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Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation
Journal of Natural Gas Science and Engineering xxx (2016) 1e9
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Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation Wei Tian a, *, Xingru Wu a, Tong Shen a, Sumeer Kalra b a b
Mewbourne School of Petroleum & Geological Engineering, University of Oklahoma, SEC 1362, 100 E Boyd, Norman, OK, USA Warwick Energy Group, 900 W Wilshire Blvd, Oklahoma City, OK, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 January 2016 Received in revised form 12 May 2016 Accepted 8 June 2016 Available online xxx
Hydraulic fracture geometry is of the interest in optimizing stimulation treatment and forecasting production potential. Current diagnostic tools such as tiltmeter and microseismic are insufficient in evaluating fracture geometry. Knowing that gas from the shale reservoir has a much higher mobility than fracking fluid, partitioning chemical tracer is employed so that tracer data can be obtained earlier and more complete. The proposed approach is examined by synthetic numerical simulations. On the semi-log plot, tracer production declined tail clearly divides into two straight-line segments. Applying the moment of methods to the entire tracer production data gives the total volume of hydraulic fracture and the invaded matrix swept by the tracer due to leak-off. Additionally, extrapolating the first segment of tracer decline tail using the exponential law yields a volume that is close to the actual hydraulic fracture volume, especially when fracture permeability is several orders larger than matrix permeability. © 2016 Elsevier B.V. All rights reserved.
Keywords: Partitioning chemical tracer Fracture diagnosis Method of moments Shale gas
1. Introduction Hydraulic fracturing has been applied in shale gas development to increase the contact area with matrix and create permeable conduits for fluid flow. Knowledge of hydraulic fracture volume is essential in determining the stimulation treatment efficiency. However, the fracture volume diagnosis is very challenging because of the complexities of rock properties and fracturing process. Davis (2009) summarized capabilities and limitations of numerous fracture diagnostic technologies, including tiltmeters, microseismic mapping and radioactive tracers. Among them, only surface tilt mapping is able to determine the hydraulic fracture volume, while its resolution decreases with depth. Chemical tracer is a powerful technology for reservoir characterization (Tomich et al., 1973; Sheely Jr and Baldwin Jr, 1982; Abbaszadeh-Dehghani and Brigham, 1984; Allison et al., 1991). In recent years, its application has been extended in hydraulic fracturing to evaluate the contribution of each fracture stage to the total hydrocarbon production in a multi-stage horizontal well (Goswick and LaRue, 2014; King and Leonard, 2011; Catlett et al., 2013). Chemical tracer can also help understand interwell communication
* Corresponding author. E-mail address: [email protected] (W. Tian).
for fractured wells (Crawford et al., 2014). Chemical tracer is rarely used to estimate fracture volume. Gardien et al. (1996) revealed that the tracer response was sensitive to an influence ratio, which was the combination of fracture half length, fracture height, formation porosity and injected volume. They noticed that tracer response in fractured reservoir was quite different with a homogeneous reservoir, indicating the possibility of hydraulic fracture diagnosis using the chemical tracer. Nevertheless, it was impossible to determine the fracture volume directly from their work because fracture width was not included in the ratio. Leong et al. (2015) utilized the conservative deuterium tracer to detect the fracture volume based on tracer residence time in a well pair setting. Their target fracture did not have two-phase flow. They also neglected the tracer swept volume in matrix due to leakoff, which could lead to an overestimation of fracture volume eventually. Elahi and Jafarpour (2015) proposed to analyze tracer test data for fracture volume using ensemble Kalman filter. However, this approach is difficult to employ because it required tremendous fracture and matrix information for the data assimilation. As seen from above discussion, none of the work could estimate fracture volume under the condition of multi-phase flow and leak-off. In this paper, we propose to evaluate fracture volume in shale gas formation using partitioning chemical tracer. The impact of matrix as well as dispersion on tracer production data will be
http://dx.doi.org/10.1016/j.jngse.2016.06.018 1875-5100/© 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Nomenclature
Normal a b B C D K k L h t
coefficient coefficient formation volume factor, fraction chemical tracer concentration, mole fraction dispersion coefficient, L2/T partition coefficient, fraction permeability, L2 length, L height, L time, T
analyzed, which has never been investigated in previous work. Method of moments (MoM) is applied to compute the swept volume and the tracer production in both phases, vapor and liquid, is accounted for correspondingly. This approach is simple to use without asking for detailed reservoir information. Synthetic numerical simulation is utilized to validate the proposed method. 2. Methodology 2.1. Motivation of using partitioning chemical tracer For many shale gas formations, more than 60% of fracking fluid is not produced back in the early production stage according to the field observations (Crafton, 2008). Therefore, for the fracking fluid soluble tracers (conservative tracers), their production history would be either too limited, which may lead to incorrect estimations of fracture volume, or the tracer information is too late to yield useful information. Another type of conservative tracer is gas soluble tracers. Given that gas from the shale reservoir has a much higher mobility than the fracking fluid and some reservoirs may even have immediate gas production right after completion (Asadi et al., 2008), we can anticipate these tracers may quickly flow back. However, gas soluble tracers fail to provide sufficient information about the fracking fluid inside the hydraulic fracture, and consequently we cannot evaluate the exact fracture volume. Upon previous discussions, we propose to use partitioning chemical tracer, which is soluble in both gas and fracking fluid. The partitioning chemical tracer partitions between gas and fracking fluid. The phase preference of such tracer is described by its partition coefficient, K, which is defined as the ratio of tracer mole fraction in gas to its mole fraction in fracking fluid (Eq. (1)). Partitioning chemical tracer production data will reflect information of both phases that it could sense during the test. In addition, it can flow back with gas, suggesting the potential of early interpretation of fracture volume.
K¼
Cg Cw
(1) eq
V w 4
swept volume, L3 width, L porosity, fraction
Subscript BHP e eq g i m swept w
bottom-hole pressure end point equilibrium gas component i matrix swept volume water
as (Oyerinde, 2005):
Z
∞
Vi Ci dVi
Vi;swept ¼ Z0
(2)
∞ 0
Ci dVi
Gas and fracking fluid could exist in the hydraulic fracture at the same time. Since partitioning chemical tracer also exists in both phases, its swept volumes in both gas and fracking fluid should be taken into account in order to get the total swept volume in hydraulic fracture. Because the produced volume is measured at surface condition, the formation volume factor (FVF) at producing bottom-hole pressure (BHP) is needed to convert volume from surface to subsurface condition (Eq. (3)).
Vswept ¼ Bg;BHP Vg;swept þ Bw; BHP Vw;swept
(3)
2.3. Exponential decline Since the measurement of tracer concentration history is often limited in time, we assume that the tracer concentration declines exponentially with time if the tracer is injected as a slug. In other words, it is possible to obtain the full tracer interpretation earlier by extrapolating the tracer production data when the exponential decline trend occurs (Fig. 1). Mathematically, the tracer exponential decline tail is expressed by (Sharma et al., 2014):
CðVÞ ¼ beaV for V > Ve
(4)
The tracer behavior in a fractured reservoir is different from that in a homogeneous reservoir (Gardien et al., 1996). By plotting the tracer tail in a semi-log plot, we would observe two distinct linear relationships, which help to distinguish the tracer swept volume in matrix and fracture respectively. We will illustrate how to analyze the tracer tail in a hydraulically fractured shale reservoir in the later sections.
3. Model description 2.2. Swept volume calculation MoM has been widely used to interpret tracer production data. The first moment gives the tracer swept volume. For the tracer production data within phase i, i.e. produced tracer concentration versus cumulative produced volume, the first moment is calculated
To validate the proposed approach, synthetic models are created. This section provides all the critical information and parameters to develop a prototype of hydraulically fractured shale gas reservoir. Adsorption and capillary pressure effects are neglected in the simulations.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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Table 1 Dimensions of model with matrix. Parameter
Value
Unit
Number of reservoir girds Formation length, y direction Formation height, z direction Formation width, x direction
(24,50,1) 300 30 449
(x,y,z) ft ft ft
properties are listed in Table 2 and will be applied to all the simulations. 3.3. Rock and fluid properties
Fig. 1. Tracer production data at later time on a semi-log plot is a straight line. This is known as the tracer exponential decline tail.
3.1. Domain construction We construct two different domains. The first one only includes the hydraulic fracture, which is used to investigate the fracture volume estimation without leak-off. The second model has the fracture as well as adjacent matrix to consider leak-off impact. Although we have different domains, the input properties of fracture, rock, fluid and well are the same for both models. 3.1.1. Hydraulic fracture only In this scenario, we consider half of the hydraulic fracture using a 1D model with 300 grids. Each grid has the dimension of 1 ft in length, 0.1 ft in width and 30 ft in height. The horizontal well perforated at the left side of the fracture as shown in Fig. 2. 3.1.2. Hydraulic fracture with matrix Half of the hydraulic fracture and a quarter of its adjacent matrix are simulated here. There are 24 grids in x direction and 50 grids in y direction. The domain dimensions are listed in Table 1. The hydraulic fracture is located at the right side, where x coordinate is 24 parallel with y-axis. Local grid refinement is implemented near the hydraulic fracture (Sun and Schechter, 2015). The fracture height is assumed identical with reservoir thickness of 30 ft. The horizontal well locates at the upper side of the domain parallel with x-axis and it only perforates at the fracture (Fig. 3).
Initial pressure inside hydraulic fracture and matrix is 4925 psi. Matrix permeability is 50 nd. There are two phases, i.e. vapor phase and liquid phase, in the system initially. The liquid phase represents initial reservoir water and the injected fracking fluid. The vapor phase represents the shale gas. The initial water saturation is 0.3 in both hydraulic fracture and matrix. The gas and water FVF at 500 psi are 0.037 and 1.0 respectively. The partition coefficient of tracer is constant as 25.6. In simulations, local equilibrium is assumed. In other words, the tracer distribution between phases reaches immediate equilibrium governed by Eq. (1) (CMG-STARS user’s guide, 2012). The tracer dispersion coefficient is assumed 0. The detailed rock and fluid properties are summarized in Table 3. To accomplish the model description, the relative permeability curve is shown as the dashed line in Fig. 4. The input values for matrix permeability and dispersion coefficient described here are set as the base case. In the following sections, these two parameters will be varied one by one to examine their influence on tracer production data. 3.4. Well plan For all simulations, well schedule has four consecutive steps: 1) slug injection of partitioning tracer with the fracking fluid; 2) injection of fracking fluid without the partitioning tracer, displacing the tracer farther into the fracture; 3) shut in the well for a short time interval (water soaking) as the well is not initiated back to produce right after the treatment (Haddad et al., 2015); 4) open the well and start to produce (Fig. 5). The first two steps are designed to simulate the hydraulic fracturing process. For injection, the well is constrained by the maximum BHP of 15,000 psi and maximum injection rate of 2000 bbl/day. The production minimum BHP is 500 psi. Table 4 shows the details of the well constraints. 4. Result and discussion
3.2. Hydraulic fracture properties 4.1. Hydraulic fracture volume estimation The fracture half-length is 300 ft and fracture height is 30 ft. Fracture flowing capacity is controlled by conductivity, which is assumed constant as 10 md-ft. In our model, the fracture width is 0.1 ft. Fracture permeability is therefore 100 md. The fracture
Fig. 6 is the result of tracer production data in vapor phase on a semi-log plot. The tracer tail section, the red section in graph, could be well fitted by an exponential decline function as shown in the
Fig. 2. Illustration of hydraulic fracture configuration. Each grid is 1 ft long. There are 300 grids and the well perforates at one end.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Fig. 3. Synthetic model configuration with hydraulic fracture and matrix. The hydraulic fraction is on the right side with red color. The horizontal well perforates in the upper right grid. The matrix is in the blue color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Generic hydraulic fracture properties. Parameter
Value
Unit
Fracture Fracture Fracture Fracture Fracture Fracture
300 30 0.1 100 0.05 0.3
ft ft ft md fraction fraction
half length height width permeability porosity initial saturation
Table 3 Rock and fluid properties. Parameter
Value
Unit
Reservoir Initial Pressure Matrix Porosity Matrix Permeability Matrix Initial Water Saturation Water FVF at 500 psi Gas FVF at 500 psi Water Viscosity Gas Viscosity Tracer Partition Coefficient Tracer Dispersion Coefficient
4925 0.05 50 0.3 1.0 0.037 0.3 0.02 25.6 0
psi fraction nd fraction rbbl/stb rsf/scf cp cp fraction ft2/day
Fig. 6. Applying Eq. (2), we can get tracer swept volume in gas at surface condition is 199 ft3 and swept volume in water is 4.7 ft3. Then, the total swept pore volume at subsurface through Eq. (3) is 12.02 ft3. Fig. 7 is the tracer distribution profile at the end of shut in period, obtained from numerical simulation output directly. The horizontal axis is the distance from the wellbore. It shows that the injected tracer has been pushed to the location of 95 ft away from the wellbore and the total contacted pore volume, if calculated based on Fig. 7, is Lwh4 ¼ 95 0:1 30 0:05 ¼ 14:25ft3 . This value is in a good agreement with the previous swept volume obtained from tracer production data. Although the hydraulic fracture is 300 ft, the tracer only flows
95 ft from wellbore because of the pressure increase in the system. Above result verifies that MoM is capable in estimating such volume swept by the tracer. In other words, tracer production data could directly tell where the tracer goes during the injection process. Therefore, we recommend injecting a slug of tracer with fracking fluid at the beginning of stimulation treatment at each stage. The fracking fluid at later fracturing steps could displace tracer farther into the induced fracture so that the tracer flowback data is informative to the entire fracture volume. In practical gas production from shale formations, multiple stages of hydraulic fractures are created in order to maximize the productivity of the well and reduce the number of wells needed for the field development. When the well is flowing back after the treatment, the tracer response curve will be the superposition of tracer responses from individual stage of the fractures if only one tracer is used in all stages. Therefore, we can get the entire fracture volume of all stages from tracer production data using MoM.
4.2. Impact of leak-off The previous case just simulates one single hydraulic fracture without matrix. However, in reality, the pressure inside fracture will increase significantly during the fracturing process and it becomes higher than the matrix pressure. As a result, the fracking fluid will leak-off into the matrix (Warpinski et al., 1998). The penetration distance of fracturing fluid into the matrix is relevant with matrix permeability. For high permeable reservoir, the injected fluid could penetrate deeper and vice versa (Chitrala et al., 2011). Such leak-off would complicate the tracer diagnosis. This section addresses the impact of matrix when using partitioning tracer to detect fracture volume. With larger matrix permeability, the partitioning chemical tracer may invade deeper into the formation. To investigate the leak-off impact, matrix permeability varies from 5 nd to 500 nd. The rest input parameters are kept the same with the previous description. The solid lines in Fig. 8 are simulation output of tracer production in gas in a semi-log plot. Its production in water has the similar
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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1.0
Relative Permeability
0.8
0.6 Krw in Fracture Krg in Fracture Krw in Matrix Krg in Matrix
0.4
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Saturation Fig. 4. Relative permeability curves in matrix and hydraulic fracture (modified from Cheng (2012)).
0.14 Partitioning Tracer in Water Partitioning Tracer in Gas
Tracer Mole Fraction
0.12 0.10 0.08 0.06 0.04 0.02
Fig. 5. The four steps of well plan. 0.00 0
20
40
60
80
100
120
140
Distance from Injector, ft
Table 4 Well constraints. Well controls
Value
Unit
Injection Maximum Bottom Hole Pressure Injection Maximum Rate Production Minimum Bottom Hole Pressure
15,000 2000 500
psi bbl/day psi
Fig. 7. Tracer distribution profile inside fracture at the end of shut in, obtained from numerical simulation output directly.
Fig. 8. Partitioning tracer production data in gas. Solid lines are simulation output. The dashed lines are the extrapolation based on the first linear section. Fig. 6. Tracer concentration vs. cumulative gas production. The dashed line is the best fitted line. Its R-square is 0.99, indicating the tracer tail is almost a straight line.
shape. Based on the direct output from simulation, the total swept volume for each case is listed in the third row in Table 5 using MoM. Figs. 9e11 shows the tracer distribution profile at the end of shut in
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Table 5 Comparison of swept volume with different matrix permeability. 5 180 137 39 134
50 300 275 43.5 232
500 635 570 45 571
(Note: ‘Total Swept Volume’ is calculated using MoM from the original tracer production data (the solid line in Fig. 8); ‘Total Contacted Volume’ is the total pore volume contacted by the tracer at end of shut in, including matrix; ‘Contacted Fracture Volume’ is the fracture volume contacted by the tracer at end of shut in, not including matrix; ‘Corrected Swept Volume’ is calculated using MoM based on the extrapolated tracer production history (the dashed line in Fig. 8).
0.06
0.04
0.02
0
0.08
0.04
0.02
0.00 50
100
150
200
250
300
Distance in Y Direction, ft Fig. 9. The tracer distribution profile inside domain at the end of shut in. km ¼ 5 nd. Obtained from simulation output directly.
0.12 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.10
0.08
0.06
0.04
0.02
0.00 0
50
100
150
200
250
100
150
200
250
300
Fig. 11. The tracer distribution profile inside domain at the end of shut in. km ¼ 500 nd. Obtained from simulation output directly.
0.06
0
50
Distance in Y Direction, ft
x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19
0.10
Tracer Mole Fraction
0.08
0.00
0.12
Tracer Mole Fraction
x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.10
Tracer Mole Fraction
Matrix Permeability, nd Total Swept Volume, ft3 Total Contacted Volume, ft3 Contacted Fracture Volume, ft3 Corrected Swept Volume, ft3
0.12
300
Distance in Y Direction, ft Fig. 10. The tracer distribution profile inside domain at the end of shut in. km ¼ 50 nd. Obtained from simulation output directly.
period, obtained from numerical simulation output. They are depicted on cross-sections in y direction. The decrease of x number indicates the deeper location into the matrix away from hydraulic fracture. We use these graphs to compute the tracer contacted volume in hydraulic fracture and in entire system respectively (Table 5). In Figs. 9e11, columns of x ¼ 24 indicate the hydraulic fracture. The results in Table 5 show that the tracer original production data provides the total swept volume rather than the hydraulic fracture volume. This is because the injected fracking fluid
penetrates into the matrix and the fluid flow from matrix will contribute to the final tracer production besides fluid in hydraulic fracture. In addition, higher matrix permeability results in larger total tracer swept volume, implying larger leak-off of the fracking fluid. Figs. 9e11 shows that tracer penetrates deeper into the formation, which is a proof of this statement. Such observations suggest that the tracer production data can help estimate the leakoff volume if hydraulic fracture volume is known. Examining the tracer tail in Fig. 8, we notice two distinct linear relationships of tracer concentration versus cumulative gas production at a later time. This is also observed in water production. For the convenience of discussion, we name the intersection of the two linear lines as the deviation point. We extrapolate the first linear section for both gas and water using the exponential decline rule (Eq. (4)). The dashed line declines more rapidly after the deviation point compared against the original plot (Fig. 8). We recalculate the swept volume based on the extrapolated curve and the results are displayed in the last row of Table 5. The swept volume obtained from the extrapolated line is closer to hydraulic fracture volume when matrix permeability decreases. This is because less matrix fluid flow contributes to the tracer production at early stage. Since the fracture permeability is much higher than the matrix, the fluid inside hydraulic fracture will come back to the wellbore much faster than the matrix. On the other hand, if matrix permeability increases, more matrix fluid with tracer is produced right after production starts and the deviation point is postponed in the regard of gas production as well. This will result in a larger difference between the contacted hydraulic fracture volume and the corrected swept volume. Therefore, the partitioning chemical tracer could provide a reliable estimation of fracture volume when the fracture permeability is several orders higher than the adjacent matrix permeability. Another advantage of using partitioning chemical tracer for fracture diagnosis is rapid feedback. Once the linear relationship occurs, we can simply use the exponential decline rule to extrapolate the tracer production data without actually measuring the tracer concentration for a long time. According to our simulations, even though only 1/3 of injected fracking is produced back after 1year production, the first linear section can be observed within 1 day of flowback or even less. The deviation point occurs within 3 days of production, indicating the second linear relationship can also be observed very quickly. Such rapid response of tracer is because of its partitioning feature.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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4.3. Impact of dispersion Gardien et al. (1996) had noticed that the tracer flow is dispersion dominated. Therefore, this section will investigate the impact of dispersion on tracer production data and estimation of hydraulic fracture volume estimation. We use three isotropic dispersion coefficients, assigned as total dispersion coefficient in simulations, to the partitioning chemical tracer to study dispersion effect. Their values are 0 ft2/day, 0.002 ft2/day and 0.2 ft2/day, respectively. These values are in the range of published data (Kausik et al., 2011; Sharma et al., 2015).
4.3.2. Hydraulic fracture with matrix Now, we investigate dispersion impact when matrix exists. The model input values are kept the same as the base case discussed in ‘Model Description’ section except the tracer dispersion coefficient, which ranges from 0 ft2/day to 0.2 ft2/day. Fig. 13 shows the original tracer production data and their extrapolated tracer decline tail based on first straight section. Figs. 14 and 15 are tracer distribution profiles at the end of shut in for cases with non-zero dispersion coefficient. The tracer distribution profile with 0 dispersion coefficient is identical with Fig. 10. Table 7 illustrates the swept volume comparison. The meaning of each term is the same with Table 5. The dispersion impact on tracer production data and distribution is more significant with matrix leak-off. From Fig. 13, we notice that tracer production peak arrives earlier in respect of cumulative produced volume with larger dispersion coefficient. Figs. 14 and 15 illustrates that dispersion makes the tracer penetrate much deeper into the matrix rather than flow farther inside hydraulic fracture. As Table 6 Comparison of swept volume inside hydraulic fracture only with different dispersion coefficient. Dispersion Coefficient, ft2/day Total Swept Volume, ft3 Contacted Fracture Volume, ft3
0 14.25 12.02
0.002 14.25 12.03
0.2 15.75 12.89
Chemical Tracer Mole Fraction
Fig. 12. Tracer distribution profile inside hydraulic fracture with three different dispersion coefficient at the end of shut in. It is obtained from numerical simulation output directly.
2 D=0 ft /day, Extrapolated 2 D=0 ft /day, Original 2 D=0.002 ft /day, Extrapolated 2 D=0.002 ft /day, Original 2 D=0.2 ft /day, Extrapolated 2 D=0.2 ft /day, Original
0.1
0.01
0.001
0.0001 10000
20000
30000
40000
50000
Cumulative Gas Production, ft3 Fig. 13. Partitioning tracer production data in gas. Solid lines are simulation output. The dashed lines are the extrapolation based on the first linear section.
0.010 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.008
Tracer Mole Fraction
4.3.1. Hydraulic fracture without matrix First, we consider the dispersion impact inside hydraulic fracture only, without any leak-off into the matrix. Hence, the model shown in Fig. 2 is applied. Input parameters other than dispersion coefficient are kept the same. The tracer production data of each case is similar with Fig. 6. Fig. 12 shows the tracer distribution profiles of three cases at the end of shut in. In Table 6, the ‘total swept volume’ is calculated from the tracer production data using MoM and the ‘contacted fracture volume’ is obtained based on the tracer distribution profile in Fig. 12. We can see from Fig. 12 that the tracer distribution profile of 0.002 ft2/day is overlapped with the case of 0 ft2/day, indicating that the dispersion effect is negligible when the dispersion coefficient is small enough. Results in Table 6 also point out that, when the dispersion coefficient is small, the swept volume calculated from tracer production data is close to the case without dispersion effect. In addition, Fig. 12 shows that tracer front becomes more slanted along with the increase of tracer dispersion coefficient. In other words, tracer could reach farther inside the fracture with larger dispersion coefficient. Tracer swept volume calculated from its production data also gets larger correspondingly. The main observation from Table 6 is that the tracer production data could provide accurate estimation of fracture volume through MoM even though tracer dispersion has impact on the total swept volume. Therefore, the proposed approach is sufficient to capture the fracture volume from tracer test with dispersion effect as long as there is no leak-off into matrix.
0.006
0.004
0.002
0.000 0
50
100
150
200
250
300
Distance in Y Direction, ft Fig. 14. The tracer distribution profile inside domain at the end of shut in. D ¼ 0.002 ft2/day. Obtained from simulation output directly.
a result, the contacted volume obtained from tracer distribution profile is getting larger as well (Table 7). However, due to the dispersion, the MoM fails to inform the correct total contacted
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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exponential decline can estimate fracture volume. Its accuracy is influenced by matrix permeability. 4. Partitioning tracer has rapid feedback even though the injected fracking fluid is trapped in the system. The tracer test is therefore time-efficient. 5. Dispersion is not favorable in tracer test to evaluate fracture volume. Dispersion impact on tracer production is significant and it will result in an inaccurate estimation of swept volume when leak-off occurs. Without leak-off, MoM could tell the correct fracture volume despite the dispersion.
0.010 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
Tracer Mole Fraction
0.008
0.006
0.004
0.002
Acknowledgement
0.000 0
50
100
150
200
250
300
Distance in Y Direction, ft Fig. 15. The tracer distribution profile inside domain at the end of shut in. D ¼ 0.2 ft2/ day. Obtained from simulation output directly.
Table 7 Comparison of swept volume with different dispersion coefficient. Dispersion coefficient, ft2/day Total swept volume, ft3 Total contacted volume, ft3 Contacted fracture volume, ft3 Corrected swept volume, ft3
0 300 275 43.5 232
0.002 2055 682 37 236
0.2 9530 892 8 97
volume from tracer production data. The estimated volume from tracer production data is much larger than the actual contacted volume. Furthermore, even though the two straight lines are still observed, it is impossible to extract fracture volume from the extrapolated first straight section. According to above discussion, we conclude that the tracer test should be less dispersion influenced. The tracer dispersion needs to be controlled at low level to ensure reliable analysis when matrix leak-off occurs. In field practices, we could consider to inject partitioning chemical tracer at the proppant stage to reduce tracer leak-off and dispersion influence. 5. Conclusion This paper introduces an approach to estimate fracture volume by injecting a pulse of aqueous solution containing a partitioning tracer into a shale gas reservoir. The tracer will continuously partition into and out of the liquid phase. The tracer in solution will penetrate into the rock matrix formation and some of them will be in the fracture. When the well is flowing back, the injected tracers are sampled, and then the tracer test can be analyzed for fracturing information. We employed the numerical simulation to validate the use of MoM in estimating fracture volume and the impacts of fracking fluid leak-off into the matrix and tracer dispersion. Adsorption and capillary pressure will be investigated in the future. Several following conclusions are made: 1. MoM is capable to determine the swept volume of partitioning tracer under two-mobile-phase condition. The partitioning tracer is therefore recommended to inject as a slug at the beginning of stimulation treatment at each stage, so that it can inform the entire fracture volume. 2. The tracer production data is indicative of the total volume of fracture and leak-off. 3. Two linear relationships of tracer tail are observed when matrix leak-off exists. Extrapolating the first straight section using
The authors kindly appreciate the Computer Modeling Group Ltd., for providing the simulation software CMG STARS and the support from the University of Oklahoma. References Abbaszadeh-Dehghani, M., Brigham, W.E., 1984. Analysis of well-to-well tracer flow to determine reservoir layering. J. Petrol. Technol. 36 (10), 1e753. http:// dx.doi.org/10.2118/10760-PA. Allison, S.B., Pope, G.A., Sepehrnoori, K., 1991. Analysis of field tracers for reservoir description. J. Petrol. Sci. Eng. 5 (2), 173e186. http://dx.doi.org/10.1016/09204105(91)90066-V. Asadi, M., Woodroof, R.A., Dumas, J.D., 2008. Post-frac analysis based on flowback results using chemical frac-tracers. In: Presented at the InInternational Petroleum Technology Conference. Kuala Lumpur, Malaysia, 3e5 December. http:// dx.doi.org/10.2523/IPTC-11891-MS. Catlett, R.D., Spencer, J.D., Lolon, E., et al., 2013. Evaluation of two horizontal wells in the Eagle Ford using oil-based chemical tracer technology to optimize stimulation design. In: Presented at the SPE Hydraulic Fracturing Technology Conference, Woodlands, Texas, USA, 4e6 February. http://dx.doi.org/10.2118/ 163846-MS. Cheng, Y., 2012. Impact of water dynamics in fractures on the performance of hydraulically fractured wells in gas-shale reservoirs. J. Can. Petrol. Technol. 51 (02), 143e151. http://dx.doi.org/10.2118/127863-PA. Chitrala, Y., Moreno, C., Songdergeld, C.H., et al., 2011. Microseismic and microscopic analysis of laboratory induced hydraulic fractures. In: Presented at the Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 15e17 November. http://dx.doi.org/10.2118/147321-MS. CMG-STARS User’s Guide (2012): Computer Modeling Group Ltd. Crafton, J.W., 2008. Modeling flowback behavior or flowback equals “slowback”. In: Presented at the SPE Shale Gas Production Conference, Fort Worth, Texas, USA, 16e18 November http://dx.doi.org/10.2118/119894-MS. Crawford, E., Senters, C.W., Bullard, K.E., et al., 2014. Granite Wash optimizationvalidating completion and production techniques. In: Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, Netherlands, 27e29 October. http://dx.doi.org/10.2118/170923-MS. Davis, E., 2009. Hydraulic Fracture Diagnostics and Reservoir Diagnostics. http:// www.ieaghg.org/docs/monitoring/5mtg/Pinnacle_BD%20Overview%20EJD.pdf. Elahi, S.H., Jafarpour, B., 2015. Characterization of fracture length and conductivity from tracer test and production data with Ensemble Kalman filter. In: Presented at the Unconventional Resources Technology Conference, San Antonio, Texas, USA, 20e22 July. http://dx.doi.org/10.2118/178707-MS. Gardien, C.J., Pope, G.A., Hill, A.D., 1996. Hydraulic fracture diagnosis using chemical tracers. In: Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6e9 October. http://dx.doi.org/10.2118/36675-MS. Goswick, R.A., LaRue, J.L., 2014. Utilizing oil soluble tracers to understand stimulation efficiency along the lateral. In: Presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, Netherlands, 27e29 October. http:// dx.doi.org/10.2118/170929-MS. Haddad, M., Sanaei, A., Al-Shalabi, E.W., et al., 2015. Major obstacles in production from hydraulically re-fractured shale formations: reservoir pressure depletion and pore blockage by the fracturing fluid. In: Presented at the Unconventional Resources Technology Conference, San Antonio, Texas, USA, 20e22 July. http:// dx.doi.org/10.2118/178587-MS. Kausik, R., Minh, C.C., Zielinski, L., et al., 2011. Characterization of gas dynamics in kerogen nanopores by NMR. In: Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 30 October e 2 November. http://dx.doi.org/10.2118/147198-MS. King, G.E., Leonard, D., 2011. Deciphering chemical tracer results in multi-fractured well backflow in shales: a framework for optimizing fracture design and application. In: Presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, the Woodlands, 24e26 January. http://dx.doi.org/10.2118/ 140105-MS. €hring, S., et al., 2015. Estimation of fracture volume beLeong, Y., de Iongh, J.E., Ba tween well pairs using deuterium tracer. In: Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, USA, 28e30 September.
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9 http://dx.doi.org/10.2118/174832-MS. Oyerinde, A.S., 2005. A Composite Tracer Analysis Approach to Reservoir Characterization. Ph.D dissertation. Texas A&M University. Sharma, A., Shook, G.M., Pope, G.A., 2014. Rapid analysis of tracers for use in EOR flood optimization. In: Presented at the SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 12e16 April. http://dx.doi.org/10.2118/169109-MS. Sharma, A., Namsani, S., Singh, J.K., 2015. Molecular simulation of shale gas adsorption and diffusion in inorganic nanopores. Mol. Simul. 41 (5e6), 414e422. http://dx.doi.org/10.1080/08927022.2014.968850. Sheely Jr., C.Q., Baldwin Jr., D.E., 1982. Single-well tracer tests for evaluating chemical enhanced oil recovery processes. J. Petrol. Technol. 34 (08), 1887e1896. http://dx.doi.org/10.2118/8838-PA.
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Sun, J., Schechter, D.S., 2015. Optimization-based unstructured meshing algorithms for simulation of hydraulically and naturally fractured reservoirs with variable distribution of fracture aperture, spacing, length and strike. SPE Reserv. Eval. Eng. 18 (04), 463e480. http://dx.doi.org/10.2118/170703-PA. Tomich, J.F., Dalton Jr., R.L., Deans, H.A., et al., 1973. Single-well tracer method to measure residual oil saturation. J. Petrol. Technol. 25 (02), 211e218. http:// dx.doi.org/10.2118/3792-PA. Warpinski, N.R., Branagan, P.T., Peterson, R.E., et al., 1998. Mapping hydraulic fracture growth and geometry using microseismic events detected by a wireline retrievable accelerometer array. In: Presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15e18 March. http://dx.doi.org/10.2118/ 40014-MS.
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Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation Wei Tian a, *, Xingru Wu a, Tong Shen a, Sumeer Kalra b a b
Mewbourne School of Petroleum & Geological Engineering, University of Oklahoma, SEC 1362, 100 E Boyd, Norman, OK, USA Warwick Energy Group, 900 W Wilshire Blvd, Oklahoma City, OK, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 January 2016 Received in revised form 12 May 2016 Accepted 8 June 2016 Available online xxx
Hydraulic fracture geometry is of the interest in optimizing stimulation treatment and forecasting production potential. Current diagnostic tools such as tiltmeter and microseismic are insufficient in evaluating fracture geometry. Knowing that gas from the shale reservoir has a much higher mobility than fracking fluid, partitioning chemical tracer is employed so that tracer data can be obtained earlier and more complete. The proposed approach is examined by synthetic numerical simulations. On the semi-log plot, tracer production declined tail clearly divides into two straight-line segments. Applying the moment of methods to the entire tracer production data gives the total volume of hydraulic fracture and the invaded matrix swept by the tracer due to leak-off. Additionally, extrapolating the first segment of tracer decline tail using the exponential law yields a volume that is close to the actual hydraulic fracture volume, especially when fracture permeability is several orders larger than matrix permeability. © 2016 Elsevier B.V. All rights reserved.
Keywords: Partitioning chemical tracer Fracture diagnosis Method of moments Shale gas
1. Introduction Hydraulic fracturing has been applied in shale gas development to increase the contact area with matrix and create permeable conduits for fluid flow. Knowledge of hydraulic fracture volume is essential in determining the stimulation treatment efficiency. However, the fracture volume diagnosis is very challenging because of the complexities of rock properties and fracturing process. Davis (2009) summarized capabilities and limitations of numerous fracture diagnostic technologies, including tiltmeters, microseismic mapping and radioactive tracers. Among them, only surface tilt mapping is able to determine the hydraulic fracture volume, while its resolution decreases with depth. Chemical tracer is a powerful technology for reservoir characterization (Tomich et al., 1973; Sheely Jr and Baldwin Jr, 1982; Abbaszadeh-Dehghani and Brigham, 1984; Allison et al., 1991). In recent years, its application has been extended in hydraulic fracturing to evaluate the contribution of each fracture stage to the total hydrocarbon production in a multi-stage horizontal well (Goswick and LaRue, 2014; King and Leonard, 2011; Catlett et al., 2013). Chemical tracer can also help understand interwell communication
* Corresponding author. E-mail address: [email protected] (W. Tian).
for fractured wells (Crawford et al., 2014). Chemical tracer is rarely used to estimate fracture volume. Gardien et al. (1996) revealed that the tracer response was sensitive to an influence ratio, which was the combination of fracture half length, fracture height, formation porosity and injected volume. They noticed that tracer response in fractured reservoir was quite different with a homogeneous reservoir, indicating the possibility of hydraulic fracture diagnosis using the chemical tracer. Nevertheless, it was impossible to determine the fracture volume directly from their work because fracture width was not included in the ratio. Leong et al. (2015) utilized the conservative deuterium tracer to detect the fracture volume based on tracer residence time in a well pair setting. Their target fracture did not have two-phase flow. They also neglected the tracer swept volume in matrix due to leakoff, which could lead to an overestimation of fracture volume eventually. Elahi and Jafarpour (2015) proposed to analyze tracer test data for fracture volume using ensemble Kalman filter. However, this approach is difficult to employ because it required tremendous fracture and matrix information for the data assimilation. As seen from above discussion, none of the work could estimate fracture volume under the condition of multi-phase flow and leak-off. In this paper, we propose to evaluate fracture volume in shale gas formation using partitioning chemical tracer. The impact of matrix as well as dispersion on tracer production data will be
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Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Nomenclature
Normal a b B C D K k L h t
coefficient coefficient formation volume factor, fraction chemical tracer concentration, mole fraction dispersion coefficient, L2/T partition coefficient, fraction permeability, L2 length, L height, L time, T
analyzed, which has never been investigated in previous work. Method of moments (MoM) is applied to compute the swept volume and the tracer production in both phases, vapor and liquid, is accounted for correspondingly. This approach is simple to use without asking for detailed reservoir information. Synthetic numerical simulation is utilized to validate the proposed method. 2. Methodology 2.1. Motivation of using partitioning chemical tracer For many shale gas formations, more than 60% of fracking fluid is not produced back in the early production stage according to the field observations (Crafton, 2008). Therefore, for the fracking fluid soluble tracers (conservative tracers), their production history would be either too limited, which may lead to incorrect estimations of fracture volume, or the tracer information is too late to yield useful information. Another type of conservative tracer is gas soluble tracers. Given that gas from the shale reservoir has a much higher mobility than the fracking fluid and some reservoirs may even have immediate gas production right after completion (Asadi et al., 2008), we can anticipate these tracers may quickly flow back. However, gas soluble tracers fail to provide sufficient information about the fracking fluid inside the hydraulic fracture, and consequently we cannot evaluate the exact fracture volume. Upon previous discussions, we propose to use partitioning chemical tracer, which is soluble in both gas and fracking fluid. The partitioning chemical tracer partitions between gas and fracking fluid. The phase preference of such tracer is described by its partition coefficient, K, which is defined as the ratio of tracer mole fraction in gas to its mole fraction in fracking fluid (Eq. (1)). Partitioning chemical tracer production data will reflect information of both phases that it could sense during the test. In addition, it can flow back with gas, suggesting the potential of early interpretation of fracture volume.
K¼
Cg Cw
(1) eq
V w 4
swept volume, L3 width, L porosity, fraction
Subscript BHP e eq g i m swept w
bottom-hole pressure end point equilibrium gas component i matrix swept volume water
as (Oyerinde, 2005):
Z
∞
Vi Ci dVi
Vi;swept ¼ Z0
(2)
∞ 0
Ci dVi
Gas and fracking fluid could exist in the hydraulic fracture at the same time. Since partitioning chemical tracer also exists in both phases, its swept volumes in both gas and fracking fluid should be taken into account in order to get the total swept volume in hydraulic fracture. Because the produced volume is measured at surface condition, the formation volume factor (FVF) at producing bottom-hole pressure (BHP) is needed to convert volume from surface to subsurface condition (Eq. (3)).
Vswept ¼ Bg;BHP Vg;swept þ Bw; BHP Vw;swept
(3)
2.3. Exponential decline Since the measurement of tracer concentration history is often limited in time, we assume that the tracer concentration declines exponentially with time if the tracer is injected as a slug. In other words, it is possible to obtain the full tracer interpretation earlier by extrapolating the tracer production data when the exponential decline trend occurs (Fig. 1). Mathematically, the tracer exponential decline tail is expressed by (Sharma et al., 2014):
CðVÞ ¼ beaV for V > Ve
(4)
The tracer behavior in a fractured reservoir is different from that in a homogeneous reservoir (Gardien et al., 1996). By plotting the tracer tail in a semi-log plot, we would observe two distinct linear relationships, which help to distinguish the tracer swept volume in matrix and fracture respectively. We will illustrate how to analyze the tracer tail in a hydraulically fractured shale reservoir in the later sections.
3. Model description 2.2. Swept volume calculation MoM has been widely used to interpret tracer production data. The first moment gives the tracer swept volume. For the tracer production data within phase i, i.e. produced tracer concentration versus cumulative produced volume, the first moment is calculated
To validate the proposed approach, synthetic models are created. This section provides all the critical information and parameters to develop a prototype of hydraulically fractured shale gas reservoir. Adsorption and capillary pressure effects are neglected in the simulations.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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Table 1 Dimensions of model with matrix. Parameter
Value
Unit
Number of reservoir girds Formation length, y direction Formation height, z direction Formation width, x direction
(24,50,1) 300 30 449
(x,y,z) ft ft ft
properties are listed in Table 2 and will be applied to all the simulations. 3.3. Rock and fluid properties
Fig. 1. Tracer production data at later time on a semi-log plot is a straight line. This is known as the tracer exponential decline tail.
3.1. Domain construction We construct two different domains. The first one only includes the hydraulic fracture, which is used to investigate the fracture volume estimation without leak-off. The second model has the fracture as well as adjacent matrix to consider leak-off impact. Although we have different domains, the input properties of fracture, rock, fluid and well are the same for both models. 3.1.1. Hydraulic fracture only In this scenario, we consider half of the hydraulic fracture using a 1D model with 300 grids. Each grid has the dimension of 1 ft in length, 0.1 ft in width and 30 ft in height. The horizontal well perforated at the left side of the fracture as shown in Fig. 2. 3.1.2. Hydraulic fracture with matrix Half of the hydraulic fracture and a quarter of its adjacent matrix are simulated here. There are 24 grids in x direction and 50 grids in y direction. The domain dimensions are listed in Table 1. The hydraulic fracture is located at the right side, where x coordinate is 24 parallel with y-axis. Local grid refinement is implemented near the hydraulic fracture (Sun and Schechter, 2015). The fracture height is assumed identical with reservoir thickness of 30 ft. The horizontal well locates at the upper side of the domain parallel with x-axis and it only perforates at the fracture (Fig. 3).
Initial pressure inside hydraulic fracture and matrix is 4925 psi. Matrix permeability is 50 nd. There are two phases, i.e. vapor phase and liquid phase, in the system initially. The liquid phase represents initial reservoir water and the injected fracking fluid. The vapor phase represents the shale gas. The initial water saturation is 0.3 in both hydraulic fracture and matrix. The gas and water FVF at 500 psi are 0.037 and 1.0 respectively. The partition coefficient of tracer is constant as 25.6. In simulations, local equilibrium is assumed. In other words, the tracer distribution between phases reaches immediate equilibrium governed by Eq. (1) (CMG-STARS user’s guide, 2012). The tracer dispersion coefficient is assumed 0. The detailed rock and fluid properties are summarized in Table 3. To accomplish the model description, the relative permeability curve is shown as the dashed line in Fig. 4. The input values for matrix permeability and dispersion coefficient described here are set as the base case. In the following sections, these two parameters will be varied one by one to examine their influence on tracer production data. 3.4. Well plan For all simulations, well schedule has four consecutive steps: 1) slug injection of partitioning tracer with the fracking fluid; 2) injection of fracking fluid without the partitioning tracer, displacing the tracer farther into the fracture; 3) shut in the well for a short time interval (water soaking) as the well is not initiated back to produce right after the treatment (Haddad et al., 2015); 4) open the well and start to produce (Fig. 5). The first two steps are designed to simulate the hydraulic fracturing process. For injection, the well is constrained by the maximum BHP of 15,000 psi and maximum injection rate of 2000 bbl/day. The production minimum BHP is 500 psi. Table 4 shows the details of the well constraints. 4. Result and discussion
3.2. Hydraulic fracture properties 4.1. Hydraulic fracture volume estimation The fracture half-length is 300 ft and fracture height is 30 ft. Fracture flowing capacity is controlled by conductivity, which is assumed constant as 10 md-ft. In our model, the fracture width is 0.1 ft. Fracture permeability is therefore 100 md. The fracture
Fig. 6 is the result of tracer production data in vapor phase on a semi-log plot. The tracer tail section, the red section in graph, could be well fitted by an exponential decline function as shown in the
Fig. 2. Illustration of hydraulic fracture configuration. Each grid is 1 ft long. There are 300 grids and the well perforates at one end.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Fig. 3. Synthetic model configuration with hydraulic fracture and matrix. The hydraulic fraction is on the right side with red color. The horizontal well perforates in the upper right grid. The matrix is in the blue color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Generic hydraulic fracture properties. Parameter
Value
Unit
Fracture Fracture Fracture Fracture Fracture Fracture
300 30 0.1 100 0.05 0.3
ft ft ft md fraction fraction
half length height width permeability porosity initial saturation
Table 3 Rock and fluid properties. Parameter
Value
Unit
Reservoir Initial Pressure Matrix Porosity Matrix Permeability Matrix Initial Water Saturation Water FVF at 500 psi Gas FVF at 500 psi Water Viscosity Gas Viscosity Tracer Partition Coefficient Tracer Dispersion Coefficient
4925 0.05 50 0.3 1.0 0.037 0.3 0.02 25.6 0
psi fraction nd fraction rbbl/stb rsf/scf cp cp fraction ft2/day
Fig. 6. Applying Eq. (2), we can get tracer swept volume in gas at surface condition is 199 ft3 and swept volume in water is 4.7 ft3. Then, the total swept pore volume at subsurface through Eq. (3) is 12.02 ft3. Fig. 7 is the tracer distribution profile at the end of shut in period, obtained from numerical simulation output directly. The horizontal axis is the distance from the wellbore. It shows that the injected tracer has been pushed to the location of 95 ft away from the wellbore and the total contacted pore volume, if calculated based on Fig. 7, is Lwh4 ¼ 95 0:1 30 0:05 ¼ 14:25ft3 . This value is in a good agreement with the previous swept volume obtained from tracer production data. Although the hydraulic fracture is 300 ft, the tracer only flows
95 ft from wellbore because of the pressure increase in the system. Above result verifies that MoM is capable in estimating such volume swept by the tracer. In other words, tracer production data could directly tell where the tracer goes during the injection process. Therefore, we recommend injecting a slug of tracer with fracking fluid at the beginning of stimulation treatment at each stage. The fracking fluid at later fracturing steps could displace tracer farther into the induced fracture so that the tracer flowback data is informative to the entire fracture volume. In practical gas production from shale formations, multiple stages of hydraulic fractures are created in order to maximize the productivity of the well and reduce the number of wells needed for the field development. When the well is flowing back after the treatment, the tracer response curve will be the superposition of tracer responses from individual stage of the fractures if only one tracer is used in all stages. Therefore, we can get the entire fracture volume of all stages from tracer production data using MoM.
4.2. Impact of leak-off The previous case just simulates one single hydraulic fracture without matrix. However, in reality, the pressure inside fracture will increase significantly during the fracturing process and it becomes higher than the matrix pressure. As a result, the fracking fluid will leak-off into the matrix (Warpinski et al., 1998). The penetration distance of fracturing fluid into the matrix is relevant with matrix permeability. For high permeable reservoir, the injected fluid could penetrate deeper and vice versa (Chitrala et al., 2011). Such leak-off would complicate the tracer diagnosis. This section addresses the impact of matrix when using partitioning tracer to detect fracture volume. With larger matrix permeability, the partitioning chemical tracer may invade deeper into the formation. To investigate the leak-off impact, matrix permeability varies from 5 nd to 500 nd. The rest input parameters are kept the same with the previous description. The solid lines in Fig. 8 are simulation output of tracer production in gas in a semi-log plot. Its production in water has the similar
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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1.0
Relative Permeability
0.8
0.6 Krw in Fracture Krg in Fracture Krw in Matrix Krg in Matrix
0.4
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Water Saturation Fig. 4. Relative permeability curves in matrix and hydraulic fracture (modified from Cheng (2012)).
0.14 Partitioning Tracer in Water Partitioning Tracer in Gas
Tracer Mole Fraction
0.12 0.10 0.08 0.06 0.04 0.02
Fig. 5. The four steps of well plan. 0.00 0
20
40
60
80
100
120
140
Distance from Injector, ft
Table 4 Well constraints. Well controls
Value
Unit
Injection Maximum Bottom Hole Pressure Injection Maximum Rate Production Minimum Bottom Hole Pressure
15,000 2000 500
psi bbl/day psi
Fig. 7. Tracer distribution profile inside fracture at the end of shut in, obtained from numerical simulation output directly.
Fig. 8. Partitioning tracer production data in gas. Solid lines are simulation output. The dashed lines are the extrapolation based on the first linear section. Fig. 6. Tracer concentration vs. cumulative gas production. The dashed line is the best fitted line. Its R-square is 0.99, indicating the tracer tail is almost a straight line.
shape. Based on the direct output from simulation, the total swept volume for each case is listed in the third row in Table 5 using MoM. Figs. 9e11 shows the tracer distribution profile at the end of shut in
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
Table 5 Comparison of swept volume with different matrix permeability. 5 180 137 39 134
50 300 275 43.5 232
500 635 570 45 571
(Note: ‘Total Swept Volume’ is calculated using MoM from the original tracer production data (the solid line in Fig. 8); ‘Total Contacted Volume’ is the total pore volume contacted by the tracer at end of shut in, including matrix; ‘Contacted Fracture Volume’ is the fracture volume contacted by the tracer at end of shut in, not including matrix; ‘Corrected Swept Volume’ is calculated using MoM based on the extrapolated tracer production history (the dashed line in Fig. 8).
0.06
0.04
0.02
0
0.08
0.04
0.02
0.00 50
100
150
200
250
300
Distance in Y Direction, ft Fig. 9. The tracer distribution profile inside domain at the end of shut in. km ¼ 5 nd. Obtained from simulation output directly.
0.12 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.10
0.08
0.06
0.04
0.02
0.00 0
50
100
150
200
250
100
150
200
250
300
Fig. 11. The tracer distribution profile inside domain at the end of shut in. km ¼ 500 nd. Obtained from simulation output directly.
0.06
0
50
Distance in Y Direction, ft
x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19
0.10
Tracer Mole Fraction
0.08
0.00
0.12
Tracer Mole Fraction
x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.10
Tracer Mole Fraction
Matrix Permeability, nd Total Swept Volume, ft3 Total Contacted Volume, ft3 Contacted Fracture Volume, ft3 Corrected Swept Volume, ft3
0.12
300
Distance in Y Direction, ft Fig. 10. The tracer distribution profile inside domain at the end of shut in. km ¼ 50 nd. Obtained from simulation output directly.
period, obtained from numerical simulation output. They are depicted on cross-sections in y direction. The decrease of x number indicates the deeper location into the matrix away from hydraulic fracture. We use these graphs to compute the tracer contacted volume in hydraulic fracture and in entire system respectively (Table 5). In Figs. 9e11, columns of x ¼ 24 indicate the hydraulic fracture. The results in Table 5 show that the tracer original production data provides the total swept volume rather than the hydraulic fracture volume. This is because the injected fracking fluid
penetrates into the matrix and the fluid flow from matrix will contribute to the final tracer production besides fluid in hydraulic fracture. In addition, higher matrix permeability results in larger total tracer swept volume, implying larger leak-off of the fracking fluid. Figs. 9e11 shows that tracer penetrates deeper into the formation, which is a proof of this statement. Such observations suggest that the tracer production data can help estimate the leakoff volume if hydraulic fracture volume is known. Examining the tracer tail in Fig. 8, we notice two distinct linear relationships of tracer concentration versus cumulative gas production at a later time. This is also observed in water production. For the convenience of discussion, we name the intersection of the two linear lines as the deviation point. We extrapolate the first linear section for both gas and water using the exponential decline rule (Eq. (4)). The dashed line declines more rapidly after the deviation point compared against the original plot (Fig. 8). We recalculate the swept volume based on the extrapolated curve and the results are displayed in the last row of Table 5. The swept volume obtained from the extrapolated line is closer to hydraulic fracture volume when matrix permeability decreases. This is because less matrix fluid flow contributes to the tracer production at early stage. Since the fracture permeability is much higher than the matrix, the fluid inside hydraulic fracture will come back to the wellbore much faster than the matrix. On the other hand, if matrix permeability increases, more matrix fluid with tracer is produced right after production starts and the deviation point is postponed in the regard of gas production as well. This will result in a larger difference between the contacted hydraulic fracture volume and the corrected swept volume. Therefore, the partitioning chemical tracer could provide a reliable estimation of fracture volume when the fracture permeability is several orders higher than the adjacent matrix permeability. Another advantage of using partitioning chemical tracer for fracture diagnosis is rapid feedback. Once the linear relationship occurs, we can simply use the exponential decline rule to extrapolate the tracer production data without actually measuring the tracer concentration for a long time. According to our simulations, even though only 1/3 of injected fracking is produced back after 1year production, the first linear section can be observed within 1 day of flowback or even less. The deviation point occurs within 3 days of production, indicating the second linear relationship can also be observed very quickly. Such rapid response of tracer is because of its partitioning feature.
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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4.3. Impact of dispersion Gardien et al. (1996) had noticed that the tracer flow is dispersion dominated. Therefore, this section will investigate the impact of dispersion on tracer production data and estimation of hydraulic fracture volume estimation. We use three isotropic dispersion coefficients, assigned as total dispersion coefficient in simulations, to the partitioning chemical tracer to study dispersion effect. Their values are 0 ft2/day, 0.002 ft2/day and 0.2 ft2/day, respectively. These values are in the range of published data (Kausik et al., 2011; Sharma et al., 2015).
4.3.2. Hydraulic fracture with matrix Now, we investigate dispersion impact when matrix exists. The model input values are kept the same as the base case discussed in ‘Model Description’ section except the tracer dispersion coefficient, which ranges from 0 ft2/day to 0.2 ft2/day. Fig. 13 shows the original tracer production data and their extrapolated tracer decline tail based on first straight section. Figs. 14 and 15 are tracer distribution profiles at the end of shut in for cases with non-zero dispersion coefficient. The tracer distribution profile with 0 dispersion coefficient is identical with Fig. 10. Table 7 illustrates the swept volume comparison. The meaning of each term is the same with Table 5. The dispersion impact on tracer production data and distribution is more significant with matrix leak-off. From Fig. 13, we notice that tracer production peak arrives earlier in respect of cumulative produced volume with larger dispersion coefficient. Figs. 14 and 15 illustrates that dispersion makes the tracer penetrate much deeper into the matrix rather than flow farther inside hydraulic fracture. As Table 6 Comparison of swept volume inside hydraulic fracture only with different dispersion coefficient. Dispersion Coefficient, ft2/day Total Swept Volume, ft3 Contacted Fracture Volume, ft3
0 14.25 12.02
0.002 14.25 12.03
0.2 15.75 12.89
Chemical Tracer Mole Fraction
Fig. 12. Tracer distribution profile inside hydraulic fracture with three different dispersion coefficient at the end of shut in. It is obtained from numerical simulation output directly.
2 D=0 ft /day, Extrapolated 2 D=0 ft /day, Original 2 D=0.002 ft /day, Extrapolated 2 D=0.002 ft /day, Original 2 D=0.2 ft /day, Extrapolated 2 D=0.2 ft /day, Original
0.1
0.01
0.001
0.0001 10000
20000
30000
40000
50000
Cumulative Gas Production, ft3 Fig. 13. Partitioning tracer production data in gas. Solid lines are simulation output. The dashed lines are the extrapolation based on the first linear section.
0.010 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
0.008
Tracer Mole Fraction
4.3.1. Hydraulic fracture without matrix First, we consider the dispersion impact inside hydraulic fracture only, without any leak-off into the matrix. Hence, the model shown in Fig. 2 is applied. Input parameters other than dispersion coefficient are kept the same. The tracer production data of each case is similar with Fig. 6. Fig. 12 shows the tracer distribution profiles of three cases at the end of shut in. In Table 6, the ‘total swept volume’ is calculated from the tracer production data using MoM and the ‘contacted fracture volume’ is obtained based on the tracer distribution profile in Fig. 12. We can see from Fig. 12 that the tracer distribution profile of 0.002 ft2/day is overlapped with the case of 0 ft2/day, indicating that the dispersion effect is negligible when the dispersion coefficient is small enough. Results in Table 6 also point out that, when the dispersion coefficient is small, the swept volume calculated from tracer production data is close to the case without dispersion effect. In addition, Fig. 12 shows that tracer front becomes more slanted along with the increase of tracer dispersion coefficient. In other words, tracer could reach farther inside the fracture with larger dispersion coefficient. Tracer swept volume calculated from its production data also gets larger correspondingly. The main observation from Table 6 is that the tracer production data could provide accurate estimation of fracture volume through MoM even though tracer dispersion has impact on the total swept volume. Therefore, the proposed approach is sufficient to capture the fracture volume from tracer test with dispersion effect as long as there is no leak-off into matrix.
0.006
0.004
0.002
0.000 0
50
100
150
200
250
300
Distance in Y Direction, ft Fig. 14. The tracer distribution profile inside domain at the end of shut in. D ¼ 0.002 ft2/day. Obtained from simulation output directly.
a result, the contacted volume obtained from tracer distribution profile is getting larger as well (Table 7). However, due to the dispersion, the MoM fails to inform the correct total contacted
Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018
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W. Tian et al. / Journal of Natural Gas Science and Engineering xxx (2016) 1e9
exponential decline can estimate fracture volume. Its accuracy is influenced by matrix permeability. 4. Partitioning tracer has rapid feedback even though the injected fracking fluid is trapped in the system. The tracer test is therefore time-efficient. 5. Dispersion is not favorable in tracer test to evaluate fracture volume. Dispersion impact on tracer production is significant and it will result in an inaccurate estimation of swept volume when leak-off occurs. Without leak-off, MoM could tell the correct fracture volume despite the dispersion.
0.010 x=24 Hydraulic Fracture x=23 x=22 x=21 x=20 x=19 x=18 x=17
Tracer Mole Fraction
0.008
0.006
0.004
0.002
Acknowledgement
0.000 0
50
100
150
200
250
300
Distance in Y Direction, ft Fig. 15. The tracer distribution profile inside domain at the end of shut in. D ¼ 0.2 ft2/ day. Obtained from simulation output directly.
Table 7 Comparison of swept volume with different dispersion coefficient. Dispersion coefficient, ft2/day Total swept volume, ft3 Total contacted volume, ft3 Contacted fracture volume, ft3 Corrected swept volume, ft3
0 300 275 43.5 232
0.002 2055 682 37 236
0.2 9530 892 8 97
volume from tracer production data. The estimated volume from tracer production data is much larger than the actual contacted volume. Furthermore, even though the two straight lines are still observed, it is impossible to extract fracture volume from the extrapolated first straight section. According to above discussion, we conclude that the tracer test should be less dispersion influenced. The tracer dispersion needs to be controlled at low level to ensure reliable analysis when matrix leak-off occurs. In field practices, we could consider to inject partitioning chemical tracer at the proppant stage to reduce tracer leak-off and dispersion influence. 5. Conclusion This paper introduces an approach to estimate fracture volume by injecting a pulse of aqueous solution containing a partitioning tracer into a shale gas reservoir. The tracer will continuously partition into and out of the liquid phase. The tracer in solution will penetrate into the rock matrix formation and some of them will be in the fracture. When the well is flowing back, the injected tracers are sampled, and then the tracer test can be analyzed for fracturing information. We employed the numerical simulation to validate the use of MoM in estimating fracture volume and the impacts of fracking fluid leak-off into the matrix and tracer dispersion. Adsorption and capillary pressure will be investigated in the future. Several following conclusions are made: 1. MoM is capable to determine the swept volume of partitioning tracer under two-mobile-phase condition. The partitioning tracer is therefore recommended to inject as a slug at the beginning of stimulation treatment at each stage, so that it can inform the entire fracture volume. 2. The tracer production data is indicative of the total volume of fracture and leak-off. 3. Two linear relationships of tracer tail are observed when matrix leak-off exists. Extrapolating the first straight section using
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Please cite this article in press as: Tian, W., et al., Estimation of hydraulic fracture volume utilizing partitioning chemical tracer in shale gas formation, Journal of Natural Gas Science and Engineering (2016), http://dx.doi.org/10.1016/j.jngse.2016.06.018