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Using Micro-positron Emission Tomography to Quantify Single and Multiphase Flow in Heterogeneous Reservoirs
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 114 (2017) 5070 – 5082
13th International Conference on Greenhouse Gas Control Technologies, GHGT-13, 14-18 November 2016, Lausanne, Switzerland
Using micro-positron emission tomography to quantify single and multiphase flow in heterogeneous reservoirs Christopher Zahaskya* and Sally M. Bensona a
Department of Energy Resources Engineering, 367 Panama St Green Earth Sciences 065, Stanford University, Stanford, CA, 94305, USA
Abstract
Understanding and quantifying the role of reservoir heterogeneity on multiphase flow and the immobilization of CO2 is essential for predicting and validating models of long-term CCS reservoir performance. In this study a novel imaging technique known as Positron Emission Tomography (PET) is used to image pulse tracer transport through a heterogeneous Berea core first during single phase water injection and then during water-gas coinjection experiments. Methods are described for using this spatially and temporally resolved tracer data to describe sub-core permeability, interstitial velocity, tracer flux, relative permeability, and water saturation. The experimental data is then used to build a multiphase, multicomponent 3D simulation model in order to confirm and validate the experimental results. The simulation results highlight the importance of sub-core heterogeneity on relative permeability and saturation distributions which has important implications for understanding and modeling CO2 distribution and trapping in heterogeneous storage reservoirs. © 2017 The Authors. Published by Elsevier Ltd. ThisLtd. is an open access article under the CC BY-NC-ND license © 2017 The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of GHGT-13. Peer-review under responsibility of the organizing committee of GHGT-13. Keywords: Positron Emission Tomography, imaging, CCS, simulation, capillary heterogeneity
1. Introduction Quantifying single and multiphase flow behavior in porous media is essential for understanding how geologically sequestered CO2 will travel and become immobilized in the subsurface. Since it is extremely difficult and expensive
* Corresponding author. Tel.: 1-715-797-3228. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of GHGT-13. doi:10.1016/j.egypro.2017.03.1660
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to study this behavior in the subsurface it is important to first perform studies of flow in porous media in the laboratory and use this data to improve our understanding of the physics of flow in the subsurface and to build more accurate numerical simulations of CO2 storage projects. While much progress has been made in characterizing and modeling the CO2-water system in porous media, uncertainty remains regarding the influence of heterogeneity on multiphase flow, specifically regarding saturation distributions, wetting phase flow, and nonwetting phase trapping. Previous work has shown the importance that capillary heterogeneity has on laboratory measured phase saturations [1] and the importance of incorporating capillary heterogeneity when modeling drainage and imbibition processes [2,3]. Previous laboratory studies have utilized X-ray Computed Tomography (CT) imaging in order to quantify multiphase flow in heterogeneous porous media. While CT imaging is a powerful tool for measuring sub-core saturations and porosity, it is limited in its ability to capture dynamic flow behavior. In this study micro-Positron Emission Tomography imaging is employed in order to measure not only phase saturations but sub-core wetting phase fluxes, interstitial velocities, relative permeability, and dispersion. Positron Emission Tomography is a non-destructive, four dimensional, reproducible, quantitative imaging technique that enables direct visualization of dynamic single phase and multiphase fluid flow in opaque materials. Emission tomography techniques are those that rely on the detection of gamma ray emissions from a radioactive tracer inside a 3D object. This is different from X-ray CT imaging which is a transmission imaging method, meaning that photons are generated externally and transmitted through the object being scanned. The advantage of PET imaging over CT is higher sensitivity and the fact that PET is a functional imaging technique as opposed to CT which is a structural imaging technique [4]. CT imaging relies on the electron density contrast between fluids (i.e. air, water) to produce different levels of attenuation allowing for saturation measurements. PET imaging relies on the presence and intensity of radioisotope imaging in the pore space to measure saturation. The contrast between no radioisotope and full pore saturation is much larger than the contrast created by the density of the fluids allowing PET to measure saturations with a greater sensitivity than CT. The direct imaging of the radioisotope dissolved in water enables 4D visualization of single and multiphase fluid displacement in a way that is often not possible with typical CT saturation information. Previously published studies utilizing PET in earth science have suffered from spatial resolution issues related to the fundamental physics of positron decay and reconstruction limits. These issues result in spatial resolutions on the order of 3mm x 3mm. For these experiments we employ a small animal micro-PET scanner which enables resolutions on the order of 1 mm due to smaller system diameter and detector element width [5]. This 1 mm resolution is approximately the same as the spatial resolution of typical medical CT scanners. In this study single phase radiotracer ([18F]FDG) pulse experiments are performed in a 3.5 inch diameter heterogeneous sandstone core in order to provide initial sub-core characterization of interstitial velocities, permeability, and dispersion. Following the single phase experiments, a drainage experiment is performed by coinjecting water, with an initial pulse of radiotracer, and nitrogen gas. Nitrogen is used in order to simplify the fluids in the system and thus focus on quantifying the influence of rock heterogeneity on fluid flow. The multiphase tracer experiments enable measurement of relative permeability, wetting phase interstitial velocity and fluxes, and saturation. Experimental results are then used to build a 3D simulation model of the experiments and are used to validate the experimental data. Quantification of these multiphase properties has important implications on relative permeability and residual, dissolution, and chemical trapping in carbon storage reservoirs. 2. Experimental methods 2.1. Core characterization The core sample used in this experiment is a 3.5 inch (8.89 cm) diameter by 5.5 inch (13.97 cm) long Berea Sandstone acquired from Cleveland Quarries. The porosity was measured using a clinical CT scanner as described in [6]. The core average porosity was found to be 20.6%, resulting in a core pore volume of approximately 200 mL. Steady state water injection at multiple flow rates was performed in order to measure the core average permeability. The measured permeability was 46 mD. The core has visible axial-parallel bedding layers due to slight variations in grain size and composition. While the bedding is subtle, it creates permeability heterogeneity that is clearly expressed in CT scans and during tracer experiments. This heterogeneity is quantified in Section 3. Multiphase characterization was performed by measuring the Mercury Injection Capillary Pressure These curves where then scaled to the coreaverage, water-nitrogen system with a Leverett-J scaling and verified with the multiphase coreflooding method
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described in [1]. Relative permeability curves were then calculated with Burdine’s method based on the capillary pressure curve [7,8]. The core average capillary pressure and relative permeability curves are shown in Figure 1.
Fig. 1. (left) Brooks-Corey capillary pressure curve that was fit to the MICP and multiphase coreflooding data. (right) Brooks-Corey relative permeability curve to water (red line) and gas (blue line) fit to relative permeability curves derived using Burdine’s method.
2.2. Coreflooding apparatus A schematic of the experimental setup used for the coreflooding experiments is shown in Figure 2. In order to perform both radiotracer injection and continuous water injection, three different Teledyne ISCO Model 500D syringe pumps were used. Nitrogen gas is injected using a Sierra C100L gas mass flow controller. Core outlet backpressure (typically around 20 psi) is maintained with an ISCO Model 1000D syringe pump. Confining pressure is applied with an ISCO 500D pump and was set to 350 psi for all experiments. Injected fluid passes through an inlet radioactivity detector prior to entering the sample holder. The effluent fluid then passes through an outlet radioactivity detector prior to being discharged into a lead-shielded waste container. Both differential (Omegadyne 150-DIFF-W/W-USBH) and absolute (Omegadyne 100-USBH) fluid pressure are measured at the inlet and outlet of the coreholder. Lead bricks and machined lead shielding is placed around several of the experiment components including the radioactivity detectors, injection syringe, tracer injection pump, backpressure pump, and the radioactivity waste reservoir. Shielding is used to reduce the radiation dose received by the experimenter and to reduce the background radiation that can increase noise during the microPET scans. The coreholder used in this study was custom built to fit in the microPET scanner and utilized a low attenuation cast nylon material for the outer confining shell. The inlet and outlet caps where machined from aluminum. There are two confining pressure ports on the inlet of the coreholder to enable temperature control via continuous fluid circulation between the coreholder and the confining pressure pump which contained a temperature control sleeve. The confining pressure water was circulated with an Eldex ReciPro Series 2000 reciprocating piston pump. The temperature of all the pumps was maintained at 20 o C during the experiments. The PET scans were performed using a Siemens pre-clinical Inveon DPET scanner at the Stanford Center for Innovation in In-Vivo Imaging (SCI3).
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Fig. 2. Schematic of experimental setup of single and multiphase PET experiments.
2.3. PET experiment summary The core was dried in a vacuum oven for several days before being loaded into the coreholder. The core was then saturated with gaseous CO2 at low pressure (~20 psi) in order to displace all the air in the core. Next, tap water was injected continuously through the sample for over 24 hours at a flow rates of 10-20 mL/min and pressures between ambient and 120 psi. Water was removed from the system and replenished with fresh tap water three times in order be sure that all of the CO2 originally in the core was either displace or dissolved into the water. Once the core was saturated with water, the coreholder was loaded into the bore of the micro-PET scanner and prior to starting the microPET scan, 4.2 millicurie of Fludeoxyglucose ([18F]FDG was injected into the ISCO tracer pump containing 75 mL of water. In order to ensure proper mixing of the tracer and water in the ISCO pump the FDG solution was first diluted with approximately 50 mL of cold water. This diluted FDG solution was then injected into the warmer water in the ISCO pump and repeatedly injected and produced from the ISCO pump six times. Once the FDG was well mixed in the ISCO pump a 60 minute PET scan was started. Shortly after the start of the scan a pulse of 2.9 mCi of radiotracer was injected at 10 mL/min for 1.5 minutes. The PET scan terminated after approximately three pore volumes of water was injected into the core. Following the 10 mL/min tracer experiment another PET scan and FDG tracer pulse was injected at 5 mL/min. In this case 1.2 mCi of tracer was injected for 3.6 min followed by water injection at 5 mL/min until the PET scan was terminated after 120 minutes. After the completion of the two single phase tracer injections a drainage experiment was started. For the drainage experiment nitrogen gas was co-injected with water at 5 mL/min each. After two hours of co-injection (roughly 6 PV of water and gas injected) a 120 minute PET scan was started. Shortly after the PET scan was started a pulse of 1.3 mCi of tracer was co-injected with the gas without changing the flow rate from 5 mL/min. The results of the single phase and multiphase experiments are described in the following sections. All of the PET scans described were reconstructed with 3D Ordered Subset Expectation Maximization using Maximum A Priori (OSEM-OP MAP)[9]. The time frames of the PET reconstructions all had equal volumes of fluid injected (10 mL per frame ~0.05 PV), so the 10 mL/min injection rate experiments have 60 second time frames and the 5 mL/min injection experiments have
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120 second time frames. The reconstructions were also corrected for deadtime between the start of the PET scan and the start of tracer injection. The images were reconstructed with voxels 0.77 mm x 0.77 mm x 0.79 mm, however the images were coarsened up to 2.5 mm x 2.5 mm x 2.5 mm in order to reduce data noise and to have a more reasonable number of grid cells for numerical simulation (~56,000 cells). 3. Single phase experimental results 3.1. Experiment repeatability PET imaging is an emerging technology for characterizing single and multiphase transport in geologic materials so it is important to verify the accuracy and repeatability of PET imaging experiments. In previous work we have demonstrated PET saturation measurement accuracy as compared with more conventional imaging techniques such as computed tomography [10]. In this study, one of our goals is to verify that the tracer injection experiments are repeatable and that PET data can be used to build sophisticated 3D numerical simulations (described in Section 5). In order to first illustrate repeatability of the tracer experiments, moment spatial analysis was used to quantify the speed and spreading of the tracer as it moved through the core. Rather than performing core-average moment analysis as is typically done via tracer inlet and outlet curves, PET imaging enables analysis of sub-core tracer transport of rows of voxels along the core parallel to the direction of flow (referred to here as streamtubes [10,11]). In order to compare the 5 mL/min tracer injection with the 10 mL/min tracer injection the normalized first moment (i.e. center of mass) was calculated for each of the streamtubes in the core at different times during the experiments. The center of mass is determined by numerical integration of the PET image tracer concentrations (C) in each streamtube (i) from the inlet of the core (x=0) to the outlet of the core (x =L) described in Equation 1. L
m1,i
³ C xdx ³ C dx i
0
L
0
(1)
i
This method of comparison was chosen for analyzing the two experiments with tracer moving at different flow rates because different flow rates produce different amounts of tracer dispersion making full core tracer curve comparisons more challenging. Figure 3 illustrates the results of streamtube tracer center of mass calculations for the 5 mL/min and 10 mL/min experiments at equivalent times during the experiment (based on pore volumes injected). From this comparison it is clear that the distribution and transport of the tracer throughout the core is very similar in the two single phase tracer injection experiments.
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Fig. 3. Center of mass comparison along the axis of the core (parallel to flow) between 5 mL/min tracer experiment and 10 mL/min tracer experiment at different times during the experiment. The dark blue dots, light blue dots, and cyan dots refer to roughly 0.2, 0.3, and 0.4 pore volumes of water injected post-tracer injection, respectively. The dashed black line indicates the trend if the center of mass in each experiment were perfectly identical.
3.2. Sub-core permeability Once the center of mass of the tracer along the core is calculated, the interstitial velocity for each streamtube can then be calculated based off the time since tracer injection began (ts). Using the assumption that the pressure drop along the core is equal to the pressure drop along each streamtube the Darcy equations for flow in the core and along each streamtube can be rearranged to obtain the permeability of each streamtube as described in Equation 2.
ki
m1,i AcIi kc tsQ
(2)
Where Q is the injection rate (5 mL/min), kc is the core average permeability, Ac is the cross sectional area of the core, and ϕi is the average streamtube porosity measured from CT scans prior to the tracer injection experiment. The resulting 2D approximation of permeability for each streamtube in the core is shown in Figure 4. This permeability map highlights the heterogeneity in permeability induced by the presence of axial-parallel bedding in the sandstone core. 4. Multiphase phase experimental results 4.1. Sub-core tracer flux calculation In order to quantify multiphase flow from the coinjection of a pulse of tracer and nitrogen gas it is essential to be able to calculate flux of water/tracer in each streamtube in the core. Using a similar methodology to the streamtube permeability measurement described in the previous section, it is possible to quantify the tracer flux in each streamtube by calculating the interstitial velocity from the difference in center of mass at two points in time and then scaling the sum of the flux to match the known injection rate of water into the core. Figure 4 shows the estimated flux for each streamtube (qw,i). From the flux map it is clear that less water is flowing into the top of the core than the bottom of the core during water-gas coinjection. Single phase flux analysis shows a much more homogeneous flux map. Since gravity effects are non-negligible, due to the density contrast between low pressure nitrogen and water, we expect the gas saturation to be slightly higher at the top of the core than the bottom of the core. This vertical saturation gradient leads to a reduction in the mobility of water across the top of the core.
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Fig. 4. (left) Sub-core permeability estimation based on center of mass travel velocity through the core during single phase tracer injection. (right) Tracer flux into core during 5 ml/min nitgrogen and tracer coinjection.
4.2. Streamtube saturation calculation Once the streamtube permeability (ki) and multiphase streamtube tracer flux have been determined it is possible to calculate the wetting phase relative permeability (krw,i) of each streamtube using the multiphase Darcy equation for the water phase described in Equation 3.
krw,i
qw,i P w L Ai ki 'p
(3)
Where L is the length of the core, Ai is the streamtube cross-sectional area, µ w is the water viscosity, and ∆p is the multiphase pressure drop in the core. Using the core-average relative permeability curves described in Section 2.1 it is possible to fit a Brooks-Corey curve (Equation 4) to the core-average result. The wetting phase residual saturation (Swir) was determined from MICP and was found to be 0.21. Lambda is the Brooks-Corey fitting coefficient and was found to be 0.2759 in order to fit the relative permeability curve shown in Figure 1.
k rw
§ S w S wir · ¨¨ ¸¸ © 1 S wir ¹
23O
O
(4)
Equation 4 can be rearranged to solve for water saturation in each streamtube (S w,i) based on the relative permeability values calculated for each streamtube in Equation 4.
S w,i
O
k rw2,i3O (1 S wir ) S wir
(5)
The resulting saturation map is shown in Figure 8. The water saturation ranges from 0.77 to 0.90, and it is clear that the gas saturation is higher in the top of the core than the bottom of the core. To our knowledge this is the first time sub-core saturations have been determined from tracer injection tests and this illustrates new utility of PET imaging for characterizing sub-core scale multiphase flow behavior. 4. Simulation model In order to validate the sub-core single and multiphase characterization and further highlight the importance of
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using laboratory data to inform simulation studies, a 3D numerical model was built of the heterogeneous Berea core used in this study. The simulation model was run using the Computer Modeling Group (CMG) STARS simulator. STARS is an advanced processes and thermal reservoir simulator. It was chosen for this study because of the ease and flexibility of modeling a water-tracer-nitrogen system, specifically the ability to handle different components in the water phase (i.e. tracers with properties that may be identical or different from the water component). The simulator is also very fast (running a ~50,000 cell multiphase model on a desktop in ~1 hr), has the option of using lab units, and using the Results 3D application it is easy to quickly visualize simulation results and export data in formats that are simple to load into other data analysis programs such as MATLAB. Replicating laboratory data with a simulation model requires detailed measurement, quantification, and accounting of several factors besides porosity and permeability. These factors include dead volume at the inlet and outlet, lateral and transverse dispersion approximation, numerical dispersion approximation, injection volume correction, and timestep control which allows direct comparison with PET experimental data. The simulation injection volume had to be corrected/reduced in order to account for the reduction in cross sectional area of the processed PET and CT data. During the coarsening process, any voxel that was not completely contained within the core was cropped from the PET datasets. This resulted in a surface area reduction of ~15% and thus the injection rate in the simulation model reduced by a similar percentage. An additional correction that is required is due to the fact that during PET reconstruction all of the decay events that are detected within a given time frame are used in reconstructing the location of the tracer during that time frame. This process leads to a ‘temporal smearing’ proportional to the timestep size. For the 5 mL/min injection experiments the reconstructed timestep length was 120 seconds, therefore the simulation output data was time-averaged every 120 seconds in order to account for this effect and enable frame-to-frame comparison between the experimental and simulation data. The last detail that is essential for accurately modeling multiphase flow is the incorporation of capillary heterogeneity [1,2,3]. Capillary heterogeneity describes small spatial variations in the capillary pressure-saturation relationship that can be related to local porosity and permeability by the widely used Leverett J-function [12] as described in Equation 6.
Pc ,i ( S w )
Ii
kc
ki Ic
Pc ,c ( S w )
(6)
Where the subscript i refers to voxel capillary pressure, porosity, and permeability and the subscript c refers to the core-average property. Capillary heterogeneity is thus implemented in the CMG simulation model by scaling the capillary pressure curve shown in Figure 1 for each grid cell by the grid cell and core-average porosity and permeability. The final simulation model was 32 x 32 x 57 grid cells, with each grid cell having dimensions of 2.5 mm x 2.5 mm x 2.5 mm. The inlet of the core was set to flow rate control of 5 mL/min for the single phase experiments and 5 mL/min water plus 5 mL/min gas injection during the drainage simulation. The tracer component was assigned identical physical and thermodynamic properties as the water. The outlet face of the core was set to pressure control of 20 psi, identical to the back pressure used during the multiphase experiments.
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4.3. Single phase comparison Single phase tracer simulation provides the most unambiguous method for validating the measured porosity and permeability maps as well as determining the sub-core dispersivity and verifying proper model setup. There are several methods that can be used to compare simulation results with laboratory and PET scan results, including inlet and outlet radioactivity tracer curves, tracer moment and center of mass comparison both for the entire core and for individual streamtubes, and qualitative visual comparisons of tracer migration through axial slices of the core. Figure 5 compares the decay corrected inlet and outlet radioactivity curves measured with the radioactivity sensors (see Figure 2) compared with the single phase simulation inlet and outlet curves. This result is produced without any history matching. There is very good agreement between the experiment and model curves which provides confidence in the model dispersion, porosity, deadvolume calculation, and permeability heterogeneity.
Fig. 5. Comparison of experimental decay corrected tracer curves (red and blue lines) with simulation derived tracer curves (black and green line)
While Figure 5 illustrates good agreement between the core average tracer migration measured in the experiments versus the simulation model, the use of PET data allows for a comparison between the sub-core scale tracer transport in the experiments versus the simulation model. Figure 6 shows the comparison of the tracer center of mass between the PET experiment the simulation model. The results of this comparison show very good agreement between the tracer transport location in time in almost all of the streamtubes.
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Fig. 6. Tracer center of mass comparison between the simulation model and the PET scan results for different timeframes (indicated by different colored points).
4.4. Multiphase phase comparison The results of the single phase experiment versus model tracer data provide confidence in the sub-core quantification of permeability heterogeneity and porosity. The next step in validating the sub-core characterization is to compare tracer and calculated saturation measurements between the PET water-gas drainage experiment and the multiphase simulation model. Figure 7 shows a comparison of the PET scan tracer transport in each streamtube versus the modeled tracer transport. The vast majority of voxels agree fairly well, however, there are a number of streamtubes in the PET data which show much slower tracer migration than expected in the simulation model. Closer analysis of these streamtubes showed that they are the tubes located at the top of the core. From the experimental tracer flux and saturation estimation described in Section 3, it is expected that the streamtubes at the top of the core will show the highest gas saturation. As the gas saturation increases it appears that the tracer transport travels more slowly than predicted by the relative permeability model used in this study. In addition to using the simulation model to compare tracer experiment results, the model can be used to assess the accuracy of the streamtube-average saturation described in Section 4.2. The right side of Figure 8 shows the streamtube-average steady-state water saturation during coinjection of water and gas at 5 mL/min each, as was done in the PET drainage experiment. The core-average saturations between the experiment and the model are 0.859 and 0.860, respectively. In order to more quantitatively compare the individual streamtube saturations derived from the PET experiments, Figure 9 plots the PET saturation calculations versus the two simulation model saturation results. The left plot shows the comparison in streamtube average saturation between the experiment and the simulation model with capillary heterogeneity (same model as the results shown in Figure 7 and 8). The right plot of Figure 9 shows the comparison of streamtube average saturation between the experiment and the simulation model which neglects capillary heterogeneity. While there is some variation between the simulation model with capillary heterogeneity and the PET experiment, the linear regression has a slope of nearly 1. This strong agreement between the model and the experimentally calculated saturation provides validation for the novel method of experimental saturation measurement
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described in this work (Section 4.2). The comparison between the model without capillary heterogeneity and the PET data shows no relationship, highlighting the importance of including capillary heterogeneity in multiphase simulations.
Fig. 7. Tracer center of mass comparison between the multiphase simulation model and the PET scan results for different timeframes (indicated by different colored points).
Fig. 8. (left) Streamtube average saturation in the core assuming the streamtube relative permeabilities are identical to the core average permeability. (right) Streamtube average saturation after water-gas coinjection for two hours in the simulation model that incorporates capillary heterogeneity.
Conclusion Micro-Positron Emission Tomography imaging of single and multiphase tracer tests enables new methods of investigation of heterogeneous porous media. The tracer tests presented in this study highlight the repeatability of micro-PET tracer studies and were used to develop a method for quantifying sub-core permeability. Following single phase tracer test characterization, nitrogen and water were coinjected in a drainage experiment. Tracer was added to the water phase during this coinjection while a PET scan was completed. Results of this experiment enabled quantification of water flux during multiphase flow and a new method for calculating sub-core relative permeabilities and saturations.
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Fig. 9. (left) Scatter plot of multiphase saturation results when capillary heterogeneity is incorporated into the model versus PET streamtube saturation results. The red line indicates the resulting linear regression, the slope is equal to 0.9975 and the line is forced through zero. (right) Scatter plot of multiphase saturation results when capillary heterogeneity is ignored versus PET streamtube saturation results.
The results derived from the experimental PET tracer tests where then compared with results from a numerical simulation model built using data extracted from the experiments. The inlet and outlet tracer curves, streamtube center of mass, and streamtube average saturations showed strong agreement between the single and multiphase experimental data and simulation results. Finally, the simulation model was used to highlight the importance of accounting for capillary heterogeneity when modeling multiphase displacement and even for identifying gravity effects during the drainage experiment. Results of this study have important implications for understanding and modeling CO 2 trapping in heterogeneous storage reservoirs, providing additional confidence in our ability to quantify and predict the longterm behavior of geologically sequestered CO2. Acknowledgements This work is funded by the Global Climate Energy Project, the Stanford Center for Carbon Storage, and the Department of Energy Resources Engineering. The Inveon DPET (microPET) scanner was funded by NIH grant number 1S10OD018130-01. Nick Vandehey, James O’Neil, Tim Doyle and Frezghi Habte provided essential radioisotope handling training, PET scanner training, instruction, and advice. Yaxin Li, Yao Yao, Daniel Hatchell, and Cindy Ni provided invaluable assistance in moving laboratory equipment across campus. References [1] Pini R, Krevor SCM, Benson SM. Capillary pressure and heterogeneity for the CO 2/water system in sandstone rocks at reservoir conditions. Advances in Water Resources 2012; 38, 48-59. [2] Li B. Modeling geological CO2 sequestration: Translations across spatial scales and advancements in nonlinear Newton solver. Stanford University PhD Thesis 2014. [3] Krevor SCM, Pini R, Li B, Benson SM. Capillary heterogeneity trapping of CO2 in a sandstone rock at reservoir conditions. Geophysical Research Letters 2011; 38, L15401. [4] Wernick MN, Aarsvold JN. Introduction to Emission Tomography. In Wernick, M. N. and Aarsvold, J. N., editors, Emission Tomography: The Fundamentals of PET and SPECT 2004; Chapter 2, pages 11-23. Elsevier. [5] Levin CS, Hoffman EJ. Calculation of positron range and its effect on the fundamental limit of positron emission tomography system spatial resolution. Physics in medicine and biology 1999; 44, 3, 781-799. [6] Akin S, Kovscek AR. Computed tomography in petroleum engineering research. Geological Society, London, Special Publications 2003; 215, 25-38. [7] Burdine NT. Relative permeability calculations from pore size distribution data. Trans. AIME 1953; 198, 71. [8] Li K, Horne RN. Comparison of methods to calculate relative permeability from capillary pressure in consolidated water-wet porous media. Water Resources Research 2006; 42.
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[9] Hudson HM, Larkin RS, Accelerated Image Reconstruction Using Ordered Subsets of Projection Data. IEEE Transactions on Medical Imaging. 1994; 13, 4, 601-609. [10] Zahasky C, Benson SM. Phase saturation validation and tracer transport quantification using microPET in a heterogeneous sandstone core. International Symposium of the Society of Core Analysts 2016; SCA2016_Temp095. [11] Pini R, Vandehey NT, Druhand J, O’Neil JP, Benson SM. Quantifying solute spreading and mixing in reservoir rocks using 3D PET imaging. Journal of Fluid Mechanics 2016; 796, 558-587. [12] Leverett MC. Capillary behaviour in porous solids. Petroleum Transactions AIME 1941; 142:152-169.
ScienceDirect Energy Procedia 114 (2017) 5070 – 5082
13th International Conference on Greenhouse Gas Control Technologies, GHGT-13, 14-18 November 2016, Lausanne, Switzerland
Using micro-positron emission tomography to quantify single and multiphase flow in heterogeneous reservoirs Christopher Zahaskya* and Sally M. Bensona a
Department of Energy Resources Engineering, 367 Panama St Green Earth Sciences 065, Stanford University, Stanford, CA, 94305, USA
Abstract
Understanding and quantifying the role of reservoir heterogeneity on multiphase flow and the immobilization of CO2 is essential for predicting and validating models of long-term CCS reservoir performance. In this study a novel imaging technique known as Positron Emission Tomography (PET) is used to image pulse tracer transport through a heterogeneous Berea core first during single phase water injection and then during water-gas coinjection experiments. Methods are described for using this spatially and temporally resolved tracer data to describe sub-core permeability, interstitial velocity, tracer flux, relative permeability, and water saturation. The experimental data is then used to build a multiphase, multicomponent 3D simulation model in order to confirm and validate the experimental results. The simulation results highlight the importance of sub-core heterogeneity on relative permeability and saturation distributions which has important implications for understanding and modeling CO2 distribution and trapping in heterogeneous storage reservoirs. © 2017 The Authors. Published by Elsevier Ltd. ThisLtd. is an open access article under the CC BY-NC-ND license © 2017 The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of GHGT-13. Peer-review under responsibility of the organizing committee of GHGT-13. Keywords: Positron Emission Tomography, imaging, CCS, simulation, capillary heterogeneity
1. Introduction Quantifying single and multiphase flow behavior in porous media is essential for understanding how geologically sequestered CO2 will travel and become immobilized in the subsurface. Since it is extremely difficult and expensive
* Corresponding author. Tel.: 1-715-797-3228. E-mail address: [email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of GHGT-13. doi:10.1016/j.egypro.2017.03.1660
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to study this behavior in the subsurface it is important to first perform studies of flow in porous media in the laboratory and use this data to improve our understanding of the physics of flow in the subsurface and to build more accurate numerical simulations of CO2 storage projects. While much progress has been made in characterizing and modeling the CO2-water system in porous media, uncertainty remains regarding the influence of heterogeneity on multiphase flow, specifically regarding saturation distributions, wetting phase flow, and nonwetting phase trapping. Previous work has shown the importance that capillary heterogeneity has on laboratory measured phase saturations [1] and the importance of incorporating capillary heterogeneity when modeling drainage and imbibition processes [2,3]. Previous laboratory studies have utilized X-ray Computed Tomography (CT) imaging in order to quantify multiphase flow in heterogeneous porous media. While CT imaging is a powerful tool for measuring sub-core saturations and porosity, it is limited in its ability to capture dynamic flow behavior. In this study micro-Positron Emission Tomography imaging is employed in order to measure not only phase saturations but sub-core wetting phase fluxes, interstitial velocities, relative permeability, and dispersion. Positron Emission Tomography is a non-destructive, four dimensional, reproducible, quantitative imaging technique that enables direct visualization of dynamic single phase and multiphase fluid flow in opaque materials. Emission tomography techniques are those that rely on the detection of gamma ray emissions from a radioactive tracer inside a 3D object. This is different from X-ray CT imaging which is a transmission imaging method, meaning that photons are generated externally and transmitted through the object being scanned. The advantage of PET imaging over CT is higher sensitivity and the fact that PET is a functional imaging technique as opposed to CT which is a structural imaging technique [4]. CT imaging relies on the electron density contrast between fluids (i.e. air, water) to produce different levels of attenuation allowing for saturation measurements. PET imaging relies on the presence and intensity of radioisotope imaging in the pore space to measure saturation. The contrast between no radioisotope and full pore saturation is much larger than the contrast created by the density of the fluids allowing PET to measure saturations with a greater sensitivity than CT. The direct imaging of the radioisotope dissolved in water enables 4D visualization of single and multiphase fluid displacement in a way that is often not possible with typical CT saturation information. Previously published studies utilizing PET in earth science have suffered from spatial resolution issues related to the fundamental physics of positron decay and reconstruction limits. These issues result in spatial resolutions on the order of 3mm x 3mm. For these experiments we employ a small animal micro-PET scanner which enables resolutions on the order of 1 mm due to smaller system diameter and detector element width [5]. This 1 mm resolution is approximately the same as the spatial resolution of typical medical CT scanners. In this study single phase radiotracer ([18F]FDG) pulse experiments are performed in a 3.5 inch diameter heterogeneous sandstone core in order to provide initial sub-core characterization of interstitial velocities, permeability, and dispersion. Following the single phase experiments, a drainage experiment is performed by coinjecting water, with an initial pulse of radiotracer, and nitrogen gas. Nitrogen is used in order to simplify the fluids in the system and thus focus on quantifying the influence of rock heterogeneity on fluid flow. The multiphase tracer experiments enable measurement of relative permeability, wetting phase interstitial velocity and fluxes, and saturation. Experimental results are then used to build a 3D simulation model of the experiments and are used to validate the experimental data. Quantification of these multiphase properties has important implications on relative permeability and residual, dissolution, and chemical trapping in carbon storage reservoirs. 2. Experimental methods 2.1. Core characterization The core sample used in this experiment is a 3.5 inch (8.89 cm) diameter by 5.5 inch (13.97 cm) long Berea Sandstone acquired from Cleveland Quarries. The porosity was measured using a clinical CT scanner as described in [6]. The core average porosity was found to be 20.6%, resulting in a core pore volume of approximately 200 mL. Steady state water injection at multiple flow rates was performed in order to measure the core average permeability. The measured permeability was 46 mD. The core has visible axial-parallel bedding layers due to slight variations in grain size and composition. While the bedding is subtle, it creates permeability heterogeneity that is clearly expressed in CT scans and during tracer experiments. This heterogeneity is quantified in Section 3. Multiphase characterization was performed by measuring the Mercury Injection Capillary Pressure These curves where then scaled to the coreaverage, water-nitrogen system with a Leverett-J scaling and verified with the multiphase coreflooding method
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described in [1]. Relative permeability curves were then calculated with Burdine’s method based on the capillary pressure curve [7,8]. The core average capillary pressure and relative permeability curves are shown in Figure 1.
Fig. 1. (left) Brooks-Corey capillary pressure curve that was fit to the MICP and multiphase coreflooding data. (right) Brooks-Corey relative permeability curve to water (red line) and gas (blue line) fit to relative permeability curves derived using Burdine’s method.
2.2. Coreflooding apparatus A schematic of the experimental setup used for the coreflooding experiments is shown in Figure 2. In order to perform both radiotracer injection and continuous water injection, three different Teledyne ISCO Model 500D syringe pumps were used. Nitrogen gas is injected using a Sierra C100L gas mass flow controller. Core outlet backpressure (typically around 20 psi) is maintained with an ISCO Model 1000D syringe pump. Confining pressure is applied with an ISCO 500D pump and was set to 350 psi for all experiments. Injected fluid passes through an inlet radioactivity detector prior to entering the sample holder. The effluent fluid then passes through an outlet radioactivity detector prior to being discharged into a lead-shielded waste container. Both differential (Omegadyne 150-DIFF-W/W-USBH) and absolute (Omegadyne 100-USBH) fluid pressure are measured at the inlet and outlet of the coreholder. Lead bricks and machined lead shielding is placed around several of the experiment components including the radioactivity detectors, injection syringe, tracer injection pump, backpressure pump, and the radioactivity waste reservoir. Shielding is used to reduce the radiation dose received by the experimenter and to reduce the background radiation that can increase noise during the microPET scans. The coreholder used in this study was custom built to fit in the microPET scanner and utilized a low attenuation cast nylon material for the outer confining shell. The inlet and outlet caps where machined from aluminum. There are two confining pressure ports on the inlet of the coreholder to enable temperature control via continuous fluid circulation between the coreholder and the confining pressure pump which contained a temperature control sleeve. The confining pressure water was circulated with an Eldex ReciPro Series 2000 reciprocating piston pump. The temperature of all the pumps was maintained at 20 o C during the experiments. The PET scans were performed using a Siemens pre-clinical Inveon DPET scanner at the Stanford Center for Innovation in In-Vivo Imaging (SCI3).
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Fig. 2. Schematic of experimental setup of single and multiphase PET experiments.
2.3. PET experiment summary The core was dried in a vacuum oven for several days before being loaded into the coreholder. The core was then saturated with gaseous CO2 at low pressure (~20 psi) in order to displace all the air in the core. Next, tap water was injected continuously through the sample for over 24 hours at a flow rates of 10-20 mL/min and pressures between ambient and 120 psi. Water was removed from the system and replenished with fresh tap water three times in order be sure that all of the CO2 originally in the core was either displace or dissolved into the water. Once the core was saturated with water, the coreholder was loaded into the bore of the micro-PET scanner and prior to starting the microPET scan, 4.2 millicurie of Fludeoxyglucose ([18F]FDG was injected into the ISCO tracer pump containing 75 mL of water. In order to ensure proper mixing of the tracer and water in the ISCO pump the FDG solution was first diluted with approximately 50 mL of cold water. This diluted FDG solution was then injected into the warmer water in the ISCO pump and repeatedly injected and produced from the ISCO pump six times. Once the FDG was well mixed in the ISCO pump a 60 minute PET scan was started. Shortly after the start of the scan a pulse of 2.9 mCi of radiotracer was injected at 10 mL/min for 1.5 minutes. The PET scan terminated after approximately three pore volumes of water was injected into the core. Following the 10 mL/min tracer experiment another PET scan and FDG tracer pulse was injected at 5 mL/min. In this case 1.2 mCi of tracer was injected for 3.6 min followed by water injection at 5 mL/min until the PET scan was terminated after 120 minutes. After the completion of the two single phase tracer injections a drainage experiment was started. For the drainage experiment nitrogen gas was co-injected with water at 5 mL/min each. After two hours of co-injection (roughly 6 PV of water and gas injected) a 120 minute PET scan was started. Shortly after the PET scan was started a pulse of 1.3 mCi of tracer was co-injected with the gas without changing the flow rate from 5 mL/min. The results of the single phase and multiphase experiments are described in the following sections. All of the PET scans described were reconstructed with 3D Ordered Subset Expectation Maximization using Maximum A Priori (OSEM-OP MAP)[9]. The time frames of the PET reconstructions all had equal volumes of fluid injected (10 mL per frame ~0.05 PV), so the 10 mL/min injection rate experiments have 60 second time frames and the 5 mL/min injection experiments have
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120 second time frames. The reconstructions were also corrected for deadtime between the start of the PET scan and the start of tracer injection. The images were reconstructed with voxels 0.77 mm x 0.77 mm x 0.79 mm, however the images were coarsened up to 2.5 mm x 2.5 mm x 2.5 mm in order to reduce data noise and to have a more reasonable number of grid cells for numerical simulation (~56,000 cells). 3. Single phase experimental results 3.1. Experiment repeatability PET imaging is an emerging technology for characterizing single and multiphase transport in geologic materials so it is important to verify the accuracy and repeatability of PET imaging experiments. In previous work we have demonstrated PET saturation measurement accuracy as compared with more conventional imaging techniques such as computed tomography [10]. In this study, one of our goals is to verify that the tracer injection experiments are repeatable and that PET data can be used to build sophisticated 3D numerical simulations (described in Section 5). In order to first illustrate repeatability of the tracer experiments, moment spatial analysis was used to quantify the speed and spreading of the tracer as it moved through the core. Rather than performing core-average moment analysis as is typically done via tracer inlet and outlet curves, PET imaging enables analysis of sub-core tracer transport of rows of voxels along the core parallel to the direction of flow (referred to here as streamtubes [10,11]). In order to compare the 5 mL/min tracer injection with the 10 mL/min tracer injection the normalized first moment (i.e. center of mass) was calculated for each of the streamtubes in the core at different times during the experiments. The center of mass is determined by numerical integration of the PET image tracer concentrations (C) in each streamtube (i) from the inlet of the core (x=0) to the outlet of the core (x =L) described in Equation 1. L
m1,i
³ C xdx ³ C dx i
0
L
0
(1)
i
This method of comparison was chosen for analyzing the two experiments with tracer moving at different flow rates because different flow rates produce different amounts of tracer dispersion making full core tracer curve comparisons more challenging. Figure 3 illustrates the results of streamtube tracer center of mass calculations for the 5 mL/min and 10 mL/min experiments at equivalent times during the experiment (based on pore volumes injected). From this comparison it is clear that the distribution and transport of the tracer throughout the core is very similar in the two single phase tracer injection experiments.
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Fig. 3. Center of mass comparison along the axis of the core (parallel to flow) between 5 mL/min tracer experiment and 10 mL/min tracer experiment at different times during the experiment. The dark blue dots, light blue dots, and cyan dots refer to roughly 0.2, 0.3, and 0.4 pore volumes of water injected post-tracer injection, respectively. The dashed black line indicates the trend if the center of mass in each experiment were perfectly identical.
3.2. Sub-core permeability Once the center of mass of the tracer along the core is calculated, the interstitial velocity for each streamtube can then be calculated based off the time since tracer injection began (ts). Using the assumption that the pressure drop along the core is equal to the pressure drop along each streamtube the Darcy equations for flow in the core and along each streamtube can be rearranged to obtain the permeability of each streamtube as described in Equation 2.
ki
m1,i AcIi kc tsQ
(2)
Where Q is the injection rate (5 mL/min), kc is the core average permeability, Ac is the cross sectional area of the core, and ϕi is the average streamtube porosity measured from CT scans prior to the tracer injection experiment. The resulting 2D approximation of permeability for each streamtube in the core is shown in Figure 4. This permeability map highlights the heterogeneity in permeability induced by the presence of axial-parallel bedding in the sandstone core. 4. Multiphase phase experimental results 4.1. Sub-core tracer flux calculation In order to quantify multiphase flow from the coinjection of a pulse of tracer and nitrogen gas it is essential to be able to calculate flux of water/tracer in each streamtube in the core. Using a similar methodology to the streamtube permeability measurement described in the previous section, it is possible to quantify the tracer flux in each streamtube by calculating the interstitial velocity from the difference in center of mass at two points in time and then scaling the sum of the flux to match the known injection rate of water into the core. Figure 4 shows the estimated flux for each streamtube (qw,i). From the flux map it is clear that less water is flowing into the top of the core than the bottom of the core during water-gas coinjection. Single phase flux analysis shows a much more homogeneous flux map. Since gravity effects are non-negligible, due to the density contrast between low pressure nitrogen and water, we expect the gas saturation to be slightly higher at the top of the core than the bottom of the core. This vertical saturation gradient leads to a reduction in the mobility of water across the top of the core.
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Fig. 4. (left) Sub-core permeability estimation based on center of mass travel velocity through the core during single phase tracer injection. (right) Tracer flux into core during 5 ml/min nitgrogen and tracer coinjection.
4.2. Streamtube saturation calculation Once the streamtube permeability (ki) and multiphase streamtube tracer flux have been determined it is possible to calculate the wetting phase relative permeability (krw,i) of each streamtube using the multiphase Darcy equation for the water phase described in Equation 3.
krw,i
qw,i P w L Ai ki 'p
(3)
Where L is the length of the core, Ai is the streamtube cross-sectional area, µ w is the water viscosity, and ∆p is the multiphase pressure drop in the core. Using the core-average relative permeability curves described in Section 2.1 it is possible to fit a Brooks-Corey curve (Equation 4) to the core-average result. The wetting phase residual saturation (Swir) was determined from MICP and was found to be 0.21. Lambda is the Brooks-Corey fitting coefficient and was found to be 0.2759 in order to fit the relative permeability curve shown in Figure 1.
k rw
§ S w S wir · ¨¨ ¸¸ © 1 S wir ¹
23O
O
(4)
Equation 4 can be rearranged to solve for water saturation in each streamtube (S w,i) based on the relative permeability values calculated for each streamtube in Equation 4.
S w,i
O
k rw2,i3O (1 S wir ) S wir
(5)
The resulting saturation map is shown in Figure 8. The water saturation ranges from 0.77 to 0.90, and it is clear that the gas saturation is higher in the top of the core than the bottom of the core. To our knowledge this is the first time sub-core saturations have been determined from tracer injection tests and this illustrates new utility of PET imaging for characterizing sub-core scale multiphase flow behavior. 4. Simulation model In order to validate the sub-core single and multiphase characterization and further highlight the importance of
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using laboratory data to inform simulation studies, a 3D numerical model was built of the heterogeneous Berea core used in this study. The simulation model was run using the Computer Modeling Group (CMG) STARS simulator. STARS is an advanced processes and thermal reservoir simulator. It was chosen for this study because of the ease and flexibility of modeling a water-tracer-nitrogen system, specifically the ability to handle different components in the water phase (i.e. tracers with properties that may be identical or different from the water component). The simulator is also very fast (running a ~50,000 cell multiphase model on a desktop in ~1 hr), has the option of using lab units, and using the Results 3D application it is easy to quickly visualize simulation results and export data in formats that are simple to load into other data analysis programs such as MATLAB. Replicating laboratory data with a simulation model requires detailed measurement, quantification, and accounting of several factors besides porosity and permeability. These factors include dead volume at the inlet and outlet, lateral and transverse dispersion approximation, numerical dispersion approximation, injection volume correction, and timestep control which allows direct comparison with PET experimental data. The simulation injection volume had to be corrected/reduced in order to account for the reduction in cross sectional area of the processed PET and CT data. During the coarsening process, any voxel that was not completely contained within the core was cropped from the PET datasets. This resulted in a surface area reduction of ~15% and thus the injection rate in the simulation model reduced by a similar percentage. An additional correction that is required is due to the fact that during PET reconstruction all of the decay events that are detected within a given time frame are used in reconstructing the location of the tracer during that time frame. This process leads to a ‘temporal smearing’ proportional to the timestep size. For the 5 mL/min injection experiments the reconstructed timestep length was 120 seconds, therefore the simulation output data was time-averaged every 120 seconds in order to account for this effect and enable frame-to-frame comparison between the experimental and simulation data. The last detail that is essential for accurately modeling multiphase flow is the incorporation of capillary heterogeneity [1,2,3]. Capillary heterogeneity describes small spatial variations in the capillary pressure-saturation relationship that can be related to local porosity and permeability by the widely used Leverett J-function [12] as described in Equation 6.
Pc ,i ( S w )
Ii
kc
ki Ic
Pc ,c ( S w )
(6)
Where the subscript i refers to voxel capillary pressure, porosity, and permeability and the subscript c refers to the core-average property. Capillary heterogeneity is thus implemented in the CMG simulation model by scaling the capillary pressure curve shown in Figure 1 for each grid cell by the grid cell and core-average porosity and permeability. The final simulation model was 32 x 32 x 57 grid cells, with each grid cell having dimensions of 2.5 mm x 2.5 mm x 2.5 mm. The inlet of the core was set to flow rate control of 5 mL/min for the single phase experiments and 5 mL/min water plus 5 mL/min gas injection during the drainage simulation. The tracer component was assigned identical physical and thermodynamic properties as the water. The outlet face of the core was set to pressure control of 20 psi, identical to the back pressure used during the multiphase experiments.
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4.3. Single phase comparison Single phase tracer simulation provides the most unambiguous method for validating the measured porosity and permeability maps as well as determining the sub-core dispersivity and verifying proper model setup. There are several methods that can be used to compare simulation results with laboratory and PET scan results, including inlet and outlet radioactivity tracer curves, tracer moment and center of mass comparison both for the entire core and for individual streamtubes, and qualitative visual comparisons of tracer migration through axial slices of the core. Figure 5 compares the decay corrected inlet and outlet radioactivity curves measured with the radioactivity sensors (see Figure 2) compared with the single phase simulation inlet and outlet curves. This result is produced without any history matching. There is very good agreement between the experiment and model curves which provides confidence in the model dispersion, porosity, deadvolume calculation, and permeability heterogeneity.
Fig. 5. Comparison of experimental decay corrected tracer curves (red and blue lines) with simulation derived tracer curves (black and green line)
While Figure 5 illustrates good agreement between the core average tracer migration measured in the experiments versus the simulation model, the use of PET data allows for a comparison between the sub-core scale tracer transport in the experiments versus the simulation model. Figure 6 shows the comparison of the tracer center of mass between the PET experiment the simulation model. The results of this comparison show very good agreement between the tracer transport location in time in almost all of the streamtubes.
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Fig. 6. Tracer center of mass comparison between the simulation model and the PET scan results for different timeframes (indicated by different colored points).
4.4. Multiphase phase comparison The results of the single phase experiment versus model tracer data provide confidence in the sub-core quantification of permeability heterogeneity and porosity. The next step in validating the sub-core characterization is to compare tracer and calculated saturation measurements between the PET water-gas drainage experiment and the multiphase simulation model. Figure 7 shows a comparison of the PET scan tracer transport in each streamtube versus the modeled tracer transport. The vast majority of voxels agree fairly well, however, there are a number of streamtubes in the PET data which show much slower tracer migration than expected in the simulation model. Closer analysis of these streamtubes showed that they are the tubes located at the top of the core. From the experimental tracer flux and saturation estimation described in Section 3, it is expected that the streamtubes at the top of the core will show the highest gas saturation. As the gas saturation increases it appears that the tracer transport travels more slowly than predicted by the relative permeability model used in this study. In addition to using the simulation model to compare tracer experiment results, the model can be used to assess the accuracy of the streamtube-average saturation described in Section 4.2. The right side of Figure 8 shows the streamtube-average steady-state water saturation during coinjection of water and gas at 5 mL/min each, as was done in the PET drainage experiment. The core-average saturations between the experiment and the model are 0.859 and 0.860, respectively. In order to more quantitatively compare the individual streamtube saturations derived from the PET experiments, Figure 9 plots the PET saturation calculations versus the two simulation model saturation results. The left plot shows the comparison in streamtube average saturation between the experiment and the simulation model with capillary heterogeneity (same model as the results shown in Figure 7 and 8). The right plot of Figure 9 shows the comparison of streamtube average saturation between the experiment and the simulation model which neglects capillary heterogeneity. While there is some variation between the simulation model with capillary heterogeneity and the PET experiment, the linear regression has a slope of nearly 1. This strong agreement between the model and the experimentally calculated saturation provides validation for the novel method of experimental saturation measurement
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described in this work (Section 4.2). The comparison between the model without capillary heterogeneity and the PET data shows no relationship, highlighting the importance of including capillary heterogeneity in multiphase simulations.
Fig. 7. Tracer center of mass comparison between the multiphase simulation model and the PET scan results for different timeframes (indicated by different colored points).
Fig. 8. (left) Streamtube average saturation in the core assuming the streamtube relative permeabilities are identical to the core average permeability. (right) Streamtube average saturation after water-gas coinjection for two hours in the simulation model that incorporates capillary heterogeneity.
Conclusion Micro-Positron Emission Tomography imaging of single and multiphase tracer tests enables new methods of investigation of heterogeneous porous media. The tracer tests presented in this study highlight the repeatability of micro-PET tracer studies and were used to develop a method for quantifying sub-core permeability. Following single phase tracer test characterization, nitrogen and water were coinjected in a drainage experiment. Tracer was added to the water phase during this coinjection while a PET scan was completed. Results of this experiment enabled quantification of water flux during multiphase flow and a new method for calculating sub-core relative permeabilities and saturations.
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Fig. 9. (left) Scatter plot of multiphase saturation results when capillary heterogeneity is incorporated into the model versus PET streamtube saturation results. The red line indicates the resulting linear regression, the slope is equal to 0.9975 and the line is forced through zero. (right) Scatter plot of multiphase saturation results when capillary heterogeneity is ignored versus PET streamtube saturation results.
The results derived from the experimental PET tracer tests where then compared with results from a numerical simulation model built using data extracted from the experiments. The inlet and outlet tracer curves, streamtube center of mass, and streamtube average saturations showed strong agreement between the single and multiphase experimental data and simulation results. Finally, the simulation model was used to highlight the importance of accounting for capillary heterogeneity when modeling multiphase displacement and even for identifying gravity effects during the drainage experiment. Results of this study have important implications for understanding and modeling CO 2 trapping in heterogeneous storage reservoirs, providing additional confidence in our ability to quantify and predict the longterm behavior of geologically sequestered CO2. Acknowledgements This work is funded by the Global Climate Energy Project, the Stanford Center for Carbon Storage, and the Department of Energy Resources Engineering. The Inveon DPET (microPET) scanner was funded by NIH grant number 1S10OD018130-01. Nick Vandehey, James O’Neil, Tim Doyle and Frezghi Habte provided essential radioisotope handling training, PET scanner training, instruction, and advice. Yaxin Li, Yao Yao, Daniel Hatchell, and Cindy Ni provided invaluable assistance in moving laboratory equipment across campus. References [1] Pini R, Krevor SCM, Benson SM. Capillary pressure and heterogeneity for the CO 2/water system in sandstone rocks at reservoir conditions. Advances in Water Resources 2012; 38, 48-59. [2] Li B. Modeling geological CO2 sequestration: Translations across spatial scales and advancements in nonlinear Newton solver. Stanford University PhD Thesis 2014. [3] Krevor SCM, Pini R, Li B, Benson SM. Capillary heterogeneity trapping of CO2 in a sandstone rock at reservoir conditions. Geophysical Research Letters 2011; 38, L15401. [4] Wernick MN, Aarsvold JN. Introduction to Emission Tomography. In Wernick, M. N. and Aarsvold, J. N., editors, Emission Tomography: The Fundamentals of PET and SPECT 2004; Chapter 2, pages 11-23. Elsevier. [5] Levin CS, Hoffman EJ. Calculation of positron range and its effect on the fundamental limit of positron emission tomography system spatial resolution. Physics in medicine and biology 1999; 44, 3, 781-799. [6] Akin S, Kovscek AR. Computed tomography in petroleum engineering research. Geological Society, London, Special Publications 2003; 215, 25-38. [7] Burdine NT. Relative permeability calculations from pore size distribution data. Trans. AIME 1953; 198, 71. [8] Li K, Horne RN. Comparison of methods to calculate relative permeability from capillary pressure in consolidated water-wet porous media. Water Resources Research 2006; 42.
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[9] Hudson HM, Larkin RS, Accelerated Image Reconstruction Using Ordered Subsets of Projection Data. IEEE Transactions on Medical Imaging. 1994; 13, 4, 601-609. [10] Zahasky C, Benson SM. Phase saturation validation and tracer transport quantification using microPET in a heterogeneous sandstone core. International Symposium of the Society of Core Analysts 2016; SCA2016_Temp095. [11] Pini R, Vandehey NT, Druhand J, O’Neil JP, Benson SM. Quantifying solute spreading and mixing in reservoir rocks using 3D PET imaging. Journal of Fluid Mechanics 2016; 796, 558-587. [12] Leverett MC. Capillary behaviour in porous solids. Petroleum Transactions AIME 1941; 142:152-169.