Effect of Gas Flow Rate on Hydrate Formation Within the Hydrate Stability Zone
Abstract
We form methane hydrate in brine-saturated, coarse-grained samples, under hydrate-stable conditions, by injecting methane vapor at various flow rates. Decreasing the flow rate results in higher hydrate saturation, lower brine saturation, a smaller affected volume, and larger average pressure differentials across the sample. We interpret that the longer execution times at lower flow rates allow for additional methane transport and hydrate formation at the hydrate-brine interface. As a result, the hydrate skin is thicker at lower flow rates and thus is capable of sustaining larger pressure differentials. In several experiments, we stop brine flow and supply methane gas to the sample for an additional 800 hrs. During this period, hydrate continues to form, pressure differentials develop, and the bulk density changes within the affected volume. We interpret that there is gas present in the sample that is disconnected from the gas source. Hydrate forms around the disconnected gas due to methane transport through the skin that surrounds it, causing the internal gas pressure to decline and leading to inward collapse and net volume decrease. This lowers the brine pressure and creates a differential pressure across the sample that induces gas flow. This study indicates that lower gas flow rates through the hydrate stability zone can produce very high saturations of hydrate but require a larger differential pressure to sustain flow. Ultimately, this process is an alternative mechanism for sustained upward gas flow and hydrate formation far above the base of the hydrate stability zone.
Key Points
- We performed five hydrate formation experiments at two applied brine flow rates and four brine shut-in experiments
- Lower flow rates allow more hydrate to form, thicken the hydrate skin, and raise the average pressure differential
- During shut-in hydrate forms to very high saturations and disconnected gas conversion to hydrate create pressure gradients that induce flow
1 Introduction
Methane hydrate is a crystalline solid composed of methane gas trapped within a water cage (Kvenvolden & McMenamin, 1980). Hydrate is stable at high pressure, low temperature, and low salinity and forms when the local methane concentration exceeds the solubility of methane in water (Sloan & Koh, 2007). Hydrates occur in marine environments and beneath permafrost regions (Boswell & Collett, 2011; Kvenvolden, 1993; Shipley et al., 1979) and are estimated to contain between 500 and 2,500 gigatons of carbon globally (Boswell & Collett, 2011; Milkov, 2004).
Hydrates in sand reservoirs are of particular interest as a potential energy resource due to their favorable production characteristics (e.g., Koh et al., 2016; Konno et al., 2017; Moridis, 2008). Some reservoirs consist of meter-scale sand layers, bounded by muds, that cross-cut the base of the hydrate stability zone. High concentrations of hydrate (60–90%) far above and free gas below the base of the hydrate stability zone have been observed in these reservoirs (Boswell et al., 2009; Boswell, Collett, et al., 2012; Crutchley et al., 2015; Tréhu et al., 2004). The processes responsible for the formation of these thick, high concentration, hydrate deposits remain a conundrum.
There are several potential mechanisms to explain hydrate formation in these reservoirs (Malinverno & Goldberg, 2015; Nole et al., 2016; Rempel, 2011; Xu & Ruppel, 1999). One primary proposed mechanism, however, is the transport of free methane gas over hundreds of kilometers into the gas hydrate stability zone from below (Crutchley et al., 2015; Liu & Flemings, 2006; Liu & Flemings, 2007; Torres et al., 2004). Methane gas, driven upward by buoyancy, preferentially accumulates in sand layers (England et al., 1987; Schowalter, 1979). The overlying mud restricts vertical gas migration, due to its high capillary entry pressure (England et al., 1987; Schowalter, 1979), forcing gas to flow updip into the gas hydrate stability zone where it forms hydrate (Liu & Flemings, 2006; Torres et al., 2004; Tréhu et al., 2004). Modeling investigations (Liu & Flemings, 2007; You et al., 2015) previously suggested that hydrate formation is limited by elevated salinities that create bulk three-phase (gas-hydrate-brine) equilibrium conditions that then allow for upward gas flow.
We previously developed an experimental method to investigate the fundamental behaviors of hydrate formation during gas injection into the hydrate stability zone (Meyer et al., 2018). Based on these experiments, we proposed that a continuous hydrate skin nucleates rapidly at the gas-brine interface upon gas injection, forming a barrier that separates the gas and brine phases. This provides an alternative mechanism for gas transport through the hydrate stability zone where hydrate formation is limited by methane transport through the hydrate skin, rather than by elevated salinities. Since those experiments were performed at the same flow rate, however, it is not clear whether the behavior is sustainable at lower flow rates.
We performed five hydrate formation experiments by removing brine, at a range of constant rates, from a brine-saturated sand sample under hydrate-stable conditions while supplying methane gas to the sample at a constant pressure. We also performed brine shut-in experiments after the brine removal period, by stopping brine flow, but continuing to supply gas to the sample for approximately 800 hrs. During brine removal, we found that decreasing the flow rate generates higher hydrate saturations and produces larger temporary pressure differentials between the upstream and downstream transducers. During brine shut-in, we found that (1) the hydrate continues to form, but at a rate decreasing with time; (2) the bulk density decreases near the gas inlet and increases near the formation front; and (3) there are periods of no gas flow associated with the development of pressure differentials. We interpret that decreasing the flow rate allows more time for hydrate skin development, resulting in higher hydrate saturations, and that, after halting brine removal, methane transport across the skin continues to drive hydrate formation. These findings suggest that hydrate formation during gas injection could form very high hydrate saturations, in coexistence with free gas, far above the base of hydrate stability in natural systems.
2 Methods
We performed three “Mid” flow experiments at a brine removal rate of 0.06 mL/hr and two “Low” flow experiments at a brine removal rate of 0.03 mL/hr (Table 1). We compared these experiments to three we performed at a “High” flow rate of 0.18 mL/hr (Table 1) that were presented in Meyer et al. (2018). In addition, for each flow rate, we performed one brine shut-in experiment for approximately 800 hrs (Table 1). We also performed one short shut-in experiment (167 hrs) after Low-1 (Table 1) in an X-ray computed tomography (CT) scanner to observe the core-scale behavior during this period. All experiments were performed in a vertical pressure vessel consisting of steel end caps and an X-ray transparent, aluminum cylinder surrounded by a cooling jacket (Figure 1). The samples were kept approximately 10.5 °C below the stability temperature (Table 1), to encourage rapid hydrate nucleation (Rees et al., 2011; Seol & Kneafsey, 2009; You et al., 2015).
| Test | Porosity, ϕgrav | Salinity, Ci (wt % NaCl) | Pressure, Ppore (MPa) | Temp, Tconf (°C) | Stable tempa (°C) | Brine flow rate (mL/hr) | CT | Shut-in |
|---|---|---|---|---|---|---|---|---|
| High-1b | 0.41 | 7 | 12.24 | 1.01 | 11.5 | 0.18 | Y | N |
| High-2b | 0.38 | 1.05 | N | N | ||||
| High-3b | 0.39 | 1.02 | N | Y | ||||
| Mid-1 | 0.40 | 0.64 | 0.06 | N | N | |||
| Mid-2 | 0.40 | 1.38 | N | N | ||||
| Mid-3 | 0.40 | 0.98 | N | Y | ||||
| Low-1 | 0.38 | 1.03 | 0.03 | Y | Yc | |||
| Low-2 | 0.39 | 0.98 | N | Y |
- a Maximum temperature at which hydrate is stable at experiment pressure and salinity conditions.
- b Experiments presented previously in Meyer et al. (2018).
- c Shut-in was only performed for 167 hrs.
We performed the experiments using the methodology described in Meyer et al. (2018), with the one exception that the samples were always kept vertical after packing. This modification to the packing procedure helped maintain more homogeneous sample porosity. The samples consisted of clean, silica sand (362-μm median grain size) mixed with 0.5 wt % smectite-rich clay (Casey et al., 2013). The clay was added to accelerate hydrate nucleation (Riestenberg et al., 2003). We packed the samples using slow, dry pluviation (Germaine & Germaine, 2009) and saturated them with 7 wt % sodium chloride brine by pulling five pore volumes of fluid through the sample while under vacuum. We used this concentration of brine to maintain consistency with the previous experiments we performed (Meyer et al., 2018). We then pressurized and cooled the sample to experimental conditions (Table 1). During brine removal, we withdrew brine from the base of the sample as a constant rate with methane gas connected to the top of the sample at a constant pressure. During shut-in, we stopped brine removal but continued to supply gas.
We performed two experiments, High-1 and Low-1, within a medical CT scanner (Table 1). We collected scans, prior to each experiment, of the samples filled with only methane (dry) and only brine (wet) and then collected scans at least every 24 hrs during the experiments. From the wet and dry CT scans, we determined the porosity (ϕCT) and bulk density endpoints of each voxel. From the CT scans taken during each experiment, we determined the bulk density (ρb) and the total affected volume (Vaff). The affected volume is defined by the region of the sample where the bulk density decrease, relative to the initial condition, exceeds the CT measurement error (±0.024 g/mL) due to either gas and/or hydrate presence. Full derivation and definition of these CT-derived results are described in Meyer et al. (2018).
3 Results
3.1 Sample Porosity
The CT-derived porosity, averaged over each slice, decreased downward from 44% to 39% in High-1 and was constant at 40% in Low-1 (Figure 2a). Sample handling created narrow, high porosity fingers extending down the edges of the sample in High-1 (Figure 2b). Our modification to the packing method (section 2) eliminated these high porosity artifacts in Low-1 (Figure 2c).
3.2 Pressure Differentials
We observed temporary pressure differentials (dP = Pin − Pout) between the inlet (Pin) and outlet (Pout) transducers (Figure 1) during both the removal and shut-in periods of each experiment (Figure 3). The pressure differentials were generally greater for the Low experiments (Figure 3c) than for the High experiments (Figure 3a). However, the rate of differential pressure increase was proportional to the brine removal rate, averaging 0.19, 0.1, and 0.06 MPa/hr in the High, Mid, and Low experiments, respectively.
We define the critical pressure differential (dPcrit) as the maximum value prior to a rapid reduction in dP. The High experiments had many pressure differentials with dPcrit magnitudes generally lower than 0.1 MPa (Figure 3d: blue bars). In contrast, the Low experiments had fewer pressure differentials with a much broader distribution of dPcrit magnitudes that reached maximum values of 0.8 (Figure 3d: green bars). The average dPcrit during brine removal in the High (Figure 3d, blue dot), Mid (Figure 3d, red dot), and Low (Figure 3d, green dot) experiments were 0.05, 0.10, and 0.16 MPa, respectively.
During shut-in, large pressure differentials developed in all experiments and generally increased with time (Figure 3e). However, in contrast to the brine removal period, there was no correlation between the average magnitude of dPcrit and the original brine removal rate.
3.3 Fluid Volumes
The volume of methane injected (Vm) during brine removal, relative to the volume of brine removed (Vl), was greatest in the Low experiments (Figure 4a: green dots) and least in the High experiments (Figure 4a, blue dots). During shut-in, methane continued to flow into the sample, but the flow rate decreased with time in all experiments (Figure 4b). The gas flow rate immediately after shut-in was highest for High-3 (Figure 4b, blue line), which had the highest brine flow rate (0.18 mL/hr) during the removal period, and lowest for Low-2 (Figure 4b, green line), which had the lowest brine flow rate (0.03 mL/hr) during the removal period. At later times (>200 hrs elapsed), the gas flow rates decreased in all experiments (Figure 4b). There were also extended periods of no methane flow into the sample followed by short periods of rapid gas flow (Figure 4b inset, green line). These cycles were associated with the development of differential pressures (dP) that were qualitatively similar (Figure 4b inset, black line) to those observed during brine removal (Figures 3a–3c). During dP development, no methane flowed into the sample, and during dP reduction, methane flowed into the sample at rates 10 times faster than the applied brine removal rate (Figure 4b inset).
3.4 CT-Derived Bulk Density
At the beginning of brine removal in High-1, bulk density decrease exceeded the CT measurement error within the top 0.5 cm of the sample (Figure 5a, solid black line) due to gas injection during experiment initialization. This density decrease was concentrated at the sample edges (Figure 5b) where the initial porosity was high (Figure 2b). After 4.7 mL of brine had been removed, Δρb exceeded the CT measurement error within 1.5 cm of the inlet (Figure 5a, dashed black line). Below this region, the density decreased along the sample edges (Figure 5c). After 9.4 mL of brine removed, Δρb exceeded the CT measurement error within 4 cm of the inlet (Figure 5a, dotted black line). Below this region, the density decreased at the sample edge and across the sample (Figure 5d).
At the beginning of brine removal in Low-1 (Figure 6a, solid black line), the only discernible change in bulk density from the initial was concentrated at the gas inlet (Figure 6b). After 5 mL of brine was removed, Δρb exceeded the CT measurement error within 1 cm of the inlet (Figure 6a, dashed black line). Below this region, the density decreased along the edges of the sample (Figure 6c). After 9.4 mL of brine was removed (Figure 6a: dotted black line), Δρb exceeded the CT measurement error within 3 cm of the inlet. Below this region, the density decreased primarily down one half of the sample (Figure 6d). The flow behavior, indicated by the progression of the low density region, is qualitatively similar to that observed in High-1 (Figures 5b–5d), despite dramatically different porosity distributions (Figures 2b and 2c).
After a 167-hr shut-in of Low-1, the bulk density within the affected volume decreased within the region from 0 to 1.5 cm by as much as 0.25 g/mL (Figure 7a, red line) and increased within the region from 1.5 to 6.3 cm by as much as 0.45 g/mL (Figure 7a, green line). Throughout the affected volume, behind the red line in Figure 7b, the average bulk density increased by 0.016 g/mL. A two-dimensional slice through the sample (Figure 7b) shows that density increased within 1.5 to 4 cm of front of the affected volume (Figure 7b, red line) and decreased near the inlet.
3.5 Affected Volumes
During brine removal, the affected volume (Vaff; section 2) increased linearly with the volume of brine removed and was always greater in High-1, compared to Low-1 (Figure 8a). During the shut-in of Low-1, Vaff decreased modestly (Figure 8b) because the bulk density in certain voxels increased (Figure 7b), which reduced Δρb to below the CT measurement error. As a result, those voxels were no longer considered “affected” in our determination of the affected volume.
4 Mass Balance Analysis
The volumetric injection ratio (Xinj) is the ratio of the volume of methane injected to the volume of brine removed. The mass conversion ratio (Xconv) is the ratio of the mass of methane converted to hydrate to the total mass of methane injected (Meyer et al., 2018). With no gas conversion (Xconv = 0), the volume of methane injected equals the volume of brine removed (Xinj = 1). We confirmed this behavior in our two-phase gas flooding experiment presented in Meyer et al. (2018). At our experimental pressure and temperature conditions, total gas conversion (Xconv = 1) results in 5.34 times more methane injected than brine removed (Xinj = 5.34); this solution is derived in Meyer et al. (2018). These cases represent the minimum (Figure 4, solid black line) and maximum (Figure 4, dashed black line) hydrate formation scenarios for our experiments.
In all experiments, Xinj was greater than the minimum end-member (Figure 9, black line) and increased over time (Figure 9), indicating the partial and increasing conversion of the injected methane into hydrate. During brine removal, Xconv was greatest in the Low experiments (Figure 9a, green dots) and lowest in the High experiments (Figure 9a, blue dots). During the shut-ins of High-3 (Figure 9b, blue line), Mid-3 (Figure 9b, red line), and Low-2 (Figure 9b, green line), Xconv continued to increase, but at rates that decreased with time.
We calculate the saturations of methane gas (Sg), liquid brine (Sl), and solid hydrate (Sh) within the affected volume (Vaff) during brine removal using brine and methane mass balance (Meyer et al., 2018). In High-1, the average bulk gas (Figure 10a: red dots), brine (Figure 10a: blue dots), and hydrate (Figure 10a: green dots) saturations within the affected volume were 22%, 67%, and 11%, respectively. By contrast, in Low-1, the average bulk gas (Figure 10b, red dots), brine (Figure 10b, blue dots), and hydrate (Figure 10b, green dots) saturations within the affected volume were 25%, 42%, and 32%, respectively.
During brine shut-in, we calculate the phase saturations using the same mass balance solution for brine removal (Meyer et al., 2018). However, we assume that the affected volume is constant and equal to the value at the end of brine removal because we know which voxels contain gas and/or hydrate at this point and do not observe an increase in Vaff during shut-in (Figure 8b). In Low-1, the hydrate saturation increased from 53% to 87% (Figure 10c, green dots) and the gas (Figure 10c, red dots) and brine (Figure 10c, blue dots) saturations decreased from 21% to 13% and from 26% to 0%, respectively. The continuous increase in hydrate saturation and complete consumption of brine suggests that brine is likely being drawn into the affected volume to supply water for additional hydrate formation. It is also possible, however, that Vaff is increasing but is offset by reductions Vaff due to the density increases. In this case, this calculation would underestimate the brine saturation and overestimate the gas and hydrate saturations.
We calculate the volume of hydrate in the sample (Vh) during the removal and shut-in periods from the gas and brine mass balance (Meyer et al., 2018). At the end of brine removal in the High experiments (Figure 11a, blue dots), an average of 4.8 mL of hydrate formed in the sample. By contrast, in the Mid (Figure 11a, red dots) and Low (Figure 11a, green dots) experiments, an average of 8.6 and 13.2 mL of hydrate formed by the end of the experiments. After shut-in, hydrate continued to form in the sample at a decreasing rate (Figure 11b), resulting in an additional 20, 18, and 9.6 mL of hydrate in the samples from High-3 (Figure 11b, blue line), Mid-3 (Figure 11b, red line), and Low-2 (Figure 11b, green line), respectively.
5 Discussion
A sixfold decrease in the brine flow rate increases the average hydrate saturation within the affected volume from 11% to 32% and decreases the average brine saturation from 68% to 47% at our experimental timescales (Figure 10). Decreasing the brine flow rate has little effect on the gas saturation (Figure 10). Lower flow rates also produce greater average pressure differentials across the sample (Figure 3) and reduce the affected volume by 21% (Figure 8).
During shut-in, methane flows into the sample at a decreasing rate with time (Figure 4a). The gas flow rate immediately after shut-in was greater for High-3 (Figure 4b, blue line) than Low-2 (Figure 4b, green line), but, at later times (>200 hrs elapsed), the gas flow rate is very low in all experiments. Throughout the shut-ins, hydrate saturations increase and brine saturations decrease significantly, while the gas saturation decreases slightly (Figure 10c). The bulk density within the affected volume increases overall but decreases near the inlet and increases near the front of the affected volume (Figure 7). Pressure differentials develop during shut-in (Figure 3d) and are associated with little to no gas flow into the sample (Figure 4b inset).
5.1 Flow Blockages During Brine Removal
The development of pressure differentials (Figures 3a–3c) is coincident with no gas flow (Figure 4b inset), indicating flow blockages. The increase in differential pressure (dP) is driven by the removal of brine from the sample. Thus, the rate of increase of dP is proportional to the brine removal rate such that, once a blockage is formed, dP rises faster for the High experiments than for the Low experiments (section 3.2). The reestablishment of flow is recorded by an abrupt decrease in dP at dPcrit and rapid gas flow into the sample (Figure 4b inset). dPcrit generally increases with time during the experiments and, on average, is greater and takes longer to develop in the Low experiments than the High experiments (section 3.2; Figure 12, dots).
) of 146 mol m−3, and a methane concentration at the brine-hydrate interface (
) of 61 mol m−3.We infer that the flow blockage is caused by the formation of a hydrate skin at the gas-brine interface (Meyer et al., 2018) and that dPcrit records the differential pressure necessary to break the hydrate skin. dPcrit is a function of the skin strength, which is related to its thickness. We describe the hydrate skin thickness with a one-dimensional diffusion model in Meyer et al. (2018). It is striking that both the skin thickness and the magnitude of dPcrit can be modeled as functions of the square root of time (Figure 12, black line); this finding suggests that these processes are interrelated. We interpret that the pressure differentials rise with time during the experiments due to the extra time for the skin thickness to increase. Furthermore, we interpret that dPcrit is greater in the Low experiments because the lower brine flow rates extend the time for the hydrate skin to thicken during the flow blockages.
5.2 Gas Flow and Hydrate Formation During Brine Removal
The CT results show that the affected volume, the region where we infer that gas and hydrate are present, is 21% smaller in the Low experiments than the High experiments for a given volume of brine removed (Figure 8a). Our mass balance results indicate that, within this region, the pore space is filled with a similar fraction of free gas and 3 times the fraction of hydrate in the Low, compared to the High experiments (Figure 10). The Low experiments had sixfold longer duration compared to the High experiments, which allowed significantly more methane transport across the hydrate skin. As a result, a lower fraction of the methane injected was available as free gas to advance farther into the sample. This behavior reduced the affected volume in the Low, compared to the High, experiments and produced a higher hydrate saturation within that region.
5.3 Hydrate Formation During Shut-in
During shut-in, the gas flow rate, and hence the hydrate formation rate, is greatest in the experiments that had the highest brine flow rate during the removal period and decreases over time in all experiments (Figure 4). We interpret that the High experiments have a thinner average hydrate skin at the end of brine removal, compared to the Low experiments, which allows for more rapid methane diffusion through the skin. As the skin thickness increases, however, the concentration gradient decreases, reducing the diffusion rate and driving the gradual decrease in gas flow rate observed in all experiments.
The pressure differentials formed during shut-in are generally larger in magnitude than those formed during brine removal and do not appear to scale with the brine flow rate during the removal period (Figure 3e). The volume of gas injected after skin failure (e.g., Figure 4b inset) indicates that the total volume change during pressure differential development is typically less than 1 mL. We interpret that this volume change is due to the conversion of water and disconnected gas to hydrate (Figure 13), similar to the collapse of a hydrate-encased gas bubble (Davies et al., 2010; Tohidi et al., 2001), which results in a 47% decrease in net volume. Initially, the disconnected gas is at the same pressure as the brine and these phases are separated by a hydrate skin (Figure 13a). As methane diffuses across the skin and forms hydrate at the gas-brine interface, the internal gas pressure declines, causing the brine to press on the hydrate skin (Figure 13b). Eventually, the pressure of the disconnected gas decreases enough that the hydrate skin fails, drawing brine into the affected volume and compressing the remaining disconnected gas (Figure 13c). This process produces the pressure differentials observed across the sample that occasionally cause gas flow into the sample along the interconnected gas network. We envision that, at the core-scale, the region where density increases (Figure 7b near inlet) is where disconnected gas is converting to hydrate, while the region where density is decreasing (Figure 7b near red line) is where gas is flowing into the pore space.
5.4 Field-Scale Implications
Our experiments indicate that hydrate formation at the gas-brine interface ultimately sustains upward gas transport through the hydrate stability zone and may limit hydrate formation. This behavior is similar to modeling results at both the microscale (Fu et al., 2018) and fieldscale (Riedel et al., 2006). Decreasing the flow rate not only increases the hydrate saturation but also requires larger pressure differentials to maintain gas flow. In our experiments, the pressure differentials during removal are created by removing brine from the sample, but in the field, this pressure differential is most likely created by the development of a continuous free gas column beneath the hydrate. The critical gas column height (h = dP/g · Δρl − g) is equal to the critical differential pressure (dPcrit) divided by the brine-gas density contrast (Δρl − g = ρl − ρg) and gravitational acceleration (g). This relationship indicates that the High, Mid, and Low experiments would require, on average, a gas column of 6, 10, and 16 m high, respectively; this is not uncommon in active hydrocarbon systems (Boswell, Frye, et al., 2012; Frye et al., 2012). The average gas flow rates in the field, however, are likely slower than can be achieved experimentally (Liu & Flemings, 2007; Torres et al., 2002), which suggests that larger pressure differentials may be required. Thus, it is possible that hydrate would form to such high saturations that upward gas flow ceases entirely. Where gas is able to flow, however, there is certain to be significant additional hydrate formation driven by methane diffusion through the skin. This work indicates that, under the right conditions, this process could produce very high saturations of hydrate distributed throughout a coarse-grained reservoir far above the base of the hydrate stability zone.
6 Conclusions
We form methane hydrate in brine-saturated sand packs under hydrate-stable conditions by removing brine at a constant rate and allowing methane gas to flow into the sample at a constant pressure. We then halt the brine flow and maintain the upstream methane pressure for approximately 800 hrs. Decreasing the brine flow rate increases the average hydrate saturation at the end of brine removal from 11% to 32% and hydrate continues to form over the course of the shut-in periods. These findings are consistent with our previous conceptual model where hydrate forms a solid skin at the gas-liquid interface that separates the gas and brine phases. We interpret that lower flow rates provide extra time for methane transport, which results in higher hydrate saturations and thicker hydrate skins. Since the mechanism for methane transport is the same during the brine removal and shut-in periods, hydrate continues to form at a decreasing rate. At our comparatively short experimental time scales, this process distributes high saturations of hydrate throughout a large portion of the sample. This result suggests that this mechanism could explain the presence of very high hydrate saturations far above the base of gas hydrate stability.
Nomenclature
| Symbol | Name | Dimension | Unit |
| C | Salinity | (M M−1) | (wt%) |
 |
Solubility of methane in water | (M L−3) | (mol m−3) |
 |
Solubility of hydrate in water | (M L−3) | (mol m−3) |
| Dm | Diffusion coefficient of methane in hydrate | (L T−2) | (m s−2) |
| dP | Differential pressure | (M L−1 T−2) | (MPa) |
| dPcrit | Critical differential pressure | (M L−1 T−2) | (MPa) |
| g | Gravitational acceleration | (M T−2) | (m s−2) |
| h | Critical gas column height | (L) | (m) |
| P | Experimental pressure | (M L−1 T−2) | (MPa) |
| Pin | Inlet pressure | (M L−1 T−2) | (MPa) |
| Pout | Outlet pressure | (M L−1 T−2) | (MPa) |
| Sg | Methane gas phase saturation | (−) | (−) |
| Sh | Solid hydrate phase saturation | (−) | (−) |
| Sl | Liquid brine phase saturation | (−) | (−) |
| T | Experimental temperature | (K) | (°C) |
| t | Time elapsed | (T) | (s) |
| Vh | Volume of hydrate | (L3) | (cm3) |
| Vaff | Affected volume | (L3) | (cm3) |
| Vl | Volume of brine removed | (L3) | (cm3) |
| Vm | Volume of methane injected | (L3) | (cm3) |
| Xconv | Mass conversion ratio | (−) | (−) |
| Xinj | Volumetric injection ratio | (−) | (−) |
| Δρb | Bulk density change | (M L−3) | (g cm−3) |
| Δρl − g | Brine-gas density contrast | (M L−3) | (g cm−3) |
| ϕgrav | Gravimetrically derived sample porosity | (−) | (−) |
| ϕCT | CT-derived sample porosity | (−) | (−) |
| ρb | Sample bulk density | (M L−3) | (g cm−3) |
| ρg | Gas phase density | (M L−3) | (g cm−3) |
| ρl | Liquid phase density | (M L−3) | (g cm−3) |
Acknowledgments
This work was supported by the U.S. Department of Energy under contracts DE-FE0010406, DE-FE0028967, and DE-FE0023919. Supporting data for this work are available upon request from the corresponding author. All of the X-ray CT images and acquired data used in the figures are archived in the Digital Rocks Portal (www.digitalrocksportal.org) with the project name “Methane hydrate formation during gas injection into saturated sand.” All other experimental and analytical data referenced in this article are accessible through the presented figures, tables, and references. These data can also be requested by e-mail from the corresponding author ([email protected]). We thank Peter Polito and Joshua O'Connell for their assistance and advice in assembling the experimental apparatus and executing these experiments.
