CFD validation of scaling rules for reduced-scale field releases of carbon dioxide

Applied Energy 115 (2014) 525–530

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

CFD validation of scaling rules for reduced-scale field releases of carbon dioxide Ji Xing a, Zhenyi Liu a,⇑, Ping Huang a, Changgen Feng a, Yi Zhou a, Ruiyan Sun b, Shigang Wang b a b

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China Oil Field Reconnaissance Designing Institute of Jilin, PetroChina Jilin Oilfield Company, Songyuan, China

h i g h l i g h t s  A series of scaling rules was introduced to scale a CO2 release field experiment.  The simulation based on the k–e model was used to evaluate the scaled results.  The scaled results showed acceptable agreement with the simulated values.  The statistical performance indicators were introduced to verify the consistency.  The scaling rules were applicable for field experiment of accidental releases.

a r t i c l e

i n f o

Article history: Received 11 June 2013 Received in revised form 17 October 2013 Accepted 29 October 2013 Available online 23 November 2013 Keywords: Heavy gas dispersion CFD simulation k–e Model Carbon dioxide Experiment

a b s t r a c t Carbon Dioxide-Enhanced Oil Recovery (CO2-EOR) has the potential for well blowouts that could cause casualties and environmental damage. To assess the consequence of such accidents, a reduced-scale field experiment of CO2 release was performed based on scaling rules instead of a full-size field test that was economically infeasible. A series of scaling rules was introduced to upscale the reduced-scale field experiment to full-size. To validate the scaling rules, numerical simulation was carried out based on the k–e turbulence model which proved to be an effective way to predict the concentration field for heavy gas dispersion. For concentration variation, the general tendencies of the simulation and experimental observations remained identical except nearby the jet nozzle where the measured CO2 concentration from the experiment was obviously higher than that in the simulation. Statistical performance indicators were introduced to verify the consistency between the scaled results and the simulated ones, and the results showed that using the scaling rules to scale the field experiment exhibited acceptable accuracy at small flow rates and these scaling rules appear applicable for field experiments of accidental releases. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Carbon capture and storage (CCS) technology is seen as one of the most promising solutions to the increasingly serious problem of global warming. Carbon Dioxide-Enhanced Oil Recovery (CO2EOR) technology, not directly targeting CO2 sequestration, can help improve oil recovery and provide a utilization option for CO2, and it has been widely used in recent years [1–3]. CO2 produces physiological effects to humans and also act as an asphyxiant by displacing atmospheric air, so physiological effects and suffocation may occur during drilling and production if accidental releases happen [4,5]. A concentration of CO2 over 7% by volume will cause death in a short time, while CO2 over 3% by volume will be danger-

⇑ Corresponding author. Address: 5 South Zhongguancun Street, Beijing 100081, China. Tel.: +86 1068918687. E-mail address: [email protected] (Z. Liu). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.10.049

ous to humans. Accidents involving well blowouts and large-scale leakage during CO2-EOR processes may cause great danger to the surrounding staff [6]. According to China’s national standards GBZ 2.1-2007 ‘‘Occupational Exposure Limits for Industrial Workplace’’, the acceptable upper limit of CO2 concentration for a short period of time (15 min) exposure is 18,000 mg/m3, equivalent to 1% by volume. CO2 has a greater density than air and its dispersion in the atmosphere follows the heavy gas dispersion law [7]. The main experimental methods of studying heavy gas dispersion include natural analogues, full-size field experiments, reduced-scale field experiments, wind tunnel experiments and brine experiments [8–12]. Natural analogues need specific scenarios such as natural CO2 emissions from cold springs, volcanic areas, etc. But these specific conditions are not easy to encounter. Although full-size field experiments can reproduce the conditions of accidents, such as weather conditions, the topography and the characteristics of the

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leaking source, they are generally too costly in labor and time. Furthermore, the requirements of environmental conditions, especially for some specific weather conditions and terrain conditions, are difficult to meet for test repeatability. Wind tunnel experiments demand close agreement in dimensionless parameters between the model and the prototype to simulate the flow of the atmospheric boundary layer, such as Reynolds number (Re), Bulk Richardson number (Ri), Rossby number (Ro), Prandtl number (Pr) and Eckert number (Ec) [13–17]. However, it is unrealistic to keep all the dimensionless parameters identical. Moreover, the scale of wind tunnel experiments is usually too small, between 1/100 and 1/1000 the physical system of interest. In such a small scaling, it is difficult to reproduce a real environment with a humid atmosphere [18–20]. The brine experiment approach can use liquid to simulate gas diffusion for visual effect, but it does not produce the quantitative results for gas concentration. Reducedscale field experiments are conducted in real terrain and weather conditions, but the parameters for the terrain and the weather conditions are scaled based on similarity criteria. It is absolutely necessary that the geometry, mechanics and kinematics for the characteristics of the source are scaled correctly according to similarity criteria. Consequently, the concentration information for the real scenario can be deduced based on the measured values of concentration at the reduced-scale site. In contrast with the full-size field test, the reduced-scale field experiment can greatly reduce the amount of hazardous materials to save cost, and decrease the potential risk from abundant hazardous materials. Compared with the wind tunnel experiment, reduced-scale field experiments are close to the realistic atmospheric environment at 1/10 to 1/100 the site. Many gas dispersion models exist like the Gaussian model, the BM model, the Sutton model and the three-dimensional (3D) CFD model, etc. [21–24]. The 3D CFD model has the ability to accurately simulate the flow field based on rigorous flow equation calculation. The Lawrence Livermore National Laboratory (LLNL) in the 1980s developed the FEM3 model based on the finite element method and single-equation k theory turbulence model and simulated the series of instantaneous release tests of Thorney Island with it, with results in good agreement. Now the model has been developed as the two-equation k–e model FEM3C model. Sklavaounos used the software CFX 5.6 to simulate the flow of the heavy gas over obstacles with the k–e and the SST equations, and found the simulated results in good agreement with the experimental data [25]. Hanna and his group used the data from Kit Fox, MUST, Prairie Grass, and EMU test to validate the FLACS CFD model based on the k–e turbulence equations [26,27]. Hence, the k–e turbulence equations have been shown reliable for calculating heavy gas dispersion [28]. In this paper, we apply similarity theory and describe scaling rules for reduced-scale field releases of carbon dioxide, and introduce reduced-scale field experiments to simulate CO2 blowouts, which were conducted by the Beijing Institute of Technology [29]. On the basis of the scaling rule, the reduced-scale field experiment was enlarged back to the full-size scenario. The CO2 concentration field in the full-size was simulated by the k–e model to verify the scaling rules that were used to scale the real CO2 releases.

2.1. Length scales The characteristic length (l, L) is described on the base of the volume of gas discharging into the ambient atmosphere, as

l ¼ v 1=3

ð1Þ

in the reduced-scale model and

L ¼ V 1=3

ð2Þ

in the full-size scale. Defining Sc as the reduced-scale/full-size length scaling factor, the same gas released into the atmosphere both in the model and in the full scale is

v V

¼

 3 m l ¼ ¼ S3c M L

ð3Þ

It is apparent that the amount of released gas required is decreased in the reduced-scale model. For instance, if Sc = 0.1, it means that the releases of 10 kilograms materials in the reduced-scale model are equivalent to the releases of 10 tonnes materials in the full-size system. 2.2. Velocity scales As to the gas dispersion, both the density ratio,

qg ; qa

ð4Þ

and the Froude number, FC, where

FC ¼

U2 ; gL

ð5Þ

are supposed to be kept identical in the reduced-scale model and the full-size scale considering the similarity theory. There is another scaling parameter in the dispersion modeling defined as the Richardson number, Ri, where

Ri ¼ g

qg  qa L qa U 2

ð6Þ

According to the similarity theory, the Richardson number should also remain identical in the different scales. However, Ri will automatically be scaled correctly if Eqs. (4) and (5) are identical between the reduced-scale model and the full-size scale. Due to the same material being released in different scales, the velocity of the release should be defined as follows to satisfy Eqs. (4) and (5),

 0:5 uh l ¼ ¼ S0:5 c L UH

ð7Þ

Thus, the inlet velocity and the wind speed are much higher in the full-size system than those in the reduced-scale model. For example, if Sc = 0.1, it means that the velocity at 100 m height in the full-size system is three times more than that at 10 m height in the reduced-scale model. 2.3. Time scales

2. Scaling rules The dimensionless rate The reduced-scale field experiment is a type of field test scaled based on similarity criteria and conducted in the real terrain and in real weather conditions. Below, capital letters are used for parameters in the full size system while all the lowercase letters represent those in the reduced scale.

UT L

ð8Þ

should remain identical in the full-size system and in the reducedscale model, so that

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UT ut ¼ : L l

ð9Þ

Due to

u U

The k–e model is one of the most effective models evaluated from the Reynolds averaged Navier–Stokes (RANS) equations [30]. The k–e model includes two main parameters, and one is k, the turbulent kinetic energy, and the other is e, the turbulence dissipation rate [31]. Launder and Spalding first proposed the classical model in 1972 [32]. Continuity equation:

¼ S0:5 c , it is easy to get the following result.

t U l ¼ ¼ S0:5 c T u L 2.4. Continuous release scales The dimensionless rate

Q

ð10Þ

2

UL

should remain identical in the full-size system and in the reducedscale model, thus

Q UL2

¼

q ul

2

;

 2 q u l ¼ ¼ S2:5 c : Q U L

4. Turbulence modeling

ð11Þ

@q @ þ ðqui Þ ¼ 0 @t @xi

ð13Þ

Momentum equation:

@ @ @p @ ðqui Þ þ ðqui uj Þ ¼  þ @t @xi @xi @xj



l

@ui  qu0i u0j @xj

 ð14Þ

The definitions for k and e are presented as follows.

ð12Þ

For example, if Sc = 0.1, it means that the release rate in the fullsize system should be three hundred times more than that in the reduced-scale model. 3. Description of the CO2 release test The reduced-scale CO2 release field test was performed by Beijing Institute of Technology in Zhangjiakou. An artificial tunnel was built with open ends. A prism of 3 m width and 3 m height and 11 m length was chosen as the experimental volume within one small part of the whole tunnel, as shown in Fig. 1. The bottom was the ground and the other five faces were open. The CO2 was released vertically upwards from the hole on the floor with radius of 1 cm, and the initial CO2 concentration released kept constant at 99.9% by volume with CO2 flow rates from 0 m3/h to 20 m3/h. In our trials, four different flow rates for discharging CO2 were 10 m3/h, 12 m3/h, 15 m3/h and 18 m3/h. Due to the fixed diameter, CO2 was discharged from the source at the speeds of approximately 8.8 m/s, 10.6 m/s, 13.3 m/s and 15.9 m/s. Sensors were arranged on the central line across the CO2 source on the ground along the downwind direction. The distances from the source to the ten sensors were 0.5 m, 1 m, 1.5 m, 2 m, 2.5 m, 3 m, 4 m, 6 m, 8 m and 10 m on the central line.

k¼

u0i u0i 1 02 ¼ ðu þ v 02 þ w02 Þ 2 2

e¼

l @u0i q @xk





@u0i @xk

ð15Þ

 ð16Þ

The k–e equation states that the turbulence viscosity is determined by both the turbulence kinetic energy and the turbulence dissipation rate.

lt ¼

C l qk

2

ð17Þ

e

As to the values of k and e, they are determined from the following equations below.

@ðqkÞ @ðqkui Þ @ þ ¼ @t @xi @xj

@ðqeÞ @ðqeui Þ @ þ ¼ @t @xi @xj







lþ

lt @k þ Gk  qe rk @xj

lþ

lt @ e e e2 þ C 1e Gk  C 2e q re @xj k k







where Gk is obtained from the given equation as follows:

Fig. 1. Experimental domain and wind direction.

ð18Þ

ð19Þ

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( "   2  2 #  2 2 @u @v @w @u @ v þ Gk ¼ lt 2 þ þ þ @x @z @y @x @y  2  2 ) @u @w @ v @w þ þ þ þ @z @x @z @y

6. Simulation results

ð20Þ

where C1e and G2e are empirically determined constants empirically, and rk and re are separate corresponding Prandtl values for k and e. These empirical constants are defined as

C 1e ¼ 1:44;

C 2e ¼ 1:92;

C l ¼ 0:09;

rk ¼ 1:0; re ¼ 1:3 ð21Þ

5. Statistical performance indicators Statistical performance indicators were introduced to assess the effects of the models for simulation. Some typical statistical performance approaches were suggested by Chang and Hanna [33], including the geometric mean bias (MG), the geometric mean variance (VG), and the fraction of predictions within a factor of two of observations (FAC2). MG is the exponential function of the difference between means of the logarithmic function of predicted values less the logarithmic function of observed value. VG is the exponential function of the mean of the square of the difference between logarithmic function of predicted values less the logarithmic function of observed values. FAC2 is defined as the percentage of predictions within a factor of two of the observed values. The definitions are shown as follows.

MG ¼ expðln Co  ln Cp Þ

ð22Þ

h i 2 VG ¼ exp ðln Co  ln Cp Þ

ð23Þ

FAC2 ¼ fraction of data that satisfy 0:5 6

Cp 6 2:0 Co

ð24Þ

In general, a perfect model should produce MG, VG and FAC = 1.0. To verify the predicted results, the acceptable range of the evaluation should be fixed in advance. According to Chang and Hanna [33], 0.7 < MG < 1.3, VG < 4 and 0.5 < FAC2 < 1 mean the acceptable criteria for heavy gas dispersion models. Furthermore, Chang and Hanna [33] presented a lower limit for the observed and predicted concentrations on the calculation of MG and VG, because these two indicators were strongly influenced by small values of less than 0.1%. Consequently, the predicted concentration values less than 0.1% were not used in calculations of MG and VG.

The simulations were carried out with FLUENT 6.3 to calculate CO2 concentration as a function of time, and transient species transport modeling was carried out [34]. Before the transient simulation, we ran the wind field to steady state. The steady state was running for approximately 200–260 iterations to achieve an acceptable convergence. The factor of 104 was chosen as a convergence residual criterion. And then we started to model the dispersion of CO2 as a transient process. The whole releasing continued 200 s (20  0.25 s + 50  0.5 s + 50  1 s + 60  2 s). The entire simulation lasted approximately 4 h on an 2.5 GHz IntelÒ Pentium Duo-Core with 3 GB RAM. The CO2 concentration field was simulated by species transport modeling, and the concentration field at the central line on the ground along the wind direction was the most significant concern, because the CO2 concentration is largest along the downwind direction, and the CO2 concentration field was directly related to personal safety for workers around the well outlet. For example, the CO2 allowable concentration in the workplace is less than 1% by volume according to the National Standards of China. That central line represents the rough forward direction of the CO2 cloud. Table 1 exhibits CO2 concentration at different positions on this line predicted by the k–e model. These concentration values were recorded at 632 s after CO2 release.

7. Comparisons between reduced-scale experimental results and simulated values The scale of 1/10 was used in the field experiment of CO2 release, so all the variables need be scaled in the original model for simulation based on the scaling rules described above. In the original model, it can be deduced that the distances between the source and sampling points were 5 m, 10 m, 15 m, 20 m, 25 m, 30 m, 40 m, 60 m, 80 m, 100 m along the central line; and CO2 flow speeds were 27.8 m/s, 33.5 m/s, 42.1 m/s and 50.3 m/s after scaling instead of 8.8 m/s, 10.6 m/s, 13.3 m/s and 15.9 m/s in the field experiment; and the release time was prolonged approximately by three times and became 632 s; and CO2 flow rates became 3162 m3/h, 3795 m3/h, 4743 m3/h and 5692 m3/h instead of 10 m3/h, 12 m3/h, 15 m3/h and 18 m3/h. Gravity was kept identical in the reduced-scale experiment and in the original model. In addition, wind speed was also scaled from 0.6 m/s at 10 m height to 1.9 m/s at 100 m height. Table 2 shows CO2 concentration at different positions on the central line after scaling in the original model.

Table 1 CO2 concentration at the central line on the ground in the simulation. Flow rate (m3/h)

10 12 15 18

CO2 concentration of different coordinates at 632 s after CO2 release (%) (15, 1.5, 0)

(20, 1.5, 0)

(25, 1.5, 0)

(30, 1.5, 0)

(35, 1.5, 0)

(40, 1.5, 0)

(50, 1.5, 0)

(70, 1.5, 0)

(90, 1.5, 0)

(110, 1.5, 0)

0.4 0.2 0.1 0.1

0.7 0.3 0.1 0.1

1.8 1.1 0.3 0.1

2.0 1.9 1.2 0.3

1.5 1.7 1.7 1.2

1.1 1.3 1.5 1.5

0.7 0.8 0.9 1.0

0.5 0.5 0.6 0.7

0.2 0.3 0.3 0.5

0.1 0.1 0.2 0.3

Table 2 CO2 concentration at the central line on the ground in the original model after scaling. Flow rate (m3/h)

CO2 concentration of different coordinates at 632 s after CO2 release (%) (15, 1.5, 0)

(20, 1.5, 0)

(25, 1.5, 0)

(30, 1.5, 0)

(35, 1.5, 0)

(40, 1.5, 0)

(50, 1.5, 0)

(70, 1.5, 0)

(90, 1.5, 0)

(110, 1.5, 0)

10 12 15 18

0.8 0.6 0.6 0.4

1.3 0.5 0.4 0.2

1.9 0.8 0.3 0.5

2.2 1.4 0.8 0.6

1.4 1.6 1.4 0.9

1.0 1.2 1.5 1.4

0.6 0.7 1.0 1.3

0.4 0.4 0.5 0.7

0.2 0.3 0.4 0.5

0.1 0.2 0.2 0.2

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CO2 concentrations at the central line on the ground were compared between the simulation and the scaled results from the field experiment at different flow rates, as shown in Fig. 2. It was apparent that the simulation and the scaled results exhibited a good agreement for the concentration except near the jet nozzle. With the flow rate increasing, the concentration near the jet nozzle became obvious. For the flow rate of 10 m3/h, the concentration trend kept identical even near the jet nozzle, but the trend discrepancy came out before 20 m for the flow rates of 12 m3/h and 15 m3/h. The lack of agreement for the flow rates of 12 m3/h continued until 30 m. The scaled results had higher CO2 concentration than the simulation. This is because the CO2 diffusion is stronger near the jet nozzle in the real scenario than in the simulation. Therefore, the difference between the simulation and the scaling methods is mainly in the area near the CO2 outlet, and the scaling method could really show the tendency of CO2 concentration variation. To verify the scaling rules, concentration values after scaling in the field experiment were compared with those in the simulation through the statistical performance indicators (see Table 3). Through the performance of MG, VG and FAC2, the effectiveness of the scaling rules could be validated. Except for a low MG = 0.678 for the flow rate of 18 m3/h which was outside the acceptable range, the other values were in the reasonable region according to Chang’s criteria [33]. The FAC2 was the most robust performance indicator because it was not considerably influenced by exceeding the limits of the high or too low criterion. The

Table 3 Summary of the statistical performance for the original model after scaling comparing to the simulated CO2 concentration values in the central ground line parallel to the wind velocity; the acceptable ranges are 0.7 < MG < 1.3, VG < 4, 0.5 < FAC2 < 2, and an ideal model produces MG = VG = FAC2 = 1.0. Flow rate (m3/h)

MG

VG

FAC2

10 12 15 18

0.912 0.889 0.876 0.678

1.10 1.25 2.14 1.78

1.0 0.9 0.7 0.8

FAC2 = 1 for the flow rate of 10 m3/h shows the best performance followed by that for 12 m3/h. The FAC2 = 0.7 for the flow rate of 15 m3/h was the worst in all the cases but was still in the acceptable arrange of FAC2 > 0.5. For MG and VG, the value nearer to MG = 1 and VG = 1 is better. As Fig. 3 shown, it is easily seen that the MG and VG of the flow rate of 10 m3/h is the most satisfied criterion due to the nearest distance from the point of MG = 1 and VG = 1, however, the MG and VG for 15 m3/h and 18 m3/h is further from the point (1, 1). Hence, we can conclude that the scaling rules are more accurate when flow rates are not too high. Because increasing the flow rate improves the CO2 outlet speed, the height of CO2 spilling becomes higher. In this case, it will take more time for spilled gas to return to the ground and the distribution of CO2 on the ground becomes harder to predict. So the accuracy of the

Fig. 2. CO2 concentration comparisons between the simulation and the scaled results from the field experiment: (a) CO2 flow rate of 10 m3/h, (b) CO2 flow rate of 12 m3/h, (c) CO2 flow rate of 15 m3/h, and (d) CO2 flow rate of 18 m3/h.

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Fig. 3. Plot of geometric mean (MG) versus geometric variance (VG) for CO2 concentration for the original model after scaling the field experiment. The solid parabola represents the minimum VG for a given value of MG.

scaling rules for concentration prediction decreases with increasing flow rate. 8. Conclusions A series of scaling rules was introduced and used to scale field experiments of CO2 dispersion, which were conducted by Beijing Institute of Technology. The length scaling factor of 1/10 was applied for scaling this field experiment. To validate the scaling rules, the successful k–e turbulence model was used to simulate the CO2 concentration distribution of the scaled original model for comparison. The tendencies of the two methods stayed the same except near the jet nozzle where the measured CO2 concentration from the experiment was obviously higher than that in the simulation. The results of comparison were evaluated using statistical performance indicators, including MG, VG and FAC2. It was shown that all the VG and FAC2 results were satisfactory at different flow rates according to the Chang’s criteria [33]. The values of MG represented a decreasing trend for accuracy with increasing flow rate, and even the MG = 0.678 for 18 m3/h was outside the acceptable range. Hence, it was concluded that using the scaling rules to scale the field experiment exhibited acceptable accuracy at small flow rates. Through the comparison with the k–e model and the statistical performance indicators, we concluded that the scaling rules were demonstrated useful for the accidental release field experiment. Acknowledgements This work was supported by the National Science and Technology Major Project of China (Project No.: 2011ZX05054). The field experiments conducted by Beijing Institute of Technology were supported by the Petroleum Production Technology Research Institute. The first author expresses his gratitude to Dr. Umberto Desideri at University of Perugia for his help to this paper. References [1] Jiang X. A review of physical modelling and numerical simulation of long-term geological storage of CO2. Appl Energy 2011;88:3557–66. [2] Zhu L, Fan Y. A real options-based CCS investment evaluation model: case study of China’s power generation sector. Appl Energy 2011;88:4320–33.

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