Transcript
Journal of Archaeological Science 35 (2008) 1453e1462 http://www.elsevier.com/locate/jas
Methods for calculating brine evaporation rates during salt production D. Glen Akridge* Arkansas Archeological Society, 5411 W. Wheeler Road, Fayetteville, AR 72704, USA Received 11 July 2007; received in revised form 17 October 2007; accepted 22 October 2007
Abstract Salt is recognized by archaeologists as an important commodity due to the biological need for sodium and other cultural uses. Numerous studies have described the various techniques used in converting brine to crystallized salt, but few, if any, have attempted to quantify the physical processes of evaporation in pre-industrial societies. Apart from the few areas where salt mining is possible, nearly all forms of salt production require evaporation of water to concentrate brine and ultimately produce salt crystals. This study quantifies three of the most common evaporation techniques and provides insight into the production rates of salt and fuel requirements. Methods of calculation are provided for determining evaporation through (1) direct solar heating of brine, (2) applied external heat to a vessel, and (3) an immersed heated object (e.g., stone). These results provide physical constraints on the evaporation process and provide investigators with techniques for estimating efficiency and total production of prehistoric and historic saltworks. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Salt; Evaporation; Brine; Stone boiling; Numerical methods
1. Introduction Saltmaking from brine has been a common worldwide industry for thousands of years, beginning by at least the fourth millennium B.C. in Europe (Olivier and Kovacik, 2006) and by the first millennium B.C. in China (Flad et al., 2005) and Central America (Andrews, 1983). Solar evaporation of brine to form salt continues to be a viable commercial process to this day along coastal areas (Kostick, 2002). The procedures used in making salt varied by geographic region and resources locally available. The quantity desired by the local population may have also influenced the choice of salt production methods. Although the process often involved techniques such as leaching, extraction, filtering, and burning of saltenriched plants (Adshead, 1992), the final step in salt production invariably required evaporation of water from brine to precipitate salt crystals. Numerous studies have focused on the techniques and archaeological remnants of saltworks. These studies have tended to leave open the question of * Tel.: þ1 479 790 0261; fax: þ1 479 575 5453. E-mail address:
[email protected] 0305-4403/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2007.10.013
efficiency and total salt production, except in the few cases where historic descriptions of saltworks exist (e.g., Chiang, 1976). Few have attempted to quantify the process of evaporation. Quantifying the process of salt production does more than provide estimates for the total salt produced. It provides insights into the required human labor expenditure and the degree to which the local economy depended on salt. The salt trade would have largely been determined by the amount of excess salt that could be produced. In the case of brine boiling to obtain salt, the need for substantial quantities of fuel (e.g., wood) often resulted in serious environmental changes to the surrounding landscape (Early, 1993). Quantifying the production of salt can be accomplished through experimentation or by numerical simulation. Experimentation is often advantageous because it can provide insights into the subtleties of the process that might not be realized otherwise, but suffers greatly from the need to control variables. Salt production is a labor intensive and time consuming task, and in the case of solar evaporation may take weeks to obtain salt. This makes experimentation difficult, especially in light of the multitude of potential variables such as ambient temperature and humidity, brine volume and
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
1454
concentration, fire temperature, and vessel heat transfer properties that need to be monitored and maintained. In addition, experimentation results are generally only relevant for the tested scenario and provide only limited insight into other untested evaporation conditions. The great utility of numerical simulations is the speed at which ‘‘experiments’’ can be performed. Simulations of processes taking hours or weeks can be performed in seconds allowing for greater exploration of variable effects and deeper understanding of the physical mechanisms underlying evaporation. This paper lays out in detail all the necessary steps in simulating evaporation in three different scenarios: (1) solar evaporation, (2) evaporation from an externally heated pan, and (3) evaporation from a hot immersed object. Each scenario involves evaporation of a fixed volume of brine to dryness resulting in the precipitation of salt crystals. For any batch evaporation the amount of salt produced can be determined by ms ¼ mw 1:52 104 S2 þ 9:50 103 S
ð1Þ
where ms is the mass (kg) of salt crystallized, mw is the mass (kg) of the water evaporated, and S is the initial salt concentration of the brine in wt% NaCl (Fig. 1). For ease of calculation, the dissolved salt is assumed to be pure sodium chloride. Sodium and chlorine make up 85% of the inorganic constituents found in seawater (Lide, 1991) and natural inland brines are often of even higher purity (Bowman, 1956). Consequently, the presence of other minor components has little impact on the numerically simulated results. Exceptions may be inland lakes containing high concentrations of sulfates. In these cases, adjustments may need to be made to account for the mass, density, and vapor pressure differences of a sulfaterich brine. 2. Solar evaporation In solar evaporation a vessel or ponded area containing brine is allowed to evaporate under the prevailing 20
NaCl Crystallized (kg)
18 16 26.2 wt%
14 12
20 wt%
10 8
15 wt%
6 10 wt%
4 2 0
5 wt% 0
5
10
15
20
25
30
35
40
45
50
Water Evaporated (kg) Fig. 1. Graphical representation of Eq. (1). The maximum sodium chloride brine concentration is 26.2 wt% (at 25 C). For comparison, seawater has a salt content of about 3.5 wt%.
environmental conditions. This technique works best at low latitudes where sunlight duration and intensity are highest and areas with low relative humidity and rainfall. Solar evaporation also becomes the default method when fuel resources are scarce and boiling of brine is unfeasible. Historically this technique was common in coastal areas (e.g., LeConte, 1862) and continues to be a viable commercial process worldwide (Kostick, 2002). Solar evaporation could have been practiced at many inland salines where brine concentrations tend to be high (e.g., Demir and Seyler, 1999) thus reducing total evaporation time. 2.1. Calculation method for solar evaporation Calculating evaporation rates for brine solutions requires a slight modification to the standard Penman (1948) equation used by hydrologists to determine evaporation from open water sources. The Penman approach combines the effects of radiation and aerodynamic forces controlling evaporation and has been shown to adequately predict evaporation in a wide variety of environments (e.g., Finch, 2001). The Penman equation is generally expressed as: lE ¼
D g Rn þ f ðuÞ ðes eÞ Dþg Dþg
ð2Þ
where E is the evaporation rate expressed as mm/day, l is the latent heat of vaporization, D is the gradient of the vapor pressureetemperature curve, g is the psychometric constant, Rn is the net solar radiation, f(u) is a function of wind speed, and es and e are the saturation vapor pressure of water and ambient water vapor pressure, respectively. In this paper the Penman equation has been modified to reflect the reduced vapor pressure of a salt solution. A similar approach has been used previously in determining evaporation from saline lakes (Calder and Neal, 1984). Additional details of the equation and its variables are discussed by Allen et al. (1998) and Shuttleworth (1993). 2.1.1. Calculating aerodynamic terms The aerodynamic forces acting on evaporation are primarily the result of environmental variables governing diffusion of water molecules away from the liquid surface of water or brine. The modified Penman equation for predicting potential evaporation rates from a free water surface requires knowledge of several local climate variables. The method shown here is for daily calculation steps and uses 24 h averages for temperature, humidity, and wind speed. For modeling past saltmaking endeavors, historical weather data including average climate conditions for each month can be obtained for a variety of locales from several sources, including the National Climatic Data Center in the United States. The latent heat of evaporation l (MJ kg1) varies with temperature according to l ¼ 2:501 0:002361T
ð3Þ
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
where T is in degrees celsius. The temperature T for daily time steps is simply defined as the mean of the daily maximum and minimum temperatures. T¼
Tmax þ Tmin 2
es ¼ 0:6108aw exp
17:27T 237:3 þ T
ð5Þ
The activity coefficient of water aw is a function of the concentration of dissolved salts. The following correlation was derived from experimental vapor pressure data published for sodium chloride (Lide, 1991). aw ¼ 0:0011m2 0:0319m þ 1
ð6Þ
where m is the concentration of sodium chloride in moles per liter of water. Density of NaCl solutions has been measured by Romanklw and Chou (1983). Based on their published data, the following equation was developed to calculate NaCl solution density over the temperature range of 25e45 C and concentration range of 0e26.2 wt%. 0:012 25 D¼ 2:754 105 S2 þ 6:872 103 S þ 0:99704 Tsol ð7Þ where D is the solution density (g cm3), S is the NaCl concentration in wt%, and Tsol is the solution temperature ( C). The saturation vapor pressure is a function of temperature and the gradient of this function (kPa C1) is also required and can be calculated by 4098es ð237:3 þ TÞ
2
ð8Þ
The psychrometric constant (kPa C1) is given by g ¼ 0:000655P
emax þ emin ð11Þ 2 The vapor pressure e (kPa) can be determined from the relative humidity e¼
ð4Þ
The saturation vapor pressure es (kPa) is determined from the average daily temperature and is an indication of the rate at which water molecules can escape from the liquid surface. When dissolved salts are present the saturation vapor pressure is lowered due to the decreased chemical potential of the liquid water. To adjust for this lowering effect the water activity coefficient aw is inserted into the basic equation.
D¼
1455
ð9Þ
where P is the atmospheric pressure (kPa). If the atmospheric pressure is unknown, an approximate value can be calculated based upon a site’s elevation 5:26 293 0:0065z P ¼ 101:3 ð10Þ 293 where z is height above sea level (m). In a similar fashion to the mean temperature, the daily mean vapor pressure is the average of the maximum and minimum values.
e¼
Hr es 100
ð12Þ
where Hr is the relative humidity (%). Wind speed is incorporated using empirically determined coefficients for the atmospheric resistance encountered in diffusion of the water vapor away from a liquid surface. For an open water surface the wind function is given by f ðuÞ ¼ 6:43ð1 þ 0:536U2 Þ
ð13Þ
where the wind speed U2 (m s1) is measured at 2 m above the surface. 2.1.2. Determining net radiation Solar radiation aids in promoting evaporation by imparting energy into the absorbing material. The radiational energy available at the ground surface is a combination of both short and long-wavelength radiation and is the difference between the upward and downward radiation fluxes. The amount of solar energy reaching the ground surface can be reduced by cloudiness and atmospheric interferences or increased with increasing altitude. This net radiation, Rn, can be determined in three ways: (1) direct measurement using a radiometer, (2) published tables based on latitude, or (3) calculations incorporating Earth’s orbital characteristics. Radiometers measure the net radiation by monitoring the temperature difference across two parallel plates. They require periodic calibration and each measurement locale must be generally free of any obstructions blocking incoming or outgoing radiation. Approximate values for the net radiation reaching the ground surface can also be found in published tables (e.g., Lide, 1991). These tables are generally organized by latitude and indicate the average net radiation for a cloudless sky during each month of the year. These tables do not usually account for altitude differences but are generally accurate to within 10% during summer months and 15% during winter months (Lide, 1991). 2.1.3. Calculating net radiation The following series of equations are required when determining the net radiation by accounting for Earth’s orbital characteristics. The extraterrestrial radiation Ra (MJ m2 day1) can be calculated for any latitude and day of year by adjusting the solar constant Gsc for the solar declination Ra ¼
24ð60Þ Gsc dr ½us sinð4ÞsinðdÞ þ cosð4ÞcosðdÞsinðus Þ p ð14Þ
where Gsc ¼ 0.0820 MJ m2 min1, dr is the inverse relative EartheSun distance, us is the sunset hour angle (rad), 4 is
1456
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
the latitude (rad), and d is the solar declination (rad). Angles in radians can be obtained by converting decimal degrees. p ½Decimal degrees ð15Þ 180 The inverse relative EartheSun distance dr is given by 2p J ð16Þ dr ¼ 1 þ 0:033 cos 365
Radians ¼
where J is the number day of the year (e.g., 1 for January 1 or 365 for December 31). The solar declination d is 2p d ¼ 0:409 sin J 1:39 ð17Þ 365 The sunset hour angle us is given by us ¼ arccos½ tanð4ÞtanðdÞ
ð18Þ
The number of daylight hours N can be determined by 24 us ð19Þ p The solar radiation is calculated by adjusting the extraterrestrial radiation for the relative sunshine duration n ð20Þ Rs ¼ as þ bs Ra N
N¼
where Rs is the solar radiation (MJ m2 day1), n is the actual duration of sunshine (hours), N is the maximum possible amount of sunshine (hours), and as and bs are regression parameters with recommended values of 0.25 and 0.50, respectively. The effective solar radiation reaching the ground surface is reduced by solar reflection caused by albedo Rns ¼ ð1 aÞRs
ð21Þ
where Rns is the net solar radiation (MJ m2 day1), and a is the albedo of the surface. For open water Shuttleworth (1993) recommends an albedo value of 0.08. However, for shallow evaporation pans the underlying reflectivity of the pan must be considered. For example, dark earthenware or wooden pans filled with water may have an albedo closer to 0.05. When evaporating brine, salt crystals will begin to form, thus increasing the reflectivity. Rife et al. (2002) found that albedo values of 0.3 were appropriate for modeling diurnal weather cycles over a salt-encrusted playa. The flux of long-wave radiation reflected by the ground back into space is given by the StefaneBoltzmann law minus that which is absorbed by clouds, water vapor, dust, and carbon dioxide. The net long-wave radiation can be determined by 4 4 pffiffiffi T þTmin Rs Rnl ¼s max 0:340:14 e 1:35 0:35 2 ðas þbs ÞRa ð22Þ where s is the StefaneBoltzmann constant (4.903 109 MJ K4 m2 day1), T is the maximum and minimum
temperature during a 24 h period (K), e is the water vapor pressure (kPa), as and bs are regression terms mentioned earlier, Rs is the solar radiation (MJ m2 day1), and Ra is the extraterrestrial radiation (MJ m2 day1). The net radiation Rn (MJ m2 day1) is simply the difference between the incoming effective solar radiation and outgoing long-wave radiation. Rn ¼ Rns Rnl
ð23Þ
2.2. Results from numerical simulations To illustrate the utility of predicting solar evaporation rates, two examples from the literature will be briefly discussed here. These examples were selected because sufficient evaporation variables are specified to allow for numerical modeling of the described saltmaking process. The first example is an ethnographic description of saltmaking from the western coast of Mexico. The second simulation uses historic descriptions of 19th century Chinese coastal tradition using portable wooden pans to evaporate brine. Each case requires the input of numerous weather data and site specific information. Historical weather data including long-term averages can be obtained from a variety of sources. The data used here were derived from the online databases of the National Climatic Data Center of the National Oceanic and Atmospheric Administration (www.noaa.gov); and Weather Underground (www.wunderground.com). Model inputs are summarized in Table 1. Williams (2002) describes a traditional Mesoamerican saltworks operating on the western coast of Mexico in the state of Michoacan. The La Placita saltworks operates during the dry season, roughly from April to mid-June. Specialists, called salineros, scrape the upper surface of soil from a nearby dry estuary. The salt-encrusted sand called salitre is first filtered through a tapeixtle using seawater and the resulting enriched brine is transferred to specially prepared evaporation pans called eras. According to Williams, La Placita has 18 eras with most measuring approximately 3 m 3 m in dimension. Each era is lined with beach sand and lime and can hold about 400 L of brine. Every day 2e3 buckets of brine must be added to maintain a consistent level. It takes 5 days of evaporation to concentrate the brine sufficiently to begin collecting salt, about 25e30 kg are then collected every other day from each era. An average of 7 tons of salt can be produced at each saltmaking site during the dry season. Table 1 Monthly weather averages for selected saltmaking locales
Latitude Month Temperature ( C) Humidity (%RH) Solar Radiation (MJ m2 day-1) Wind Speed (m s1)
Michoacan, Mexico
Shanghai, China
16.83 N May 2000 27.2 77 29.1 5
31.17 N July 28.4 83 30.8 4
Weather data were obtained from the National Climatic Data Center of the U.S. National Oceanic and Atmospheric Administration (www.noaa.gov). Solar radiation for a cloudless day was calculated from Section 2.1.3.
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
Based on the information that Williams (2002) supplies, an estimate for the average evaporation rate can be derived. During the first 5 days of evaporation, the brine concentrates up to a maximum value of about 26.2 wt%. Once the maximum value is reached, further evaporation results in the formation of salt crystals. Eq. (1) indicates that producing 12.5e15 kg of salt per day requires the evaporation of 35e43 kg of water. Converting the mass of the water evaporated to volume and dividing by the surface area of an era (w9 m2) results in an evaporation rate of 3.9e4.8 mm day1. Using the steps outlined in Section 2.1 we can numerically simulate the evaporation process during Williams’ field season at La Placita in 2000. Input values used for the model are listed in Table 1. The albedo of the pan is expected to be relatively high (w0.3) owing to the lime-lined pan and the constant precipitation of salt crystals at the bottom of the pan. Results for the numerical simulation suggest that the evaporation rate should be in the range of 4.1e4.7 mm day1 following the initial 5-day concentration period, essentially identical to that obtained in practice. The range in evaporation rate given by the numerically calculated results reflects the potential variation in cloud cover from 0 to 20%. Assuming an initial brine concentration of about 15 wt% and an average cloud cover of 10%, Fig. 2 represents model results from the numerically simulated evaporation occurring from a single era at La Placita during the first 20 days of May 2000. Interestingly, extrapolating the production rate of the era in Fig. 2 to the entire field season (w75 days) yields approximately 790 kg of salt. This correlates to an average of about 9 eras in use at La Placita based on the estimate of 7 tons of salt produced each season. This agrees well with Williams’ (2002: p. 243) assertion that not all of the 18 eras are in use at one time. Similarly, solar evaporation along the coastal margin of China utilized enriched brine obtained by leaching salty earth or in some cases from ashes that were spread onto the ground (Chiang, 1976). The practice of using portable wooden pans for evaporation began in the 18th century in the Hangchou Bay area. Although variations in size were common, the typical wooden pan was about 2.5 m long, 1 m wide, and 3e 6 cm deep. Chiang (1976: p. 526) states that ‘‘crystallization
7
200 Evaporation Rate, mm/day Salt Produced, kg
180 160 140
6
120 100
5
80 60
4
Salt Produced (kg)
Evaporation Rate (mm/day)
8
40 20
3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Day of Month (May 2000) Fig. 2. Numerical simulation results for a 9 m2 era at La Placita saltworks in Michoacan, Mexico.
1457
of salt in these portable pans took only 1 day under fine weather in summers.’’ Although we are not told of the brine strength or volume in these pans, some reasonable assumptions can be made. If the brine is near saturation (26.2 wt%) and averages 3 cm in depth, then numerical calculations indicate that the evaporation rate would be 4.8 mm day1 (see Table 1 for model inputs). Upon complete evaporation the depth of the salt crystals would be about 5 mm indicating the total evaporation time to be about 5 days. This is somewhat longer than the estimate given by Chiang (1976) unless he was referring to incipient crystallization which could begin on the first day. The two examples provided here illustrate the value of numerical modeling in addition to historic descriptions. Computer simulation of the well documented La Placita saltworks in Mexico provides remarkable agreement between the author’s observations and numerical results. However, historic descriptions of 18th century Chinese saltmaking appear to differ from the numerically calculated evaporation rate. Numerical modeling provides an independent means for validating historical claims regarding salt production.
3. Evaporation from an externally heated pan This technique typically involves the suspension of a vessel over a fire or the emplacement of a vessel directly onto a bed of hot coals. Heat is transferred through the base and walls of the vessel and warms the interior fluid. The amount of heat transferred to the brine is governed by the energy output of the fire and efficiency of heat transfer in a particular brineboiling setup. The efficiency is defined as the amount of heat transferred into the brine relative to the total heat produced by the fire. For an open fire efficiency is low owing to the loss of heat by combustion gases escaping around the vessel. Glanville (2005) calculated an efficiency of about 20% for the 19th century methods of brine boiling in iron vessels described by LeConte (1862) along the east coast of the United States. This value is somewhat better than the approximately 15% efficiency for boiling water in cooking vessels over an open fire (McCracken and Smith, 1998) but less than the more optimal 28e40% efficiency of well vented wood stoves (Joshi et al., 1991). For earthenware vessels with substantially lower thermal conductivity than iron (Table 2), efficiency is reduced even further and may be as low as 2e5% (Glanville, 2005). Although efficiency is a poorly known variable and is unique to each setup for brine boiling with externally applied heat, the amount of salt produced can be determined by simply estimating the temperature on the exterior surface of the vessel. This method eliminates (or sidesteps) the issue of efficiency and focuses directly on the heat being transferred through the vessel and into the brine. Thus, the amount of heat calculated would be the absolute minimum required to accomplish evaporation and would represent a system of 100% heat transfer efficiency. Heat loss by escaping combustion gases, evaporating water molecules, and conduction through
1458
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
Table 2 Physical properties of various materials at 20 C Material
Density (g cm3)
Thermal conductivity (W m1 K1)
Specific Heat (J g1 K1)
Source
Clay (9.3e18.3 wt% H2O) Brick, clay Iron (100%Fe) Cast iron (3.16%C) Copper Bronze (89%Cu þ 11%Sn) Lead
1.33e1.50 1.60e1.82 7.87 7.15 8.96 8.77 11.36
0.4e0.7 0.41e0.63 74.48 46.9 393.7 70.6 34.7
0.92 0.4473 0.837 0.3846 0.3771 0.1287
C A, B, F D D, G D E D
Data from [A] Dondi et al. (2004); [B] Bhattacharjee and Krishnamoorthy (2004); [C] Abu-Hamdeh and Reeder (2000); [D] Davis (1998); [E] Copper Development Association (2007); [F] Lange (1952); [G] MatWeb (2007).
vessel walls to surrounding air all contribute to lowering the overall efficiency.
E¼
q l
ð26Þ
using Eq. (3) to determine the latent heat of vaporization. 3.1. Calculation method for evaporation by externally applied heat
3.2. Numerical simulation of applied external heat
By concentrating solely on the heat transferred through a vessel’s wall, a one-dimensional steady-state heat transfer equation can be applied k q ¼ A ðTe Ti Þ Dx
ð24Þ
where q is the heat transfer rate in joules per second (J/s), A is the heated surface area, Dx is vessel thickness, k is the thermal conductivity in watts per meter-kelvin (W m1 K1), and Te and Ti are the temperature (K) of the vessel exterior and interior surfaces, respectively (Geankoplis, 2003). This equation assumes that a constant flow of heat is applied to the vessel exterior. Materials of high thermal conductivity (Table 2) allow for substantially more heat to be transferred through the vessel whereas increasing the vessel’s wall or basal thickness reduces heat flow. For most practitioners of brine boiling, the primary means of evaporation control comes from varying the amount of external heat applied to the vessel which in turn determines the temperature of the vessel’s exterior. The temperature of the internal surface Ti is typically the same as the boiling point of the brine and will change as evaporation proceeds and the brine concentrates to a maximum value of about 29.0 wt% at the boiling point. Although at very high external temperatures, the interior surface may exceed that of the boiling brine. The boiling point of sodium chloride brine can be estimated by the boiling point elevation equation Tb ¼ Kb mi þ 100 C
ð25Þ
where Tb is the boiling temperature ( C) of the brine, Kb is the proportionality constant for water (0.512 C/m), m is the brine concentration (mol NaCl per L of water), and i is the number of dissociated ions per formula unit (NaCl ¼ 2). At high altitudes where pure water boils at temperatures below 100 C, the appropriate boiling point should instead be inserted into the equation. Finally, the evaporation rate (g/s) can be determined by
Simulating the effects of brine boiling requires knowledge of both the physical characteristics of the pan and the amount of applied heat (i.e. temperature on pan exterior). Often one or the other of these criteria is unknown for a specific saltwork. The discovery of several late Roman age lead pans in Britain provides constraints on these variables which can be used to demonstrate the numerical model. Lead melts at 327 C and salt practitioners would likely have kept the external temperature well below this value to avoid accidental melting of the pan. At Shavington, Cheshire, a lead pan measuring 100 cm by 90 cm by 14 cm deep was found cut into eight pieces, presumably as a first step to recycling the material (Penney and Shotter, 1996). At 0.8 cm thickness, the original weight of the pan would have been approximately 118 kg. Although none of the surviving Roman era lead pans have been found in situ, they likely would have been placed across earthen flue trenches much like many ceramic salt pans elsewhere in Britain (e.g., Bradley, 1992). Fires were presumably kept relatively low, 200e250 C, to prevent damage to the pan. Numerically simulating the evaporation from the Shavington salt pan requires only an estimation of the initial brine concentration. Here an arbitrary 10 wt% is used, but this value has only a minor impact on the duration of the evaporation process. Even if the temperature on the pan’s exterior is kept relatively low (w200 C), Fig. 3 demonstrates a fairly quick evaporation for the Shavington pan. Neglecting substantial heat loss, the brine is brought to a boil in only 3 min and continues until 14 min, whereby evaporation has resulted in the maximum allowable brine concentration. Further evaporation after 14 min results in salt crystals forming inside the pan. Ultimately, about 14 kg of salt can be recovered in less than 20 min of boiling, assuming 10 wt% brine in a 126 L pan. 4. Evaporation using hot immersed objects A third evaporation scenario considered here is that of a hot object (e.g., stone) placed inside a pan of brine. This method is believed to have been utilized for salt production in eastern
35
20
30
Brine Concentration 18 16
25
Crystallized Salt
14 12
20
10 15
8 6
10
4 5 0
Crystallized Salt (kg)
Brine Concentration (wt% NaCl)
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
2 0
5
10
15
20
25
0 30
1459
analytical solution to the conduction equation becomes considerably more complex. Finite difference methods can be used to obtain a numerical solution to Eq. (27), which involves computing temperature changes after small positional (n) and time (t) steps are incremented (Geankoplis, 2003: pp. 386e387; Carslaw and Jaeger, 1959). The positional steps effectively divide the object into concentric rings that are Dx (m) thick. For a sphere, the temperature can be determined by
1 2n þ 1 2n 1 T nþ1 þ ðM 2Þt T n þ T n1 ð29Þ tþDt T n ¼ M 2n t 2n t
Time (min) Fig. 3. Brine evaporation from a lead pan placed over fire. Pan conditions are: pan exterior ¼ 200 C, pan volume ¼ 126 L, pan thickness ¼ 0.8 cm, and pan heated area ¼ 0.9 m2. Initial pan heat-up time is negligible.
where M ¼ Dx2/(aDt). At the center (n ¼ 0) the equation changes to tþDt T 0
North America from about A.D. 1000e1400 (Brown, 1980, 1981). Stone boiling as a cooking technique probably began with the introduction of pottery (ca. 2500 B.C.), if not earlier, and continued into the historic period (Sassaman and Rudolphi, 2001). Thick-walled ceramic ‘‘pans,’’ most in association with salines, have been found with capacities ranging from 40 to 400 L. The enormous size and weight of these vessels when filled with brine would have made them practically immovable and suspension over a fire seems equally unlikely. Brown (1980, 1981) concluded that these salt pans were placed in basin-shaped ground depressions and heated stones from nearby fires were dropped into the pan to facilitate evaporation. The lack of exterior discoloration from fires on many pans and the occasional find of stones inside pans (e.g., Bushnell, 1907) lend support to the conclusion that stone boiling was at least one method utilized by Native Americans to evaporate brine. 4.1. Calculation method for stone boiling A hot object transfers its internal heat energy to the surrounding fluid through convective heat transfer at the object’s surface. This transfer of heat is governed by the unsteady-state conduction equation vT v2 T ¼a 2 vt vx
ð27Þ
where a is the thermal diffusivity (m2/s), t is time (s), and T is the temperature (K) of the object. Thermal diffusivity is simply k a¼ rCp
ð28Þ
where k is the thermal conductivity (W m1 K1), r the density (kg m3), and Cp the heat capacity of the object (J g1 K1). For simplicity, here it is assumed that the object is spherical and that only the one-dimensional direction need be considered. For irregularly shaped objects, the
¼
4 M4 T1 þ T0 Mt M t
ð30Þ
where M 4 for both Eqs. (29) and (30). At the surface, equations accounting for convection must be utilized assuming that the heat capacity of the outer half-slab can be neglected tþDt T n
¼
nN ð2n 1Þ=2 tþDt T a þ 2n 1 tþDt T n1 2n 1 þ nN þ nN 2 2
ð31Þ
where Tn represents surface temperature and Tn1 the temperature at 1 positional step below the surface. 4.2. Numerical simulation of stone boiling Solving these equations allows for the determination of the average stone temperature with time after immersion. Initially, the heat transferred raises the temperature of the brine up to its boiling point. Any additional heat released by the stone serves to evaporate water and concentrate brine. Eventually the brine is concentrated to a maximum value of about 29.0 wt% at its boiling point with further evaporation resulting in the formation of salt crystals. For the numerical model, the boiling stone is assumed to be chert. Chert was well known to Native Americans and was commonly used to make stone tools. Although the physical properties of chert are not well studied, there are numerous studies on the analogous material of amorphous or fused quartz. The thermal conductivity of chert can be determined from a polynomial fit of published data by Kanamori et al. (1968) and Clauser and Huenges (1995) k ¼ 4:67 109 T 3 8:53 106 T 2 þ 6:29 103 T 9:85 102
ð32Þ
where k is thermal conductivity (W m1 K1), and T is the stone temperature (K). Similarly, Robie et al. (1978) have developed expressions for the heat capacity of quartz Cp ¼ 44:603 þ 3:7754 102 T 1:0018 106 T 2
ð33Þ
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
where Cp is the heat capacity (J mol1 K1) and T is the temperature (K) for the range of 298e844 K. At higher temperatures the equation changes to Cp ¼ 58:928 þ 1:0031 102 T
ð34Þ 3
20
0.50
18
0.45
16
0.40
14
0.35
12
0.30
10
0.25
8
0.20
6
0.15
4
0
0.10
Heat transferred, MJ Salt Produced, kg
2 0
1
2
3
4
5
6
7
8
Salt Produced (kg)
Heat Transferred (MJ)
for the range 844e1800 K. The density of chert is 2.6 g cm . This information together can be used to determine the thermal diffusivity (a) properties of chert for the numerical model. Fig. 4 graphically represents a simulated evaporation of placing 700 C chert stone(s), representing 25% of the total 40 L volume, into a salt pan containing 10 wt% brine at 25 C. Boiling begins immediately for brine surrounding the stone and continues for about 4 min, by which time the stone temperature now equals that of the brine and no further heat is transferred. During the first 2 min the evaporating brine concentrates from 10 wt% up to 29.0 wt%. At 1.6 min salt crystals begin forming and continue until the stone and brine reach thermal equilibrium. For this scenario, 373 g of crystallized salt would be produced. Emplacement of additional hot stones into the pan would continue the evaporation process. From the short timescales involved to obtain salt, it seems this method would clearly be effective in evaporating brine. Unlike suspension of a pan over a fire, stone boiling releases all of its internal heat directly into the brine. However, there may be practical limitations for manipulating large volumes of very hot stones. Stones heated to high temperatures often shatter and large stones would be difficult to transport from a fire to the brine pan. Smaller stones would make handling easier, but would require more repeated firings to achieve the same evaporation as large stones. The smallest salt pan found at the Kimmswick site near St. Louis (Bushnell, 1907) had a volume of approximately 40 L. Assuming a scenario similar to that outlined above, emplacement of 25 vol% stone into the salt pan would translate to 26 kg of extremely hot stone(s) that would have been manipulated. This seems to suggest that stone boiling may actually require a tremendous amount of human labor to achieve significant quantities of salt. Fig. 5 indicates the potential evaporation that could be
0.05 9
0.00
Time (minutes) Fig. 4. Numerical simulation results for Native American stone boiling. Represented here are results for placing a 700 C stone with a volume of 10 L into a ceramic pan containing 30 L of 10 wt% brine initially at 25 C. The stone is assumed to be a spherical nodule of chert.
25
Water Evaporated (kg)
1460
20
Volume Ratio Brine/Stone 1.0 2.0 3.0 4.0
15
10
5
0 200
300
400
500
600
700
800
900
1000
Initial Stone Temperature (°C) Fig. 5. Evaporation curves for stone boiling with various brine:stone volume ratios. Curves represent an initial brine temperature of 25 C and 10 wt% concentration.
obtained with various brine/stone volume ratios. The 10 wt% brine is assumed to initially be at 25 C before emplacement of a hot spherical stone of chert. Even for a Vb/Vs ¼ 1 and an initial stone temperature of 1000 C, the mass of the stone would still exceed the mass of the evaporated water by a factor of 2.5. Lower stone temperatures or smaller volumes of stone would result in greater discrepancies between stone mass and evaporated water mass. 4.3. Hot objects with negligible internal resistance An alternative mathematical treatment can be applied when the hot object has negligible internal resistance to the flow of heat. These objects (e.g., copper and iron) have high thermal conductivities and will have an approximately uniform internal temperature profile at any given time following immersion into brine. To maintain an energy balance, heat loss through the vessel wall or to the atmosphere is assumed to be minimal relative to the rapid rise in brine temperature. The total amount of heat transferred at any given time can be determined by Q ¼ Cp rVðT0 TN Þ 1 eðhA=Cp rVÞt ð35Þ where Q (J) is the total heat transferred, V (m3) is the volume of the object, h is a heat transfer coefficient for natural convection (w5000 W m2 K), A is the heated area (m2), and t is the elapsed time (s) after immersion (Geankoplis, 2003: pp. 277e 286, 357e359). 5. Conclusions The goal of this paper is to develop a mathematical basis for brine evaporation that can be used by investigators to quantitatively describe salt production activities. The methods described herein cover three distinct techniques for evaporating brine: (1) solar evaporation, (2) boiling due to an externally applied heat source, and (3) boiling caused by a hot immersed object. Historically these techniques were sometimes used in combination to achieve the desired evaporation results. Input
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
parameters for the three models range from common weather variables for solar evaporation to pan and stone physical dimensions for brine boiling. No one evaporation method can be considered superior since other factors such as fuel availability, sunshine intensity, brine concentration, and even the cultural value placed on human labor make the choice of evaporation technique unique to each culture. However, the calculation methods given here do allow for direct comparisons to be made regarding evaporation efficiency. Brine boiling offers the quickest means of evaporation, typically on the order of minutes for the examples given here, but this does not account for the time spent acquiring fuel. Solar evaporation does not require fuel but may take days or weeks to accomplish and is limited to geographic areas with high evaporation and little precipitation. Although beyond the scope of the current paper, quantifying salt production opens up new areas of research that can be addressed. Changes in production methods through time can be the result of either cultural or technological factors, or both. In a simple least-cost model, humans would be expected to seek strategies to minimize labor and fuel requirements in the salt production process. Salt production has often been described as a labor intensive endeavor requiring, in the case of brine boiling, extraction of substantial quantities of fuel from the local environment. The calculations presented herein offer a direct means to evaluate technological changes for improved evaporation efficiency. For example, Eq. (24) describes the direct relationship between vessel thickness and the rate of heat transfer. Thinner vessel walls require proportionately less fuel to achieve evaporation. In addition, determinations of minimum energy (fuel) requirements can be made which provide insight into local deforestation or other resource depletion. Early (1993) noted that the removal of fruit bearing plants and nut bearing trees from the vicinity of a saltworks may have altered diet and even changed the local population of wild animals that depend on these resources. These and other concerns can now be better addressed by quantifying the brine evaporation process. Acknowledgments The author thanks Ann M. Early and Dan F. Morse for helpful discussions on this subject. Ashley Dumas and Robert C. Mainfort provided insightful comments on an early draft of this paper. Valuable comments were also received from two anonymous reviewers that greatly improved this manuscript. References Abu-Hamdeh, N.H., Reeder, R.C., 2000. Soil thermal conductivity: effects of density, moisture, salt concentration, and organic matter. Soil Science Society of America Journal 64, 1285e1290. Adshead, S.A.M., 1992. Salt and Civilization. St. Martin’s Press, New York. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: guidelines for computing crop water requirements. In: Irrigation and Drainage Paper, 56. Food and Agriculture Organization of the United Nations, Rome.
1461
Andrews, A., 1983. Maya Salt Production and Trade. University of Arizona Press, Tucson. Bhattacharjee, B., Krishnamoorthy, S., 2004. Permeable porosity and thermal conductivity of construction materials. Journal of Materials in Civil Engineering 16, 322e330. Bowman, H.H.M., 1956. Salinity data on marine and inland waters and plant distribution. The Ohio Journal of Science 56 (2), 101e106. Bradley, R., 1992. Roman salt production in Chichester Harbour: rescue excavations at Chidham, West Sussex. Britannia 23, 27e44. Brown, I.W., 1980. Salt and the Eastern North American Indian: an archaeological study. In: Lower Mississippi Survey Bulletin, No. 6. Peabody Museum, Harvard University. Brown, I.W., 1981. The Role of Salt in Eastern North American Prehistory. Louisiana Archaeological Survey and Antiquities Commission Anthropological Study No. 3. Department of Culture, Recreation and Tourism, Baton Rouge. Bushnell, D.I., 1907. Primitive salt-making in the Mississippi Valley, I. Man No. 13. London. Calder, I.R., Neal, C., 1984. Evaporation from saline lakes: a combination equation approach. Hydrological Sciences Journal 29, 89e97. Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids, second ed. Clarendon Press, Oxford. Chiang, T.C., 1976. The production of salt in China, 1644e1911. Annals of the Association of American Geographers 66, 516e530. Clauser, C., Huenges, E., 1995. Thermal conductivity of rocks and minerals. In: Ahrens, T.J. (Ed.), Rock Physics and Phase Relations e a Handbook of Physical Constants. AGU Reference Shelf, vol. 3. American Geophysical Union, Washington, pp. 105e126. Copper Development Association.
(accessed 03.07.07.). Davis, J.R. (Ed.), 1998. Metals Handbook. ASM International, Materials Park, Ohio. Demir, I., Seyler, B., 1999. Chemical composition and geologic history of saline waters in Aux Vases and Cypress Formations, Illinois Basin. Aquatic Geochemistry 5, 281e311. Dondi, M., Mazzanti, F., Principi, P., Raimondo, M., Zanarini, G., 2004. Thermal conductivity of clay bricks. Journal of Materials in Civil Engineering 16, 8e14. Early, A.M., 1993. Caddoan saltmakers in the Ouachita Valley: the Hardman Site. In: Research Series, No. 43. Arkansas Archeological Survey, Fayetteville. Finch, J.W., 2001. A comparison between measured and modeled open water evaporation from a reservoir in south-east England. Hydrological Processes 15, 2771e2778. Flad, R., Zhu, J., Wang, C., Chen, P., von Falkenhausen, L., Sun, Z., Li, S., 2005. Archaeological and chemical evidence for early salt production in China. Proceedings of the National Academy of Sciences of the United States of America 102, 12618e12622. Geankoplis, C.J., 2003. Transport Processes and Separation Process Principles, fourth ed,. Prentice Hall, New Jersey. Glanville, J., 2005. Brine transport and woodland salt making in southwestern Virginia: an hypothesis. Paper presented at the Eastern States Archeological Federation Meeting, Williamsburg, Virginia, USA, November 12, 2005. Joshi, V., Venkataraman, C., Ahuja, D.R., 1991. Thermal performance and emission characteristics of biomass-burning heavy stoves with flues. Pacific and Asian Journal of Energy 1, 1e19. Kanamori, H., Fujii, N., Mizutani, H., 1968. Thermal diffusivity measurement of rock-forming minerals from 300 to 1100 K. Journal of Geophysical Research 73 (2), 595e605. Kostick, D.S., 2002. Salt. In: Metals and Minerals. U.S. Geological Survey Minerals Yearbook, vol. 1. U.S. Government Printing Office, pp. 1e17 (Chapter 64). Lange, N.A., 1952. Handbook of Chemistry, eighth ed. Handbook Publishers, Sandusky, Ohio. LeConte, J., 1862. How to Make Salt from Sea-Water? Governor and Council of South Carolina, Columbia. Lide, D.R. (Ed.), 1991. CRC Handbook of Chemistry and Physics, 72nd ed. CRC Press, Boca Raton.
1462
D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462
MatWeb, 2007. Material Property Database. Available from: http://www.matweb.com (accessed 03.07.07.). McCracken, J.P., Smith, K.R., 1998. Emissions and efficiency of improved woodburning cookstoves in highland Guatemala. Environment International 24 (7), 739e747. Olivier, L., Kovacik, J., 2006. The ‘Briquetage de la Seille’ (Lorraine, France): proto-industrial salt production in the European Iron Age. Antiquity 80, 558e566. Penman, H.L., 1948. Natural evaporation from open water, bare soil, and grass. Proceedings of the Royal Society, Series A 193, 120e145. Penney, S., Shotter, D.C.A., 1996. An inscribed Roman salt-pan from Shavington, Cheshire. Britannia 27, 360e365. Rife, D.L., Warner, T.T., Chen, F., Astling, E.G., 2002. Mechanisms for diurnal boundary layer circulations in the Great Basin Desert. Monthly Weather Review 130, 921e938.
Robie, R.A., Hemingway, B.S., Fisher, J.R., 1978. Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 pascals) pressure and at higher temperatures. In: USGS Survey Bulletin, 1452. U.S. Government Printing Office, Washington. Romanklw, L.A., Chou, I.-M., 1983. Densities of aqueous NaCl, KCl, MgCl2, and CaCl2 binary solutions in the concentration range 0.5e6.1 m at 25, 30, 35, 40, and 45 C. Journal of Chemical and Engineering Data 28, 300e 305. Sassaman, K.E., Rudolphi, W., 2001. Communities of practice in the early pottery traditions of the American Southeast. Journal of Anthropological Research 57, 407e425. Shuttleworth, W.J., 1993. Evaporation. In: Maidment, D.R. (Ed.), Handbook of Hydrology. McGraw-Hill, New York. Williams, E., 2002. Salt production in the coastal area of Michoacan, Mexico. Ancient Mesoamerica 13, 237e253.
