PROCEEDINGS, Thirty-Seventh Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 30 - February 1, 2012 SGP-TR-194
LABORATORY AND THEORETICAL RESULTS FROM INVESTIGATIONS OF CO2 SOLUBILITY IN GEOTHERMAL RESERVOIRS Sarah Pistone and Roland Horne Stanford University 367 Panama Street, Rm 67 Stanford, CA 94305 e-mail:
[email protected]
ABSTRACT This paper considers the idea of CO2 injection into deep thermal reservoirs. The application of this research is either to the goal of carbon sequestration or the use of CO2 as the working fluid in an Engineered Geothermal Systems (EGS). Sequestration may occur in a number of ways such as via: solubility trapping, mineralization, impermeable caprocks, or capillary forces. This research presents evidence for a new phenomenon named ―active phase change‖ (APC), which refers to the combined effect of CO2 solubility with standard hydrodynamics on the multiphase flow of CO2 and water through porous media. Laboratory experiments and theoretical work were designed to investigate thermodynamic effects that may occur when solubility is taken into account. A core-scale experiment measured relative permeabilities in the two-phase system, a micromodel experiment qualitatively observed the dynamic dissolution phenomenon, and theoretical analyses put the findings in context and provided a framework to predict results under varied conditions. The purpose of this research was to analyze and quantify the magnitude of dissolution effects through laboratory and theoretical work. An additional goal was to evaluate the time and length-scales of dissolution and diffusion effects relative to standard hydrodynamic behavior. This paper concludes with recommendations for improvements to the experimental set-up and for future work. BACKGROUND The concept of using carbon dioxide (CO2) as a working fluid in an Engineered Geothermal Systems (EGS) is not new and has received increased attention over recent years. Multiple conference sessions have been dedicated to the topic with contributions related to: multiphase flow (Bennion
and Bachu, 2008; Chen, 2005; Pistone, 2011; Stacey, 2008; Stacey et al., 2010), numerical modeling (Chang et al., 1998; Pruess 2006), geochemistry and field experiments (Kaieda et al., 2009; Ueda et al., 2009; Yanagisawa et al., 2007, 2008, 2010). The research presented herein was designed to investigate ―active phase change‖ (APC); a phenomenon wherein a miscible fluid may enter pore spaces via chemical gradient rather than by hydrodynamic forces alone (Chen, 2005; Stacey 2008). In the context of CO2 EGS, this would be important since it may allow CO2 to flow in a disconnected phase in advance of the main CO2 front. Furthermore, APC may allow for the residual water saturation to decrease over multiple cycles of drainage and imbibition. Prior studies demonstrated decreasing residual water saturation in laboratory experiments (Bennion and Bachu, 2008 and Stacey, 2008). Figure 1 provides a conceptual model of how the residual water saturation may decrease over time in a CO2 -water system: (1) the pore space is fully saturated, (2) residual water saturation after primary drainage and CO2 may enter the smallest pore spaces via chemical gradient without overcoming capillary forces, (3) after drainage CO2 comes out of solution and forces some water that was previously immobile into the higher permeability pathways, whereby (4) the immobile water is made mobile and the residual water saturation in frame 4 is less than the residual water saturation after primary drainage (frame 2).
Figure 1 Schematic showing reduction in residual water saturation over time.
Table 1 Summary of previous relative permeability experiments.
Previous laboratory studies have been conducted to date that measured relative permeabilities using steady and unsteady methods with various fluids. Table 1 summarizes rock types, experimental method, and some settings of the different experiments (compiled from Müller, 2011). There is high variability in sample type, sample properties, and experimental settings. As noted by Müller (2011), these inconsistencies led to variable results that are difficult to compare. Table 2 lists some relative permeability results from CO2-water or CO2brine systems. Table 2 Summary of results from previous relative permeability experiments.
EXPERIMENTAL WORK Experimental studies for this research were divided into two main sections: micromodel experiments and core flooding experiments. The micromodels were intended to be a qualitative check of two-phase flow behavior of CO2 and water, and to observe the phenomenon of APC visually. The core flood experiments were a method to measure relative permeabilities quantitatively and evaluate the significance of CO2 solubility and APC. The two experiment sets complemented each other and provided insight into the physical flow behavior of a CO2-water system. Experimental apparatus and methods for both micromodel and core experiments are described in detail in Pistone, 2011. Micromodel The micromodel experiments served as a visual analogue to observe pore-scale behavior. The models are made out of etched silicon that mimics the characteristics of Berea Sandstone (Table 3). Table 3 Micromodel properties Micromodel Properties dimensions 5x5 cm grain size 30 - 200 μm permeability 500 mD porosity 0.20
micromodel was near the edge of the inlet side of the model. In the following frames you can see bubble shrinkage and dissolution, which clearly show that mass transfer was occurring within the pore space.
Figure 2 Diagram of micromodel (not to scale). Red oval represents area of observation.
In the current study, only drainage experiments were conducted with the micromodel to observe the disconnected flow of CO2 as a result of dissolution and mass transfer through the water. Later, it may be insightful to continue consecutive imbibition and drainage cycles to see if it is possible to visually verify the conceptual model that the residual water saturation may decrease over time as a result of APC (Figure 1).
The model is fit into a holder with a glass cover plate with a channel on the inlet and outlet ends that approximates a uniform pressure gradient (Figure 2). The model was saturated with water and then drained with CO2 at a low pressure (about 2 psig) that is below the expected capillary entry pressure (8 psig).
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Results Observations were focused on the inlet portion of the model where the CO2 front was visible in the constant pressure channel abutting the etched pore network (red oval in Figure 2). The first signs that CO2 gas entered the pore space occurred in the center of the micromodel on the inlet interface. CO2 flow phenomena observed included disconnected bubbles and bubble dissolution. The first bubbles were observed within the pore space after about 20 min. Figures 3 shows that the results are similar to previous observations by Stacey (2008). In Figure 3 (left) the CO2 front is visible on the left side of each frame where it abuts the edge of the pore network. In one location (identified by red arrow) the interface is advancing and retreating into a pore throat. At the same time, the bubbles within the pore space change size and shape with each time step. Similarly, in Stacey’s images (Figure 3, right) the bubbles were shown to grow, shrink, nucleate and dissolve with each time step. The direction of CO2 flow was from left to right. Another distinct observation was that the CO 2 front seemed to remain in a period of stasis interrupted by a rapid advancement that occurred within a fraction of a second. This behavior agrees with observations that were noted in previous micromodel studies (Li and Yortsos, 1995 and Tsimpanogiannis and Yortsos 2002). Bubble dissolution was observed in the micromodel too. Figure 4 shows a series of frames recorded about 3 hours into the experiment. The location on the
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Figure 3
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(left) Pistone 2011 micromodel results. (right) Stacey 2008 micromodel results.
Figure 4 Bubble dissolution in micromodel. Core Unsteady-state core flood experiments were completed with a Berea Sandstone core fit into a horizontal titanium core holder to which a confining pressure was applied. Specific core properties are included in Table 4. During each flow experiment, the inlet was held at a constant pressure of 4 psi for the duration of the drainage and imbibition experiments; the pressure was supplied by a gas canister and controlled with a pressure regulator. Outlet pressure was to atmosphere. Results Figure 6 shows inlet and outlet pressure data for a full series of drainage and imbibition experiments.
Each cycle consists of 1 hr of gas drainage, a 10 min rest period followed by 20 min of water injection. There were some instrumentation malfunctions after the first gas drainage cycle where the shapes of the curves were reasonable, but the magnitudes were wrong for the inlet pressure transducers. As a fix a constant pressure difference (2 psi) was used to correct the data (Figure 6 represents ―corrected‖ data).
Table 4 Core properties
Because the cumulative gas injection volume is so great (11–14 liters), The difference between the gas injected and the gas produced is not visible. The cumulative volume of water produced declined with each cycle of drainage and imbibition (Figure 5). This makes sense because the first drainage is of a water-saturated core where the largest volume of water may be displaced. After the first imbibition, water is returned to the pore space, but not to complete saturation due to the immobile gas phase. Based upon totals of fluid injected and produced a mass balance was maintained to calculate residual water saturations (Table 5). Residual water saturations calculated with the JBN method did not match the mass balance values (Figure 8). This may have been because some water mass was produced during the breaks between cycles. The JBN method cannot account for this mass because there are no gas flow rates registered during the breaks.
Figure 5 Cumulative water production in grams.
Figure 6 Pressure data; assumes a constant dP. Table 5 Calculations of residual water saturation based upon mass balance: Initial Vol injected removed Final Vol S
Drainage 1 Imbibition 1 Drainage 2 Imbibition 2 Drainage 3 Imbibition 3 Water CO2 Water CO2 Water CO2 Water CO2 Water CO2 Water CO2 128.50 0.00 50.76 77.74 115.37 13.13 48.31 80.19 104.01 24.49 45.75 82.75 0.00 234.30 0.00 170.40 0.00 170.40 77.74 169.69 67.06 114.70 58.26 115.23 50.76 77.74 115.37 13.13 48.31 80.19 104.01 24.49 45.75 82.75 100.92 27.58 0.40 0.60 0.90 0.10 0.38 0.62 0.81 0.19 0.36 0.64 0.79 0.21
So, for the mass balance calculations the mass production during the breaks was accounted for, whereas in the JBN calculations it was not. This resulted in lower residual water saturation (Swr) calculated from the mass balance because more water was recorded as removed. The relative permeability curves calculated using the JBN method are displayed in Figure 7. Drainage 3 provided puzzling results. The residual water saturation calculated from the mass balance continues the decreasing trend seen in cycles 1 and 2, however the relative permeability curves calculated from the JBN method are much higher and inconsistent with the previous two cycles. It was not possible to conclude if this was a result of an analysis or an instrumentation error. Regardless, the first and second cycles of drainage result in a decreasing residual water saturation and the third drainage cycle data is inconclusive. All residual water saturation values are within a range comparable to data previously reported by Stacey (2008) (Figure 8).
THEORETICAL WORK A simple one-dimensional diffusion model was generated to simulate diffusion of CO2 through water, where concentration in the water (C) was calculated as a function of position (x) and time (t) given the general 1-D diffusion equation (Equation 1; Crank, 1975):
C( x, t ) 2C( x, t ) D t x2
(1)
The model assumed a semi-infinite slab with an interface at x = 0 (assumed stationary) with a constant concentration boundary condition (Co) (Figure 9).
Co
x
x=0 Figure 9 Schematic of semi-infinite slab diffusion model. Given the boundary conditions, Kreft and Zuber (1978) presented a full solution to the diffusion equation using the complimentary error function, which can be simplified to Equation 2:
æ x öïü ïì C = Co íerfc ç ÷ý ïî è 4Dt øïþ Figure 7
Relative permeability curves for drainage 1, 2, and 3. Residual Water Saturation
0.6 0.5
Swr
0.4 0.3 0.2 0.1
JBN Mass Balance Stacey, 2008
0 1
2
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Drainage Cycle
Figure 8 Residual water saturation over time.
(2)
A diffusion coefficient (D) was selected based upon experimental and modeled diffusivities reported in Tamimi et al, (1994) values ranged from 1.60×10-5 to 1.76×10-5 cm2/s at atmospheric temperature (20 °C). A diffusion coefficient of D = 1.70x10-3 mm2/s in units applicable to the pore scale range. Model results showed a normalized concentration that gave a sense of relative rate of concentration increase versus distance (Figure 10). A Berea sandstone pore throat length is on the order of 100 μm. In Figure 11 it appears that the concentration at the end of the pore throat would reach one-half the concentration at the interface (Co) in about 7 sec and would reach ¾ Co in about 30 sec. Previous work indicated a maximum injection velocity of about 8.5 cm/min, which corresponds to about 1.4 mm/sec. The speed at which the front moved through the core under the current conditions is orders of magnitude higher than the rate of
water saturation was decreasing over time. However, the last drainage cycle was inconclusive and disrupted the decreasing trend of residual water saturation (Swr). In contrast to the JBN results, Swr data calculated from the mass balance did continue its decreasing trend over all three drainage cycles. The reason for this discrepancy is not clear at this time, but may be related to the fact that the mass balance includes water production data over the break period, which appear resulted in a larger volume of water removed, thus lower Swr.
1 t = 1 sec t = 10 sec t = 30 sec
The simple one-dimensional diffusion model seemed to indicate that diffusion and bubble nucleation may not be relevant in the flow behavior of the advancing front, but it does have the potential to interact with immobile water that would be left behind after drainage.
0.9
t = 1 min t = 5 min t = 10 min
0.8 0.7
C/C
o
0.6 0.5
For CO2 EGS, a primary concern is drying the reservoir quickly of its connate water so that the corrosive effects of hydrochloric acid may be avoided. APC makes it possible for CO2 to enter the smallest pore spaces that it would not be able to enter assuming pure hydrodynamic forces. An injection scheme could be designed to use the APC phenomenon strategically. For example, injection could be cyclically paused and restarted, with a lowpressure break in between. This way, it may be possible to lower the residual water saturation quicker than by maintaining a constant injection rate.
0.4 x = 10 m
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x = 50 m
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x = 100 m x = 200 m
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x = 500 m x = 1 mm
0
Figure 10
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Diffusion model results: normalized concentration versus distance for lines of constant time.
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Recommendations for future work It is recommended that work on this project continues to define the constraints of APC and its effect under various experimental conditions, considering variables such as: gas, salinity, flow rate, pressure, temperature, or rock type. Care should be taken to change only one variable at a time. There is limited work that has been reported about unsteady-state relative permeability experiments, which was summarized in Table 1. The issue with a lot of this work is the differing experimental setups, methods, x = 10 m and data collection techniques xmake comparison = 50 m between datasets difficult or meaningless. Some x = 100 m x = 200 m recommendations for future work include:
1 t = 1 sec t = 10 sec t = 30 sec
0.9
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t = 1 min t = 5 min t = 10 min
0.8 0.7
0.8 0.7
0.6 o
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C/C
0.8
C/C o
6 m)
concentration increase as a result of diffusion. For example, about one-half the concentration at the interface would reach 1 mm after 10 min. As noted above the time-scale is on order of tens of seconds for shorter lengths (50-100 μm), which is reasonable for the pore scale. As such, it appears that at high injection rates diffusion may not be immediately relevant to the advancing gas-liquid interface, but may be relevant to the immobile water that remains after drainage.
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Figure 11
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0.4 0.6 Distance (mm)
0.8
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Diffusion model results: normalized concentration versus time for lines of constant distance.
CONCLUSIONS The core-scale experimental results provided data that could be used with the JBN method to calculate relative permeabilities and indicate that the residual
0
x = 500 m x = 1 mm
0
• A vertical core setup to eliminate gravity 0.5 1 1.5 2 effect and improvetime core sweep efficiency (min) • X-ray tomography would be helpful to observe core heterogeneity or determine saturation profiles • More than three cycles of drainage and imbibition should be conducted. Cycles should be continued until the residual water saturation stabilizes to constant values.
Aside from the experimental methods, it would be informative to repeat both the micromodel and the core experiments at higher pressures and temperatures to see if a similar behavior is observed. One concern with the higher temperatures may be chemical alteration of the core, corrosion, or mineral precipitation. It is easier to control pressure, so it may be advisable to first investigate the effect of pressure before modifying the temperature of the experiment. A pore network model seems like it would be a natural extension to this work. Li and Yortsos (1999) used a pore network simulation to look at bubble nucleation and growth in micromodels. Chalbaud et al. (2007) also generated a pore network model to match relative permeabilities and residual gas saturation. ACKNOWLEDGEMENTS The authors are grateful for financial support from the American Chemical Society that made this research possible. Also, many thanks to Professor Roland Horne and colleagues at Stanford University for unending support and guidance both inside the laboratory and out. REFERENCES Bennion, D.B, and Bachu, S. (2008), ―Drainage and Imbibition Relative Permeability Relationships for Supercritical CO2/Brine and H2S/Brine Systems in Intergranular Sandstone, Carbonate, Shale, Anhydrite Rocks,‖ SPE Reservoir Evaluation & Engineering, 11(3), June 2008, 487-496.
Kaieda, H., Ueda, A., Kubota, K., Wakahama, H., Mito, S., Sugiyama, K., Akiko, O., Kuroda, Y., Sato, H., Yajima, T., Kato, K., Ito, H., Ohsumi, T., Kaji, Y., and Tokumaru, T., (2009), ―Field Experiments for Studying CO2 Sequestration in Solid Minerals at the Ogachi HDR Geothermal Site, Japan,‖ Proceedings 34th Workshop on Geothermal Reservoir Engineering, Stanford University, SGP-TR-187. Kreft, A., and Zuber, A. (1991), ―On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions,‖ Chemical Engineering Science, 33, 1471-1480. Li, X. and Yortsos, Y.C. (1995), ―Visualization and Simulation of Bubble Growth in Pore Networks,‖ American Institute of Chemical Engineers, Col. 41, No.2, 214-222. Müller, N. (2011), ―Supercritical CO2-Brine Relative Permeability Experiments in Reservoir Rocks— Literature Review and Recommendations,‖ Transport in Porous Media, 87, 367-383. Pistone, S. (2011), ―The Significance of CO2 Solubility in Deep Subsurface Environments,‖ MS Thesis, Stanford University. Pruess, K. (2006), ―EGS using CO2 as Working Fluid – A Novel Approach for Generation Renewable Energy with Simultaneous Sequestration of Carbon‖ Geothermics, 35, 351-367. Stacey, R. (2008), ―The Impact of Dynamic Dissolution on Carbon Dioxide Sequestration in Aquifers,‖ Engineer Thesis, Stanford University.
Chang, Y., Coats, B.K., and Nolen, J.S. (1998), ―A Compositional Model for CO2 Floods Including CO2 Solubility in Water,‖ Society of Petroleum Engineers, 155-160.
Stacey, R., Pistone, S., and Horne, R.N. (2010), ―CO2 as an EGS Working Fluid – The Effects of Dynamic Dissolution on CO2-Water Multiphase Flow,‖ GRC Transactions.
Chen, CY (2005), ―Liquid-Gas Relative Permeabilities in Fractures: Effects of Flow Structures, Phase Transformation and Surface Roughness,‖ PhD thesis, Stanford University.
Tsimpanogiannis, I.N. and Yortsos, Y.C. (2002), ―Model for the Gas Evolution in a Porous Medium Driven by Solute Diffusion,‖ Environmental and Energy Engineering, 48, No. 11, 2690-2710.
Crank, N. (1975), The Mathematics of Diffusion, Oxford University Press, Oxford, England. Duan, Z., and Sun, R., (2003), ―An Improved Model Calculating CO2 Solubility in Pure Water and Aqueous NaCl Solutions from 273 to 533 K and from 0 to 2000 bar,‖ Chemical Geology, 193, 257-271.
Ueda, A., Nakatsuka, Y., Kunieda, M., Kuroda, Y., Yajima, T., Satoh, H., Sugiyama, K., Ozawa, A., Ohsumi, T., Wakahama, H., Mito, S., Kaji, Y., and Kaieda, H., (2009), ―Laboratory and Field Tests of CO2-Water Injection into the Ogachi Hot Dry Rock Site, Japan,‖ Energy Procedia, 1, 3669-3674.
Duan, Z., Sun, R., Zhu, C., and Chou, I, (2005), ―An Improved Model for the Calculation of CO2 Solubility in aqueous Solutions Containing Na+, K+, Ca2+, Mg2+, Cl-, and SO42-,‖ Marine Chemistry, 98, 131-139.
Yanagisawa, N., Matsunaga, I., and Sugita, H., (2007), ―Estimation of Mineral Transportation in HDR Circulation Test,‖ 32nd Workshop on
Geothermal Reservoir Engineering, Stanford University, SGP-TR-183. Yanagisawa, N., Matsunaga, I., Sugita, H., Sato, M., and Okabe, T., (2008), ―Temperature-Dependent Scale Precipitation in the Hijiori Hot Dry Rock System, Japan,‖ Geothermics, 37, 1-18. Yanagisawa, N., (2010), ―Ca and CO2 Transportation and Scaling in HDR System,‖ Proceedings World Geothermal Congress.
