PROCEEDINGS, Fortieth Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January 26-28, 2015
SGP-TR-204
Heat Transfer Properties and Dissolution Behavior of Barre Granite as Applied to
Hydrothermal Jet Drilling with Chemical Enhancement
Sean D. Hillson* and Jefferson W. Tester
Cornell Energy Institute, Cornell University, Ithaca, NY 14853, USA
*corresponding author: sdh93@cornell.edu
Keywords: Drilling, spallation, dissolution, silica, SiO2, sodium hydroxide, NaOH, high temperature flow reactor, heat transfer
coefficient, Barre granite
ABSTRACT
Hydrothermal jet drilling is a non-contact drilling technology that has the potential to improve the development prospects of
geothermal energy, by increasing the rate of penetration and decreasing overall drilling costs. In particular, this improvement
would facilitate development of lower grade resources where deeper drilling is required. The mechanism involves impingement of
a heated fluid jet onto the formation in the wellbore, where the high heat flux from the jet to the rock induces a steep temperature
gradient and thermal stresses at the surface. If the resulting stress field is sufficient to induce microcrack growth, thermal spallation
can occur, which is known to have high penetration rates in hard crystalline rocks such as granite and quartzite.
Our research program is focused on improved understanding of the physical attributes and interaction of the hydrothermal jet and
the rock surface, the heat flux, heat transfer coefficient, and dissolution phenomena. Barre granite has been selected as model hard
rock relevant to deep EGS resources in conduction dominated environments. Experimental studies have examined pressure / jet
temperature conditions of: 1) 250 bar / 389℃, 2) 225 bar / 370℃, and 3) 200 bar / 358℃. Heat flux delivered to the rock surface at
these conditions ranged from 410-670 kW/m2 (41-67 W/cm2) with estimated surface temperatures of 369℃, 345℃, and 328℃, for
conditions 1, 2, and 3, respectively. Additionally, hydrothermal jet drilling may be enhanced by application of chemically active
solutions along with the hydrothermal jet to facilitate the dissolution of silicate minerals and weaken the structure of the rock.
Results show that a 0.08 m NaOH solution injected at these elevated temperatures leads to a rock dissolution rate of 0.05-0.1
g/m2s, several orders of magnitude greater than dissolution in pure water at these temperature and pressure conditions.
1. MOTIVATION
Engineered/Enhanced Geothermal Systems (EGS) have the potential to create opportunities for geothermal energy development for
both electricity and direct thermal use in areas not generally considered to have high-grade resources (Tester et al., 2006). EGS
differs from conventional high-grade hydrothermal areas in that the rock mass of interest typically lacks one or more of the
following attributes: 1) a high geothermal gradient allowing for shallower well depth to reach the desired temperature; 2) the
presence of artesian water in the reservoir which can be extracted and circulated; and 3) the formation has sufficiently high matrix
or fracture permeability for inter-well hydraulic connectivity to occur with a relatively low pressure loss.
While the lack of any of these characteristics hinders the feasibility of geothermal energy utilization, a critical limiting factor at
present is the cost and difficulty of drilling wells to depths greater than 5 km which would be required to reach useful temperatures
for mid- to lower -grade EGS resources where average geothermal gradients are less than 40℃/km. Lukawski et al (2014) analyzed
historical drilling cost data of geothermal and oil and gas wells. Figure 1 shows the relationship of well costs with depth; it is
estimated that a 5 km well would cost approximately $15 million US and a well of 10 km would cost more than $30 million US.
Considering that a commercial EGS field will involve drilling several injection and production wells, the high costs of drilling
quickly diminishes the economic feasibility of many EGS projects because of the large up-front capital costs for drilling and
delayed payback periods before revenues are realized while wells are drilled and completed, and the field’s productivity is assessed.
Figure 1: Well cost as a function of depth using conventional drilling methods (from Lukawski et al, 2014).
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Hillson and Tester
The aspect of drilling that correlates most strongly with higher costs is the net penetration rate, which decreases non-linearly with
depth because of increased frequency of bit replacement as harder rocks are encountered, as well as the associated trip time for
these replacements or other drilling activities (Silverman, Lukawski, and Tester, 2015). By means of a Monte Carlo simulation,
these authors found that for an 8,000 ft (2.4 km) well, the average well cost is approximately $7 million US varying between $6.65
million (-5%) to $7.55 million (+8%) for a range of penetration rates. For deeper wells, the cost distribution broadens, meaning
that the impact of rate of penetration also becomes stronger. Therefore, a technology that can reliably increase drilling rates and/or
decrease the need for bit replacement has the potential to dramatically reduce total drilling costs. To put this perspective, deep
wells using conventional drilling techniques could have costs reduced by 10% or more if an alternative drilling technology could
significantly improve the rate of penetration.
2. SUMMARY OF PREVIOUS WORK
2.1 Spallation Drilling
Several novel drilling technologies have been investigated worldwide (Maurer, 1980; Pierce, Livesay, and Finger, 1996;
Timoshkin, Mackersie, and MacGregor, 2004), with Thermal Spallation Drilling (TSD) among the most promising for penetrating
hard crystalline rocks that are particularly resistant to conventional rotary drilling methods. Hard rock formations are commonly
found in many geothermal resource areas, for example as crystalline basement rock in conduction-dominated EGS resources. In
current practice, TSD impinges a high temperature flame-jet jet to generate a high heat flux (500-3,000 kW/m2) on the surface of
the rock, thereby inducing significant thermal stresses in a thin layer on that surface. These thermal stresses cause microfracture
growth and coalescence, rapidly leading to rock failure and the ejection of small, disc-shaped “spalls”. The process continues as
new, cooler rock surface is exposed to the high temperature jet (Potter and Tester, 1998; R.M. Rauenzahn and Tester, 1991;
Wideman, Potter, Dreesen, Potter, and Unzelman-Langsdorf, 2010; Wilkinson and Tester, 1993; E. Williams et al., 1988; R. E.
Williams, Potter, and Miska, 1996).
TSD has been used in the past to drill blast holes in quarries and for mining operations. Penetration rates in silicate-bearing igneous
rocks can be as high as 30 m/hr (100 ft/hr) (Browning, 1981; Wilkinson and Tester, 1993); these rates are much greater than the 10
m/hr (30 ft/hr) rates or less that results with conventional rotary drilling methods (Jimeno, Jimeno, and Carcedo, 1995).
Furthermore, the rock destruction mechanism does not require mechanical contact with the rock surface, reducing wear to the
bottom-hole assembly, effectively increasing bit lifetime and reducing the frequency of drill string trips. Previous TSD operations
have to date been fairly shallow (less than 0.5 km), and the spalls were adequately cleared from the hole by the hot, high velocity
exhaust gases; air drilling methods have reached depths of 10,000 ft (3 km) (Nas, Gala, and Cox, 2010), indicating that TSD could
reach much deeper than has been achieved thus far without spall removal being a limiting factor.
However, there are instances where a higher density fluid (e.g., water) must be circulated through the well, either due to natural
infiltration or to remove comminuted material and to ensure stability of the wellbore. At depths greater than about 2.3 km (7500
ft), the hydrostatic pressure at the bottom of a water-filled borehole will exceed the critical pressure of water (221 bar); furthermore,
TSD relies on high temperature fluid jets exceeding the critical temperature of water (374℃). Under these conditions the process is
also known as hydrothermal drilling, as depicted in Figure 2. Various technical aspects of the hydrothermal drilling environment
have been studied by other researchers. Earlier in our group, we conducted research related to hydrothermal flame phenomena
(Augustine and Tester, 2009). More recently, several investigators at ETH Zurich have carried out experimental measurements and
computational fluid dynamics modeling focusing on the behavior of supercritical jets injected into sub-critical concurrent flow
(Rothenfluh, Schuler, and von Rohr, 2011; Schuler, Rothenfluh, and Rohr, 2013). They also characterized the heat flux delivered
to a calorimeter (and consequent heat transfer coefficient) by a confined supercritical jet in a geometry that more closely resembles
a borehole (Rothenfluh, Schuler, and Rudolf von Rohr, 2013; Schuler, Rothenfluh, and von Rohr, 2015).
Figure 2: Conceptual illustration of the hydrothermal drilling process.
2.2 Mineral Dissolution
To improve and broaden the application of hydrothermal drilling, the rate of penetration may be accelerated by using active
chemical dissolution in conjunction with the imposed heat flux. Supplementing spallation with dissolution as a removal
mechanism may act to weaken the rock so spallation occurs more quickly, or allow for continued penetration in rocks that are not
as conducive to spallation because of their inherent physical properties. Chemical dissolution may also be useful with conventional
drilling techniques again by weakening the rock, which may lead to faster penetration rates and improved bit life. There has been
extensive work in the geochemical community investigating the dissolution behavior of minerals under a multitude of conditions,
including (but not limited) to variation of temperature, pressure, pH, and dissolved species (Balitsky, Kurashige, Balitskaya, and
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Hillson and Tester
Iwasaki, 2002; Blake and Walter, 1999; Dove, 1999; Rimstidt and Barnes, 1980); however, under the specific conditions
investigated in the present study (high temperature and pressure, basic pH), the literature is less robust, particularly with respect to
granite dissolution. Worley et al (1996) experimentally determined the dissolution rates of silica in basic, single phase solutions
from 100-200℃; the rates ranged from 10-10 to 10-5 molSi/m2∙s (geometric area basis), increasing for higher temperature and higher
pH conditions. Polizzotti et al (2004) investigated a higher temperature regime up to 450℃ (multiple phases present), and found
quartz dissolution rates as high as 0.352 molSi/m2∙s (geometric area basis).
3. EXPERIMENTAL APPROACH
3.1 Research Objectives
The experimental program described in the next section sought to investigate the heat transfer properties of sub- and super-critical
water jets impinging on a core of Barre granite, chosen as a representative crystalline rock for conduction dominated EGS. The
heat transfer properties of interest include the heat flux delivered to the rock surface from the jet, and the surface temperature of the
rock at the stagnation point. These quantities relate directly to the efficacy of thermal spallation, where heat fluxes on the order of
1,000 kW/m2 and surface temperatures of approximately 450℃ are needed to initiate spallation (R. M. Rauenzahn and Tester,
1989; Wilkinson and Tester, 1993).
The second objective of this work was to probe the dissolution behavior of Barre granite, the composition of which is given in
Table 1. Dissolution of quartz in the pressure, temperature, and pH range of interest has been fairly well characterized, but less so
for the feldspar components. These initial experiments will assess simple bulk dissolution, with future work developing a more
detailed breakdown of the preferential dissolution behavior of the various minerals.
Percent (by point
Mineral
counter analysis)
Plagioclase (primarly albite)
35.2
Quartz
27.2
Potassium Feldspar
19.4
Muscovite
8.3
Biotite
8.1
Other
1.8
Table 1: Mineral composition of Barre granite (from Chayes 1950)
3.2 Apparatus and Procedures
The apparatus used for the experiments was initially constructed by Potter Drilling, with some of the equipment repurposed from
work by Augustine (Augustine, 2009). Several modifications have been made over the last few years, including a new core reactor.
A flow diagram of the high-temperature flow system and a magnification of the core reactor are shown in Figure 3, which was
designed to mimic a miniaturized borehole geometry.
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Hillson and Tester
Figure 3: Simplified flow diagram of the high temperature flow system and the locations of thermocouples 1 to 6. A
schematic of the rock core reactor where the jet impinges on the rock surface is also shown at the right. The core
reactor is contained within an external cooling water jacket.
Deionized water is delivered from a metering pump and flows through a series of preheaters to reach the desired temperature. For
the heat transfer experiments, the jet temperature was varied over the course of the run to 3 temperatures, each at its corresponding
temperature along the boiling/ pseudo-critical curve of water, as shown in figure 4. The pressure / jet temperature conditions for
each set of experiments were: 1) 250 bar / 389℃ , 2) 225 bar / 370℃, and 3) 200 bar / 358 ℃. The hot water then flows through a
4-way valve just prior to entering the pressure vessel/cooling water jacket, which contains the core reactor. The other inlets to the
4-way valve are a thermocouple (which is used as an effective measure of the jet temperature) and 1/16” tubing that runs coaxially
through the 1/4” injection tube before mixing with the hot water inside the core reactor just before impinging on the rock. This
delayed coaxial mixing approach was taken so that high temperature chemical mixtures were confined within several layers of
containment and to limit possible corrosion to just the bottom and outside of the injection tubing and the internal core reactor walls
(which are cooled). The chemical solution is delivered by a separate metering pump, but the flow from this pump starts as
deionized water while the system is brought up to the desired operating temperature; once the desired temperature is reached, the
flow is switched to the chemical solution by means of a ball valve. The flow rate of the hot water and water/chemical solution for
all experiments was 184 mL/min and 16 mL/min, respectively; only water was during heat transfer runs used to maintain
consistency of flow conditions. Using this ratio of flow rates, the concentration of the chemical solution decreased from 1 m NaOH
being delivered from the pump to 0.08 m NaOH upon mixture in the reactor.
Figure 4: Pressure and jet temperature conditions investigated in this study: 1) 250 bar / 389℃, 2) 225 bar / 370℃, and 3)
200 bar / 358℃. Solid line is the boiling curve of water; star is the critical point of water (221 bar, 374℃); dashed
line is the pseudo-critical curve.
For the heat transfer experiments, multiple cores were used, with each having a different thickness between the injection tubing and
the obscured thermocouple (3). The rock samples used had thicknesses of 2.6 mm, 4 mm, 7.3 mm, 9.4 mm, and 11.6 mm. The
standoff distance, H, of the injection tubing for the 11.6 mm was ~6 mm, which for injection tubing with ID of 3.9 mm yields an
H/ID of 1.6; for the 2.6 mm core H/ID was 3.9, still less than H/ID ratio of greater than 5 where the axial velocity along the
centerline would start decreasing before approaching the impinged surface (Amano and Brandt, 1984). Therefore, we can expect
similar stagnation flow profiles for all experiments.
The cooling water is delivered by a pump powered by a variable frequency motor, and the flowrate is measured by a separate
flowmeter. For the heat transfer experiments, the cooling water flow is varied such that the final effluent temperatures were
approximately 80℃, 70℃, or 60℃. Multiple effluent temperatures were examined to observe whether the far-field temperature has
an impact on the surface temperature or heat transfer coefficient. For dissolution runs, the effluent temperature was kept constant at
70℃; the cooling water is also pre-treated with carbon filtration and ion exchange tanks. Early dissolution runs with hard tap
cooling water resulted in the precipitation of calcite after the hydroxide was injected, which gradually clogged a downstream filter
thereby increasing system pressure.
Thermocouples are placed at 6 locations throughout the system, as identified in Figure 3. Thermocouple 1 is the temperature of the
hot water leaving the pre-heating system – it is set so as not to exceed the boiling temperature of water at the operating pressure to
ensure single phase flow. Thermocouple 2 is in the 4-way valve just prior to injection of the hot water – calibration runs were
conducted to ensure the temperature at this location and of the jet were roughly the same with a combined flow rate of 200 mL/min.
Thermocouple 3 is obscured by the impinged surface of the rock and is not used in this study, but may be used in future work to
directly measure the surface temperature of the rock face and for validating computational modeling of the system. Thermocouple
4 is the core reactor exhaust temperature – it is used to calculate the average heat flux to the rock over its entire exposed internal
surface. Thermocouple 5 is at the base of the cooling water jacket and records the final effluent temperature. Thermocouple 6
measures the temperature of the cooling water before being injected; thermocouples 2, 5, and 6 were used to estimate the overall
instantaneous power balance of the system:
𝑝𝑜𝑤𝑒𝑟 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = Σ𝑚̇ 𝑖 𝐻𝑖 [𝑊]
(1)
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Hillson and Tester
where ṁi is the mass flow rate of stream i and Hi is the enthalpy of stream i (at points 2, 5, or 6). The total enthalpy flux for the
injected fluids and effluent ranged from 6,600 to 10,000 W depending on the experimental conditions. The time-averaged power
balances ranged in error from +2.3 to -3.6%, a reasonable degree of precision considering the various sources of error.
A sample experimental readout from a heat transfer run is shown in Figure 5. The run consists of 5 parts: 1) prep/ramp up; 2-4)
data gathering at the pressure/temperature conditions described earlier (shown in figure 4), with 3 sub-steps at each jet temperature
condition where the effluent temperature is varied; and 5) cool down. Temperatures in each sub-step were allowed to stabilize for
several minutes. Data (collected every 2 s) from a steady 2-minute period was then selected and analyzed; no major data anomalies
were found and the data spanning the 2-minute period was averaged to provide a single set of temperatures at each operating
condition. Dissolution runs consist of just 3 parts: prep/ramp up, data gathering at one of the pressure/temperature conditions, and
cool down. Once the desired conditions were reached, the NaOH solution was injected for about 30 minutes.
Figure 5: Temperature and pressure readout for a heat transfer run using the core with an impinged surface thickness of
9.4 mm. Each line corresponds to the thermocouple with the same color and number as identified in Figure 3. “Eff”
is an abbreviation for “Effluent”; “CW” is an abbreviation for “Cooling Water”.
4. RESULTS AND DISCUSSION
4.1Heat Flux and Surface Temperature
The average heat flux to the rock from the jet was determined using the following equation:
ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑡𝑜 𝑟𝑜𝑐𝑘 = 𝑞̇ =
𝑚̇𝑖𝑛𝑗 Δ𝐻
𝐴𝑖𝑛𝑡
𝑘𝑊
[ 𝑚2 ]
(2)
where ṁinj is the combined mass flow rate of the hot and injected water streams (200 g/min), ΔH is the change in enthalpy of the
injected water between Thermocouples 2 (jet) and 4 (reactor outlet), and Aint is the internal area of the blind hole. The pressures at
the locations of thermocouples 2 and 4 were assumed to be equal (i.e., the pressure drop between these points is minimal). The heat
flux typically fell within certain ranges for each condition, and increased with lower far-field cooling water temperatures: condition
1) 500-670 kW/m2; 2) 440-550 kW/m2; and 3) 410-520 kW/m2. The heat flux through the rock was then used to estimate the
surface temperature of the impinged face with the following expression:
𝑞̇ = ℎ(𝑇𝐽 − 𝑇𝑆 )
(3)
where h is the heat transfer coefficient, TJ is the jet temperature and TS is the surface temperature. With equation 3, the heat transfer
coefficient can be plotted as a function of TS, an example of which is shown in Figure 6. All curves exhibited the same general
behavior, with good agreement between runs using different rock thicknesses and for different far-field cooling water temperatures.
However, without specification of the expected heat transfer coefficient for a given condition, the range of possible surface
temperatures is quite broad. Rothenfluh (2013) investigated the surface temperature and heat transfer coefficient for an Inconel
calorimeter for pressure and temperature conditions similar to those investigated in this study. Note that the thermal conductivity
of Inconel is 11 W/mK, while for Barre granite it is 3 W/mK. The magnitudes of the heat fluxes for these two materials are
comparable for similar pressure/temperature conditions (Inconel: 700-900 kW/m2; Barre granite: 410-670 kW/m2). The slightly
lower heat flux for granite is logical considering its lower thermal conductivity, and should also lead to slightly higher surface
temperatures for granite. Table 2 provides the relevant information from Rothenfluh and estimated surface temperature for Barre
granite using the same range of heat transfer coefficients. The resulting surface temperature estimates are in fact slightly higher
than equivalent surface temperatures for Inconel, as expected. However, more precise surface temperature measurements are
needed to validate the range of heat transfer coefficient values applied to Barre granite.
P [bar]
TJ [℃]
250
225
225 (200)
389
370
358
h (range)
[W/m2K]
30 (25-35)
20 (15-25)
16 (13-18)
5
TS,Inconel
TS,Barre (range)
360
340
313
369 (363-374)
345 (335-354)
328 (320-335)
Hillson and Tester
Table 2: Comparison of heat transfer coefficients and surface temperature data for Inconel (Rothenfluh, 2013) and Barre
granite (present study)
Figure 6: Heat transfer coefficient, h, vs. surface temperature, TS, for various core thicknesses at condition 1: P=250 bar,
TJ=389℃.
Earlier in our group, Rauenzahn (1986) found that the onset of spallation in Barre granite occurred at temperatures ranging from
412-496℃ for a surface exposed to open atmosphere, results which were confirmed by Wilkinson (1993), albeit with a slightly
wider temperature range. This previous work also showed that the heat flux necessary to generate spallation could be as low as 300
kW/m2 (laser induced) to 600 kW/m2 (welding torch). This level of heat flux has already been reached in the current system, and
attaining sufficient surface temperatures are possibly within reach using lower injected water flowrates and higher jet temperatures.
However, Schuler (2015) noted that in the near critical region the temperature at the impinged surface will typically not exceed the
pseudo-critical temperature due to the fact that water in the boundary layer approaches the pseudo-critical point where the heat
capacity is elevated. Another complicating factor is that many drilling methods typically perform worse under higher confining
pressures encountered at practical well depths as comminuted rock is not as easily removed from the surface (Maurer, 1980),
although it is unclear whether this tendency is also true for thermal spallation. Future work will attempt to achieve hydrothermal
spallation by investigating this higher pressure and temperature environment.
4.2 Mineral Dissolution
The mass of the granite core is measured before and after the run to determine the amount of material removed. The bulk
dissolution rate of minerals has been calculated with the following equation:
𝑏𝑢𝑙𝑘 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = 𝑟𝑏𝑢𝑙𝑘 = 𝐴
Δ𝑚𝑟𝑜𝑐𝑘
𝑔
𝑒𝑥𝑝 ∙𝑡𝑁𝑎𝑂𝐻
[𝑚2 𝑠 ]
(4)
where Δmrock is the change in mass of the granite sample, Aexp is the exposed surface area of the core (blind hole + upper annulus,
no evidence of chemical attack on outer or lower surface), and tNaOH is the amount of time the 0.08 m NaOH solution was injected.
Dissolution during the ramp up and cool down phases is neglected, as the dissolution rate in pure water at the conditions
investigated is approximately 2 orders of magnitude below the anticipated dissolution rate, so the material dissolved during these
phases is likely negligible.
Figure 6 plots, in Arrhenius coordinates, the mass dissolution rate data for granite from the present study, and quartz/silica mass
dissolution rate data from previous investigators for comparison (Worley 1994; Polizzotti et al. 2004). Arrhenius coordinates – in
this case log(rate) vs. 1000/T[K] – are helpful for interpreting kinetic data because if the solution is far from saturation, then the
dissolution rate effectively follows 0th order kinetics (i.e., rbulk ∝ k, independent of the concentration of reactants) and the plot of
dissolution rate in Arrhenius coordinates would yield a linear trend. The empirical rate equation for silica dissolution and the
Arrhenius equation for the rate constant of this reaction are:
𝑚
𝐴
𝑛𝑒𝑡 𝑑𝑖𝑠𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝑟𝑛𝑒𝑡 = 𝑘𝑓 𝑀 𝑆 (1 − 𝑚𝐻𝑠𝑎𝑡4 𝑆𝑖𝑂4 )
𝑊
𝐻4 𝑆𝑖𝑂4
𝐸
𝑓𝑜𝑟𝑤𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝑘𝑓 = 𝐴 exp (− 𝑅𝑇)
𝑚𝑜𝑙
[ 𝑚2 𝑠𝑆𝑖 ]
𝑚𝑜𝑙𝑆𝑖
[𝑘𝑔
𝑤𝑎𝑡𝑒𝑟 𝑠
]
(5)
(6)
where AS is the surface area of the rock, MW is the mass of water, 𝑚𝐻4𝑆𝑖𝑂4 is the concentration of silicic acid (dissolved silica),
𝑠𝑎𝑡
𝑚𝐻
is the saturation concentration (solubility) of dissolved silica, A is the Arrhenius coefficient, E is the activation energy of
4 𝑆𝑖𝑂4
the dissolution reaction, R is the gas constant, and T is the absolute temperature. Note that the bulk dissolution rate calculated in
this study is actually equivalent to the dissolution rate constant of the equation for silica dissolution; in this case, the difference is
primarily one of units and this approach simplifies the comparisons for flow systems. With respect to the applicable temperature
for the present study, several uncertainties exist because of the reactor properties. First, there is a difference between the fluid and
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Hillson and Tester
surface temperatures of the rock; second, there is a temperature gradient between the jet vicinity and the outlet. The temperatures
that have been plotted here are 347, 312, and 293℃ which are averages of the estimated impinged surface temperatures (found in
Table 1) and outlet surface temperatures of 325, 280, and 260℃, which correspond to the surface temperature from a jet at the
outlet fluid temperature at thermocouple 4.
3.5
102
Dissolution Rate [g/m2s]
1000/T[K]
2.5
3
2
1.5
1
Present Study, log mOH -1.1
Polizzotti, multiple conc. and phases
Worley, log mOH -2.5
Worley, log mOH -4
Pure Water
1
10-2
10-4
10-6
10-8
10-10
10-12
25
50
100
150
200
250
300 350 400
500 600 700
T [℃]
Figure 7: Mass dissolution rate data in solutions of elevated OH- concentration (i.e., high pH) for granite (present study)
and quartz/silica (Worley 1994; Polizzotti et al. 2004)
Results from the present study agree reasonably previous work, despite the differences in rock type, experimental configuration,
and the variable nature of the temperature in the present study. Over the conditions studied, the dissolution rate ranged from 0.05 to
0.1 g/m2s on a geometric area basis. An estimation of the average dissolved silica mass fraction in the reactor product was
calculated with the following equation, using the assumption that all material removed from the rock was dissolved silica:
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐻4 𝑆𝑖𝑂4 𝑚𝑎𝑠𝑠 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑥𝐻4𝑆𝑖𝑂4 =
Δ𝑚𝑟𝑜𝑐𝑘 𝑀𝑊𝑤𝑎𝑡𝑒𝑟
𝑡𝑁𝑎𝑂𝐻 𝑚̇ 𝑖𝑛𝑗 𝑀𝑊
𝑆𝑖𝑂
2
𝑚𝑜𝑙
4 𝑆𝑖𝑂4
[ 𝑚𝑜𝑙𝐻𝑤𝑎𝑡𝑒𝑟
]
(7)
where MWi is the molecular weight of the specified component and all units in the equation have been made internally consistent.
With this equation, the average mole fraction of dissolved silica for the various dissolution runs ranged from 1×10-5 to 5×10-5,
whereas the estimated solubility of silica at these conditions is 10-7.5 to 10-6.5 (Carr and Tester, 2013). Clearly, this simple
calculation likely does not accurately describe the nature of the reaction actually occurring in the core reactor. Instead, the
dissolution in likely generating silica polymers of various lengths, as well as other dissolution products, that require a more rigorous
analysis. The system has the capability to extract fluid from the reactor, so future research will examine the composition of the
product to determine the composition and better describe any preferential dissolution that may be occurring from the various
minerals.
5. CONCLUSIONS AND FUTURE WORK
An initial investigation of the heat transfer and dissolution behavior of Barre granite has yielded results that largely agree with
previous work. Experimental conditions covered pressures /jet temperatures of 1) 250 bar / 389℃, 2) 225 bar / 370℃, and 3) 200
bar / 358℃. Over these conditions, heat fluxes ranged from 410-670 kW/m2 and jet impingement surface temperatures were
estimated to be 369℃, 345℃, and 328℃, although more precise measurements will be taken to validate the heat transfer
coefficients used to make these estimates. In order to reach surface temperatures greater than 400℃ that are capable of achieving
spallation, higher temperature jets will be injected and similar heat transfer properties will be studied.
Dissolution rates also agreed reasonably with earlier work and ranged from 0.05 to 0.1 g/m2s (geometric area basis). However, the
reactor product composition is unknown; it will be extracted in future work for further analysis to determine whether polymeric
silica is being removed from the exposed rock face and whether there is any preferential dissolution of the silicate minerals
composing Barre granite. The dissolution experiments will also extend into higher temperatures to better describe granite
dissolution at these elevated pressure, temperature, and pH conditions, as well as whether the presence of a basic solution effects or
enhances the spallation process.
ACKNOWLEDGMENTS
We’d like to thank the NSF Earth-Energy IGERT, the Cornell Energy Institute, the Department of Energy for each funding various
aspects of this project. We are also grateful to our early collaborators Adam Carr and everyone at Potter Drilling, particularly Jared
Potter, Tom Wideman, and Robert Potter, all of whom provided support in the initial stages of this work. Many thanks must also
be given to all members of the Tester group, the faculty and staff of Chemical Engineering and Earth and Atmospheric Sciences
Departments at the Cornell College of Engineering, and Glenn Swan, George Hade, and Tim Bond who helped greatly with
equipment fabrication and core preparation.
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