oA

Wh

rm

ueto car

uceand

millennium B.C. in Europe (Olivier and Kovacik, 2006) and

to form salt continues to be a viable commercial process to this

the techniques and archaeological remnants of saltworks.These studies have tended to leave open the question of

than provide estimates for the total salt produced. It provides

trade would have largely been determined by the amount of

variables. Salt production is a labor intensive and timeconsuming task, and in the case of solar evaporation maytake weeks to obtain salt. This makes experimentation diffi-cult, especially in light of the multitude of potential variablessuch as ambient temperature and humidity, brine volume and

* Tel.: 1 479 790 0261; fax: 1 479 575 5453.E-mail address: dgakridge@hotmail.com

Journal of Archaeological Science 35day along coastal areas (Kostick, 2002). The procedures usedin making salt varied by geographic region and resources lo-cally available. The quantity desired by the local populationmay have also influenced the choice of salt productionmethods. Although the process often involved techniquessuch as leaching, extraction, filtering, and burning of salt-enriched plants (Adshead, 1992), the final step in salt produc-tion invariably required evaporation of water from brine toprecipitate salt crystals. Numerous studies have focused on

excess salt that could be produced. In the case of brine boilingto obtain salt, the need for substantial quantities of fuel (e.g.,wood) often resulted in serious environmental changes to thesurrounding landscape (Early, 1993).

Quantifying the production of salt can be accomplishedthrough experimentation or by numerical simulation. Experi-mentation is often advantageous because it can provideinsights into the subtleties of the process that might not berealized otherwise, but suffers greatly from the need to controlCentral America (Andrews, 1983). Solar evaporation of brine

by the first millennium B.C. in China (Flad et al., 2005) and insights into the required human labor expenditure and the de-

gree to which the local economy depended on salt. The salting 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 andtotal production of prehistoric and historic saltworks. 2007 Elsevier Ltd. All rights reserved.

Keywords: Salt; Evaporation; Brine; Stone boiling; Numerical methods

1. Introduction

Saltmaking from brine has been a common worldwide in-dustry for thousands of years, beginning by at least the fourth

efficiency and total salt production, except in the few caseswhere historic descriptions of saltworks exist (e.g., Chiang,1976). Few have attempted to quantify the process of evapora-tion. Quantifying the process of salt production does moreMethods for calculating brine evap

D. Glen

Arkansas Archeological Society, 5411 W.

Received 11 July 2007; received in revised fo

Abstract

Salt is recognized by archaeologists as an important commodity dstudies have described the various techniques used in converting brineprocesses of evaporation in pre-industrial societies. Apart from the fewrequire evaporation of water to concentrate brine and ultimately prodration techniques and provides insight into the production rates of salt0305-4403/$ - see front matter 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.jas.2007.10.013ration rates during salt production

kridge*

eeler Road, Fayetteville, AR 72704, USA

17 October 2007; accepted 22 October 2007

to the biological need for sodium and other cultural uses. Numerousrystallized salt, but few, if any, have attempted to quantify the physicaleas where salt mining is possible, nearly all forms of salt productionsalt crystals. This study quantifies three of the most common evapo-fuel requirements. Methods of calculation are provided for determin-

(2008) 1453e1462http://www.elsevier.com/locate/jas

concentration, fire temperature, and vessel heat transfer prop-erties that need to be monitored and maintained. In addition,experimentation results are generally only relevant for thetested scenario and provide only limited insight into other un-tested evaporation conditions. The great utility of numericalsimulations is the speed at which experiments can be per-formed. Simulations of processes taking hours or weeks canbe performed in seconds allowing for greater exploration ofvariable effects and deeper understanding of the physicalmechanisms underlying evaporation.

This paper lays out in detail all the necessary steps insimulating evaporation in three different scenarios: (1) solarevaporation, (2) evaporation from an externally heated pan,and (3) evaporation from a hot immersed object. Each scenarioinvolves evaporation of a fixed volume of brine to drynessresulting in the precipitation of salt crystals. For any batch a slight modification to the standard Penman (1948) equation

arilyn of

water molecules away from the liquid surface of water or

1454 D.G. Akridge / Journal of Archaeologievaporation the amount of salt produced can be determined by

ms mw1:52 104S2 9:50 103S 1

where ms is the mass (kg) of salt crystallized, mw is the mass(kg) of the water evaporated, and S is the initial salt concentra-tion of the brine in wt% NaCl (Fig. 1). For ease of calculation,the dissolved salt is assumed to be pure sodium chloride. So-dium and chlorine make up 85% of the inorganic constituentsfound in seawater (Lide, 1991) and natural inland brines areoften of even higher purity (Bowman, 1956). Consequently,the presence of other minor components has little impact onthe numerically simulated results. Exceptions may be inlandlakes containing high concentrations of sulfates. In thesecases, adjustments may need to be made to account for themass, density, and vapor pressure differences of a sulfate-rich brine.

2. Solar evaporation

In solar evaporation a vessel or ponded area containingbrine is allowed to evaporate under the prevailing

0

2

4

6

8

10

12

14

16

18

20

0 10 15 20 25 30 35 40 45 50Water Evaporated (kg)

NaC

l C

rystallized

(kg

)

5 wt%

10 wt%

15 wt%

20 wt%

26.2 wt%

5

Fig. 1. Graphical representation of Eq. (1). The maximum sodium chloridebrine concentration is 26.2 wt% (at 25 C). For comparison, seawater hasa salt content of about 3.5 wt%.brine. The modified Penman equation for predicting potentialevaporation rates from a free water surface requires knowledgeof several local climate variables. The method shown here isfor daily calculation steps and uses 24 h averages for temper-ature, humidity, and wind speed. For modeling past saltmakingendeavors, historical weather data including average climateconditions for each month can be obtained for a variety of lo-cales from several sources, including the National ClimaticData Center in the United States.

The latent heat of evaporation l (MJ kg1) varies with tem-perature according toThe aerodynamic forces acting on evaporation are primthe result of environmental variables governing diffusioused by hydrologists to determine evaporation from openwater sources. The Penman approach combines the effectsof radiation and aerodynamic forces controlling evaporationand has been shown to adequately predict evaporation ina wide variety of environments (e.g., Finch, 2001). The Pen-man equation is generally expressed as:

lE DD gRn

g

D g f u es e 2

where E is the evaporation rate expressed as mm/day, l is thelatent heat of vaporization, D is the gradient of the vapor pres-sureetemperature curve, g is the psychometric constant, Rn isthe net solar radiation, f(u) is a function of wind speed, and esand e are the saturation vapor pressure of water and ambientwater vapor pressure, respectively. In this paper the Penmanequation has been modified to reflect the reduced vapor pres-sure of a salt solution. A similar approach has been used pre-viously in determining evaporation from saline lakes (Calderand Neal, 1984). Additional details of the equation and its var-iables are discussed by Allen et al. (1998) and Shuttleworth(1993).

2.1.1. Calculating aerodynamic termsenvironmental conditions. This technique works best at lowlatitudes where sunlight duration and intensity are highestand areas with low relative humidity and rainfall. Solar evap-oration also becomes the default method when fuel resourcesare scarce and boiling of brine is unfeasible. Historicallythis technique was common in coastal areas (e.g., LeConte,1862) and continues to be a viable commercial process world-wide (Kostick, 2002). Solar evaporation could have been prac-ticed at many inland salines where brine concentrations tend tobe high (e.g., Demir and Seyler, 1999) thus reducing totalevaporation time.

2.1. Calculation method for solar evaporation

Calculating evaporation rates for brine solutions requires

cal Science 35 (2008) 1453e1462l 2:501 0:002361T 3

logiwhere T is in degrees celsius. The temperature T for daily timesteps is simply defined as the mean of the daily maximum andminimum temperatures.

T Tmax Tmin2

4

The saturation vapor pressure es (kPa) is determined from theaverage daily temperature and is an indication of the rate atwhich water molecules can escape from the liquid surface.When dissolved salts are present the saturation vapor pressureis lowered due to the decreased chemical potential of the liq-uid water. To adjust for this lowering effect the water activitycoefficient aw is inserted into the basic equation.

es 0:6108aw exp 17:27T237:3 T 5

The activity coefficient of water aw is a function of the con-centration of dissolved salts. The following correlation was de-rived from experimental vapor pressure data published forsodium chloride (Lide, 1991).

aw 0:0011m2 0:0319m 1 6

where m is the concentration of sodium chloride in moles perliter of water. Density of NaCl solutions has been measured byRomanklw and Chou (1983). Based on their published data,the following equation was developed to calculate NaCl solu-tion density over the temperature range of 25e45 C and con-centration range of 0e26.2 wt%.

D25

Tsol

0:0122:754 105S2 6:872 103S 0:99704

7

where D is the solution density (g cm3), S is the NaCl con-centration 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 requiredand can be calculated by

D 4098es237:3 T2 8

The psychrometric constant (kPa C1) is given by

g 0:000655P 9

where P is the atmospheric pressure (kPa). If the atmosphericpressure is unknown, an approximate value can be calculatedbased upon a sites elevation

P 101:3293 0:0065z

293

5:2610

where z is height above sea level (m).In a similar fashion to the mean temperature, the daily

D.G. Akridge / Journal of Archaeomean vapor pressure is the average of the maximum and min-imum values.e emax emin2

11The vapor pressure e (kPa) can be determined from the rel-

ative humidity

e Hres100

12

where Hr is the relative humidity (%). Wind speed is incorpo-rated using empirically determined coefficients for the atmo-spheric resistance encountered in diffusion of the watervapor away from a liquid surface. For an open water surfacethe wind function is given by

f u 6:431 0:536U2 13

where the wind speed U2 (m s1) is measured at 2 m above the

surface.

2.1.2. Determining net radiationSolar radiation aids in promoting evaporation by impart-

ing energy into the absorbing material. The radiationalenergy available at the ground surface is a combination ofboth short and long-wavelength radiation and is the differ-ence between the upward and downward radiation fluxes.The amount of solar energy reaching the ground surfacecan be reduced by cloudiness and atmospheric interferencesor increased with increasing altitude. This net radiation, Rn,can be determined in three ways: (1) direct measurementusing a radiometer, (2) published tables based on latitude,or (3) calculations incorporating Earths orbital characteris-tics. Radiometers measure the net radiation by monitoringthe temperature difference across two parallel plates. Theyrequire periodic calibration and each measurement localemust be generally free of any obstructions blocking incom-ing or outgoing radiation. Approximate values for the netradiation reaching the ground surface can also be found inpublished tables (e.g., Lide, 1991). These tables are gener-ally organized by latitude and indicate the average netradiation for a cloudless sky during each month of theyear. These tables do not usually account for altitudedifferences but are generally accurate to within 10% duringsummer months and 15% during winter months (Lide, 1991).

2.1.3. Calculating net radiationThe following series of equations are required when deter-

mining the net radiation by accounting for Earths orbital char-acteristics. The extraterrestrial radiation Ra (MJ m

2 day1)can be calculated for any latitude and day of year by adjustingthe solar constant Gsc for the solar declination

Ra 2460p

Gscdrus sin4sind cos4cosdsinus14

where Gsc 0.0820 MJ m2 min1, dr is the inverse relative

1455cal Science 35 (2008) 1453e1462EartheSun distance, us is the sunset hour angle (rad), 4 is

temperature during a 24 h period (K), e is the water vaporpressure (kPa), as and bs are regression terms mentioned ear-lier, Rs is the solar radiation (MJ m

2 day1), and Ra is the ex-traterrestrial radiation (MJ m2 day1). The net radiation Rn(MJ m2 day1) is simply the difference between the incomingeffective solar radiation and outgoing long-wave radiation.

Rn Rns Rnl 23

2.2. Results from numerical simulations

ing site during the dry season.

logical Science 35 (2008) 1453e1462the latitude (rad), and d is the solar declination (rad). Angles inradians can be obtained by converting decimal degrees.

Radians p180

Decimal degrees 15The inverse relative EartheSun distance dr is given by

dr 1 0:033 cos2p

365J

16

where J is the number day of the year (e.g., 1 for January 1 or365 for December 31). The solar declination d is

d 0:409 sin2p

365J 1:39

17

The sunset hour angle us is given by

us arccos tan4tand 18The number of daylight hours N can be determined by

N 24pus 19

The solar radiation is calculated by adjusting the extrater-restrial radiation for the relative sunshine duration

Rs as bs n

N

Ra 20

where Rs is the solar radiation (MJ m2 day1), n is the actual

duration of sunshine (hours), N is the maximum possibleamount of sunshine (hours), and as and bs are regression pa-rameters with recommended values of 0.25 and 0.50, respec-tively. The effective solar radiation reaching the groundsurface is reduced by solar reflection caused by albedo

Rns 1 aRs 21

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, forshallow evaporation pans the underlying reflectivity of thepan must be considered. For example, dark earthenware orwooden pans filled with water may have an albedo closer to0.05. When evaporating brine, salt crystals will begin toform, thus increasing the reflectivity. Rife et al. (2002) foundthat albedo values of 0.3 were appropriate for modeling diur-nal weather cycles over a salt-encrusted playa.

The flux of long-wave radiation reflected by the groundback into space is given by the StefaneBoltzmann law minusthat which is absorbed by clouds, water vapor, dust, and car-bon dioxide. The net long-wave radiation can be determinedby

RnlsT4maxT4min

2

0:340:14 ep

1:35

RsasbsRa0:35

22

1456 D.G. Akridge / Journal of Archaeowhere s is the StefaneBoltzmann constant (4.903109 MJ K4 m2 day1), T is the maximum and minimumTable 1

Monthly weather averages for selected saltmaking locales

Michoacan, Mexico Shanghai, China

Latitude 16.83N 31.17NMonth May 2000 July

Temperature (C) 27.2 28.4Humidity (%RH) 77 83

Solar Radiation (MJ m2 day-1) 29.1 30.8Wind Speed (m s1) 5 4

Weather data were obtained from the National Climatic Data Center of theTo illustrate the utility of predicting solar evaporation rates,two examples from the literature will be briefly discussed here.These examples were selected because sufficient evaporationvariables are specified to allow for numerical modeling ofthe described saltmaking process. The first example is an eth-nographic description of saltmaking from the western coast ofMexico. The second simulation uses historic descriptions of19th century Chinese coastal tradition using portable woodenpans to evaporate brine. Each case requires the input of numer-ous weather data and site specific information. Historicalweather data including long-term averages can be obtainedfrom a variety of sources. The data used here were derivedfrom the online databases of the National Climatic Data Cen-ter of the National Oceanic and Atmospheric Administration(www.noaa.gov); and Weather Underground (www.wunder-ground.com). Model inputs are summarized in Table 1.

Williams (2002) describes a traditional Mesoamerican salt-works operating on the western coast of Mexico in the state ofMichoacan. The La Placita saltworks operates during the dryseason, roughly from April to mid-June. Specialists, called sal-ineros, scrape the upper surface of soil from a nearby dry es-tuary. The salt-encrusted sand called salitre is first filteredthrough a tapeixtle using seawater and the resulting enrichedbrine is transferred to specially prepared evaporation panscalled eras. According to Williams, La Placita has 18 eraswith most measuring approximately 3 m 3 m in dimension.Each era is lined with beach sand and lime and can hold about400 L of brine. Every day 2e3 buckets of brine must be addedto maintain a consistent level. It takes 5 days of evaporation toconcentrate the brine sufficiently to begin collecting salt, about25e30 kg are then collected every other day from each era.An average of 7 tons of salt can be produced at each saltmak-U.S. National Oceanic and Atmospheric Administration (www.noaa.gov). So-

lar radiation for a cloudless day was calculated from Section 2.1.3.

Based on the information that Williams (2002) supplies, anestimate for the average evaporation rate can be derived. Dur-ing the first 5 days of evaporation, the brine concentrates up toa maximum value of about 26.2 wt%. Once the maximumvalue is reached, further evaporation results in the formationof salt crystals. Eq. (1) indicates that producing 12.5e15 kgof salt per day requires the evaporation of 35e43 kg of water.Converting the mass of the water evaporated to volume and di-viding by the surface area of an era (w9 m2) results in anevaporation rate of 3.9e4.8 mm day1.

Using the steps outlined in Section 2.1 we can numericallysimulate the evaporation process during Williams field seasonat La Placita in 2000. Input values used for the model are listedin Table 1. The albedo of the pan is expected to be relativelyhigh (w0.3) owing to the lime-lined pan and the constant pre-

heat transferred into the brine relative to the total heat pro-duced by the fire. For an open fire efficiency is low owing

D.G. Akridge / Journal of Archaeologicipitation of salt crystals at the bottom of the pan. Results forthe numerical simulation suggest that the evaporation rateshould be in the range of 4.1e4.7 mm day1 following theinitial 5-day concentration period, essentially identical to thatobtained in practice. The range in evaporation rate given bythe numerically calculated results reflects the potential varia-tion in cloud cover from 0 to 20%. Assuming an initial brineconcentration of about 15 wt% and an average cloud cover of10%, Fig. 2 represents model results from the numerically sim-ulated evaporation occurring from a single era at La Placita dur-ing the first 20 days of May 2000. Interestingly, extrapolatingthe production rate of the era in Fig. 2 to the entire field season(w75 days) yields approximately 790 kg of salt. This correlatesto an average of about 9 eras in use at La Placita based on theestimate of 7 tons of salt produced each season. This agreeswell with Williams (2002: p. 243) assertion that not all ofthe 18 eras are in use at one time.

Similarly, solar evaporation along the coastal margin ofChina utilized enriched brine obtained by leaching salty earthor in some cases from ashes that were spread onto the ground(Chiang, 1976). The practice of using portable wooden pansfor evaporation began in the 18th century in the HangchouBay area. Although variations in size were common, the typ-ical wooden pan was about 2.5 m long, 1 m wide, and 3e6 cm deep. Chiang (1976: p. 526) states that crystallization

3

4

5

6

7

8

1 10 11 12 13 14 15 16 17 18 19 20Day of Month (May 2000)

Evap

oratio

n R

ate (m

m/d

ay)

0

20

40

60

80

100

120

140

160

180200

Salt P

ro

du

ced

(kg

)

Evaporation Rate, mm/daySalt Produced, kg

98765432Fig. 2. Numerical simulation results for a 9 m2 era at La Placita saltworks inMichoacan, Mexico.to the loss of heat by combustion gases escaping around thevessel. Glanville (2005) calculated an efficiency of about20% for the 19th century methods of brine boiling in iron ves-sels described by LeConte (1862) along the east coast of theUnited States. This value is somewhat better than the approx-imately 15% efficiency for boiling water in cooking vesselsover an open fire (McCracken and Smith, 1998) but lessthan the more optimal 28e40% efficiency of well ventedwood stoves (Joshi et al., 1991). For earthenware vesselswith substantially lower thermal conductivity than iron(Table 2), efficiency is reduced even further and may be aslow as 2e5% (Glanville, 2005).

Although efficiency is a poorly known variable and isunique to each setup for brine boiling with externally appliedheat, the amount of salt produced can be determined by simplyestimating the temperature on the exterior surface of the ves-sel. This method eliminates (or sidesteps) the issue of effi-ciency and focuses directly on the heat being transferredthrough the vessel and into the brine. Thus, the amount ofheat calculated would be the absolute minimum required to ac-complish evaporation and would represent a system of 100%of salt in these portable pans took only 1 day under fineweather in summers. Although we are not told of the brinestrength or volume in these pans, some reasonable assump-tions can be made. If the brine is near saturation (26.2 wt%)and averages 3 cm in depth, then numerical calculationsindicate that the evaporation rate would be 4.8 mm day1

(see Table 1 for model inputs). Upon complete evaporationthe depth of the salt crystals would be about 5 mm indicatingthe total evaporation time to be about 5 days. This is somewhatlonger than the estimate given by Chiang (1976) unless he wasreferring to incipient crystallization which could begin on thefirst day.

The two examples provided here illustrate the value ofnumerical modeling in addition to historic descriptions. Com-puter simulation of the well documented La Placita saltworksin Mexico provides remarkable agreement between theauthors observations and numerical results. However, historicdescriptions of 18th century Chinese saltmaking appear todiffer from the numerically calculated evaporation rate.Numerical modeling provides an independent means for vali-dating historical claims regarding salt production.

3. Evaporation from an externally heated pan

This technique typically involves the suspension of a vesselover a fire or the emplacement of a vessel directly onto a bedof hot coals. Heat is transferred through the base and walls ofthe vessel and warms the interior fluid. The amount of heattransferred to the brine is governed by the energy output ofthe fire and efficiency of heat transfer in a particular brine-boiling setup. The efficiency is defined as the amount of

1457cal Science 35 (2008) 1453e1462heat transfer efficiency. Heat loss by escaping combustiongases, evaporating water molecules, and conduction through

inesf thent of

Britain (e.g., Bradley, 1992). Fires were presumably kept rel-

Numerically simulating the evaporation from the Shaving-

ndu

4);

logithe brine and will change as evaporation proceeds and thebrine concentrates to a maximum value of about 29.0 wt%at the boiling point. Although at very high external tempera-of external heat applied to the vessel which in turn determthe temperature of the vessels exterior. The temperature ointernal surface Ti is typically the same as the boiling poivessel walls to surrounding air all contribute to lowering theoverall efficiency.

3.1. Calculation method for evaporation by externallyapplied heat

By concentrating solely on the heat transferred througha vessels wall, a one-dimensional steady-state heat transferequation can be applied

q A kDxTe Ti 24

where q is the heat transfer rate in joules per second (J/s), A isthe heated surface area, Dx is vessel thickness, k is the thermalconductivity in watts per meter-kelvin (Wm1 K1), and Teand Ti are the temperature (K) of the vessel exterior and inte-rior surfaces, respectively (Geankoplis, 2003). This equationassumes that a constant flow of heat is applied to the vessel ex-terior. Materials of high thermal conductivity (Table 2) allowfor substantially more heat to be transferred through the vesselwhereas increasing the vessels wall or basal thickness reducesheat flow. For most practitioners of brine boiling, the primarymeans of evaporation control comes from varying the amount

Table 2

Physical properties of various materials at 20 C

Material Density (g cm3) Thermal co

Clay (9.3e18.3 wt% H2O) 1.33e1.50 0.4e0.7

Brick, clay 1.60e1.82 0.41e0.63

Iron (100%Fe) 7.87 74.48

Cast iron (3.16%C) 7.15 46.9

Copper 8.96 393.7

Bronze (89%Cu 11%Sn) 8.77 70.6Lead 11.36 34.7

Data from [A] Dondi et al. (2004); [B] Bhattacharjee and Krishnamoorthy (200

ment Association (2007); [F] Lange (1952); [G] MatWeb (2007).

1458 D.G. Akridge / Journal of Archaeotures, the interior surface may exceed that of the boiling brine.The boiling point of sodium chloride brine can be estimated bythe boiling point elevation equation

Tb Kbmi 100 C 25

where Tb is the boiling temperature (C) of the brine, Kb is the

proportionality constant for water (0.512 C/m), m is the brineconcentration (mol NaCl per L of water), and i is the numberof dissociated ions per formula unit (NaCl 2). At high alti-tudes where pure water boils at temperatures below 100 C,the appropriate boiling point should instead be inserted intothe equation. Finally, the evaporation rate (g/s) can be deter-mined byton salt pan requires only an estimation of the initial brine con-centration. Here an arbitrary 10 wt% is used, but this value hasonly a minor impact on the duration of the evaporation pro-cess. Even if the temperature on the pans exterior is kept rel-

atively low, 200e250 C, to prevent damage to the pan.E ql

26

using Eq. (3) to determine the latent heat of vaporization.

3.2. Numerical simulation of applied external heat

Simulating the effects of brine boiling requires knowledgeof both the physical characteristics of the pan and the amountof applied heat (i.e. temperature on pan exterior). Often one orthe other of these criteria is unknown for a specific saltwork.The discovery of several late Roman age lead pans in Britainprovides constraints on these variables which can be used todemonstrate the numerical model. Lead melts at 327 C andsalt practitioners would likely have kept the external tempera-ture well below this value to avoid accidental melting of thepan. At Shavington, Cheshire, a lead pan measuring 100 cmby 90 cm by 14 cm deep was found cut into eight pieces, pre-sumably as a first step to recycling the material (Penney andShotter, 1996). At 0.8 cm thickness, the original weight ofthe pan would have been approximately 118 kg. Althoughnone of the surviving Roman era lead pans have been foundin situ, they likely would have been placed across earthenflue trenches much like many ceramic salt pans elsewhere in

ctivity (Wm1 K1) Specific Heat (J g1 K1) Source

C

0.92 A, B, F

0.4473 D

0.837 D, G

0.3846 D

0.3771 E

0.1287 D

[C] Abu-Hamdeh and Reeder (2000); [D] Davis (1998); [E] Copper Develop-

cal Science 35 (2008) 1453e1462atively low (w200 C), Fig. 3 demonstrates a fairly quickevaporation for the Shavington pan. Neglecting substantialheat loss, the brine is brought to a boil in only 3 min and con-tinues until 14 min, whereby evaporation has resulted in themaximum allowable brine concentration. Further evaporationafter 14 min results in salt crystals forming inside the pan. Ul-timately, about 14 kg of salt can be recovered in less than20 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 hotobject (e.g., stone) placed inside a pan of brine. This method isbelieved to have been utilized for salt production in eastern

980,egan

T T T 31

logiwith the introduction of pottery (ca. 2500 B.C.), if not earlier,and continued into the historic period (Sassaman and Rudol-phi, 2001). Thick-walled ceramic pans, most in associationwith salines, have been found with capacities ranging from 40to 400 L. The enormous size and weight of these vessels whenfilled with brine would have made them practically immovableand suspension over a fire seems equally unlikely. Brown(1980, 1981) concluded that these salt pans were placed in ba-sin-shaped ground depressions and heated stones from nearbyfires were dropped into the pan to facilitate evaporation. Thelack of exterior discoloration from fires on many pans andthe occasional find of stones inside pans (e.g., Bushnell,1907) lend support to the conclusion that stone boiling wasat least one method utilized by Native Americans to evaporatebrine.

4.1. Calculation method for stone boilingNorth America from about A.D. 1000e1400 (Brown, 11981). Stone boiling as a cooking technique probably b0

5

10

15

20

25

30

35

0 10 15 20 25 30Time (min)

Brin

e C

on

cen

tratio

n (w

t%

N

aC

l)

0

2

4

6

8

10

12

14

16

18

20

Crystallized

S

alt (kg

)

Brine Concentration

Crystallized Salt

5

Fig. 3. Brine evaporation from a lead pan placed over fire. Pan conditions are:

pan exterior 200 C, pan volume 126 L, pan thickness 0.8 cm, and panheated area 0.9 m2. Initial pan heat-up time is negligible.

D.G. Akridge / Journal of ArchaeoA hot object transfers its internal heat energy to the sur-rounding fluid through convective heat transfer at the objectssurface. This transfer of heat is governed by the unsteady-stateconduction equation

vT

vt av

2T

vx227

where a is the thermal diffusivity (m2/s), t is time (s), and T isthe temperature (K) of the object. Thermal diffusivity issimply

a krCp

28

where k is the thermal conductivity (Wm1 K1), r the den-sity (kg m3), and Cp the heat capacity of the object(J g1 K1). For simplicity, here it is assumed that the objectis spherical and that only the one-dimensional directionneed be considered. For irregularly shaped objects, thewhere Tn represents surface temperature and Tn1 the temper-ature at 1 positional step below the surface.

4.2. Numerical simulation of stone boiling

Solving these equations allows for the determination of theaverage stone temperature with time after immersion. Initially,the heat transferred raises the temperature of the brine up to itsboiling point. Any additional heat released by the stone servesto evaporate water and concentrate brine. Eventually the brineis concentrated to a maximum value of about 29.0 wt% at itsboiling point with further evaporation resulting in the forma-tion of salt crystals.

For the numerical model, the boiling stone is assumed to bechert. Chert was well known to Native Americans and wascommonly used to make stone tools. Although the physicalproperties of chert are not well studied, there are numerousstudies on the analogous material of amorphous or fusedquartz. The thermal conductivity of chert can be determinedfrom a polynomial fit of published data by Kanamori et al.(1968) and Clauser and Huenges (1995)

k 4:67 109T3 8:53 106T2 6:29 103T 9:85 102 32

where k is thermal conductivity (Wm1 K1), and T is thestone temperature (K). Similarly, Robie et al. (1978) have de-veloped expressions for the heat capacity of quartztDt n 2n 12

nNtDt a 2n 1

2 nN

tDt n1analytical solution to the conduction equation becomes con-siderably more complex.

Finite difference methods can be used to obtain a numericalsolution to Eq. (27), which involves computing temperaturechanges after small positional (n) and time (t) steps are incre-mented (Geankoplis, 2003: pp. 386e387; Carslaw and Jaeger,1959). The positional steps effectively divide the object intoconcentric rings that are Dx (m) thick. For a sphere, the tem-perature can be determined by

tDtTn 1

M

2n 12n t

Tn1 M 2tTn2n 12n t

Tn1

29

where MDx2/(aDt). At the center (n 0) the equationchanges to

tDtT0 4

MtT1M 4

M tT0 30

where M 4 for both Eqs. (29) and (30). At the surface, equa-tions accounting for convection must be utilized assuming thatthe heat capacity of the outer half-slab can be neglected

nN 2n 1=2

1459cal Science 35 (2008) 1453e1462Cp 44:603 3:7754 102T 1:0018 106T2 33

where Cp is the heat capacity (J mol1 K1) and T is the tem-

perature (K) for the range of 298e844 K. At higher tempera-tures the equation changes to

Cp 58:928 1:0031 102T 34

for the range 844e1800 K. The density of chert is 2.6 g cm3.This information together can be used to determine the ther-mal diffusivity (a) properties of chert for the numerical model.

Fig. 4 graphically represents a simulated evaporation ofplacing 700 C chert stone(s), representing 25% of the total40 L volume, into a salt pan containing 10 wt% brine at25 C. Boiling begins immediately for brine surrounding thestone and continues for about 4 min, by which time the stonetemperature now equals that of the brine and no further heat istransferred. During the first 2 min the evaporating brine con-

of heat transferred at any given time can be determined by

Q CprVT0 TN1 ehA=CprVt 35

where Q (J) is the total heat transferred, V (m3) is the volumeof the object, h is a heat transfer coefficient for natural convec-tion (w5000 Wm2 K), A is the heated area (m2), and t is theelapsed time (s) after immersion (Geankoplis, 2003: pp. 277e286, 357e359).

5. Conclusions

The goal of this paper is to develop a mathematical basisfor brine evaporation that can be used by investigators to quan-titatively describe salt production activities. The methods de-scribed herein cover three distinct techniques for evaporatingbrine: (1) solar evaporation, (2) boiling due to an externallyapplied heat source, and (3) boiling caused by a hot immersed

1460 D.G. Akridge / Journal of Archaeologicentrates from 10 wt% up to 29.0 wt%. At 1.6 min salt crystalsbegin forming and continue until the stone and brine reachthermal equilibrium. For this scenario, 373 g of crystallizedsalt would be produced. Emplacement of additional hot stonesinto the pan would continue the evaporation process.

From the short timescales involved to obtain salt, it seemsthis method would clearly be effective in evaporating brine.Unlike suspension of a pan over a fire, stone boiling releasesall of its internal heat directly into the brine. However, theremay be practical limitations for manipulating large volumesof very hot stones. Stones heated to high temperatures oftenshatter and large stones would be difficult to transport froma fire to the brine pan. Smaller stones would make handlingeasier, but would require more repeated firings to achievethe same evaporation as large stones. The smallest salt panfound at the Kimmswick site near St. Louis (Bushnell, 1907)had a volume of approximately 40 L. Assuming a scenariosimilar to that outlined above, emplacement of 25 vol% stoneinto the salt pan would translate to 26 kg of extremely hotstone(s) that would have been manipulated. This seems to sug-gest that stone boiling may actually require a tremendousamount of human labor to achieve significant quantities ofsalt. Fig. 5 indicates the potential evaporation that could be

02

4

68

1012

14

161820

0 2 4 6 8Time (minutes)

Heat T

ran

sferred

(M

J)

0.000.050.100.150.200.250.300.350.400.450.50

Salt P

ro

du

ced

(kg

)

Heat transferred, MJSalt Produced, kg

97531

Fig. 4. Numerical simulation results for Native American stone boiling. Rep-

resented 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 isassumed to be a spherical nodule of chert.An alternative mathematical treatment can be applied whenthe hot object has negligible internal resistance to the flow ofheat. These objects (e.g., copper and iron) have high thermalconductivities and will have an approximately uniform inter-nal temperature profile at any given time following immersioninto brine. To maintain an energy balance, heat loss throughthe vessel wall or to the atmosphere is assumed to be minimalrelative to the rapid rise in brine temperature. The total amount4.3. Hot objects with negligible internal resistanceobtained with various brine/stone volume ratios. The 10 wt%brine is assumed to initially be at 25 C before emplacementof a hot spherical stone of chert. Even for a Vb/Vs 1 andan initial stone temperature of 1000 C, the mass of the stonewould still exceed the mass of the evaporated water by a factorof 2.5. Lower stone temperatures or smaller volumes of stonewould result in greater discrepancies between stone mass andevaporated water mass.

0

5

10

15

20

25

200 300 400 500 600 700 800 900 1000Initial Stone Temperature (C)

Water E

vap

orated

(kg

) 1.02.03.04.0

Volume Ratio

Brine/Stone

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.

cal Science 35 (2008) 1453e1462object. Historically these techniques were sometimes used incombination to achieve the desired evaporation results. Input

calculation methods given here do allow for direct compari-

ing salt production opens up new areas of research that can

logibe addressed. Changes in production methods through timecan be the result of either cultural or technological factors,or both. In a simple least-cost model, humans would be ex-pected to seek strategies to minimize labor and fuel require-ments in the salt production process. Salt production hasoften been described as a labor intensive endeavor requiring,in the case of brine boiling, extraction of substantial quantitiesof fuel from the local environment. The calculations presentedherein offer a direct means to evaluate technological changesfor improved evaporation efficiency. For example, Eq. (24)describes the direct relationship between vessel thicknessand the rate of heat transfer. Thinner vessel walls requireproportionately less fuel to achieve evaporation. In addition,determinations of minimum energy (fuel) requirements canbe made which provide insight into local deforestation or otherresource depletion. Early (1993) noted that the removal of fruitbearing plants and nut bearing trees from the vicinity of a salt-works may have altered diet and even changed the local pop-ulation of wild animals that depend on these resources. Theseand other concerns can now be better addressed by quantifyingthe brine evaporation process.

Acknowledgments

The author thanks Ann M. Early and Dan F. Morse forhelpful discussions on this subject. Ashley Dumas and RobertC. Mainfort provided insightful comments on an early draft ofthis paper. Valuable comments were also received from twoanonymous reviewers that greatly improved this manuscript.

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1462 D.G. Akridge / Journal of Archaeological Science 35 (2008) 1453e1462

Methods for calculating brine evaporation rates during salt productionIntroductionSolar evaporationCalculation method for solar evaporationCalculating aerodynamic termsDetermining net radiationCalculating net radiation

Results from numerical simulations

Evaporation from an externally heated panCalculation method for evaporation by externally applied heatNumerical simulation of applied external heat

Evaporation using hot immersed objectsCalculation method for stone boilingNumerical simulation of stone boilingHot objects with negligible internal resistance

ConclusionsAcknowledgmentsReferences