservoirs, we used the established numerical calculation method for non-equilibrium multiphase wellbore flow to obtain the wellbore temperature, pressure, gas holdup, solid phase content, and gaseliquidesolid phase velocity curve, as shown in Fig. 2. The numerical calculation results are compared with the data from the scale physical simulation experiment of solid fluidization exploitation of marine gas hydrate made by Zhou Shouwei et al. [5,34,35]. According to the experimental basic data in the literature, the seawater depth is 1315 m, the well depth is 1500 m, the wellbore diameter of the experimental pipe section is 0.076 m, the simulated sea surface temperature is 308 K, the abundance of hydrate in the solid phase particles is 70%, the simulated construction displacement is 0.008 m3/s, the liquid phase density is 1030 kg/m3, and the solid phase throughput is 0.54 m3/h. It can be seen from Fig. 2 that the obtained numerical calculation value has little error compared with the experimental value in the literature, and the change trend is consistent. In order to further quantitatively analyze the error between the numerical calculation value and the experimental value in the literature, the following error definition equation is used:
Tm ðzH ; tÞ ¼ Tw ðzH Þ
s ¼ xs xr
ð15Þ where, Dpi represents the inner diameter of the wellbore, m; similarly, rg, rl and rs: respectively the gas, liquid and solid phase density in the wellbore, kg/m3; vg, vl and vs: respectively the gas, liquid and solid phase velocities in the wellbore, m/s; Eg, El and Es: respectively the gas holdup, liquid holdup and solid phase content, dimensionless; mhydg and mhydl: respectively the mass change rate of gas and liquid phase per unit length, kg/(s$m). 2. Numerical calculation method 2.1. Boundary and initial conditions In order to simplify the model, it is assumed that the solid phase particles of hydrate can be safely migrated in the horizontal section, and the migration velocity is equal to the liquid phase velocity, which is expressed as follows: vs ðzHo ; tÞ ¼ vl ðzHo ; tÞ
ð16Þ
ð17Þ
The wellhead pressure is equal to the wellhead back pressure, which is expressed as follows: pm ð0; tÞ ¼ pb
ð18Þ
where, zHo represents the well depth of the horizontal subsea section, m; similarly, vs(zHo, t) and vl (zHo, t): respectively the solid and liquid phase velocity in the subsea horizontal wellbore, m/s; zH: the vertical depth of the subsea horizontal section, m; Tm(zH, t) and Tw(zH): respectively the temperature of mixed fluid in the subsea horizontal wellbore and the temperature of outside seawater, K; pm(0,t) and pb: respectively the wellhead pressure and wellhead back pressure, MPa. 2.2. Numerical calculation method In order to study the non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation of marine gas hydrate reservoirs, we used the finite difference numerical calculation method. The space domain is the wellbore, and the time domain is the hydrate solid phase particles being transported from the bottom of the well to the wellhead. Assuming that at time n, the parameters of any two nodes i and i þ 1 in the wellbore are known, the numerical calculation process is illustrated by taking node i and i þ 1 from the time n to n þ 1
ð19Þ
where, s represents the error, dimensionless; similarly, xs: the numerical calculation value; xr: the experimental value in the literature. The average wellbore temperature error is calculated to be 0.022 C, the average wellbore pressure error is 0.023 MPa, the average gas holdup error is 0.010%, the average solid phase content error is 0.004%, and the average gas phase velocity error is 0.005 m/s, the average liquid phase velocity error is 0.003 m/s and the average solid phase velocity error is 0.004 m/s. It can be seen that the numerical model and calculation method proposed in this study have a high accuracy, which lays a foundation for the analysis of nonequilibrium multiphase wellbore flow characteristics. 3. Non-equilibrium multiphase wellbore flow characteristics in solid fluidization exploitation The solid fluidization exploitation of marine gas hydrate reservoir is shown in Fig. 3. The well depth is 1400 m, the vertical depth is 1000 m, the vertical well depth is 0e830 m, the depth of deviated section is 830e1100 m and the horizontal well depth is 1100e1400 m; the outer diameter of the wellbore is 0.508 m, the inner diameter of the wellbore is 0.476 m and the density of the liquid phase of the pipe is
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Fig. 1. Flow chart of numerical calculation of non-equilibrium multiphase wellbore flow in solid fluidization exploitation.
1030 kg/m3. Gas hydrate reservoir characteristics in the South China Sea: the depth of seawater is 1000 m; the sea surface temperature is 293 K; the abundance of hydrate in solid phase particles is 70%. In order to obtain the non-equilibrium multiphase wellbore flow characteristics in the process of gas hydrate solid phase
particles being transported up to the surface platform in airtight pipeline, the established mathematical model and numerical calculation method are used to analyze the non-equilibrium multiphase wellbore flow characteristics of solid fluidization exploitation under different liquid phase displacement, solid throughput and wellhead back pressure conditions.
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Fig. 2. Comparison of numerical calculation values (xs) with experimental values in the literatures (xr).
3.1. Wellbore flow characteristics under different liquid phase displacements As to the numerical calculation parameters, the liquid phase displacement is 0.03 m3/s, 0.05 m3/s and 0.07 m3/s, respectively, the solid throughput is 1.5 m3/h (corresponding to the daily gas production of about 4133 m3), and the wellhead back pressure is 0.1 MPa. Through numerical calculation, the
Fig. 3. Schematic diagram of non-equilibrium multiphase wellbore flow in solid fluidization exploitation of marine gas hydrate reservoirs.
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wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different liquid phase displacements in the solid fluidization exploitation of marine gas hydrate reservoirs were obtained, as shown in Fig. 4. It can be seen from Fig. 4a and b that, when the hydrate solid phase particles are transported upwards to the sea surface platform, the wellbore temperature is equal to the external seawater temperature in the horizontal subsea section from 1400 to 1100 m. In the deviated section and the vertical section of 1100 to 0 m, the wellbore temperature rises with the increase of external seawater temperature. With the increase of liquid phase displacement, the heat exchange time between the mixed fluid in the wellbore and the seawater is shortened and the heat transfer amount of seawater to the wellbore decreases, so the wellbore temperature drops and then the phase equilibrium pressure calculated by the hydrate phase equilibrium model decreases (Fig. 4b). With the increase of liquid phase displacement, the solid phase content (Es) in the wellbore decreases under the same solid throughput (Fig. 4i), resulting in a decrease in the density of mixed fluid in the wellbore, which in turn reduces the wellbore pressure. However, the increase of the velocity of each phase in the wellbore (Fig. 4def) will increase the frictional pressure drop and increase the wellbore pressure. Therefore, the wellbore pressure does not change significantly (Fig. 4b). In Fig. 4b, the intersection of the wellbore pressure curve and the phase equilibrium pressure curve under any determined liquid phase displacement condition is the critical position at which the hydrate solid phase particles decompose when they are transported upward with seawater. Later, as the hydrate solid particles rise in the wellbore, the amount of substance continues to decrease (Fig. 4c) and the hydrate is completely decomposed at the position where the amount of substance is 0. From the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the critical position of hydrate decomposition moves upward and the complete decomposition position moves up. It can be seen from Fig. 4def that in the horizontal subsea section from 1400 to 1100 m, according to the previous assumption, the hydrate solid phase particle velocity of the horizontal section is equal to the liquid phase velocity; the gas phase is not contained in the wellbore, and the gas phase velocity is 0. In the deviated section of 1100 to 830 m, since the cross-sectional area of the flow passage in the wellbore is constant (the inner diameter of the wellbore is constant), the liquid phase velocity is constant and the solid phase velocity gradually decreases. In the vertical section of 830 to 0 m, based on the critical position of hydrate decomposition in Fig. 4b and c, when the hydrate does not decompose, the gas phase velocity is still 0, and the liquid phase velocity and solid phase velocity remain stable. When the hydrate solid phase particles are transported upward to the decomposition critical position, the hydrate in the solid phase particles is decomposed into gas and water. Therefore, the liquidesolid two-phase flow
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Fig. 4. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different liquid phase displacements (0.03, 0.05 and 0.07 m3/s).
in the wellbore changes into the complex gaseliquidesolid multiphase flow. As the multi-phase flow continues to rise, the well depth decreases, the gas expands and the volume becomes larger, the gas phase velocity increases, and the carrier action causes the liquid phase velocity to increase. However, due to the decrease in the density of the mixed fluid in the wellbore, the carrying capacity is decreased. Therefore, the solid phase velocity decreases as the well depth decreases. At the same time, from the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the gas, liquid and solid phase velocities in the wellbore increase. In Fig. 4gei, combined with Fig. 4def, it can be seen that in the horizontal subsea section from 1400 to 1100 m, the gas holdup is 0 and the liquid holdup and solid phase content remain stable. In the deviated section of 1100 to 830 m, the solid phase velocity gradually decreases, causing the solid phase content to gradually increase, and the liquid holdup in the corresponding wellbore decreases. In the vertical section of 830 to 0 m, according to Fig. 4c, when the hydrate does not decompose, the gas holdup is 0 and the liquid holdup and solid phase content remain stable. When the hydrate solid phase particles are transported upward to
the decomposition critical position with seawater, the hydrate in the solid phase particles is decomposed into gas and water. Therefore, during the decomposition of hydrate, the gas holdup increases, the liquid holdup increases and the solid phase content decreases. When the hydrate solid phase particles are transported up to the position of complete decomposition with seawater, the liquid holdup no longer increases and the solid phase content no longer decreases. Meanwhile, as the well depth decreases, the gas expansion volume becomes larger and the gas holdup increases, resulting in a decrease in the density of mixed fluid in the wellbore, which in turn causes a decrease in the carrying capacity. Therefore, the solid phase content increases and the corresponding liquid holdup decreases. At the same time, from the comparison of the effects of different liquid phase displacement, it can be seen that as the liquid phase displacement increases, the gas holdup in the wellbore decreases, the liquid holdup increases and the solid phase content decreases. When the liquid phase displacement is at least 0.03 m3/s, the solid phase velocity rises abruptly (Fig. 4f) and the solid phase content suddenly decreases (Fig. 4i) near the wellhead (well depth is close to 0). It shows if other conditions are certain and the displacement is
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Fig. 5. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different solid throughputs (1.5, 3.0, and 4.5 m3/h).
small, the multi-phase flow pattern changes due to the high gas holdup at the wellhead, which leads to the transformation of the mixed fluid carrying capacity. At the same time, the flow pattern change poses a high challenge to well control safety. As can be seen from Fig. 4, in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, in order to prevent well control safety problems and improve the hydrate solid-phase particle transport capacity, it is necessary to appropriately increase the liquid phase displacement. 3.2. Characteristics of pipe flow under different solid throughputs As to the numerical calculation parameters, the solid throughput is 1.5 m3/h, 3.0 m3/h and 4.5 m3/h (corresponding to gas production of approximately 4133 m3/d, 8266 m3/d and 12399 m3/d), respectively, the liquid phase displacement is 0.03 m3/s and the wellhead back pressure is 0.1 MPa. Through numerical calculation, the wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different solid throughputs were obtained, as shown in Fig. 5.
In Fig. 5a and b, as the solid throughput increases, the amount of heat transfer from the seawater to the wellbore does not change much. Therefore, the wellbore temperature and the calculated phase equilibrium pressure do not change much. In Fig. 5b, a higher solid throughput will result in more solid phase entering the wellbore per unit time, which will increase the density of mixed fluid in the wellbore. In the well section where the hydrate does not decompose (the lower part of the wellbore), the flow in the wellbore is a liquidesolid two-phase flow, so the density of the mixed fluid in the wellbore increases, the gravity pressure drop increases and the wellbore pressure rises in the lower well section; In the well section after the decomposition of hydrate (the upper part of the wellbore), the gas is decomposed from the hydrate and the flow in the wellbore becomes a gaseliquidesolid multiphase flow. The gas phase has a tendency to reduce the density of mixed fluid in the wellbore, and the influence of the solid phase content is also considered. Therefore, the wellbore pressure does not change significantly with the increase of the solid throughput in the upper well section. At the same time, the critical position for the decomposition of hydrate solid phase particles rising upward with seawater does not change significantly with the increase of solid throughput and the
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Fig. 6. Wellbore temperature and pressure, hydrate dynamic decomposition and multiphase flow characteristics under different wellhead back pressures (0.1, 1.0, 2.0 MPa).
complete decomposition position also does not change significantly (Fig. 5c). In Fig. 5dei, the higher the solid throughput, the higher the solid phase content (Fig. 5i). When the hydrate solid phase particles are transported upward to the decomposition critical position with seawater, the more gas generated by the decomposition of the hydrate, the higher the gas holdup (Fig. 5g), the lower the corresponding liquid holdup (Fig. 5h). As the well depth decreases, the larger the solid throughput, the larger the gas volume after expansion, the higher the gas phase velocity (Fig. 5d), and the higher the liquid phase velocity due to its carrying capacity (Fig. 5e). At the same time, under the condition of high solid throughput, the gas holdup at the wellhead is higher, resulting in more intense multi-phase flow pattern transformation, which leads to greater transformation of the carrying capacity. Therefore, the more the solid phase velocity at the wellhead rises (Fig. 5f), the more the solid phase content decreases (Fig. 5i). At the same time, it poses a greater challenge to well control safety. As can be seen from Fig. 5, in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, the increase of solid throughput can result in the increase of the amount of hydrate delivered to the surface platform per unit time, thereby increasing gas production. However, the well
control safety problems will be more serious. Therefore, solid throughput should be increased on the premise of well control safety. 3.3. Wellbore flow characteristics under different wellhead back pressures As to the numerical calculation parameters, the wellhead back pressure is 0.1 MPa, 1.0 MPa and 2.0 MPa, respectively; the liquid phase displacement is 0.03 m3/s and the solid phase transport is 1.5 m3/h (corresponding gas production is about 4133 m3/d). Through numerical calculation, the wellbore temperature, wellbore pressure, hydrate dynamic decomposition law in multiphase riser pipe flow and the wellbore multiphase flow characteristics of the coupled hydrate dynamic decomposition under different liquid phase displacements were obtained, as shown in Fig. 6. In Fig. 6aec, as the wellhead back pressure increases, the amount of heat transfer from the seawater to the wellbore does not change much. Therefore, the wellbore temperature and the phase equilibrium pressure do not change much. The pressure in the wellbore obviously increases. The critical position of decomposition and the complete decomposition position of hydrate both move up.
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In Fig. 6dei, before hydrate solid phase particles are transported upwards to the critical position of decomposition, the flow in the wellbore is liquidesolid two-phase flow. As the back pressure of the wellhead increases, the velocity of each phase and the content of each phase remain unchanged. After the hydrate solid phase particles are transported upwards to the critical position of decomposition, the hydrate decomposes to generate gas. The higher the wellhead back pressure, the smaller the gas expansion, the lower the gas phase velocity and gas holdup (Fig. 6d and g), the lower the liquid phase velocity (Fig. 6e), and the higher the liquid holdup (Fig. 6h). Moreover, the higher the density of mixed fluid in the wellbore, the higher the carrying capacity, the higher the solid phase velocity (Fig. 6f), and the lower the solid phase content (Fig. 6i). At the same time, under a high wellhead back pressure, the smaller the change of solid phase velocity and solid phase content (Fig. 6f and i) at the wellhead, the more helpful it is to ensure well control safety. It can be seen from Fig. 6 that increasing wellhead back pressure can significantly increase wellbore pressure and reduce well control safety risks caused by gas expansion at the wellhead. Therefore, the wellhead back pressure should be properly applied in the field construction of solid fluidization exploitation of marine gas hydrate reservoirs. 4. Conclusions 1) Increase of liquid phase displacement can result in a significant reduction of wellbore temperature and hydrate phase equilibrium pressure to shift up the critical position of hydrate decomposition; and can result in a significant increase of gas, liquid and solid phase velocities, thus decreasing gas holdup and solid phase content. 2) With the increase of solid throughput, the wellbore temperature and hydrate phase equilibrium pressure do not change, the wellbore pressure rises in the lower well section and does not change significantly in the upper well section, the critical position of hydrate decomposition does not change, the solid phase content increases significantly, the gas holdup at the wellhead increases significantly, the liquid holdup decreases significantly, and the gaseliquidesolid phase velocity increases. 3) Increase of the wellhead back pressure can result in a significant increase of the wellbore pressure and the critical position of hydrate decomposition moving up; it can also result in a significant reduction of the gas holdup after hydrate decomposition, the decrease of gas and liquid phase velocity, the increase of the solid phase velocity, the decrease of the solid phase content and the increase of the liquid holding rate. 4) In the field construction of solid fluidization exploitation of marine gas hydrate reservoirs, proper increase of solid throughput can increase gas production, but problems such as well control risks will be intensified. In order to prevent the wellbore flow safety
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problems such as well control risks and improve the hydrate solid phase particle transport capacity, it is necessary to appropriately increase the liquid phase displacement and the wellhead back pressure.
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