Investigating Effects of Pore Size Distribution and Pore Shape on

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Investigating Effects of Pore Size Distribution and Pore Shape on Radon Production in Marcellus Shale Gas Formation Wei Tian, Xingru Wu, Dehua Liu, Amanda S. Knaup, Changlong Chen, and Carl Sondergeld Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b03311 • Publication Date (Web): 15 Jan 2019 Downloaded from http://pubs.acs.org on January 21, 2019

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Investigating Effects of Pore Size Distribution and Pore Shape on Radon Production in Marcellus Shale Gas Formation Wei Tiana, Xingru Wu*,a ,Dehua Liub, Amanda Knaupa, Changlong Chena Carl Sondergelda a Mewbourne

School of Petroleum & Geological Engineering, University of Oklahoma, Norman, Oklahoma 73071, United States b. Petroleum Engineering College, Yangtze University

Corresponding Author: Xingru Wu. E-mail: [email protected]; phone: +1(405)325-1207

Highlights   

Develop the formulas to calculate radon concentration in spherical shape pores Pore size distribution and pore shape both influence wellhead radon concentration Radon production at wellhead in Marcellus Shale is above safe level

Abstract Marcellus Shale gas development brings significant economic impact to the United States and local areas. However, potential negative impacts on health, safety and environment also draw public attention. Numerous studies have documented the production of radon along with shale gas. Because of radon’s severe damage to human health, it is imperative to quantitatively evaluate radon emission in hydraulically fractured systems. This work proposes the equations to calculate the radon generation in spherical pores. Then, through numerical simulation, it is noticed that pore shape as well as pore size distribution are influential factors in wellhead radon concentration. Moreover, the simulation results show that radon concentration at the wellhead ranges from 36 pCi/L to 100 pCi/L, which is above the safe standard. Most importantly, the short transport time for such contaminated shale gas will result in high radon concentration in residential buildings, which is a hazard to the public health.

Keywords: Radon; Marcellus Shale Gas; Environment and Energy; Hazard materials

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35 30

Case A, slit model

25 Case B, spherical model

20

Case C, slit model from literature [32]

15 10 5 0 11000

12000

13000 14000 Rondon in-situ Concentration, pCi/L

15000

16000

Introduction Marcellus Shale in the Appalachian basin is a middle Devonian-age shale and lies between limestone (Tristates Group) and shale (Hamilton Group) [1]. Pennsylvania has become the second largest shale gas producing state because of the Marcellus Shale production [2]. In order to economically produce natural gas from extremely low permeable shale formation, operators rely on hydraulic fracturing to increase the reservoir contact area, creating high permeable conduits for natural gas to flow [3]. Radon gas associated with shale gas production has come under the scrutiny of medical and environmental societies because of its potential negative impacts on public health and the environment [4-6]. Radon is the daughter product of radium. Its most stable isotope is 222Rn with a half-life of 3.8 days. Radon is commonly found in the gaseous phase, but it can also partition into aqueous phase such as contaminated brine and flowback fluids from hydraulic fracturings [7-12]. Epidemiological and toxicological surveys show that exposure of radioactive radon causes lung cancer [13, 14]. Considering radon’s hazard to the public, the EPA set the safe level of radon concentration at 4 pCi/L. Picocuries per liter (pCi/L) is a unit of radioactivity. Radon production from the Marcellus Shale is particularly more severe than other shale gas reservoirs and it is worth more attention. Firstly, Marcellus Shale contains highly concentrated uranium and radium, inferring possibly high concentration of radon. Uranium concentration in rock can reach about 8.9-83.7 ppm, which is much higher than other US shale formations [15]. Laboratory test measured radium concentration in hydraulic fracturing flowback water to be 1.7×104 pCi/L [16]. Kondash et al. [17] also pointed out that flowback water from Marcellus Shale contained unusually high levels of radium. Secondly, field measurements confirmed the existence of radon at a wellsite [4] and inside a natural gas pipeline [6]. Both observations indicated the radon level was higher than the safe standard. Thirdly, Marcellus Shale is close to highly populated residential area, which implies a short transportation time for radon to decay from wellsite to residential buildings. Consequently, residents would be at risk of being exposed to hazardous 2 ACS Paragon Plus Environment

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radon. Therefore, it is imperative to critically evaluate the potential danger of produced radon from Marcellus Shale. Although radon hazard in indoor air quality has been thoroughly studied [14,18], radon production from shale gas is little understood. Before estimating wellhead radon concentration, we need to understand the radon generation process so that the radon in-situ concentration (i.e., radon concentration in pore space) could be known. Radon is the decay product of radium. It is emanated from shale rock grains into pore space. The emanation process is controlled by both pore size and pore shape. These two parameters should be included in a realistic model for radon generation process [19]. Radon in pore space will flow through porous media to surface when shale gas reservoir is fractured and produced. The study of radon transport in subsurface porous media need to be further carried out to investigate how much radon will be produced to wellhead. Andrews [20] and Fleischer [21] studied radon emanation process from radium in rock grains into slit shape pores. Based on the same pore shape, Tian et al. [22] proposed a method to evaluate in-situ radon concentration including the radium contribution in formation water. Nevertheless, in addition to slit pores, spherical pore shape is also commonly seen in shale [23] and none of research discussed the calculation of radon in-situ concentration in spherical pores. Resnikoff [15] simulated radon transport and production from Marcellus Shale. However, Resnikoff’s reservoir model was oversimplified without considering hydraulic fracturing, which might affect radon production. Tian et al. [22] included hydraulic fracture in the model when they simulated radon production, but they did not assess the impact of pore features. This present research aims to investigate the effects of pore size distribution and pore shape on wellhead radon concentration produced from shale gas reservoirs. We first develop the formulas to calculate radon in-situ concentration in spherical pores. Then, we have characterized the pore structure of a sample from the Marcellus Shale with scanning electron microscopy (SEM) and subcritical nitrogen gas adsorption. These characterization methods yield critical information such as pore shape as well as the pore size distribution. Next, we calculate the distribution of radon in-situ concentration based on the pore features obtained from experiments. Finally, we input representative data of Marcellus Shale into the reservoir simulator to examine how pore size distribution and pore shape affect the radon production and its wellhead concentration.

Pore Size Analysis The Marcellus Shale sample used for this study was obtained from a gas producing well. The sample was measured with a total organic carbon (TOC) of 4.1 wt% and clay content of 72 wt%, with illite as the dominant clay. Five grams of the sample were crushed to a particle size less than 150 µm (100 mesh). One gram of the homogenized powder was collected and degassed at 373K under vacuum for twelve hours, prior the subcritical nitrogen gas adsorption measurements. Nitrogen isotherm adsorption measurements were conducted in subcritical temperature (49.3K), to allow the condensation of nitrogen gas onto the pore walls. Pore volume is measured by the number of molecules needed to fill the pore space at different relative pressures. A Density Functional Theory (DFT) statistical model was used to determine the pore size distribution. Unlike other analytical methods, this approach took into account the concentration of pores whose sizes are in the nanometer order [24]. It assumes that the pores act independently and contribute to the total isotherm adsorption in pore size distribution calculations. Lastoskie et al. [24] and Adesida et al. [25] provided more details of using DFT and the derivation of the pore volume calculation. 3 ACS Paragon Plus Environment

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We also applied scanning electronic microscopy (SEM) to observe the pore structure of shale sample. In order to receive a smooth surface, the sample was polished in sequence using 400, 600 and 800 grit abrasives and then the surface was broad beam argon ion milled before SEM images were taken.

Radon Generation in Pore Space The radon atoms acquire kinetic energy after the alpha decay of radium. This energy defines a finite distance, known as the recoil range [27]. The kinetic energy allows the radon atoms to travel inside materials. Once the atoms lose all the energy, they stop moving. This process is known as alpha recoil. The distance traveled is material dependent. Usually, solid materials like rock grain require more energy than air for example to travel equivalent distances. In other words, radon recoil range is shorter in the material with higher density. Typically, recoil range in rock, water and gas is 36nm, 100nm and 60,000nm, respectively [27]. Since radium was located in the rock grains and formation water [22], we consider radon in pore space comes from these two sources. Radon produced from radium that pre-exists in pore space is dominated by alpha recoil. Some of the produced radon may stay in pore space while some may penetrate into the adjacent grains. On the other hand, for radon emanated from rock grains into pore space, alpha recoil process is assumed as the primary mechanism. Given that radon’s half-life is 3.8 days and its low diffusivity (in range of 10-31 to 10-69 m2/s) in rock grains [28], diffusion contribution to radon emanation is negligible compared to recoil. Therefore, only radon produced within the distance of recoil range to grain-pore surface has non-zero probability of escaping the grain. Eq. 1 is modified from Hammond [29] to estimate the radon concentration in pores contributed by radium in rock grains. (1) 𝐴𝑅𝑛 = (𝐴𝑅𝑎 ∙ 𝑉𝑒 ∙ 𝑒)/𝑉𝑝 Where, ARa is the radioactivity of radium and ARn is the radioactivity of radon, both in unit of pCi/L. Ve is the grain volume in which the radon generated from radium has non-zero possibility entering the pore space, in unit of L3. e is the emanation efficiency of recoil and Vp is pore volume in unit of L3. Emanation efficiency e consists of two parts (Eq. 2). First, not all produced radon near the grain-pore surface will be emitted into the pore space (fe). Some of the produced radon atoms remain inside the grain due to the inappropriate recoil direction. Second, radon atoms that enter the pore space may maintain sufficient kinetic energy so that they could enter neighboring grains eventually (1- fi). Both of these factors should be included in evaluating efficiency e [24]: (2) 𝑒 = 𝑓𝑒 ∙ 𝑓𝑖 Slit pore shape is one commonly used pore geometry, defined by two parallel planes (grain surface) [26]. Andrews [20] analytically calculated the radon release fraction from grains into pore space (fe) for slit pores. Fleischer [21] further studied the fraction of radon atoms ejected from grains that are trapped in pores (fi). Tian et al. [22] investigated how much radon produced from radium in the pore space will remain in slit pores after alpha recoil. Besides slit pore shape, spherical pores also occur in shale, which require different formulas to calculate radon in-situ concentration. Emanation efficiency, e, is defined in Eq. 2. The point O1 is the center of spherical pore with radius of R as shown in Figure 1. Radium atom is initially located at O2. The radon recoil range inside fluid filled pore space is Rf and recoil range in solid material is Rs. The solid circle in Figure 1 represents the pore wall and, therefore, the inside of the circle is the pore space. If the trajectory of radon after recoil is O2AB, it is helpful to convert 4 ACS Paragon Plus Environment

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the stopping power in fluid to solid [21]. In other words, the distance b in pore filled by fluid is modified to an equivalent distance bRs/Rf if the pore space is assumed to be filled by solid. Radon particle could possibly be ejected and trapped into the pore if the following criteria are satisfied: 𝑏𝑅𝑠 𝑅𝑓

(3)

+𝑎 > 𝑅𝑠 & 𝑎 < 𝑅𝑠

Where (derivation in Appendix), 𝑎=

2(𝑥 + 𝑅)𝑐𝑜𝑠𝜃 ― 4(𝑥 + 𝑅)2𝑐𝑜𝑠2 𝜃 ― 4𝑥2 ― 8𝑅𝑥 2 2 2 2

(4)

𝑏 = 4(𝑥 + 𝑅) 𝑐𝑜𝑠 𝜃 ― 4𝑥 ― 8𝑅𝑥

(5)

For a specific x, when the radon trajectory is within the range of angles [1, 2] it will stay in the pore space. The corresponding probability is ratio of spherical area between these two angles to the entire spherical area: 𝑒𝑥 =

2𝜋𝑅𝑆[(𝑅𝑠 ― 𝑅𝑠𝑐𝑜𝑠𝜃2) ― (𝑅𝑠 ― 𝑅𝑠𝑐𝑜𝑠𝜃1)] 4𝜋𝑅2𝑠

=

𝑐𝑜𝑠𝜃1 ― 𝑐𝑜𝑠 𝜃2 2

The overall emanation efficiency e is: 1 1 𝑅 𝑒 = 𝑉∫𝑒𝑥𝑑𝑉 = 4 ∫0 𝑠𝑒𝑥4𝜋(𝑅 + 𝑥)2𝑑𝑥 4 3 3

(3𝜋(𝑅 + 𝑅𝑠)

― 3𝜋𝑅

)

(6)

(7)

Figure 1. Schematic cross-section view of spherical pore shape. The radon generated from radium in grains (outside of the solid circle) may enter the pore space (inside the solid circle). O2A section has length of a. AB section has length of b. O2C section has length of x. O2 represents the location of a radium molecule. After alpha decay, it radon molecule could fall inside the solid circle, it is considered to be ejected into the pore space.

Figure 2 shows the geometry considered in the calculation of the remaining radon in pore after alpha decay of radium in the pore space. The radium atom is located at position O2. If produced radon falls on to the curve 𝐴𝐵 outside the pore space (solid circle), it is regarded as entering into adjacent grains. The remaining ratio F is defined to represent how much of the

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produced radon will be kept in the pore space. By assuming radium is uniformly distributed in the pore space, we get F ,which was derived from Flügge and Zimens, [25]: 3 (8) 𝐹 = 1 ― 4𝛼(1 ― 𝛼2/12) Where, 𝛼 = 𝑅𝑓/𝑅

(9)

The remaining ratio F becomes zero when Rf >=2R.

Figure 2. Schematic cross-section view. Radon generated from radium in pore space (inside the solid circle) may remain in pore space. O2 represents the location of a radium molecule. After alpha decay, it radon molecule falls the solid circle, it is considered to be ejected into the adjacent grains.

Numerical Reservoir Model Construction Shale pores are divided into two types: organic pores and inorganic pores. Organic pores are expected to contain hydrocarbons while inorganic pores contain water. Water plays an important role to radon generation in pore space because of the strong stopping power of water. In the reservoir model, we assume that water fills the pores from smaller size to larger size, which is also known as the blocked configuration [32]. A 3D compositional model was built up using a numerical simulator to investigate the radon production along with shale gas development. Considering the symmetry, we simplified the reservoir model. It included half of a bi-wing hydraulic fracture and a quarter of the stimulated reservoir. We implemented local grid refinement (i.e. grid size is logarithm) near the fracture to accurately model the mass transport between low permeable matrix and high permeable fracture [33]. The horizontal well is only perforated at the fracture. Gas and water were the only two phases in the formation. For this study, we divided the stimulated reservoir into two sections: the far formation zone and near fracture zone. The near fracture zone reaches up to 35ft away from the hydraulic fracture as shown in Figure 3.The near fracture zone are far fracture zone were determined arbitrarily. 6 ACS Paragon Plus Environment

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Figure 3. Synthetic model configuration. The horizontal well is located at the top. It is perforated at hydraulic fracture at the left side. The stimulate reservoir is devided into two sections: near fracture zone and far formation zone.

The radium was located in the rock grains and the formation water, as the source of radon. Due to existence of radium, radon reached secular equilibrium[22], which indicates that the concentration of radioactive atom remains constant as a result of the balance between production rate and decay rate. The radium concentration in water was taken to be 1.73×104 pCi/L [16]. The radium concentration in solid phase was determined corresponding to radon in-situ concentration. Radon was initially trapped in pore space but can partition between gas and water. The partitioning coefficient is described in Eq. 10 [34]. 222

𝐾=

𝑅𝑛𝑤

222

𝑅𝑛𝑔

= 0.105 + 0.405 × 𝑒 ―0.5027𝑇

(10)

Once the shale reservoir development starts, radon escapes to surface through conductive hydraulic fractures, being entrained in shale gas and formation water. The alpha decay of radium and radon in reservoir was simulated by first-order chemical reaction since decay rate was dependent on their concentrations (Eq. 11). During the simulation, fresh water was injected into the formation for 0.5 day to mimic the hydraulic fracturing process. The injected fracking fluid did not contain any radon or radium. The well was then brought back to production under a constant bottom-hole pressure after 0.5-day shut in. This work adapted model set-up from Tian et al. [22]. 𝑑𝑁 (11) 𝑑𝑡 = ― 𝜆𝑁 Where, N is the concentration or radioactivity, and 𝜆 is the exponential decay constant.

Results and Discussions Marcellus Pore Characterization Backscattered SEM images are shown in Figure 4. Both spherical and slit shape pore exist in the sample. In general, organic pores have spherical shape. On the other hand, the large fractional 7 ACS Paragon Plus Environment

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volume of illite caused the inorganic pores to exhibit slit shape. Our observation of pore shape variation is in agreement with other research work[19-21].

Figure 4. Backscattered SEM images for Marcellus Shale. (a) Shows organic and inorganic pores at 3 µm. The inorganic pores show slit shape and organic pores shows spherical shape. In (b), the image shows more slits and sheets of illite. Illite is the dominant matrix mineral and is more visible as sheets in (c) and (d), creating inorganic pores around the sample.

Since both geometries are observed in SEM images, two distinct pore size distributions are obtained using DFT based on slit and spherical pore shapes respectively. For simplification, in each calculation, we assume all the pores are either slit or spherical shape. As shown in Figure 5, the solid line represents pore size distribution for slit shape model, and the dashed line stands for the spherical shape pores. For the slit shape pores (Case A), the pore size is related to the pore width, the separation between grain plates [35]. In this case, it is noticed that the majority of pore volume consisted of pores with a size about 10nm. The overall pore size ranges from 2~200nm. On the other hand, the pore size for spherical pores (Case B) is related to the pore radius. Its distribution is generally shifted to the larger size compared with distribution of slit model.

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Volume Fraction, %

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16 14 12 10 8 6 4 2 0

Case A, slit model, our measurements Case B, spherical model, our measurements Case C, slit model, literature [32]

1

10

100 Pore Size, nm

1000

10000

Figure 5. Pore size distribution for Marcellus Shale. Case A and Case B are calculated through DFT using our adsorption measurements. Case C is obtained from literature [30].

Pore size distribution may vary from location to location within a same formation. Case C in Figure 5 shows a distinct pore size distribution for Marcellus Shale with the assumption of slit pore shape reported in other literatures[36]. Although it assumes the same pore shape with Case A and both cases are from Marcellus Shale, the distribution is obviously different. Most pores in Case C have the pore size of 3nm, which is smaller than Case A, and Case C has a wider range of pore size. We selected Case C to study the impact of pore size distribution by comparing with Case A in the following sections.

In-situ Radon Concentration To investigate the impacts of pore size distribution and pore shape on in-situ radon concentration, we generated 3000 pores following the pore size distribution for each case in Figure 5. For simplification, radon recoil range in pore space is assumed as 100nm. The radium concentration in a shale grain is taken to be 40.4 ppm [9].The radium concentration in formation water is determined by the lab measurement of 1.7×104 pCi/L [16]. Figure 6 shows the distribution of radon in-situ concentration for all the three cases. The radon is generated from radium in rock grains as well as radium in formation water. As Case A and Case C assumed slit pore shape, we employed the formulas in Tian et al. [22] to calculate radon in-situ concentration. In Case B, the equations derived in this work for spherical pore shape were utilized. Figure 6 shows that both pore shape and pore size distribution influence the radon concentration in pore space. The distribution of radon in-situ concentration in Case A is more stretched than Case C, which is caused by the difference in pore size distribution as shown in Figure 5. Nevertheless, radon in-situ concentrations in these two cases are mostly concentrated at the level of 1.17 ×104 pCi/L. Such similarity is attributed to the majority of their pore sizes are both in the range of 1-10nm. If the general pore size in Case C is 10 times larger than Case A, we should expect a quite different distribution of radon in-situ concentration. On the other hand, pore shape is another critical factor. The radon in-situ concentration obtained from spherical model is generally shifted to the right of the slit model. The mode value of radon concentration for Case B is 1.22×104 pCi/L, larger than the mode value of Case A. This observation indicates that pore shape will influence the pore size distribution and it will further affect the radon in-situ 9 ACS Paragon Plus Environment

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concentration. Therefore, an accurate description of the pore size distribution as well as pore shape is essential to evaluate the radon in-situ concentration. 50 45 40 35 Fraction, %

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30

Case A, slit model

25 Case B, spherical model

20

Case C, slit model from literature [32]

15 10 5 0 11000

12000

13000 14000 Radon in-situ Concentration, pCi/L

15000

16000

Figure 6. Radon in-situ concentration distribution for the three cases.

Wellhead Radon Production Our simulation assumed the initial water saturation was 25%. As we previously assumed blocked configuration of saturation, water saturated the small pores first. Larger pores were filled with gas. We used average pore sizes to represent water filled pores and gas filled pores for simplification instead of explicitly assigning different radon concentration in pores space. Average pore size for each case and their corresponding radon in-situ concentration in pores are shown in Table 1. As pore size in Case A and Case C is concentrated at the magnitude of 1-10nm, their calculated average pore size of water filled pores is close to each other. Table 1. Radon in-situ concentration

Case A Case B Case C

Water Filled Pores Avg. Size, nm Radon in-situ Conc. pCi/L 4.0 1.175×104 5.5 1.220×104 3.2 1.171×104

Avg. Size, nm 26 40 198

Gas Filled Pores Radon in-situ Conc. pCi/L 23 85 48

Radon diffusivity in water is 1.13×10-9 m2/s and 10-5 m2/s [37] in air. Although radon concentration in water pores and gas pores right after the generation from radium are dramatically different as seen in Table 1, the diffusion process could balance radon concentration in these two types of pore, especially over the long geological time. Consequently, after being buried underground for millions of years, it is safe to assume that the radon atoms are uniformly distributed. Gas pores shall eventually have the identical radon concentration with water pores. 10 ACS Paragon Plus Environment

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Therefore, for each case, the radon in-situ concentration in water pores was used as the initial radon concentration in simulation. Radium content in rock grains was designed correspondingly. Figure 7 shows the wellhead radon concentration for the three cases. Wellhead radon concentration in Case A gradually increases from 36 pCi/L to 100 pCi/L in 100 days. Subsequently, it remains at 100 pCi/L for late production time. The injected fracking fluid pushes the radon and radium away from the wellbore. After a certain period, highly concentrated radon gas will then flow back to wellbore. As a result, the wellhead radon concentration at early time is relatively low. The other two cases behave a similar pattern in radon production history with Case A. Case C has an identical radon production history with Case A because of their similar initial radon in-situ concentration in Table 1. Since Case B has a higher initial radon concentration, it produces higher wellhead radon concentration as well. This observation indicates that the wellhead radon concentration is directly related with the in-situ concentration. Furthermore, pore size distribution and pore shape will influence the radon in-situ concentration, which will further determine the wellhead radon concentration. 110.0 100.0

Radon Concentration in Gas, pCi/L

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90.0 80.0 70.0 60.0

Case A

50.0

Case B

40.0

Case C

30.0 20.0 0.0001

0.001

0.01

0.1 1 10 Production Time, days

100

1000

10000

Figure 7. Wellhead radon concentration with multiple initial radon in-situ concentrations. Wellhead radon concentration is directly related with the in-situ concentration

Impact of Spatial Distribution of Pore Size Shale formations are highly heterogeneous. The pore shape and pore size could vary dramatically from location to location within a same formation, leading to heterogeneous radon in-situ concentration. This section studies the impact of heterogeneity. As discussed in the model construction, we divided the stimulated reservoir into two sections: near fracture zone and far formation zone. By doing this, we can understand how heterogeneously distributed radon could affect wellhead radon concentration. The Case A and Case B in Figure 7 were used as the lower and upper bounds. We designed another two scenarios, whose initial radon in-situ concentrations are listed in Table 2. Their results are plotted in Figure 8. 11 ACS Paragon Plus Environment

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Simulation results show wellhead radon concentrations in both cases are constrained by the upper and lower bounds. This can be explained by material balance. Since the overall radon mass will not be higher than Case B or lower than Case A, the produced radon mass will not exceed the limit as well. Another trend we get from Figure 8 is that the near fracture zone determines the early radon production. If the near fracture zone has a higher radon in-situ concentration, the produced wellhead radon concentration will be higher. On the other hand, the far formation zone influences the late time radon production. A high radon in-situ concentration in far formation zone will lead to a rapid increase of wellhead radon concentration from early to late time. For highly heterogeneous shale reservoir, various pore size and shape will result in heterogeneous radon in-situ concentration. Although diffusion could equilibrate radon concentration in different pores to some degree, the geological compartments cause radon in-situ concentration vary from location to location. If a horizontal well is drilled in a zone with high radon in-situ concentration, its wellhead radon concentration would be higher, and vice versa. Clearly, new wells should be drilled in a ‘clean’ area to reduce the radon production. Table 2. Radon in-situ concentration in near fracture zone and far formation zone for Case D and Case E.

Radon in Near Fracture Zone, pCi/L Radon in Far Formation Zone, pCi/L

Case D 1.220×105 1.175×104

Case E 1.175×104 1.220×105

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Figure 8. Wellhead radon concentration to investigate heterogeneity impact. Near fracture zone determines the early radon production.

Discussion We present formulas to capture the radon generation process in spherical pores, considering the fluid stopping power and radium existence in pore space. Our primary result indicates that the pore shape as well as pore size distribution strongly influence the in-situ radon concentration, which in turn will directly affect the wellhead radon concentration. Our simulation utilized representative data of Marcellus Shale and revealed that wellhead radon concentration increases from 36 pCi/L to 110 pCi/L. This result is in agreement with the field measurement [4] that pointed out the on-site radon concentration in Marcellus Shale ranged from 1 pCi/L to 79 pCi/L, with a median value of 37 pCi/L. In addition, the radon in-situ concentration near the hydraulic fracture influences radon production in early time, while the impact of radon that is far away from fracture affects at late time assuming those pore space are connected to the wellbore. More importantly, our work suggested an approach to simulate radon transport in shale gas reservoir and simulation using representative field input data indicated the radon wellhead concentration could be indeed above the safe standard.

Transport time in surface facility from wellhead to consumers could reduce the radon levels, but radon may still be dangerous to human health. For example, assuming it takes natural gas one week to be transported from wellhead to users, radon will decay to approximately 25% of its original concentration considering 3.8 days half-life. That is to say, the radon concentration that 13 ACS Paragon Plus Environment

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entered residential buildings would be in the range of 9 to 25 pCi/L (based on Case A), which is far above the safe standard of 4 pCi/L. Therefore, radon monitoring and protection should be implemented during Marcellus Shale gas development.

Acknowledgement The authors kindly appreciate the support from Computer Modeling Group Ltd. for the simulation software and the financial support from University of Oklahoma. The authors would also like to thank Dr. Mark Curtis for providing the SEM images. This research was partially supported by funding from Yangtze University.

Nomenclature A ARa ARn a b e ex F fe fi K R Rf Rs T Ve Vp x α θ λ pCi/L

= = = = = = = = = = = = = = = = = = = = = =

radioactivity, T-1L-3 radium radioactivity, T-1L-3 radon radioactivity, T-1L-3 one parameter, L one parameter, L emanation efficiency, dimensionless emanation efficiency at specific location x, dimensionless remaining fraction, dimensionless emanation efficiency from grains into pores, dimensionless trapping efficiency, dimensionless partition coefficient, dimensionless radius, L recoil length of fluid, L recoil length of solid, L temperature, K grain volume in which the radon can enter the pore space, L3 pore volume, L3 distance to pore wall, L one parameter, dimensionless angle, degree exponential decay constant, dimensionless picocuries per liter

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Appendix

Draw a line perpendicular to AB from O1, intersecting at E. We have:

(𝑎 + 2𝑏) 𝑥+𝑅

= 𝑐𝑜𝑠𝜃

Based on the law of cosines: 𝑎2 + (𝑥 + 𝑅)2 ― 2𝑎(𝑥 + 𝑅)𝑐𝑜𝑠𝜃 = 𝑅2 Solving above two equations, we obtain:

𝑎=

2(𝑥 + 𝑅)𝑐𝑜𝑠𝜃 ― 4(𝑥 + 𝑅)2𝑐𝑜𝑠2 𝜃 ― 4𝑥2 ― 8𝑅𝑥 2 𝑏 = 4(𝑥 + 𝑅)2𝑐𝑜𝑠2 𝜃 ― 4𝑥2 ― 8𝑅𝑥

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