Experimental and analytical study of oxygen consumption during air injection in shale oil reservoirs

Experimental and analytical study of oxygen consumption during air injection in shale oil reservoirs

Fuel 262 (2020) 116462 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Full Length Article Experimen...

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Fuel 262 (2020) 116462

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Full Length Article

Experimental and analytical study of oxygen consumption during air injection in shale oil reservoirs

T



Yao Zhanga,b, Siyuan Huanga, , James J. Shenga,b, Qi Jianga a b

Southwest Petroleum University, China Texas Tech University, United States

A R T I C LE I N FO

A B S T R A C T

Keywords: Air injection Low temperature oxidation Thermal effect Oxygen consumption Enhanced oil recovery

AIP (air injection process) is applied as an EOR (Enhanced oil recovery) method in conventional oil reservoirs, while the implementation of AIP in shale oil reservoirs has rarely been studied. The thermal effect of AIP in shale oil reservoirs is insignificant considering its low air injectivity, and the main challenge is whether the produced oxygen concentration at the production well can be reduced below 10% to avoid the potential safety hazards. In this paper, an analytical method was proposed to estimate the produced oxygen concentration during AIP, where the oxygen reaction rate was measured by the SBR (small batch reactor) experiments. In the SBR tests, a constant oxygen reaction rate was observed at a corresponding reservoir temperature. A higher reservoir temperature resulted with greater oxygen consumption. The air flooding tests were conducted with shale core and the proposed analytical method was validated by the air flooding tests. The analytical method was further applied to investigate the AIP feasibility in the air flooding tests. The results indicate that a core needs to be a longer than 0.132 m, or the injection pressure is lower than 2.68E + 06 Pa (388.70 psi), to satisfy the produced oxygen concentration requirement for AIP. This study can explore the potential of air injection in developing shale oil reservoirs and provide insights to the AIP projects in field level.

1. Introduction AIP (air injection process) is an EOR (enhanced oil recovery) method which has been applied for many years. It can be classified as ISC (in situ combustion) and HPAI (high pressure air injection). The ISC is usually applied for the heavy oil development, where the ignition and combustion sustention are critical for the success of an ISC process. The HPAI is often applied for light oil reservoirs. The feasibility of applying AIP in shale oil reservoirs has been discussed in recent studies [1–6]. It was stated that air injection may bring economic benefits due to air’s wide availability and low cost. Also, the reactions between injected oxygen and oil could generate thermal effect which may benefit the recovery process. For AIP in conventional reservoirs, some researches stated that the key aspects for HPAI are spontaneous ignition and combustion sustention [7–9], while some other researches claimed that the ignition is not necessary and the AIP in light oil reservoir is under the LTO mode [10–14]. Huang and Sheng [4,6] stated that the spontaneous ignition is hard to initiate due to insufficient LTO (low temperature oxidation) exothermic intensity. The thermal conductivity of a shale reservoir is generally higher than that of a conventional reservoir since the rock thermal



conductivity is much higher than the fluid, and the thermal conductivity will increase with the decrement of porosity [15]. In other words, heat loss in shale reservoir is more significant than conventional reservoir. As a result, high temperature reactions such as combustion reactions are difficult to be achieved in the shale reservoirs. In addition, the low gas injection rate in shale reservoirs also restrict the occurrence of combustion reactions. Huang and Sheng [16] presented that the typical temperature range for LTO is between 25 °C and 364 °C. Therefore, when applying the AIP to a shale oil reservoir, the LTO is more likely to be the dominant reaction. In this case, when investigating the AIP in shale oil reservoirs, the main concern is to restrict the oxygen concentration to a safety level before it reaches to the production end. The mechanisms of LTO reactions to a light oil have been extensively studied by researchers for a long time [17–21]. In particular, the oxygen consumption intensity of LTO was studied by different experiments including SBR (small batch reactor), oxidation tube and slim tube experiments [10,11,13,22]. The SBR is one of the most often practiced apparatuses, where the crude oil is reacted with the oxygen in a sealed container under a certain temperature and pressure condition. The gas composition was collected from the container and the oxygen concentration is measured by the GC (gas chromatography). Then, the

Corresponding author. E-mail address: [email protected] (S. Huang).

https://doi.org/10.1016/j.fuel.2019.116462 Received 27 August 2019; Received in revised form 8 October 2019; Accepted 18 October 2019 Available online 01 November 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A CO2 k air L m oil nair n o2rea n o2 ninitial nfinal Pin Pout

Px Qout Qx R Sor Tr t tf ug Vxo vo2 x ρoil

cross section area of the porous medium,cm2 oxygen concentration in the produced gas, % effective air permeability, Darcy total length of the porous medium, cm oil weight, g mole of air, mole mole of consumed oxygen, mole mole of oxygen, mole initial mole of oxygen in SBR, mole final mole of oxygen in SBR, mole inlet pressure, Pa outlet pressure, Pa

pressure at location x, Pa outlet flow rate,cm3/s flow rate at location x,cm3/s universal gas constant which equals to 8.314 J/(K*mol) residual oil saturation, fraction reservoir temperature, K reaction time in SBR, hr time for gas flow from inlet to location x, s air viscosity, cp gas filled volume from inlet to x under Pout condition,cm3 oxygen reaction rate, mole/(hr*g) length from the inlet to any location along L, cm oil density,g/cm3

minimum oxygen concentration for the formation of flammable mixtures [25]. The fire and explosion can be prevented by the following three methods. First, control the ambient temperature to be lower than the flash point temperature; second, reduce the fuel concentration to be lower than the flammability limit; third, decrease the oxygen concentration to be lower than the LOC. In this study, we are focusing to investigate the third method, which is to compare the oxygen concentration with the LOC at the production well. The ignition or explosion of the paraffin series cannot be achieved when the oxygen concentration is lower than 10% [25–27]. Based on the experience, it was stated that the oxygen concentration of 5% in the production well should be applied as the alarming limit, therefore, in this study, a 5% oxygen concentration was utilized as the safety level to evaluate the AIP feasibility in shale oil reservoir [28].

oxygen reaction rate can be calculated based on the mass balance [10,12]. Ren et al. [10] performed the SBR experiments with four North Sea light crude oils and it was reported that less than 3% of oxygen was measured after the SBR test under 120 °C with 120 h reaction time. The reaction rate ranges from 8.92 ∗ 10−6gmolo2 /hr − cm3ofsand to 9.1 ∗ 10−6 gmolo2 /hr − cm3ofsand . Chen et al.[14] used the oil from Changqing oil field in China in the SBR test and reported that the oxygen concentration decreased from 21% to 1% under 140 °C with a 108 h reaction. In addition, it was reported a higher temperature will increase the reaction rate, where a 170 °C test only took 6 h to reduce the oxygen concentration from 21% to 0.2%. Ren et al. [10] performed the oxidation tube tests to study the oxygen consumption by LTO, and they reported that the produced oxygen concentration was less than 2% under the 120 °C oxidation tube experiments, which also matches to the oxygen reaction rate measured from the SBR experiments. Niu et al. [13] conducted the slim tube experiments with an oil collected from Zhongyuan oil field in China, and they reported that when the temperature was higher than 100 °C, the produced oxygen concentration will be less than 2%. Although extensive researches have been performed in the oxygen consumption topic during AIP, a more quantitative method need to be proposed. On the other hand, the AIP feasibility in a shale oil reservoir also need to be studied. In this paper, the flammability limit theory is firstly reviewed and a restricted oxygen concentration is provided when evaluating the AIP feasibility. Then an analytical method is proposed to estimate the produced oxygen concentration during AIP, where the oxygen reaction rate is obtained by the SBR experiments. The air flooding tests were conducted with a shale core to validate the proposed analytical method, and further applications of the analytical method is performed to study the AIP feasibility in a shale oil reservoir. This study can provide insights to researchers when designing the AIP, and help researchers quickly evaluate the feasibility of AIP regarding the oxygen consumption issue.

3. Analytical method for estimating oxygen consumption during AIP Based on the review shown in the previous section, it reveals that the oxygen consumption is critical to the feasibility of an AIP project. An analytical method was proposed in this study to estimate the produced oxygen consumption after gas breakthrough. The analytical model was built for a 1-D single gas flow condition, where the air flows through the pore channel which is surrounded by the residual oil. It was assumed that the oxygen will constantly react with the surrounded residual oil, as a result, the oxygen will be consumed. As Huang and Sheng [6] discussed, the shale oil air injection process is most likely undergo only the LTO reaction process. Therefore, a single reaction with a corresponding single constant oxygen reaction rate is considered in this analytical model and the residual oil is assumed to be sufficient for the oxidation reactions. According to Ahmed [29], the air viscosity is a function of temperature and is independent of pressure when the pressure is lower than 2000 psi. The air is treated as an ideal gas since the Z factor is around 1 and will not change significantly when the temperature varies from 100 °C to 140 °C and the pressure is lower than 2000 psi. The main inputs required in this analytical method are oxygen reaction rate, rock properties (diameter, length, porosity and permeability) and operation condition (temperature, inlet and outlet pressure). This method is mainly used to estimate the oxygen consumption, and it can also be applied to evaluate the feasible injection length and pressure under a certain condition. More details can be found in a latter section. Fig. 1 shows the 1-D single gas flow model used for the analytical method, where the cylinder describes the simplified pore channel. The cross section area is A and the pore space outside the gas flowing channel is filled with residual oil. The total length of the channel is L and x defines the distance from the inlet to any location. Pin and Pout are the inlet and outlet pressure, respectively. Qout is the outlet flow rate at pressure of Pout . Due to the space limitation of the paper, the detailed

2. Flammability limit theory In order to prevent the potential fire and explosion hazards in the production well, the hydrocarbon flammability characteristics including FPT (flash point temperature), flammability limits and LOC (limiting oxygen concentration) need to be well understood. The FPT is the minimum temperature at which a liquid gives off sufficient vapors for an external ignition source to cause a flame [23]. The FPT of a paraffin series increases with increasing molecular weight. The flammability limits defines the fuel concentration criteria where a gas mixture in air can ignite with an ignition source. When the fuel concentration is lower than the LFL (lower flammability limit), there is no enough fuel to burn. If the fuel concentration is greater than the UFL (upper flammability limit), the oxygen is insufficient for combustion occurrence [24]. The LOC (limiting oxygen concentration) defines the 2

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0.21 − 4.53 ∗ 1012 ∗ vo2 ∗ CO2 = 1 − 4.53 ∗ 1012 ∗ vo2 ∗

Sor ∗ Tr ∗ ρoil ∗ug ∗ L2 (1 − Sor ) ∗ k air ∗ (Pin2 − Pout 2) Sor ∗ Tr ∗ ρoil ∗ug ∗ L2

∗ 100

(1 − Sor ) ∗ k air ∗ (Pin2 − Pout 2)

(5)

4. Experimental section 4.1. SBR test As mentioned in the previous section, the SBR test needs to be performed to obtain the oxygen reaction rate. After obtaining the oxygen reaction rate, the oxygen concentration in the produced gas can be estimated based on Eq. (5). For the SBR test, the oxygen reaction rate was measured under different temperature conditions, 100 °C, 120 °C and 140 °C. The test temperature conditions are selected according to the possible shale reservoir temperatures which may favor for implementing the AIP [5]. The crude oil used for SBR has a density of 0.83 g/cm3 (38.98 API) and the viscosity of the oil is 3.66cp at 25 °C and atmospheric pressure condition. The crude oil was collected from the Wolfcamp reservoir, and more detailed properties can be found in Ref. [18]. The SBR setup is shown in Fig. 2. For each test, around 70 cm3 crude oil was loaded into the container, where the inner volume of the container is 145 cm3 . Then the container was placed into the oven and the oven was turned on to increase the temperature to the test temperature. After the oven and also the container reached the thermal equilibrium, air was pumped into the container till the target pressure was achieved. The pressure inside the container will increase at the beginning due to the thermal expansion of the air and till a certain point, the pressure will start to decrease, which was due to the oxygen consumption by the crude oil LTO reactions. The oxygen concentration was measured by GC after the gas sample was collected from the air collector. It is worth to mention that the shale oil consists different types of hydrocarbons: light oil, resins-asphaltenes and kerogen. During the air injection process, under relatively high temperature, oxygen will be consumed by all these types of hydrocarbons. During the SBR test, the initial and final mole of gas was estimated according to the ideal gas law shown in Eq. (6),

Fig. 1. Schematic of oxygen consumption model.

analytical method derivation is provided in the Appendix section, and only the main equations are presented in this section. According to Darcy’s law, the outlet gas flow rate can be estimated by Eq. (1):

Qout =

kair ∗ A ∗ (Pin 2 − Pout 2) 2 ∗ Pout ∗ ug ∗ L

(1)

where Qout is the outlet gas flow rate, cm3/ s ; kair is the effective permeability of air, Darcy; A is the cross section area, cm2 ; Pin and Pout are the inlet and outlet pressure, respectively, atm; L is the length of the pore channel, cm; ug is the gas viscosity, cp. It was assumed that the reaction time equals to the gas flowing time in the porous medium. Therefore, the total reaction time equals to the time for the gas to flow through the porous medium. In order to find the reaction time, the volume of gas at reservoir condition was converted to the volume of gas at atmospheric condition (Pout = atmospheric pressure). Hence, the reaction time can be estimated by dividing the volume of gas at atmospheric condition by the outlet flow rate which is also measured at the atmospheric condition. As a result, the reaction time can be expressed by Eq. (2): 3

4 ∗ ug ∗ L2 ∗ (Pin3 − (Pin2 − b ∗ x ) 2 ) V t f = xo = 2 2 Qout 3 ∗ kair ∗ (Pin2 − Pout )

(2)

where t f is the reaction time when gas flows from the inlet to location x, s; Vxo is the gas volume from inlet to location x under Pout condition, cm3 ; 2 ∗ Qout ∗ Pout ∗ ug . and b equals to A ∗ k air Assuming nair mole of air is injected and the mole of consumed oxygen can be estimated by Eq. (3):

no2rea =

where the R, V and T are fixed values here, hence the mole of gas can be estimated according to the pressure. Then, by combining the oxygen concentration profile measured from GC and the total mole of gas inside the SBR, the mole of oxygen can be obtained. In this study, it was assumed that a constant reaction rate will be applied to the crude oil through the LTO stage, therefore, the oxygen reaction rate can be estimated by dividing the change of mole of oxygen by the time and oil mass as shown in Eq. (7).

2 ∗ ug ∗ vo2 ∗ ρoil ∗ sor ∗ nair ∗ R ∗ Tr ∗ L2 2 (1 − sor ) ∗ kair ∗ (Pin2 − Pout )

(3)

where no2rea is the mole of consumed oxygen, mole; vo2 is the oxygen reaction rate, mole/(hr*g); ρoil is the oil density, kg / m3 ; Sor is the residual oil saturation, fraction; R is the universal gas constant which equals to 8.314 J/(K*mol); nair is the mole of air, mole; and Tr is the reservoir temperature, K. After obtaining the mole of consumed oxygen, the oxygen concentration in the produced gas can be estimated by Eq. (4):

CO2 =

nO2 − no2rea ∗ 100 nair − no2rea

(6)

PV = nRT

v O2 =

ninitial − nfinal (7)

t ∗ moil

where vO2 is the oxygen reaction rate, mole/hr/gram(oil); ninitial is the initial mole of oxygen, mole; nfinal is the final mole of oxygen, mole; t is the reaction time, hour and moil is the oil weight, g. More details of the Table 1 Units used for Eq. (5).

(4)

where CO2 is the oxygen concentration in the produced gas, %; and nO2 is the mole of oxygen which equals to 0.21*nair , mole. After combined Eq. (3) with Eq. (4), the oxygen concentration in the produced gas can be obtained by Eq. (5). And the units applied for Eq. (5) can be found in Table 1. In Eq. (5), the oxygen reaction rate (vo2 ) can be obtained from the SBR test and other parameters can be obtained based on the reservoir properties and operation conditions. More details of the analytical method derivation can be found in the Appendix section. 3

Symbol

Unit

vo2 T Pin Pout ρoil

mole/g/hr K Pa Pa

kair L ug

g/cm3 Darcy m cp

Sor

fraction

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flooding. Since the highest oven temperature can only reach 120 °C, the air flooding tests were only applied under 100 °C and 120 °C to stay consistent with the SBR tests. In order to show the repeatability of the experimental work, the same shale core plug was used through the air flooding tests, and at each temperature, the air flooding was performed twice. Table 3 summarized all the performed air flooding tests. It is worth to mention that the gas flow rate is increased with the injection pressure. The length of the shale core sample is only 5.04 cm. If a high injection pressure is applied, the gas will flow through the core very quickly and the oxygen consumption cannot be measured due to less reaction time. Therefore, injection pressure of 1014.7 was selected for all the flooding experiments. Fig. 2. Schematic of the SBR experimental apparatus.

5. Results and discussion oxygen reaction rate calculation can be found in our previous work [22].

5.1. SBR test Table 4 shows the experimental conditions applied for the SBR tests under 100 °C, 120 °C and 140 °C, respectively. Also, the initial and final pressure and oxygen concentration for each SBR test were provided in Table 4. Fig. 6 shows the oxygen consumption profiles for the SBR tests, where the mole of oxygen is plotted vs. time*oil mass. In Fig. 6, a continuous decreasing trend of oxygen moles was observed with time. Also, it can be seen that different reservoir temperature will result in different oxygen reaction rate, where a higher temperature shows a faster oxygen consumption. In addition, stable oxygen reaction rates were observed for all three SBR tests, where the R square values are close to one after linear regression. According to Eq. (7), the oxygen reaction rate can be obtained as the slope of the curve in Fig. 6. The results were also summarized in Table 5, where the oxygen reaction rate at 100 °C, 120 °C and 140 °C are 1.27E-06 mol/hr/g, 2.01E-06 mol/ hr/g and 3.71E-06 mol/hr/g, respectively. The obtained oxygen reaction rate can be applied in the previously proposed analytical method to predict the produced oxygen concentration, and evaluate the AIP feasibility. A practical study will be presented in a latter section.

4.2. Air flooding test In addition, an air flooding tests were performed to validate the analytical method and also to directly investigate the AIP recovery efficiency to the shale core plugs. To validate the analytical method, the produced gas was collected after gas breakthrough and the oxygen concentration in the produced gas was measured by GC. Then the experimentally measured produced oxygen concentration was compared with the one which was estimated from the analytical method to validate the analytical method. The oil used in the air flooding test is the same as the ones used in the SBR test. The shale core plug used in the air flooding test was collected from the Eagle ford with 3.81 cm diameter as shown in Fig. 3. The length of the core plug is 5.04 cm. The porosity of the shale core plug is around 10.4% and the permeability for the shale core plug is around 400 nD. The detailed lithology and geochemical properties of the shale core can be found in Ref. [30]. The oil saturation setup is shown in Fig. 4. To saturate the core plug with oil, the shale core was firstly placed into the core container and then the core was vacuumed for 24 h under the room temperature of around 20 °C. Next, the crude oil was injected into the container through the accumulator till the container was fully filled. Then, the pressure will be increased and maintained at 2000 psi for 72 h. The saturation results are shown in Table 2, and it can be observed that the shale core was fully saturated with the crude oil. After the shale core was saturated with the crude oil, the air flooding test was conducted. The air flooding apparatus is shown in Fig. 5, where the air source was provided by the compressed gas cylinder. An accumulator and a core holder with maximum operating pressure of 10,000 psi were placed inside the oven. The confining pressure and the injection pressure were applied by the syringe pump (Model 100DX). The oil was displaced out due to the pressure difference between the injection end and the production end. A separator was used which locates at the outlet of the gas flooding apparatus, and a flow meter (SmartTrak 100) was placed behind the separator to measure the gas flow rate after breakthrough. The produced gas was finally collected by a gas collector which was located behind the gas flow meter. To perform the air flooding test, the saturated shale core was firstly placed into the core holder, and the gas was pumped from the cylinder to the accumulator till it reached the target pressure. Then the temperature was increased to the target temperature by controlling the oven heater and the whole system will be maintained at the target temperature for three to four hours to reach the thermal equilibrium. After applied the confining pressure, the gas was injected to the core. The produced gas was collected and measured by the GC to find the oxygen reaction rate in the air flooding test, and the recovery factor was estimated by measuring the shale core weight before and after the air

5.2. Air flooding test As mentioned previously, the air flooding tests were performed under 100 °C and 120 °C, respectively. During all the air flooding tests, the gas breakthrough occurred at around 50 min. After breakthrough, the air injection continued around 3 h till no more oil can be produced. Due to the limitation of the equipment, the heat generated from the oxidation reaction cannot be measured. Therefore, in this study, the oxygen consumption during the air flooding process is the main focus, and more experimental work need to be performed in order to

Fig. 3. Eagle ford core plug samples. 4

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Table 3 Experimental condition for air flooding test. Test

Temperature (°C)

Injection pressure (psi)

Outlet pressure (psi)

Confining pressure (psi)

Total injection time (hr)

No. 1 2 3 4

100 100 120 120

1014.7 1014.7 1014.7 1014.7

14.7 14.7 14.7 14.7

1614.7 1614.7 1614.7 1614.7

3 3 3 3

Table 4 Experimental conditions for SBR tests.

Fig. 4. Schematic of the oil saturation apparatus.

Temperature

Table 2 Shale core saturation results. Parameters

Value

Unit

cm3 g %

Bulk volume

57.51

Dry weight Porosity Oil density

126.63 10.40 0.83

Saturated weight @ 20 °C Saturated oil weight @ 20 °C Oil volume

131.52 4.89 5.89

Oil saturation

98.50

g/cm3 g g

(°C)

Initial pressure (psi)

Final pressure (psi)

Initial oxygen concentration (%)

Final oxygen concentration (%)

100 120 140

1114 1096 1196

1027 998 1063

21 21 21

17.85 13.75 5.51

it can be seen that the oxygen consumption was increased with the temperature increase, which is consistent with the SBR results. After obtaining the produced oxygen concentrations for the air flooding tests, the results were used to compare with the previously developed analytical model as shown in Eq. (5). The parameters of shale core air flooding tests under both 100 °C and 120 °C were applied in Eq. (5), respectively, where the oxygen reaction rate was obtained from the SBR test, the air viscosity was obtained from Engineering ToolBox [31] and the effective air permeability was estimated based on the Darcy’s law after gas breakthrough according to the average outlet gas rate. The detailed parameters used here are presented in Table 7. After applied the data listed in Table 7 in Eq. (5), the estimated produced oxygen concentration was compared with the experimentally obtained produced oxygen concentration, and the results are shown in Table 8. It can be seen that the errors between experimentally obtained produced oxygen concentrations and analytically obtained oxygen concentrations are very small, which proves the practicability of the proposed method.

cm3 %

investigate the heat generation process. The final recovery factor for air injection tests were obtained based on the shale core weight before and after air flooding, and the dry core weight. The recovery results are shown in Table 6, and the repeatability can be observed by comparing the tests which were performed at the same operation conditions, where the recovery factors are around 25.99% at 100 °C and 28.65% at 120 °C. It can also be observed that a 20 °C temperature difference does not show a significant effect on the recovery performance during the air injection process, where only around 2.5% recovery factor was increased which is around 0.12 g of extra oil because very small amount of oil was saturated in the shale core plug. After gas broke through, several produced gas samples were collected and the GC was utilized to measure the oxygen concentration in the produced gas. The results are shown in Fig. 7, and it can be observed that the oxygen concentration in the produced gas stays at the same level after gas breakthrough, where the oxygen concentration was around 18.9% under 100 °C and was around 17.7% under 120 °C. Also,

5.3. Feasibility of AIP in shale core regarding oxygen consumption As reviewed previously, the produced oxygen concentration needs to be reduced lower than 5% to avoid any potential explosion or fire hazardous at the production well for an AIP project. In this section, the

Fig. 5. Schematic of the core flooding apparatus. 5

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0.05

oxygen mole at 100 C y = -1.271E-06x + 4.135E-02 R² = 9.689E-01

Oxygen (mole)

0.04

oxygen mole at 120 C oxygen mole at 140 C

0.03 0.02

y = -2.009E-06x + 4.027E-02 R² = 9.875E-01

y = -3.712E-06x + 3.805E-02 R² = 9.750E-01

0.01 0 0

2500

5000

7500

10000

Reaction time * oil mass (hr*g) Fig. 6. Oxygen mole profiles for SBR tests.

The produced oxygen concentration of 5% was used as the restricted condition in the analytical method, and it was expressed in Eq. (8):

Table 5 Oxygen reaction rates for SBR tests. Temperature

Initial oxygen (mole)

Finial oxygen (mole)

Reaction time

(°C)

Mass of oil (g)

(hr)

Oxygen reaction rate (mole/hr/g oil)

100 120 140

58.1 58.1 58.1

0.040 0.038 0.038

0.030 0.023 0.009

138 129 134

1.27E − 06 2.01E − 06 3.71E − 06

0.21 − c ∗ CO2 = 1−c∗

Temperature (°C)

Dry core weight (g)

Oil saturated core weight (g)

Core weight after flooding (g)

Recovery factor (%)

No. 1 2 3 4

100 100 120 120

126.6301 126.6301 126.6301 126.6301

131.5124 131.5228 131.5298 131.5276

130.2487 130.2456 130.1312 130.1190

25.88 26.10 28.54 28.76

L2 (Pin2 − Pout 2)

(Pin

2

L2 > 3.55 ∗ 10−16 (m2 / Pa2) − Pout 2)

(9)

The pressure applied during the air flooding tests are used in Eq. (9), where it shows that in order to satisfy the oxygen consumption criterion, the length of the core needs to be longer than 0.132 m. On the other hand, when using the length of the core in Eq. (9) and the

21

Oxygen concentration (%)

(8)

where c = 4.53 ∗ 1012 ∗ vo2 ∗ (1 − S ) ∗ k . or air It can be seen that the variable c is determined based on the oxygen reaction rate and the reservoir properties. When using the experimental data of 100 °C air flooding test to find the value of c, the relation between L2 and pressure square difference can be found as shown in Eq. (9). It can be seen that a lower pressure difference or a longer gas passing length will favor the AIP feasibility regarding the oxygen consumption. This makes sense since both of these two cases will increase the oxygen reaction time during the AIP, as a result, the produced oxygen concentration will be decreased.

previously proposed analytical method was applied to study the screening criteria for the shale core AIP test feasibility regarding the oxygen consumption.

20

∗ 100 < 5 Sor ∗ Tr ∗ ρoil ∗ug

Table 6 -Experimental results for air flooding tests. Test

L2 (Pin2 − Pout 2)

test 1_100 C test 2_100 C test 3_120 C test 4_120 C

18.99% @ 100 C

19 17.74% @ 120 C

18 17

Breakthrough time

16 0

0.5

1

1.5

2

Time (hrs) Fig. 7. Oxygen concentration profiles for air flooding tests. 6

2.5

3

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Table 7 Air flooding tests data used for analytical method. Test No.

vo2 (mole/g/hr)

T (K)

Pin (Pa)

Pout (Pa)

ρoil (g/cm3 )

kair (Darcy)

L (m)

ug (cp)

Sor (fraction)

1 2 3 4

1.27E − 06 1.27E − 06 2.01E − 06 2.01E − 06

373.15 373.15 393.15 393.15

6996110.23 6996110.23 6996110.23 6996110.23

101352.93 101352.93 101352.93 101352.93

0.83 0.83 0.83 0.83

2.30E − 07 2.30E − 07 2.30E − 07 2.30E − 07

5.04E − 02 5.04E − 02 5.04E − 02 5.04E − 02

2.16E − 02 2.16E − 02 2.24E − 02 2.24E − 02

0.74 0.74 0.71 0.71

• An analytical model was proposed to estimate the produced oxygen

Table 8 Oxygen concentration from analytical method and experiments. Test

Oxygen concentration from experiments (%)

Error

No.

Oxygen concentration from analytical method (%)

1 2 3 4

19.01 19.01 17.98 17.98

18.97 19.00 17.86 17.62

0.21 0.05 0.67 2.04



(%)

concentration of an AIP, and the produced oxygen concentration of 5% was used as the restricted condition for determining the AIP feasibility. The shale core air flooding tests were performed and the analytical method was validated by the experimental data. By applying the analytical method, the results show that for this experimental study, in order to meet the oxygen consumption criteria, a longer than 0.132 m core or a lower than 2.68E + 06 Pa (388.70 psi) injection pressure with atmospheric production pressure need to be applied.

production pressure of atmospheric pressure, the maximum injection pressure that can be applied in the test can be estimated, which equals to 2.68E + 06 Pa (388.70 psi). The utilizations of this analytical method could be much more, based on the research interests. Although this analytical method was built based on some simplified assumptions, it can still be used as an effective screening method when designing an AIP project. Also, further modifications can be added to this analytical model to increase its applicability.

SI Metric Conversion Factors

6. Conclusions

Declaration of Competing Interest

°API

141.5/(131.5+°API )

atm cp Darcy

× 1.01325∗ × 1.0∗ × 9.869233∗ K − 273.15 × 6.894757∗

K psi

= E + 02 E-03 E-13

= = =

E + 00

= =

g/cm3 kPa Pa∙s m2 °C kPa

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Based on this study, the following conclusions are drawn.

• The oxygen reaction rate can be obtained from the SBR test, and a

constant oxygen reaction rate was observed at a specific reservoir temperature, where a higher temperature shows a faster oxygen consumption. The oxygen reaction rate for this tested crude oil at 100 °C, 120 °C and 140 °C are 1.27E-06 mol/hr/g, 2.01E-06 mol/hr/ g and 3.71E-06 mol/hr/g, respectively.

Acknowledgment This work is supported by the Science & Technology Department of Sichuan Province under Award No. 2018FZ0070.

Appendix

• Pressure Distribution from Inlet to Outlet Assume the pressure at location x is Px , according to the Boyle’s law, (A-1)

Qx ∗ Px = Qout ∗ Pout

where Qx is the flow rate at location x; Px is the pressure at location x; Qout is the flow rate at outlet pressure condition; and Pout is the outlet pressure. Based on the Darcy’s law,

kair = −

Q x ∗ ug A



Qout ∗ Pout ∗ ug dx dx =− ∗ dPx A Px dPx

(A-2)

The integration of (A-2) from Pin to Px will yield Eq. (A-3),

∫P

Px

in

kair ∗ Px ∗ dPx = −

∫0

x

Qout ∗ Pout ∗ ug A

dx

(A-3)

Hence, the pressure at location x can be obtained by Eq. (A-4),

Px =

Pin2 −

2Qout ∗ Pout ∗ ug A ∗ kair

∗x

(A-4)

In Eq. (A-4), when x equals to L, Qout can be obtained by:

Qout =

2 A ∗ kair ∗ (Pin2 − Pout ) 2 ∗ Pout ∗ ug ∗ L

(A-5)

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• Reaction Time for Gas Flowing from Inlet to Location x The reaction time equals to the gas flow time, which can be estimated by dividing the volume of gas at atmospheric condition by the outlet flow rate measured at the atmospheric condition. According to Boyle’s law, (A-6)

Px ∗ dVx = Pout ∗ dVxo

where dVx is the gas volume at x under pressure of Px , which can be expressed by dVx = A ∗ dx After substituted Px with (A-4), the integration on both sides of Eq. (A-6) will yield Eq. (A-7),

∫0

Vxo

dVxo =

∫0

Vx

2Qout ∗ Pout ∗ ug

Assume b =

∫0

Vxo

dVxo =

Px dVx = Pout A ∗ k air

A Pout

∫0

x

∫0

x

A ∗ Px A dx = Pout Pout

∫0

x

Pin2 −

2Qout ∗ Pout ∗ ug

∗ x dx

A ∗ kair

(A-7)

, A-6 can be expressed by Eq. (A-8)

Pin2 − b ∗ x dx

(A-8)

Vxo can be expressed by Eq. (A-9), Vxo =

A Pout

∫0

x

Pin2 − b ∗ x dx = −

1 A ∗ b Pout

∫0

x

1

(Pin2 −b ∗ x ) 2 d (Pin2 −b ∗ x )=

2∗A 3 ((Pin3 − (Pin2 − b ∗ x ) 2 ) 3 ∗ b ∗ Pout

(A-9)

Then, the reaction time, t f , can be estimated by Eq. (A-10), 2∗A 3 ∗ b ∗ Pout

V t f = xo = Qout

3

((Pin3 − (Pin2 − b ∗ x ) 2 ) Qout

3

=

4 ∗ ug ∗ L2 ∗ (Pin3 − (Pin2 − b ∗ x ) 2 ) 3 ∗ kair ∗

(Pin2



2 2 Pout )

(A-10)

• Moles of Consumed Oxygen in AIP Assume nair moles of air are injected, the volume of oil which reacts with the air under pressure Px can be expressed by Eq. (A-11),

Voil =

Sor Sor n ∗ R ∗ Tr Vair = ∗ 1 − Sor 1 − Sor Px

(A-11)

The moles of consumed oxygen can be estimated by Eq. (A-12),

dno2rea = vo2 ∗ ρoil ∗ Voil ∗ dt f = vo2 ∗ ρoil ∗ Assume m = vo2 ∗ ρoil ∗

Sor 1 − Sor

Sor n ∗ R ∗ Tr ∗ air ∗ dt f 1 − Sor Px

(A-12)

∗ nair ∗ R ∗ Tr , based on Eq. A-4 and Eq. A-10, the integration of Eq. (A-12) will yield Eq. (A-13), 3

∫0

no2rea

dno2rea =

∫0

tf

m dt f = Px

∫0

m

L

Pin2 − b ∗ x

d

4 ∗ ug ∗ L2 ∗ (Pin3 − (Pin2 − b ∗ x ) 2 ) 2 2 3 ∗ kair ∗ (Pin2 − Pout )

(A-13)

Then, the moles of consumed oxygen no2rea can be calculated by Eq. (A-14),

no2rea =

4 ∗ m ∗ ug ∗ L2 2 2 3 ∗ kair ∗ (Pin2 − Pout ) 1

∫0

L

1

(

3

)

(Pin2 − b ∗ x )− 2 d Pin3 − (Pin2 − b ∗ x ) 2 =

∗ (Pin2 − b ∗ x ) 2 d (Pin2 −b ∗ x )=

2 ∗ m ∗ ug ∗ L2 kair ∗

(Pin2



2 2 Pout )

∗b∗L=

4 ∗ m ∗ ug ∗ L2

1 3 (Pin2 − b ∗ x )− 2 ∗ ⎛− ⎞ ⎝ 2⎠ ∗ R ∗ Tr ∗ ug ∗ L2

2 2 3 ∗ kair ∗ (Pin2 − Pout )

2 ∗ vo2 ∗ ρoil ∗ Sor ∗ nair

∫0

L

2 kair ∗ (Pin2 − Pout ) ∗ (1 − Sor )

(A-14)

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