Impact of ambient temperature on evaporation from surface-exposed fractures


  • Tamir Kamai,

    1. Department of Environmental Hydrology and Microbiology, Zuckerberg Institute for Water Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel
    2. Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, Beer Sheva, Israel
    3. Now at Department of Land, Air and Water Resources, University of California, Davis, California, USA.
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  • Noam Weisbrod,

    1. Department of Environmental Hydrology and Microbiology, Zuckerberg Institute for Water Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel
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  • Maria Inés Dragila

    1. Department of Crop and Soil Sciences, Oregon State University, Corvallis, Oregon, USA
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[1] Surface-exposed fractures (SEFs) form a unique link between the atmosphere and the deep vadose zone. Quantifying evaporation and salt-accumulation rates within these SEFs is essential for understanding processes leading to groundwater salinization and contamination via these fractures. In this study, evaporation from SEFs (ESEFs) was quantified, mainly as a function of ambient atmospheric temperature, by using large-scale laboratory experiments and measuring evaporation under controlled conditions. In addition, ESEF was theoretically quantified based on the physical processes that govern it. The theoretical model was used to analyze ESEF rates as a function of ambient temperature, temperature gradient, fracture-aperture, and matrix pore size. ESEF was experimentally found to increase as the ambient temperature decreased. Measured evaporation rates were between about 110 and 260 g d−1 per square meter of fracture surface, for temperature differences between rock-bottom and the atmosphere of 0° and 13°C, respectively. Comparing these values with model results suggests that convection is the driving process for enhanced evaporation at low ambient temperatures. Finally, we show that ESEF rates decrease as a result of salt precipitation. During a ∼9-month period, with an imposed temperature difference of 13°C, ESEF decreased from ∼260 to ∼95 g d−1 m−2 due to salt accumulation near and on the fracture surfaces. Evaporation rates began decreasing after about 100 g m−2 of salt had precipitated and decreased to less than 50% of the initial rate after 160 g m−2 of salt had precipitated. We thus show that not only temperature, but also salt precipitation, largely affect ESEF rates.

1. Introduction

[2] Vadose zone fractures that are open at the soil surface (hereinafter referred to as surface-exposed fractures, or SEFs) can act as major conduits, enabling flow from land surface downward to underlying aquifers. In low-permeability deep vadose zones, the role of this route is intensified, often providing the only conduits through which transport of water, salts, and contaminants to groundwater can occur [Nativ et al., 1995]. Near the surface, these same fractures also participate in enhancing evaporation from the vadose zone and redirecting salts toward the fracture system.

[3] Weisbrod et al. [2000] explored in situ accumulation, dissolution, and mobility of salts in a SEF and found that salt accumulated within the fracture at rates significantly higher than would be expected from evaporation driven by diffusive venting of the fracture. Weisbrod et al. [2005] and Weisbrod and Dragila [2006] suggested air convection as a potential mechanism for fracture venting, leading to the enhanced accumulation of salts within SEFs. Convective venting can potentially remove moist air from the fracture aperture at rapid rates, increase water vapor loss, and subsequently enhance salt precipitation and accumulation on the fracture walls. Adams and Hanks [1964], Adams et al. [1969], Selim and Kirkham [1970], and Ritchie and Adams [1974], who explored evaporation from cracked soil, concluded that (1) the presence of a crack increases the total evaporation from a bare plot; (2) the water content in the soil zone adjacent to the crack is lower than the average soil water content at the same depth, indicating that the solution is drawn toward the crack; and (3) evaporation is enhanced in the presence of a surface wind. Weisbrod and Dragila [2006] suggested that in addition to infrequent events of forced (wind-driven) convection, cracks vent on a regular basis, nightly, by thermally driven convection. They demonstrated, theoretically, that during the night, when atmospheric air is cooler and denser than the fracture air, convection can discharge large quantities of moist air from the fracture. Using a Hele-Shaw cell, Nachshon et al. [2008] developed an empirical relationship between vertical thermal gradients and mass transfer rates. They showed that for thermal gradients within the range expected in natural settings, there is a significant increase in mass transfer rates due to convection compared with diffusive venting.

[4] Evaporation and salt accumulation are coupled processes. Evaporation from fracture walls dries out the matrix, creating a capillary gradient that drives solutes toward the evaporation surface. While back-diffusion directs salts back from the surface toward the matrix, continuing evaporation results in net salt accumulation on the fracture surfaces. Efflorescent crusts that develop near these surfaces interfere with the evaporation process by reducing the vapor pressure and consequently reducing evaporation rates [Nassar and Horton, 1999; Salhotra et al., 1985]. Modeling has shown that even before a crust is formed, evaporation from the soil is strongly affected by saline concentration and changes in the chemical composition of the solute [Yakirevich et al., 1997]. In addition, salt precipitates can cause pore clogging, which could reduce the evaporation rate by decreasing the evaporative surface area and decreasing the porous media permeability [Shimojima et al., 1996]. The net effect of these processes can significantly suppress the long-term evaporation rate. In one case, the evaporation rate was reduced to less than 10% of the potential evaporation [Chen, 1992].

[5] Unlike the case of soil-surface salinization where the accumulated salt remains near the surface, salts that have accumulated along fracture walls can be dissolved by surface water that enters and flows through these SEFs during flood or intensive rain events and move downward toward groundwater [Weisbrod et al., 2000]. This salinization mechanism is of great importance because dissolved salts and other chemicals in the vadose zone pore water are only required to travel a relatively short distance to the fractures and from there migrate to the underlying groundwater.

[6] This study explores evaporation from SEFs (ESEFs) driven by thermally induced free convection of fracture air. Imposed thermal gradients between a fractured-rock bottom and ambient atmosphere were used to experimentally explore the impact of nighttime and daytime conditions on ESEF rates. These rates were compared with equivalent rates of potential (pan) evaporation (PE), emphasizing the significance of the convective venting mechanism on ESEF. We further explored the importance of various parameters that may influence ESEFs by mathematically modeling the convective-venting mechanism. In addition, because we measured the evaporation rate but not the convective motion, the significance of convection controlling ESEF rates is shown by modeling convection and comparing the evaporation rates predicted by the model with experimental evaporation rates. Finally, the effect of salt accumulation on ESEF rates was experimentally studied by long-term monitoring.

2. Materials and Methods

2.1. Experiment

[7] The experimental setup was designed to mimic natural environmental conditions and comprised two main components: (1) the fracture simulator (FS), an assembly designed to simulate natural field conditions for a host fractured rock, namely, rock saturation, pore water chemistry, and rock temperature; and (2) the climate control room (CCR), a large room that permits control of atmospheric environmental conditions, namely, temperature and wind. No-wind conditions were imposed on all experiments in order to exclusively explore the impact of atmospheric air temperature on ESEFs. In addition, ESEF rates were compared with PE by placing an evaporation pan in the CCR to measure both rates under the same conditions.

2.1.1. Fracture Simulator (FS)

[8] Two FSs were constructed. Rocks for the FS were obtained from the Avdat Group chalk formation, in the northern Negev desert, Israel. For this chalk formation, Dagan [1977] reported an average porosity of 40%, and horizontal and vertical permeability of 1.1–2 and 0.7–2 mdarcy, respectively. Similar values have been reported in other studies [Nativ et al., 1995; Weisbrod et al., 1999]. Nativ and Adar [2001] reported pore diameters of 0.009–0.296 μm with an average of 0.151 μm. Four FS rock fragments were cut to dimensions of 25 × 50 × 50 cm. Two quadrants of the (inner) fracture surface of each rock fragment were lightly scratched (Figure 1), creating a grid of grooves (about 1 mm wide × 1 mm deep) to investigate the effect of surface roughness on salt precipitation (not part of the study presented here).

Figure 1.

Orientation of rocks in the fracture simulator (FS) assembly showing dimensions, labels for each block wall, and location of surface grooving. The distance between the rocks, which forms the fracture, is not drawn to scale in order to visualize the grooving in the inner surfaces.

[9] For each rock fragment, all rock faces (Figure 1) except for the (inner) fracture surface and the (outer) surface opposite to it were sealed with epoxy cement (Duralite®, Bolidet, Netherlands). Previous work has shown excellent adhesion of this epoxy to chalk, with complete prevention of leaking [Weisbrod et al., 1998, 1999]. Inner and outer surfaces were left unsealed to allow evaporation from the fracture (inner) surface and solution inflow from the (outer) surface opposite to it. Solution containers were directly connected to the outer surfaces, providing the inflow solution source. A Mariotte bottle controlled liquid tension in the solution to −5 cm of gauge pressure with respect to the bottom of the rock. The containers were attached to the rocks with epoxy, sealing all possible gaps and providing a strong sealed cast (Figure 2). In addition, an aluminum heat shield covered the containers, providing thermal insulation and minimizing biofilm growth from light exposure.

Figure 2.

The FS system. (a) Illustration of the FS (mirror image of Figure 2c, and not to scale). (b) Placement of instruments inside the rock. (c) Photograph of one FS. Numbers indicate 1, top surface with epoxy cement; 2, side surfaces with epoxy cement and polyurethane insulation; 3, solution containers with aluminum thermal cover; 4, small mass scales with Mariotte bottles; 5, large mass scale with the FS system; 6, thermocouples inside the rock; 7, spiral cylinder heaters inside the rock; and 8, second FS system.

[10] The fracture aperture was oriented vertically between rock pairs separated by 10-mm spacers. Each rock provided a fracture surface of ∼2500 cm2. Apart from the top of the aperture, the fracture-aperture perimeter was sealed with silicon RTV (Tambour, Netania, Israel). To thermally insulate the rocks from the chamber, the entire system (except for the top opening of the fracture) was additionally coated with a thick layer of polyurethane fixing foam (diphenylmethane-4, 4-diisocyanate). The total weight of each FS system was approximately 350 kg.

[11] A suite of electronic instruments was installed within the FS, including thermocouples (TCs; Copper-Constant thermocouple wire, Omega Engineering Limited, Manchester, UK), relative humidity sensors (RH; Hygroclip SC04, Rotronic, Zurich, Switzerland; and CS-500, Campbell Scientific Inc., Utah), and cylindrical spiral heaters (Isaac Dery, Haifa, Israel). Ten TCs monitored the temperature in each rock fragment. Seven TCs were situated inside the rock, 10 cm from the fracture surface and distributed vertically, 7 cm apart, from 5 to 47 cm, as measured from the top surface. Three TCs were situated inside the rock 5 cm from the fracture surface and distributed vertically 14 cm apart, from 5 to 33 cm, as measured from the top surface. The cylindrical spiral heaters were installed along the bottom of each rock and used to maintain a constant temperature (23°C) at the bottom of the rock. The heaters were monitored and controlled by the lowest TC located in the rock at a depth of 47 cm (i.e., just above the heaters).

[12] The air within the fracture aperture was monitored with TCs and relative RH sensors. Seven TCs were located within the aperture at the same elevation as the TCs inside the rock. Four RH sensors were used within the aperture: One was located at the top surface at the interface between the top of the fracture and the ambient air of the CCR; the other three RH sensors were semimobile and were used mostly at depths of 12, 26, and 40 cm.

[13] Artificial groundwater (AGW) [Arnon et al., 2005] was used for the feeding solution. The AGW contained 7738 mg L−1 total dissolved solids (TDS), with specific concentrations (mg L−1) of 345 Ca, 200 Mg, 2184 Na, 22 K, 3608 Cl, 1089 SO4, and 291 HCO3. Solution exiting the Mariotte bottles, representing evaporation from the fracture, was monitored by placing the Mariotte bottles on mass scales (BB 3100 ± 0.01 g, M.R.C., Tel-Aviv, Israel). The total weight of each FS, excluding the bottles, was also monitored (Rabbit 400 kg ± 25 g, Shekel Electronic Scales, Karmiel, Israel), such that changes in the overall rock water content could be distinguished from changes due to evaporation. In principle, if mass changes only occurred in the Mariotte bottles, this meant that all of the solution entering the rocks also left the rocks by evaporation from the fracture surface.

[14] In order to capture and mimic field conditions with the laboratory setup, and to minimize the disparity between field and laboratory situations, special attention was paid to thermal and fluid boundary conditions. It was assumed that the bottom of the rock, corresponding to a depth in the field of 50 cm, is not influenced by diurnal thermal variability and is at a constant temperature corresponding to the seasonal vadose zone temperature. A constant temperature of 23°C was selected and sustained by the cylindrical heaters. This was the average temperature measured in spring and fall at 50 cm depth at a field site in the Negev desert (same chalk rock that was used for the experimental work described here) [Pillersdorf, 2007]. With respect to pore-solution availability, it was assumed that under natural conditions the rock matrix provides an infinite source. In the laboratory, this was reproduced by the solution containers. Mimicking the natural fracture aperture required significant simplification as natural fractures vary in inclination, aperture, and connectivity with other fractures that can be sources and sinks for air [Dahan et al., 2000; Dragila and Weisbrod, 2004a, 2004b; Nativ et al., 1995]. These complexities were not simulated in the FS, which imposed ideal conditions consisting of a vertical fracture with a fixed aperture and limited cavity volume.

2.1.2. Climate Control Room (CCR)

[15] A CCR was used to test whether variability in atmospheric temperature influences evaporation, and to quantify its impact. Since the bottom boundary of the rock was kept at a constant temperature, changes in CCR ambient temperature resulted in temperature gradients between the atmospheric boundary and the rock bottom (ΔT = TrockTatm). The CCR was constructed inside an insulated shipping container, 6 m long, 2.5 m wide, and 2.5 m high. Cooling was obtained by flowing cool air (from an air conditioner) through aluminum pipes in a double-layered ceiling, which was sealed but noninsulated, thus cooling the room by radiation to impose no-wind conditions [Kamai, 2006]. Heating was controlled by six spiral heaters that were located around the CCR, 1.5 m above the floor. The temperature in the CCR was monitored with six TCs, and controlled by two of the TCs that were located at the same elevation as the FS aperture opening. Barometric pressure was monitored by a pressure transducer (MPX2100AP/GP, Motorola, Schaumburg, Illinois) located inside the CCR.

[16] PE within the CCR was measured using an evaporation pan. Space limitations in the CCR prevented the use of a standard Class A evaporation pan; instead, we used an insulated metal pan, 20 cm in diameter and 40 cm deep, a heating plate, and a Mariotte bottle for keeping the solution at a fixed level in the pan. The Mariotte bottle was set on a mass scale to monitor the evaporation rate. The same AGW solution used in the FS was used for the pan. PE was quantified under two conditions: (1) with the evaporation pan bottom heated to the same temperature as the rock bottom; and (2) without heating the pan bottom, i.e., ambient temperature.

2.1.3. Experimental Procedure

[17] Before initiating the experiments, the rocks were saturated with solution under positive hydraulic head by raising the level of the Mariotte bottles to the top level of the FS. Mariotte bottle mass was monitored to determine the solution flux entering the rocks and calculate the sorptivity (S) for each rock [Jury et al., 1991]. Because all four rocks were exposed to identical conditions, outside without cover, for more than a year prior to their assembly, it was assumed that the initial water content and matric potential distribution within them were similar. Thus differences in S values were interpreted as differences in permeability between rocks. Rock saturation continued for 2–3 weeks until the imbibition rate dropped significantly and a water film appeared on the fracture surfaces. Note that previous studies have shown that due to the existence of very small pores, chalk cannot be completely saturated without using a vacuum; the maximum saturation without vacuum is about 70–75% of the porosity [Zvikelsky and Weisbrod, 2006]. Saturation by gravity satisfied the requirements of this study, as it more realistically mimics field conditions. Following the saturation stage, the Mariotte bottles were lowered to attain a pressure of −5 cm at the bottom of the container. About 250 mL (∼1% pore volume) returned to the bottles as they were lowered from the top to bottom position. The bottles remained in the same lowered position, namely, at constant head, for all subsequent experiments.

[18] Experiments were initiated once the FS systems stabilized at the applied constant head. As an initial stage for these measurements, the fracture opening was temporarily sealed with a nylon cover for 7 days to evaluate no-evaporation conditions and to ensure that the systems had no leaks. After no-evaporation conditions were demonstrated, the cover was removed and evaporation was measured continuously for 9 months. The two FS systems were denoted FS1 with rocks A and B, and FS2 with rocks C and D. Because of experimental problems in rock A, mainly having to do with erroneous evaporation rates, data from this particular rock are not reported, nor are they included in any of the analyses.

[19] Experiments consisted of measuring evaporation while maintaining a constant temperature of 23 ± 0.5°C at the bottom of all rocks, and varying ambient temperature in the CCR. Each time the CCR temperature was set to a new value, the fracture opening was sealed with a nylon cover to prevent vapor transport while the CCR temperature stabilized. This nylon cover served to reset and calibrate the system, and to verify that solution migration ceased when no vapor exited the fracture. For each temperature setting, evaporation rates were quantified only after steady state conditions had been reached.

[20] Within the 9-month experimental period, a 60-day experiment was performed to quantify the functional dependence of ESEF on thermal gradient. The 60-day period began 20 days after the FS systems were initiated, and consisted of varying the CCR air temperature as follows: 10°, 25°, 20°, 15°, and 10°C. This sequence was selected to achieve the following conditions and objectives: (1) identical conditions in the first and last stages for comparison, especially since salt precipitation accumulating during the experiment may also affect evaporation rates, and (2) a stepwise decrease in CCR temperature, which was expected to increase convective venting and subsequently ESEF rates. Following the 60-day experiment, CCR temperature was kept constant at 9°–10°C for the remainder of the observation period (a total of 270 days), imposing a maximum thermal gradient and consequently leading to maximum ESEF rates. This long-term period of constant temperature conditions enabled us to investigate the impact of salt precipitation on evaporation rate.

[21] It should be noted that while the intent of the first 60-day experiment was to evaluate the role of thermal gradient on evaporation, salt precipitation was likely occurring and potentially affecting the evaporation rate. To assess how valid it was to use this period of data to isolate the effect of thermal gradient only, the initial conditions (10°C in the CCR) were repeated at the end of the 60 days and the evaporation rate was monitored; it was found to be similar (±2 g d−1 m−2) to the initial rate. In addition, the specific temperature sequence was conducted to counteract the impact of possible salt precipitation. Thus the impact of temperature reported herein is conservative. If there was no salt precipitation during the 60-day experiment, evaporation rate changes due to the increasing temperature gradient could only be larger.

2.2. Theory: The model

[22] A theoretical analysis was used to study parameters that might affect ESEF but could not be tested experimentally, namely, fracture aperture and matrix pore size, and to compare theoretical predictions with experimental results. Note that the comparison between model and experimental results was made without model calibration.

[23] The theoretical model does not account for osmotic potential, back-diffusion of solutes within the matrix, or salt accumulation, and assumes that the matrix is saturated. Furthermore, it assumes a uniform pore size, constant aperture width, vertical fracture surfaces, and no roughness. The conceptual model assumes that within a fracture, water evaporates at the fracture surface and then diffuses horizontally as vapor from the fracture surface toward the midplane of the fracture aperture, from where it is transported vertically upward to the atmosphere by diffusion and convection. Only convection in the form of free convection driven by density gradients is considered. Venting morphology is assumed to be composed of finger flow, where sections of the fracture experience downward flow, with upward flow in other sections. With this convection pattern (by mass conservation), half of the fracture participates in upward venting of moist air, while atmospheric air invades downward into the other half.

[24] The mathematical model comprises three linked mechanisms. The evaporation rate is controlled by the temperature and matrix capillary pressure at the wall boundary, and vapor density at the fracture midplane. The latter, in turn, is limited by the atmospheric exchange rate and the atmospheric vapor pressure. Atmospheric exchange is, in turn, controlled by the thermal gradient. The governing equations, described below, are linked by steady state conservation of vapor-mass flux with the aperture being the control volume, such that vapor flux from the fracture walls equals vapor flux to the atmosphere.

2.2.1. Governing Equations Evaporation and Diffusion

[25] Derivation of the evaporation portion of the mathematical model is based on the work of Ghezzehei et al. [2004], who provided a mathematical description of the various physical processes involved in evaporation from porous media into a cavity. The evaporation process sustains a saturated vapor pressure immediately above the evaporation surface. Capillary forces in porous media suppress the vapor pressure, where the capillary pressure Pc (Pa) is given by the classical Young-Laplace equation [Jury et al., 1991]

equation image

where σ (N m−1) is the interfacial surface tension, α is the liquid-solid contact angle, and r (m) is the radius of the capillary tube, denoted here as the pore size radius. The interfacial surface tension for pure water as a function of interfacial temperature is given by (see J. R. Cooper and R. B. Dooley, IAPWS release on surface tension ordinary water substance, 1994; available at

equation image

where b1 = 0.2358 N m−1, b2 = 1.256, b3 = −0.625, and b4 = 647.096 K are constants, and τ is a binding parameter that is determined by the interfacial temperature Tk (K).

[26] The vapor pressure e (Pa) over a moist porous surface is then given by equation (3), obtained by subtracting equations (1) and (2), and combining with equations (1)–(3) of Ghezzehei et al. [2004] that describe the relationship between vapor pressure, temperature, and matric potential:

equation image

where Tc (°C) is the interfacial temperature, and a1 = 21.87, a2 = 265.5°C, a3 = 6.41 are constants. Additionally, ρw (kg m−3) is the water density, Mw (kg mol−1) is the molecular mass of liquid water, and R (J K−1) is the universal gas constant.

[27] Equation (3) gives the vapor pressure near the fracture wall. The vapor pressure within the aperture is controlled by the upward venting process, to be derived next. Vapor transfer between the fracture wall and the fracture midplane is a first-order Fickian diffusive process that in one dimension with steady state conditions is described by equations (4)–(6) of Ghezzehei et al. [2004], taken from Rohsenow and Choi [1961] and Vargaftik [1975]. Convection

[28] Free convection is driven by vertical air density gradients, which are a function of temperature and vapor pressure [Weast and Astle, 1979]:

equation image

where ρA (kg m−3) is the moist air density, PHg (mm Hg) is the ambient (atmospheric) pressure, and eHg (mm Hg) is the vapor pressure (equation (3)). Equation (4) can be cast in terms of measurable parameters (T and RH) by substituting with equation (3), to give

equation image

where con is a unit conversion constant, equal to 7.5006156 × 10−3 Pa (mm Hg)−1.

[29] Sensitivity analysis of equation (5) reveals that the moist air density is not very sensitive to changes in RH, but is more strongly controlled by temperature. For example, within the range of temperatures and pressures expected in the field, the difference in moist air density between the extreme RH values of 0 and 100% is only 2%. More realistic RH values of 30 to 60% lead to air density differences of less than 1%. In contrast, a 10°C air temperature difference (at constant RH) changes the moist air density by about 5%.

2.2.2. Model Assumptions

[30] Convective airflow is assumed to be fully developed and laminar (Figure 3). Assuming no-slip conditions at the wall leads to a vertical air velocity within the aperture (m s−1) of U(x = 0) = U0 = 0, that increases to U(x) = U at x = δUb, where δU (m) is the boundary layer thickness and b (m) is half the aperture width (Figure 3). The vapor concentration gradient is analogous but in the opposite direction [Rohsenow and Choi, 1961]; the vapor concentration decreases from an equilibrium value C(x = 0) = C0, to the free air vapor concentration C(x) = C at x = δCb. At 20°C and 1 atm pressure, both boundary layer thicknesses can be assumed to be equal, δ = δU = δC [Ghezzehei et al., 2004, equation (8)]. Horizontal gradients in moist air density along the fracture plane were neglected in the model.

Figure 3.

Schematic showing half of a fracture aperture [after Ghezzehei et al., 2004]. The airflow velocity profile (U) and the vapor concentration profile (C) vary from U0 and C0 at the fracture surface, to U and C at the end of the boundary layer, which is determined by the boundary layer thickness, δ = δU = δC.. The fracture half width (b) ends at the aperture midplane (plane of symmetry). No variability is assumed in the direction normal to the drawing.

[31] Under steady state and assuming isothermal conditions in the horizontal x-direction (normal to the fracture plane), the vapor concentration gradient (dC/dx) is constant throughout the boundary layer, giving a vapor flux of [Ghezzehei et al., 2004, equation (11)]

equation image

where D (m2 s−1) is the vapor diffusion coefficient, the subscript HD denotes horizontal diffusion from a vertical wall, and JHD (g m−2) describes mass flux per unit area of the fracture wall surface. By combining equations (3), (5), and (6), the vapor diffusion flux from the evaporating fracture surface toward the center of the fracture aperture is described by

equation image

The vertical advective vapor flux due to convection (JV) describes the mass flux per aperture area (across the plane normal to the direction of flow), and is given by

equation image

Vertical air velocity within the fracture aperture can be described by Poiseuille flow between two parallel smooth walls which, for an incompressible viscous fluid, is described as a function of distance from the fracture wall by

equation image

with the first term being the vertical moist-air density gradient. Although convection in fractures theoretically occurs beyond a critical Rayleigh number (Rac = 27) [Nield, 1982; Nield and Bejan, 1992], this threshold was not used in the model. Instead, convective flow initiated with a positive moist-air density gradient (equation (9)).

[32] Governing conditions for airflow and vapor concentration along the fracture aperture midplane fall into two categories. The first category of behavior is for boundary layers that are smaller than or equal to the half aperture, δb. In this case, U and C are determined solely by the vertical density gradient and the atmospheric vapor concentration. The second category of behavior occurs for boundary layers that are theoretically larger than the half aperture (δ > b), but are limited by it. In this case, conditions at the symmetry plane are dominated by the boundary layer value for U(b) and C(b). In this second case, conditions of U and C are not reached within the aperture.

[33] Since δ = δU = δC, and assuming that C(x) varies with a similar function to U(x) (equation (9)), the vapor concentration can be also defined as a function of distance from the fracture surface:

equation image

with the vapor concentration at the fracture surface (C0) being a function of vapor pressure and capillary potential [Ghezzehei et al., 2004, equations (2) and (6)].

[34] The vapor removal rate by convection is given by the flux velocity and the difference between the vapor content of the exiting fracture air and the atmospheric air replacing it,

equation image

where Caper is the vapor concentration within the aperture as a function of distance from the fracture surface (x) and depth (z), evaluated by using equation (10) and integrating over the aperture domain in the z-direction. CA is the vapor concentration of atmospheric air entering the top (fracture-aperture) boundary. Since the assumption of a constant aperture requires (by conservation of mass) that half of the fracture volume be active in removing air from the aperture while ambient air enters the other half, the boundary layer thickness becomes an effective parameter for the fracture system.

2.2.3. Model Solution

[35] The model was used to calculate evaporation assuming steady state conditions, namely, constant linear temperature gradient, atmospheric vapor concentration, and evaporation rate. By conservation of mass, vapor leaving the matrix equals that leaving the fracture system through the upper boundary. Evaporation from the SEF (ESEF), which includes two fracture surfaces, was modeled using one surface only by assuming symmetry about the aperture midplane. Fracture-surface boundary conditions were controlled by the porosity and the capillary pressure (i.e., pore size, equation (1)). An average value of 40% porosity was used, with a range of pore-diameter values between 0.009 and 0.296 μm, average 0.151 μm [Nativ and Adar, 2001]. The temperature was assumed to vary only vertically, linearly between the top and bottom temperatures, also assuming equilibrium between rock and air temperature at each depth. Convection was calculated by using the air density difference between the bottom and top boundaries to give an average vertical density gradient. While the bottom boundary was kept at constant temperature (23°C), the top boundary temperature was changed for different simulations in accordance with the CCR temperatures used for the experiments.

[36] Solutions to the theoretical model, for steady state vapor removal rate, were obtained by iterating the boundary layer thickness (δ) (Figure 3) until the horizontal diffusive flux was equal to the vertical flux by both diffusion and convection, with an accuracy of 10−6 g m−2 d−1. For the case in which δb (first category), C was set equal to the atmospheric vapor concentration (CA), while for δ > b (second category), the vapor concentration at the center of the aperture was C(b) (equation (10)). Vapor flux solutions were obtained for a range of ambient temperatures (upper boundary), matrix pore sizes (fracture-surface boundary), and fracture aperture. A unique solution was found for each scenario; that is, only one value of boundary layer thickness resulted in equality between fluxes, i.e., JHD = JV (equations (7) and (11), respectively).

3. Results and Discussion

3.1. Experiments

[37] Apart from saturating the rocks, the initial rock imbibition stage served to determine the similarity in rock permeability between the different rock fragments of the FS systems. Since initial water content was unknown but was assumed equal in all the rocks, we used sorptivity (S) instead of permeability. The calculated S values were 4.93 × 10−2, 2.99 × 10−2, and 1.88 × 10−2 g d−0.5 for rocks B, C, and D, respectively, with a linear regression r2 ≥ 0.99. We therefore assumed that the permeability of the different rocks was within the same order of magnitude, and that the small differences in permeability could be neglected when comparing ESEF rates among the rocks.

3.1.1. Impact of Atmospheric Ambient Temperature

[38] ESEF rates were obtained by a linear fit of each data segment taken while constant CCR ambient temperature was sustained and after steady state conditions had been reached (see example in Figure 4). Only data segments that were statistically significant (r2 ≥ 0.96) were considered. The relationship between evaporation rate and ambient temperature (Figure 5) was compared with model results (discussed in section 3.2). Average evaporation rate values in Figure 5 are reported as mass flux per area (g d−1 m−2), where the area referred to is the area of each fracture wall surface (0.25 m2).

Figure 4.

Measured cumulative solution transferred from the Mariotte bottle of rock C as a function of climate control room (CCR) ambient temperature (mainly 20°C), with rock-bottom temperature of 23°C. Vertical dashed lines mark periods of temperature change from 25° to 20°C (time = 0 days) and from 20° to 15°C (time = 7 days). The evaporation rate (28.3 g d−1) corresponding to 20°C was evaluated for the period of 1 to 7 days.

Figure 5.

Evaporation rates versus CCR ambient temperature. Error bars represent the standard deviation of mean evaporation. The dashed curve shows the model prediction, using average pore size radius (0.0755 μm), experimental aperture (1 cm), and varying temperatures as in the experiment. The bottom x axis indicates the ambient temperature, and the top x axis indicates the temperature difference between the rock bottom at 23°C and ambient air.

[39] The comparison between evaporation rate from the fracture per unit of land surface area (i.e., fracture aperture opening to the atmosphere, ∼0.005 m2) and the pan (PE) is presented in Table 1, showing the enhanced evaporation that SEFs can cause. Even for a CCR temperature of 25°C (i.e., minimal convective venting of the fracture), evaporation rate from the SEFs is already about double that of the PE. When CCR temperature is decreased to 10°C, corresponding to maximum convective venting conditions in the fracture, the ESEF rate is 3 times higher than the PE. Note that the PE also increased with a decrease in CCR temperature because the bottom of the pan was being heated to 23°C while the CCR was at 10°C. Although the PE of the heated pan (Table 1) was markedly higher than natural PE conditions due to the contribution of heat energy [Sene et al., 1991], the ESEF rates were even higher.

Table 1. Comparison Between Potential Evaporation (PE) and the Average Evaporation From a Surface-Exposed Fracture (ESEF)a
Climate Control Room Temperature (°C)PE (g d−1 m−2) Pan Bottom Not HeatedPE (g d−1 m−2) Pan Bottom Heated to 23°CESEF (g d−1 m−2) per Unit Land Surface AreaESEF (g d−1 m−2) per Unit Fracture-Wall Surface Area
  • a

    ESEF values represent the average from both FS systems in the climate control room.


[40] These results demonstrate the potential importance of fractures in the hydrological cycle and in the vadose zone water balance, as fractures significantly enhance evaporation per land surface area. Our results concur with previous studies performed in soil with cracks that showed enhanced drying of the soil profile [Adams and Hanks, 1964; Adams et al., 1969; Ritchie and Adams, 1974], and support the theoretical work of Weisbrod et al. [2005] that suggested that rock fractures enhance evaporation by convective venting. In addition to quantifying the relationship between ESEF and the imposed thermal gradient that drives convective venting, this study highlights the contribution of fractures to land surface evaporation.

3.1.2. Salt Accumulation

[41] Evaporation from within the fracture is expected to result in an accumulation of salt along the fracture walls and within the matrix near the walls. Salt accumulation is known to reduce evaporation rates [Chen, 1992; Shimojima et al., 1996; Yakirevich et al., 1997]. Figure 6 displays the mean evaporation rate as a function of salt accumulation and time over the 270-day study period; for the last 160 days, the CCR temperature was kept constant at 9°–10°C (i.e., corresponding to the highest expected evaporation rates; see Figure 5). Each data point was calculated by regression on 5- to 7-day segments with steady ambient temperature, and exhibiting steady evaporation rates (r2 ≥ 0.97). Mass of accumulated salt was calculated assuming that all the evaporated water left salt along the fracture plane. Although there is a large data gap between days 20 and 80 (Figure 6), a general trend of suppressed evaporation rate with both time and salt accumulation is clear from then onward. The data gap exists because the 60-day experiment was conducted during that time period and much of the time, Tatm > 10°C (i.e., maximum evaporation rate was not measured). Evaporation rate suppression was observed only after ∼150 days (i.e., after the second data point) and a salt accumulation of ∼100 g m−2. By the end of the 270-day study period and after ∼160 g m−2 of salt had accumulated, the average evaporation rate was less than half of that observed at ∼150 days.

Figure 6.

Mean evaporation rates as a function of time and salt precipitation, at an ambient temperature of 9°–10°C. Dots are average values, with error bars representing standard deviation.

[42] In natural fractures, salt accumulation is cyclic (diurnally), with higher accumulation expected at night corresponding to higher venting/evaporation rates. Estimates for daytime and nighttime salt-accumulation rates can be made from the evaporation rates observed for a CCR temperature of 25°C and 10°C, respectively, corresponding to evaporation rates of 55 and 134 mL d−1 m−2, respectively (Figure 5), and salt-accumulation rates of 0.43 and 1.04 g d−1 m−2, respectively. Weisbrod et al. [2000] measured a slightly higher average salt-accumulation rate of 1.43 ± 0.29 g d−1 m−2 in the same Avdat formation from which the rocks used for this study originated. In contrast to the present study, which imposed either daytime or nighttime conditions continuously for many days at a time, for their estimation Weisbrod et al. [2000] used in situ salts collected from a natural fracture that experienced diurnal thermal cycles. Samples were collected from a chalk fracture after a 7-month dry period to determine an average accumulation rate. The results from these two studies are surprisingly similar, considering the inherent differences in fracture inclination, aperture, and aperture variability between the field-site fracture [Weisbrod et al., 2009] and our laboratory setup. In another study, using small-scale laboratory experiments, Weisbrod et al. [2005] suggested a maximum salt accumulation of 0.54 and 4.79 g d−1 m−2 for chalk and sandstone, respectively. Again, these values are of the same order of magnitude as those calculated in this study.

[43] At the end of the experimental period (270 days), a layer of accumulated salt was observed on the fracture surfaces, with a thicker salt layer where the aperture widened slightly (Figure 7). Distribution of salt precipitation on the surface and within the pores was not analyzed. However, Weisbrod et al. [2000] observed that salt precipitation also occurs within the pores near the fracture surface, in addition to the surface crust. An approximate value for pore clogging could be estimated from the salt-accumulation values found in this study. Assuming that all salt precipitates in the outer millimeter of the rock, that NaCl is the primary salt (70% of the AGW used), and using a NaCl density of 2.165 g cm−3 as the effective salt-accumulation density and 40% porosity, a mass of 100 and 160 g m−2 of salt will occupy 11.6% and 18.5% pore volumes, respectively, for the 1-mm depth. This could have a significant impact on permeability. Quantifying the distribution of salt precipitation around the fracture surfaces is part of an ongoing investigation.

Figure 7.

Photograph of accumulated salt on the fracture surface of a FS ∼9 months after it was assembled. Figure 7a shows the upper part of the FS fracture aperture, displaying excess accumulation in a section with slightly wider aperture, denoted 1. The part denoted 2 is shown magnified in Figure 7b from a different angle, to show detail of the grooved area (groves denoted by 3) on the fracture surface.

3.2. Model

[44] The model was used to predict evaporation rates for both diffusive and convective venting conditions for a range of atmospheric temperatures (1°–30°C) and pore sizes (0.009–0.296 μm diameter). Evaporation fluxes from vertical diffusive venting were 0.80 ± 0.02 g d−1 m−2, corresponding to approximately 1% of the rate from convective venting, for the range of temperatures tested and an average pore diameter of 0.151 μm. In convective venting, evaporation rate was most strongly influenced by the temperature difference between the top and bottom boundaries (Figure 8), and was not very sensitive to pore diameter, with the exception of pore sizes close to the minimum (0.009 μm), which significantly suppressed evaporation rates. Note that the model uses one pore size for the entire matrix and does not account for pore size distribution, heterogeneity, or unsaturated conditions.

Figure 8.

Model results for evaporation rate as a function of various parameters. Temperature at rock bottom was set to 23°C. (top) Evaporation rate as a function of ambient (CCR) temperature and matrix pore radii, with the fracture half aperture set to 0.005 m. (bottom) Evaporation rate as a function of CCR ambient temperature and fracture half-aperture width, with pore radius set to 0.0755 μm (mean value for the experimental chalk).

[45] The model also allowed investigation of the boundary layer thickness as a function of different parameters. The boundary layer corresponds to the region of effective vapor removal; beyond it, toward the aperture midplane, there is no vapor removal as we assume that atmospheric conditions exist there. Boundary layer thickness ranged between values of 0.6 and 1.1 cm: It varied as a function of convection magnitude and was sometimes constrained by fracture width. Ghezzehei et al. [2004] reported similar boundary layer thicknesses of 0.5 to 2.0 cm for evaporation in cavities. The resulting evaporation rate strongly depended on the interplay between the boundary layer thickness and the aperture (Figure 8). Evaporation rate was strongly influenced by aperture for b < ∼5 mm: While evaporation rates still increased with increasing temperature gradient, the temperature effect was smaller as compared with the behavior for the larger apertures. For ∼5 < b < ∼10 mm, evaporation rates increased with aperture and temperature gradient. Evaporation rate peaked for an ambient temperature in the range of 5 to 15°C (ΔT = 18°–8°C, respectively). Aperture widths in this range (5–10 mm) restricted convective airflow and thus ESEF rates increased with aperture increase. Beyond a certain aperture threshold value of about b = 10 mm (not displayed in Figure 8), ESEF rates were no longer influenced by increasing aperture. This threshold coincided well with the maximum boundary layer thickness (11 mm). In natural fractures, wind-driven forced convection may lead to increased evaporation for larger apertures; however, this issue is beyond the scope of this paper.

[46] Model results for the functional dependence of evaporation rate on thermal gradient corresponded very well to the experimental data, as shown by the dashed line in Figure 5. Even relatively small thermal gradients significantly enhanced evaporation; for example, a ΔT of only 3°C (Figure 5) resulted in twice the evaporation rate compared with no thermal gradient. Interestingly, the model predicts evaporation even for negative thermal gradients, with the evaporation increasing as soon as the temperature difference reaches ΔT = −3°C (Figure 5). This result was observed for all aperture widths, apart from the very small ones. The explanation for this apparent anomaly is that convection is driven by the moist-air density gradient, which is a function of both temperature and vapor concentration (equation (5)). Thus, even with atmospheric temperature being slightly higher than aperture temperature, convection can theoretically occur as result of a gradient in vapor concentration provided by differences in RH between atmospheric and aperture air. Moreover, vertical diffusion continues regardless of convection. It should be noted that the temperature and RH measured at the interface between the aperture and the atmosphere were used for the upper boundary values in the model (30–40% RH, and reported CCR temperatures). The model predicts that evaporation will cease when the CCR temperature is increased to ∼27°C (i.e., ΔT = −4°C). In other words, to achieve a condition of no evaporation from the fracture, the model requires a negative thermal gradient to oppose diffusive venting. For convection, the model exhibited a maximum value at the peculiar ambient temperature of about 7°C, for the experimental conditions. This is explained by the lower ability of air to hold vapor at lower temperatures. Thus, although convective airflow is faster at lower ambient temperature [Nachshon et al., 2008], the resulting ESEF rates are lower because the limiting factor is the ability of air to carry vapor.

[47] ESEF rates were experimentally and theoretically shown to be driven by temperature gradients at rates commensurate with convective venting. The model predicts evaporation even for small temperature gradients, corresponding to a Rayleigh number smaller than its critical value (Rac) [Nield, 1982; Nield and Bejan, 1992]. The model did not use Rac as a critical limit, but rather allowed the moist-air density gradient to control convection regardless of conditions. Although convection might not have been fully developed at these low gradients, it was still the main process for vapor removal. It is important to note that convection was not studied directly, and the above statements regarding convection at lower Rayleigh numbers warrant further investigation.

4. Conclusions

[48] Evaporation from surface-exposed fractures (ESEFs) was quantified in the laboratory and modeled mathematically. The model was used to investigate properties beyond those studied experimentally. As hypothesized by Weisbrod and Dragila [2006], net evaporation from a fractured matrix is significantly enhanced by convective venting of the air within the fractures, which is driven by the diurnal variability in atmospheric temperature. Specifically, evaporation rates varied over twofold between minimum and maximum convective conditions. In contrast, diffusive venting could explain only about 1% of the measured evaporation rates. ESEF rates reached values that were at least twice the PE per land surface area, showing the significance of this mechanism to the hydrological cycle. In addition to enhancing net evaporation, SEFs facilitate evaporation from greater depths in the vadose zone, accessing pore water that may otherwise not participate in the evaporation cycle.

[49] The model successfully predicted the functional relationship between thermal gradient, ambient temperature, and evaporation rate. Modeled ESEF rates were affected by aperture and temperature gradient, with aperture being a stronger controlling factor for smaller apertures (less than about 5 mm) and temperature more strongly controlling the system at larger apertures. Matrix pore size influenced ESEF rates at extremely small sizes only (<0.009 μm).

[50] Evaporation also results in the development of evaporative crusts that concentrate salts on the surface of and just within the fracture walls. Salt accumulation was found to reduce the evaporation rate. For the chalk matrix used in the study, suppression of the evaporation rate began after ∼100 g of salt precipitated per square meter of fracture surface. The evaporation rate was reduced to less than half its initial value by the time ∼160 g m−2 had accumulated.

[51] An important implication of salt-crust accumulation within SEFs is the potential for salts to be transported downward during an infiltration event. This enhanced evaporation cycle during dry periods, which was quantified in this laboratory study, can therefore provide a platform for collecting and then transporting salts to the groundwater, bypassing the porous matrix. Results from this study can therefore serve as a first estimate of the rate at which vadose zone salts are redirected toward fractures and downward to aquifers. The role of SEFs may be especially important in low-permeability rocks and in arid environments where the vadose zone is typically thick. Chemical or radioactive deposits are commonly located over low-permeability vadose zones that are thought to provide protective media for these deposits [Winograd and Roseboom, 2008]. This work emphasizes the potential of lateral solute movement driven by evaporation from SEFs. When the distance required for solutes to move laterally through the matrix toward a fracture is significantly smaller than the thickness of the vadose zone, the lateral route effectively shortens the protective thickness of the vadose zone.


[52] This work was supported by the Binational Science Foundation (2002058), National Science Foundation (0510825), Israeli Science Foundation (70/06), and International Arid Land Consortium (03R-19). We would also like to acknowledge Uri Nachshon and Michael Kugel for assisting in the construction of the experimental setup, and Yossef H. Hatzor and Eyal Shalev for their valuable comments. Additional valuable comments provided by three anonymous reviewers served to improve the manuscript.