Geothermics 34 (2005) 133–160

Measurement of heat flux from steaming ground Manfred P. Hochstein a, ∗ , Christopher J. Bromley b b

a Geothermal Institute, University of Auckland, Bag 92019, Auckland, New Zealand Institute of Geological and Nuclear Sciences, Wairakei, Bag 2000, Taupo, New Zealand

Received 2 October 2003; accepted 19 April 2004

Abstract The total thermal flux at the surface of ‘steaming ground’ consists of a convective and a conductive component, even in the absence of any visible steam discharge at the surface. The total flux and its convective component can be measured separately and directly using a water-filled ground calorimeter. The conductive component is given by the difference between the two fluxes, but can also be assessed independently using measured near-surface soil parameters and temperature gradients, retaining the thermal conductivity as parameter. The conductivity is controlled, in turn, by the thermal diffusivity and the specific moisture content of the near-surface layer. The observed total flux values range between 0.03 and 2 kW/m2 at sites where boiling temperatures occur at depths of about 4 m and <0.1 m, respectively; the convective flux can reach 50% of the total flux at most sites. Analysis of various soil parameters and soil temperature sections points to a ‘heat pipe’ transfer mechanism that maintains a high conductive transfer in a thin near-surface layer where sub-surface steam condensation is enhanced. An empirical power-law function can be used to assess the total heat flux from the boiling point depth at single sites with known soil temperature profiles. © 2004 CNR. Published by Elsevier Ltd. All rights reserved. Keywords: Thermal manifestations; Steaming ground; Surface heat flux; Convection; Conduction; Calorimetry; Soil thermal conductivity; Heat-pipe mechanism

1. Introduction The term ‘steaming ground’ has been used to describe thermal manifestations where vapour from the upper part of a liquid- or vapour-dominated geothermal reservoir (or a ∗

Corresponding author. Fax: +64 9 373 7435. E-mail addresses: [email protected] (M.P. Hochstein), [email protected] (C.J. Bromley).

0375-6505/$30.00 © 2004 CNR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.geothermics.2004.04.002

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Nomenclature A c C h L m q q r S t T z

area (m2 ) specific heat [J/(K kg)] compressibility factor (soil sample) specific enthalpy (J/kg) loss component (W/m2 ) mass (kg) specific heat flux (W/m2 ) variable (externally controlled) flux component repeat (site) saturation of pores time (s) temperature (K, ◦ C) depth (m)

Greek symbols α thermal diffusivity (m2 /s) λ thermal conductivity (W/mK) σ with subscript: specific density (kg/m3 ); without subscript: standard deviation φ porosity Φ specific moisture content of soil sample (kg/m3 ) ω radian frequency Subscripts a apparent value of a parameter c condensate dy pertaining to daily variations dr pertaining to temperature drift filt pertaining to infiltration yr pertaining to annual variations rd pertaining to recorded (calorimeter) temperatures v pertaining to volume (soil sample) g gas phase l (or f) liquid (fluid) phase d, w, p for density modes: dry, ‘wet’, and particle, respectively z soil parameter at a given depth z o soil parameter at free surface conv, cond, tot for heat flux modes: convective, conductive, and total, respectively eff, mix parameter derived from mixed components BP boiling point Superscripts numerically revised parameter average value



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volcanic-hydrothermal reservoir) reaches the surface. A steep temperature gradient develops close to the surface, which enhances heat transfer by conduction within a thin near-surface soil layer. Some minor steam can be diffusively discharged through the surface as well; significant steam is often discharged directly to the air through cracks, vents and fumaroles. Thus, both convective and conductive heat transfer occur in areas of steaming ground. This was recognised when the term was introduced by Banwell et al. (1957) who were the first to assess the heat transferred by steaming ground over several liquid-dominated geothermal reservoirs in New Zealand. At Wairakei and Orakei Korako, for example, the heat discharges from steaming ground were estimated in the order of 150 MW (Benseman, 1959a,b). Steaming ground also occurs over other liquid-, vapour-dominated, and volcanichydrothermal reservoirs in many parts of the world. Large steaming ground areas are observed over high-temperature systems in arid settings, such as in some segments of the East African Rifts, where steaming ground is often the only thermal manifestation. The Olkaria system (Kenya) is such a prospect, associated with extensive steaming ground (Hochstein and Kagiri, 1997). Geothermal systems that discharge heat dominantly by steaming ground have been called ‘steaming ground systems’ (Hochstein and Browne, 2000). One of the better known volcanic-hydrothermal systems associated with extensive steaming ground is that beneath the Phlegrean Fields in southern Italy (Chiodini et al., 2001). Areas with intense steaming ground usually exhibit a few larger steam vents (fumaroles or solfataras). The terms ‘fumarolic ground’ and ‘areas with soffioni’ are synonyms for steaming ground. Throughout this paper ‘vapour’ is considered to be the gas phase of water without condensation that exists strictly below the ground surface, whereas ‘steam’ is vapour with minor condensation that occurs in the air at and above the surface. Since the near-surface heat transfer raises the temperature of the ground surface, the areal extent of steaming ground can be mapped from the air by infrared (IR) methods. IR surveys are well suited to monitoring changes in the area of steaming ground over reservoirs under exploitation (Bromley and Hochstein, 2000). However, previous attempts to assess the magnitude of heat transfer over steaming ground from IR data have not been satisfactory because of vegetation screening. For surveys conducted under optimum conditions, IR data over ‘bare ground’ (hot ground clear of vegetation) can be used to infer actual ground surface temperatures (T0 ), but where there is vegetation the data are difficult to interpret. Such interpretations are open to criticism if there is no ground control of the surface heat flux. Until recently, the magnitude of heat transferred by steaming ground in New Zealand prospects was assessed with reference to rather dated studies (Benseman, 1959a; Thompson et al., 1964; Dawson, 1964). As awareness of the environmental changes associated with the extraction of thermal fluids from New Zealand reservoirs has increased, it was necessary to study, in more detail, the magnitude and the mechanisms of heat transfer at steaming ground. The problem was split into two projects: (a) assessment of the total heat transferred by steam-clouds over fumaroles and smaller vents in a large steaming ground area (an idealized setting is shown in Fig. 1a); (b) assessment of the heat loss of steaming ground not associated with any significant steam discharge at the surface (the various heat flux components for this setting are shown in Fig. 1b).

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Fig. 1. Sketch showing two different settings of ‘steaming ground’: (a) area with concentrated steam discharge from different types of surface vents; (b) area with no visible steam at the surface but with convective and conductive heat transfer.

The first study (i.e. setting of Fig. 1a) has been completed (Hochstein and Bromley, 2001); the results of the second study (setting in Fig. 1b) are presented here. In order to assess the steaming ground associated with the Wairakei, New Zealand, system, we developed and tested new methods to measure various components of heat transfer at test sites using simple experimental methods. An attempt was also made to obtain representative soil parameters at all test sites and to develop a model that explains the actual heat transfer mechanism causing the steaming ground phenomenon.

2. Terminology and basic model Our heat flow studies were made over two separate steaming ground areas of the greater Wairakei system whose reservoir has been exploited since 1958. Earlier measurements (Bromley and Hochstein, 2001; Hochstein and Bromley, 2002) have shown that various heat flux modes are involved in transferring heat from a boiling liquid subsurface to the free ground surface (see Fig. 1b). These include:

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1. Convective transfer of minor steam through the surface associated with a heat flux component qconv . 2. Conductive transfer qcond through a thin, near-surface layer. The conductive flux contains a time-variable flux component (qdy ) causing daily variations of near-surface temperature and near-surface temperature gradient (T/z0 ) (z positive downwards). 3. An episodic component qfilt caused by water infiltrating the ground after a long period of rainfall, which cools the near-surface layer of steaming ground; this component can be neglected during dry periods (>5 dry days, from our experience). 4. A seasonal component qyr causes, in colder seasons, a decline of ground temperatures and an increase in the depth below which boiling temperatures prevail. The component is smallest during the summer months when the total flux reaches a maximum. Steaming ground can also be affected by secular changes in total heat output, which could not be detected during the few years of this study. All heat flux modes and flux components listed above refer to a specific heat flux (in W/m2 ). For dry periods and during the summer, the heat flux measured at the surface qtot is therefore approximately given by: qtot = qconv + (qcond + qdy )

(1)

Small variations of the vapour flux occur at depths (zBP ) where boiling temperatures (TBP ) prevail. These are revealed by temperature changes and correlate with small periodic atmospheric pressure changes (Bromley and Hochstein, 2001). All surface heat flux components (including the total flux qtot ) are therefore time-variable parameters. We started the study with an assessment of the total conductive flux (qcond + qdy ), referred to henceforth as qcond (λ), using near-surface temperature gradients and soil parameter surveys (Bromley and Hochstein, 2001). The study was extended by using a calorimeter method to assess the total flux (qtot ) (Hochstein and Bromley, 2002). Recently, the condensation rate of the diffuse steam flux through the surface was also measured, providing independent estimates for the convective component (qconv ). The studies are presented here in a sequence of increasing uncertainty; we therefore begin with measurements of the total flux, followed by assessments of the convective flux, and, finally, the conductive flux.

3. Measurement of total flux (qtot ) 3.1. Earlier attempts The total flux of steaming ground of several New Zealand geothermal prospects was first measured almost 50 years ago by Banwell et al. (1957), who used a water calorimeter (closed bottom) and a surface calorimeter with an open bottom (differential psychrometer). The prototype psychrometer was refined by Benseman (1959a), who measured total flux values between 0.04 and 2 kW/m2 over ground with near-surface temperatures between 30 and 100 ◦ C, respectively. The reproducibility of the data was poor. The Benseman calorimeter was used together with disks of known conductivity to obtain additional information about the total heat loss of the Karapiti area (Thompson et al., 1964). Calorimeter studies of steaming ground in New Zealand were discontinued after 1965.

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A ground calorimeter with an open bottom, similar to that of Benseman, was also used by Le Guern et al. (1980) to assess the heat flux of fumarolic ground in Italy. The measured fluxes were within the range 0.4–4 kW/m2 for near-surface soil temperatures between 25 and 100 ◦ C, respectively. The Benseman calorimeter has also been used in Japan to assess the heat output of smaller areas of steaming ground (Yuhara et al., 1981). The melting rate of snowfall over areas with steaming ground has been used to obtain an order of magnitude estimate for the associated heat flux (White, 1969). The accuracy is low and application is restricted since continuous and simultaneous observations over large areas are required. ‘Snow melting’ calorimetry was used in Japan for calibration of IR data (Sekioka and Yuhara, 1974). Since soil temperatures of hot and steaming ground at a given reference depth control plant growth, order-of-magnitude estimates of total heat flux can be assigned to areas with similar types of stressed vegetation. The concept was introduced by Benseman (1959b), extended by Dawson (1964), and modified by Allis (1979). The simplified classification of Allis was used until recently to assess local steaming ground heat losses in New Zealand since representative data allowing a quantitative interpretation of IR data were not available (Bromley and Hochstein, 2000). 3.2. A new calorimeter to measure qtot A new ground calorimeter was built during this study to obtain representative heat flux data for steaming ground. Little is known about the old ‘water calorimeter’ referred to by Banwell et al. (1957). Their open bottom ground calorimeter (‘air calorimeter’) is, in principle, well suited for heat flow studies. However, the low heat capacity of air and the poor reproducibility of the ‘air calorimeter’ measurements cited above led us to construct a new ground calorimeter. A section of our calorimeter is shown in Fig. 2; design details have already been presented (Hochstein and Bromley, 2002). The calorimeter consists of a flat, cylindrical vessel with a capacity of up to 1.5 litres. It has a very thin stainless steel bottom. A stirrer provides good mixing of the water fill. The temperature change of the water mass is monitored by three mini-bead type thermistors. Conductive losses or gains through mantle and lid are reduced by an insulating double layer of polystyrene (lid) and a felt-polystyrene layer (mantle). The temperature of the lid is monitored by another thermistor. Calibration tests in the laboratory showed that an anomalous amount of heat in an electrically heated plate of the same diameter as the calorimeter bottom could be transferred with small losses (less than 6%), allowing for a reduction of a small amount of heat stored in the mantle and the bottom plate during the tests. The calibration results also showed that the thermal resistance of the thin bottom plate is small; its effect upon heat transfer was neglected when analysing the field data. Field tests were conducted at selected sites in the Karapiti steaming ground area (Fig. 3) and at a few sites in the nearby Tauhara sector during the past 3 years. All sites are covered by pumice soils exhibiting different degrees of thermal alteration. For close contact each test site was levelled by using a wooden base block of the same dimension as the calorimeter; at a few sites minor surface plant material was removed to improve contact. New sites reached stable temperatures after one day. While the calorimeter was on the ground, the water temperature, given by the resistance of the thermistors, was monitored with a ‘Fluke

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Fig. 2. Section of the ground calorimeter used in this study.

Hydro logger’, usually at 15 s intervals. The starting temperature of the calorimeter water was within a few degrees of ambient to minimize drift. Soil temperatures at 0.01, 0.05, 0.1, 0.15 and 0.19 m depth were measured at four points within the ground contact area (0.045 m2 ) to assess the temperature gradient within the topsoil layer. Only sites with no visible steam discharges at the surface were occupied. Air temperature and sometimes soil temperature at 0.05 m depth were also monitored. The water temperature in the calorimeter was always less than the surface temperature at each site during the flux measurements; hence, heat transfer was always from the ground to the calorimeter. The heat flux qtot entering the calorimeter through the bottom was computed using a time-based temperature gradient approach. Any temperature difference between the water and the lid of the calorimeter induces minor heating or cooling and causes a small drift in water temperature. The recording procedure followed was to occupy a site for 5 min periods separated by an ‘off-the-ground’ period of 2 min. This is shown by the original monitoring record at site KP10 (Fig. 4a). The background temperature drift rate (Tdr /t) of the liquid can be predicted from the characteristics of the lid temperature curve. Denoting the recorded steep temperature rise during a recording time interval t by (Trd /t), the total heat flow is given by: qtot =

mc{(Trd /t) − (Tdr /t)} A

(2)

where m is the water mass, c its specific heat, and A the area covered by the calorimeter. The uncertainty in computing mean (T/t) values was reduced by using a least-squares, linear fit applied to successive segments of the record.

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Fig. 3. Map of the Karapiti steaming ground area showing the location of the calorimeter sites (the distance and direction to sites in the Tauhara field are indicated). Boundaries of cold ground were taken from an airphoto (18 February 2000).

3.3. Results A comparison of the calorimeter records from all 24 test sites showed different types of heating response. Decreasing heating rates within the first 5 min showed up in almost 70% of the records, often decreasing quasi-exponentially with time. Most of the remaining records showed almost constant heating rates (see Fig. 4b), and a few showed an irregular pattern with a late small secondary maximum recorded during site occupation. Initially it was assumed that for sites with a constant heating rate (Fig. 4b) the heat transfer was almost entirely by conduction and that at sites with a declining heating rate, for example at KP13 (Fig. 5a and b), both conductive and convective transfer occurred. Recent assessment of the convective flux (see Section 4), however, showed that

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Fig. 4. (a) Calorimeter record from site KP10 (measured on 21 March 2002). Soil surface temperature beneath calorimeter was 46 ◦ C. (b) Reduced heating rate vs. recording time—taken from the record shown in (a).

even at sites with a quasi-constant heating rate, a significant convective flux could also be measured. At sites where qtot was greater than 0.2 kW/m2 , the ground was usually slightly moist at the surface and traces of condensate were visible on the underside of the calorimeter when it was lifted. Temperature records from shallow depths (about 0.05 m) beneath the calorimeter indicate small irregular changes, usually <1 ◦ C, of soil temperature. A decrease between 1 and 3 ◦ C at 0.01 m depth was observed at eight out of 12 sites where spatial temperature measurements were taken before and after the calorimeter survey. This caused a small increase in near-surface gradient between 3 and 10%, which increased the conductive flux

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Fig. 5. (a) Calorimeter record from site KP13 (measured on 21 March 2002). Soil surface temperature beneath calorimeter was 40 ◦ C. (b) Reduced heating rate vs. recording time; taken from record shown in (a).

component. At two sites with higher fluxes (>1 kW/m2 ), these temperatures had increased by a few degrees; at two other sites no changes were observed. The quasi-exponential decline in heating rate (Fig. 5b) is probably caused by a decline of the convective component. The decrease in convective transfer might be the result of diverting the vapour flux as soon as the calorimeter is placed on the ground, effectively reducing its permeability and thus reducing the flux reaching the calorimeter. The decline of the apparent total flux is proportional to the elapsed period τ when the meter was placed on the ground, i.e. q/q is proportional to τ. This points to an exponential decay of the form: ln q = cτ + b. For a few sites with exponentially decaying heating curves, an ‘undisturbed’ total flux (see Fig. 5b) can be assessed; for most other sites, a mean of the observed fluxes during each 5 min recording period was used to compute qtot . The short-term and long-term reproducibility of the qtot measurements was checked by re-occupying the same site days and months later. The results of some repeated tests are

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Table 1 Measured (qtot , qconv ) and computed (q  cond ) heat fluxes at 10 selected steaming ground sites at Karapiti and Tauhara (“r” denotes repeat) Site ID

KP1 KP1r KP3 KP3r KP6r2 KP6r3 KP6r5 KP10r2 KP10r3 KP10ar KP13a KP13ar KP15 KP15r KP16 KP16r KP17 KP17r TH1 TH1r TH2 TH2rV1 TH2r1

Survey date

20/11/2001 31/01/2003 20/11/2001 11/04/2002 19/04/2002 17/09/2002 26/03/2003 21/03/2002 16/04/2002 30/01/2003 20/01/2003 25/03/2003 30/01/2003 25/03/2003 30/01/2003 26/03/2003 31/01/2003 26/03/2003 21/11/2001 3/12/2002 21/11/2001 25/02/2002 3/12/2002

1

2

3

4

5

6

7

8

T grad

Rel. error

qtot-1

qtot-2

qconv-1

qconv-2

q  cond

zBP

150 183 35 56 264 215 243 713 843 622 721 856 393 566 516 546 254 250 1019 883 166 293 243

16.3 17.6 20.1 8.5 11.9 11.4 4.2 33.6 9.2 11.4 11.5 15.9 7.8 8.9 8.2 8.5 2.8 6.6 10.2 11.4 5.2 6.3 10.4

326 372 30 59 268 190 259 909 947 1040 1237 1065 559 465 728 683 267 330 1802 1055 270 274 214

385 321 31 52 222 158 226 902 969 1014 1044 962 462 473 562 566 247 276 1691 999 225 255 170

211

173

165

136

544 584 584 235 255 331 314 97 151

461 634 534 193 206 327 242 81 123

457

508

24

23

89 127 21 29 175 142 160 513 566 468 457 529 286 347 341 391 165 167 591 501 65 112 83

0.80 0.81 4.34 4.34 0.67 0.74 0.55 0.10 0.10 0.11 0.12 0.11 0.26 0.16 0.20 0.20 0.66 0.47 0.05 0.08 0.99 1.02 0.99

Explanation of labelled columns: Column 1: Average near-surface temperature gradient between 0.01 and 0.05 m depth (◦ C/m). Column 2: Relative error of T gradient measurements at four points (normalized standard deviation in %). Column 3: Total heat flux qtot (W/m2 ) observed during the first 5 min of recording. Column 4: Total heat flux qtot (W/m2 ) from the second 5 min recording period. Column 5: Convective heat flux qconv (W/m2 ) given by the condensation rate at the bottom of the calorimeter during the first 5 min of recording. Column 6: Convective heat flux qconv (W/m2 ) during the second 5 min period. Column 7: Computed conductive heat flux q  cond (W/m2 ) using the revised thermal conductivity listed in column 8 of Table 2. Column 8: Boiling point depth zBP (m) computed from linearized temperature-depth profile taken at survey date.

listed for ten sites in Table 1. The sites selected cover a representative set of all 24 stations occupied. The observed total flux qtot at sites with repeated surveys lies between 0.03 and 2 kW/m2 . The scatter increases for higher qtot values (qtot > 1 kW/m2 ). At four sites qtot measurements were repeated after a day or a few days; the results differ from the mean by <7%; for six sites re-measured after 3–8 weeks the repeat values of qtot differ between 0 and 10% from the mean (on average by about 7%). The differences do not correlate with changes in the near-surface gradient (T/z)0 and are probably caused by small changes in the effective ground contact of the calorimeter. At several sites where three or more qtot measurements were taken during a year, including a reading taken during the cold season, the normalized standard deviation [σ(qtot )/mean (qtot )] lies between 7 and 27%, reflecting the influence of the seasonal component qyr , which also causes changes in the boiling depth beneath each site (see Section 6). However, when measurements were

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repeated during the summer months a year or so later, the difference from the mean was usually <7% (see data from KP06 and KP10 in Table 1). An exception was at site TH1 in Tauhara. Poor reproducibility at this high heat-flux, bare-ground site can be attributed to laterally variable permeability combined with mis-location of the site when reoccupied. Any long-term monitoring of qtot should therefore be made during the same (dry) summer months, and repeat sites should be marked to allow for accurate reoccupation.

4. Assessment of the convective flux (qconv ) In the early 1950s, an attempt was made to assess the latent heat of vapour condensing at the bottom of a water calorimeter (Banwell et al., 1957). This method, however, was not developed further. Measurements of a gas species (CO2 ) transferred to the surface by the vapour flux were used by Chiodini et al. (2001) to assess the heat flux of steaming ground over the Phlegrean Fields. The average CO2 /H2 O ratio of many steam vents within the Karapiti steaming ground area is known (Glover et al., 1999); it varies locally and amounts to about 190 ± 26 mmol CO2 per 100 mol H2 O. We tested the CO2 method across the Karapiti area. For this a LI-COR infrared gas analyser with an accumulation chamber was used, as described by Werner and Brantley (2000). Repeat measurements were made at 12 test sites, selected to cover the whole range of the observed qtot values. In general, there was an approximate correlation between CO2 and qtot values. At Karapiti, the predicted steam mass flux values were between 15 × 10−3 and 170 × 10−3 g/(m2 s) with a median (anomalous) value of about 65 × 10−3 g/(m2 s), pointing to a total diffuse steam discharge of the order of 20 kg/s for the steaming ground area (0.33 km2 ). This is about half that discharged separately by all fumaroles and visibly steaming centres in the area (Hochstein and Bromley, 2001). The previously mentioned phenomenon of condensation of diffuse steam at the cool (stainless steel) bottom of the calorimeter when measuring qtot can also be used to estimate qconv . Tests using dry tissue paper to collect all the condensate (mass mc ) at the bottom showed that the rate of condensation (mc /t) is similar for repeat surveys at the same site, after the vessel had been on the ground for a given period (5 min). The associated heat transfer rate qconv (from latent heat) is therefore:
 (mc /t) qconv = (3) [hg − hc ] + L A where A is the area of the calorimeter bottom plate, hg the specific enthalpy of steam escaping at the surface with the known near-surface temperature T0 , hc the enthalpy of the condensate droplets with respect to the temperature of the water mass in the calorimeter, and L a liquid loss component (droplets becoming attached to the ground). The moist tissues were stored in small, air-tight plastic bags at low temperature to avoid evaporation. Measurement of moist and air-dried tissues in the laboratory determined the condensate mass (mc ). This showed that condensation rates varied between 10 × 10−3 and 150 × 10−3 g/(m2 s) for sites that had previously been occupied by the CO2 flux survey. The range of mass flux rates of diffuse steam is therefore similar for the two methods. However, a few sites at the periphery of the Karapiti thermal area (with low heat flux), and at Tauhara, revealed rather high CO2

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Fig. 6. Plot of qconv vs. qtot (using all data from 5 min recording periods).

fluxes, presumably because of deeper condensation. We continued with the ‘tissue method’ since uncertainties due to heat flux variations were less than those affecting the CO2 flux. The qconv data are also listed in Table 1. A plot of qconv versus qtot (Fig. 6) shows a clear positive correlation. The qconv values vary between 0 and 0.6 kW/m2 for qtot between 0.2 and 1.2 kW/m2 , respectively. The scatter is small for qconv < 0.2 kW/m2 but increases for larger values. At sites with repeat measurements, the normalized standard deviation [σ(qconv )/mean qconv )] lies between 7 and 30%. The effect of the loss component L (Eq. (3)) cannot be assessed yet; hence, the qconv data in Table 1 and Fig. 6, computed assuming that L can be neglected, are ‘apparent’ flux data. Convective transfer starts to increase once the conductive flux exceeds 0.2 kW/m2 ; convective transfer can account for up to 50% of the total heat transfer from steaming ground (with no visible steam discharge).

5. Assessment of the conductive flux qcond (λ) The conductive heat flux at the surface (z = 0) is given by:   T λ(z)0 qcond (λ) = z 0

(4)

where (T/z)0 is the vertical temperature gradient and λ(z)0 the thermal conductivity of the surface (contact) layer. The temperature gradient decreases with depth and consists of a constant and a variable component; the latter reflects the effect of the variable daily flux qdy . The thermal conductivity of soils also varies with depth (Bromley and Hochstein, 2001). We used the mean of temperatures measured at four points at 0.01 and 0.05 m depth at each site (in very hot ground at 0.01 and 0.03 m depth) to obtain a representative value for

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(T/z)0 . However, assessment of a representative value for λ(z)0 turned out to be more complex. Several methods have been used in the past to estimate the magnitude of the conductive flux. This involved direct measurement of qcond at some shallow depth using disks of known thermal conductivity or computing qcond values based on estimates of the thermal conductivity of the soil layer and observed shallow temperature gradients. The conductive component of steaming ground flux was assessed in the late 1950s at Karapiti (Fig. 3) by using a disk (Lee’s disk) of known thermal conductivity (Thompson et al., 1964). A heat flow ‘disk’ at 0.1 m depth was used to assess an apparent conductive flux over small steaming ground areas in Japan (Yuhara et al., 1981). The disk method produced widely differing results when condensation occurred. 5.1. Conductive heat flux and thermal constants of steaming ground The friable nature of the pumice soils at Wairakei did not allow measurement of their thermal conductivity in the laboratory. We therefore used an indirect method to estimate this parameter. The conductivity λ(z) is given by the product of three thermal constants: λ(z) = αceff σw

(5)

where α is the thermal diffusivity [m2 /s], ceff the effective thermal capacity per unit mass [J/kg K], and σ w the bulk (‘wet’) density [kg/m3 ] of a soil sample at depth z. Measurement of the parameters in Eq. (5) was used, for example, by Nassar and Horton (1989) and Evett (1994) to assess the thermal conductivity of soils. An approximate value of the thermal diffusivity α of a soil layer can be obtained from the analysis of the downward propagation in time of the diurnal flux (temperature) pulse with amplitude T(0) and period P (radian frequency ω = 2␲/P) at the surface. Its attenuated amplitude T(z) at depth z and time t can be described by a Fourier series whose first term is, for example:       ω 0.5  ω 0.5 cos ωt − z (6) T(z) = T(0) exp −z 2α 2α Independent solutions for (ω/2α) can therefore be obtained from an analysis of the amplitude decay of the daily maximum with depth (first term) and its phase shift (second term) assuming conductive heat transfer. The effective heat capacity of a soil sample in Eq. (5) is: ceff =

cp (1 − φ)σp + cf φ S1 σf σw

(7)

where cp is the mean specific heat capacity of the soil particles (about 0.8 kJ/kg K for most minerals), φ the porosity of the sample, σ p the particle density of the soil matrix [kg/m3 ], cf the heat capacity of the saturating liquid in the pores (about 4.18 kJ/kg K for water), S1 the degree of liquid saturation of the pores, and σ f the fluid density. The fluid parameters cf and σ f vary slightly with the temperature T(z) prevailing at depth z. The density terms are

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related by: σw = (1 − φ)σp + φS1 σf = σd + Φ

(8)

where {(1 − φ)σ p } is the so-called ‘dry’ density σ d and {φS1 σ f } the specific moisture content Φ (kg/m3 ) of the sample. In soil science literature, the dimensionless ‘volumetric’ moisture content (Φ/σ f ) is used to describe the water content of a soil sample. Substituting these parameters in (5), λ(z) can be expressed by: λ(z) = α [cp σd + cf (σw − σd )]

(9)

5.2. Thermal diffusivity of soils To assess the thermal diffusivity α, the daily temperature variations were recorded at shallow depths (down to 0.2 m) at several sites in the Karapiti area using a calibrated thermistor probe and the Fluke Hydra data logger. An example of such a record from site KP02 is shown in Fig. 7 (from Bromley and Hochstein, 2001). Fourier series analysis (Newson et al., 2001) showed that the value of α obtained from the amplitude decay term differed significantly from that of the phase shift term (about 0.2 × 10−6 and 0.6 × 10−6 m2 /s, respectively, for the record shown in Fig. 7). The same behaviour and a similar range of α values were found at other Karapiti sites and at sites in the Wairakei area where temperatures had been monitored previously (Dawson and Fisher,

Fig. 7. Temperature monitoring logs at site KP02 showing propagation of diurnal temperature pulses down to 0.2 m depth.

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1964). The phenomenon was also found in agricultural ‘cold’ soils in the US (Nassar and Horton, 1989). Since a similar range of diffusivity values had been found in Wairakei ‘thermal’ ground and in nearby ‘cold’ ground, their average value of α = 0.40 ± 0.13 × 10−6 m2 /s (from six sites) was adopted to obtain the thermal conductivity at other sites using Eq. (9). Little was known prior to our study about the thermal properties of partly saturated pumice soils and tuffs with high porosity apart from the results of the earlier study by Dawson and Fisher (1964) and a small reference in Somerton (1992) quoting a diffusivity value of 0.5 × 10−6 m2 /s for dense tuffs with unknown saturation. Eq. (9) implies a linear dependence of λ upon the moisture content Φ (and saturation S1 ). However, experimental studies, cited in Clauser and Huenges (1995) and conducted on moderately porous rocks, point to a rather small effect of S1 upon λ (for S1 > 0.2). This indicates that the thermal diffusivity of porous rocks and soils decreases with increasing saturation, as it has indeed been reported for soils with S1 > 0.2 (Williams, 1982). We therefore refer to the thermal conductivity computed from soil parameters using an average diffusivity value as ‘apparent’ thermal conductivity λa . 5.3. Physical properties of near-surface soil samples Soil parameters were assessed for 22 sites in the Karapiti steaming ground area and for six sites in the adjacent Tauhara sector. Almost 25% of all sites were on hot ‘bare’ ground, while the other sites were covered by moss and stunted shrubs (Karapiti) or grass (Tauhara sites). The pumice soils at most of the Karapiti sites are thermally altered, their clay content (with significant smectite and kaolinite) varying between 20 and 80%; pumice soils at the Tauhara sites are unaltered and contain almost no clay, thus pointing to a recent development of thermal activity in this area. Over 150 soil samples were taken using 160 mm long, cylindrical brass tubes (38 mm diameter). Initially, soil samples were taken over 0.15 m depth intervals. However, in active thermal ground most soil parameters show significant variations over this interval and more detailed sampling (at 0–0.05 m and 0–0.1 m intervals, see Table 2) was used later. At sites with thermal alteration, the cores usually suffered some compression both during sampling and recovery. A core compressibility factor Cv was introduced, given by the ratio of the volume of the recovered core to that of the in situ sample. Apparent bulk (σ wa ) and dry density (σ da ) were measured in the laboratory, the latter after a drying period of >2 days (at 105 ◦ C). In-situ densities were computed using Cv (for example, σ w = Cv σ wa ). The dried sample was ground to a fine powder (with more than 50% of the mass passing through a 150 ␮m mesh) and the particle density (σ p ) was measured using a pycnometer after removing air bubbles under high vacuum. Porosity φ, specific moisture content Φ, liquid saturation S1 , and apparent thermal conductivity λa were computed using the values of the three density modes and Eqs. (8) and (9). The results of the soil parameter survey for selected sites are listed in Table 2. Most soil properties varied with moisture content and intensity of alteration. A characteristic feature of the pumice soils in both study areas is their anomalously high porosity (0.6 > φ > 0.8). High values of liquid saturation (S1 up to 0.8) occur at sites with high heat flux values reflecting an accumulation of condensates close to the surface. Measured par-

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Table 2 Measured and computed soil parameters at ten selected steaming ground sites listed in Table 1 Sample ID

Sampling date

1

2

3

4

5

7

8

Sample interval

Dry density

Wet density

Particle density

Porosity Volume moisture

6

Therm. conduct.

Revised conduct.

KP1 KP1r KP3 KP3r KP6r2 KP6r3 KP6r5 KP10r2 KP10r3 KP10ar KP13a KP13ar KP15 KP15r KP16 KP16r KP17 KP17r TH1 TH1r TH2 TH2rV1 TH2r1

20/11/2001 1/02/2003 20/11/2001 11/04/2002 19/04/2002 17/09/2002 26/03/2003 21/03/2002 16/04/2002 31/01/2003 20/01/2003 25/03/2003 31/01/2003 25/03/2003 31/01/2003 26/03/2003 1/02/2003 26/03/2003 21/11/2001 3/12/2002 21/11/2001 25/02/2002 3/12/2002

0–0.15 0–0.10 0–0.15 0–0.05 0–0.15 0–0.05 0–0.05 0–0.05 0–0.05 0–0.05 0–0.10 0–0.05 0–0.10 0–0.05 0–0.10 0–0.05 0–0.10 0–0.05 0–0.15 0–0.05 0–0.15 0–0.07 0–0.10

638 823 951 872 524 580 734 744 734 812 434 370 728 689 654 775 630 720 665 649 632 679 535

967 1231 1193 1051 1005 1019 1117 1258 1157 1352 923 838 1280 1034 1084 1249 1034 1124 988 956 779 875 738

2551 2511 2367 2406 2234 2414 2341 2310 2291 2346 2267 2152 2372 2349 2373 2343 2428 2376 2235 2227 2306 2204 2341

0.750 0.672 0.598 0.638 0.766 0.760 0.686 0.678 0.680 0.654 0.809 0.828 0.693 0.707 0.725 0.669 0.740 0.697 0.702 0.708 0.726 0.692 0.772

0.750 0.939 0.708 0.579 0.957 0.913 0.869 1.076 0.922 1.148 0.931 0.884 1.132 0.786 0.912 1.024 0.871 0.899 0.735 0.707 0.445 0.542 0.508

0.594 0.697 0.601 0.514 0.663 0.660 0.659 0.720 0.671 0.752 0.634 0.619 0.729 0.613 0.661 0.715 0.649 0.670 0.581 0.567 0.404 0.475 0.443

0.333 0.412 0.242 0.179 0.491 0.444 0.387 0.530 0.435 0.552 0.509 0.480 0.570 0.352 0.441 0.483 0.408 0.408 0.336 0.316 0.148 0.198 0.205

Column 1: Depth interval (m) of core sample from the surface layer. Column 2: Measured dry density σ d (kg/m3 ). Cohmm 3: Measured (in situ) wet density σ w (kg/m3 ). Column 4: Measured particle (matrix) density σ p (kg/m3 ). Column 5: Computed porosity φ of sample (dimensionless). Column 6: Computed ‘volumetric’ moisture content (Φ/σ f ) of sample (dimensionless) with the ‘specific’ moisture content Φ given by (σ w – σ d ). Column 7: Apparent thermal conductivity λa (W/mK) of sample assuming a constant value for its thermal diffusivity α. Column 8: Revised thermal conductivity λ (W/mK) of sample using a best-fit thermal diffusivity α .

ticle densities are lower than those of silicic rocks (about 2650 kg/m3 ); ␴p values between 2250 and 2350 kg/m3 are typical for unaltered pumice soils at Wairakei, indicating poor connection between gas (air)-filled voids. In thermally-altered soils, the particle density increases to values of up to 2550 kg/m3 . The computed apparent thermal conductivity values λa lie within the range of 0.4 to 1.3 W/mK (see Bromley and Hochstein, 2001; Hochstein and Bromley, 2002). The approach described here to obtain thermal conductivity data of a soil layer is similar to that of Evett (1994) who used the time-domain reflectometry (TDR) method to assess the specific moisture content Φ. We tested the TDR method at several steaming ground sites in the Karapiti area but found that the inferred specific moisture values differed significantly from those of the core samples. It is likely that high temperatures and variable matrix resistivities (caused by thermal alteration) affect the TDR results. After the failed tests, we continued with the time-consuming core (weighing) method to determine the specific parameters Φ and S1 .

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5.4. Reducing the uncertainties in λa and qcond (λ) For sites where all three flux components could be assessed, an estimate of the uncertainty in λa can be obtained from an auto-correlation plot of conductive heat flux qcond (λa ) computed from soil parameters (Eq. (9)) versus the same component given by Eq. (1) since: qcond (λ) = qtot − qconv

(10)

The auto-correlation plot (Fig. 8a) shows that most data points lie above the correlation line y = x. Most of the computed qcond (λa ) values appear to be too high by about 30%, which implies that the thermal diffusivity α is not a constant since the shift of data points cannot be explained by the error of the mean surface gradient (Table 1). The value of qcond (λ), however, is constrained because the thermal diffusivity of clayrich and highly porous soils tends to decrease almost linearly between about 0.5 × 10−6 and 0.35 × 10−6 m2 /s for samples with a volumetric moisture content (S1 φ) between 0.1 and 0.5, respectively (Williams, 1982). For the thermally-altered soils at Karapiti (0.2 < (S1 φ) < 0.6), an appropriate function α = f(S1 φ) was found by a trial-and-error approach; sets of autocorrelation plots were computed until data were closest to the best fit (x = y) line. This indicates an empirical function of the type: α = [−0.25(S1 φ) + 0.4] × 10−6 m2 /s

(11)

A new set of thermal diffusivities (α ) and resultant thermal conductivities (λ a ) was then computed. The revised λ a values lie between 0.4 and 0.8 W/mK and exhibit a smaller spread than the λa data (see Table 2). An auto-correlation plot using the revised flux q  cond (λ ) is shown in Fig. 8b. The data point of site KP14r appears to be an ‘outlier’. We also computed another set of thermal conductivities (λmix ), using a compositional model (arithmetic mixing law model) and matrix conductivities as listed, for example, in Midttomme and Roaldset (1999). A comparison between the three λ values (i.e. λa , λ a , and λmix ) and the resulting scatter of data points showed that for most sites the λ a value is still the best. The resultant uncertainty of the qtot and qconv values can also be assessed. For this, the auto-correlation plot of qtot versus [q  cond (λ ) + qconv ] can be used. The plot (Fig. 8c) confirms that the total flux can indeed be obtained by separate measurement of the convective and the conductive flux components. The relative error of qtot and [q  cond (␭ ) + qconv ] lies for most stations between 15 and 25%; the effect of the unknown loss component L is therefore small.

6. Structure of steaming ground and likely heat and mass transfer mechanisms Only a few studies of the structure of steaming ground have been made. Earlier studies focussed on temperature (T)–depth (z) profiles. It was known by the early 1960s that, after appropriate reduction of the effect of daily and seasonal temperature variations, the reduced T–z profiles of steaming ground exhibit a quasi-exponential shape from the surface down to the depth zBP where boiling temperatures prevail (Banwell et al., 1957; Robertson and

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Fig. 8. (a) Auto-correlation plot of conductive flux, given by the difference [qtot − qconv ] between the measured fluxes qtot and qconv , vs. the computed conductive flux qcond (λ) (assuming that the average thermal diffusivity α is constant). (b) Auto-correlation plot of conductive flux, given by the difference [qtot − qconv ], vs. the computed conductive flux q  cond (λ ), using a thermal conductivity (λ a ) and a variable thermal diffusivity α = f (S1 φ). (c) Auto-correlation plot of the observed total flux (qtot ) vs. the sum [q  cond (λ ) + qconv ]; all qtot and qconv values are the average of two successive 5 min recordings.

Dawson, 1964). The same phenomenon was described as a characteristic feature of temperature profiles in steaming ground in Japan (Ehara and Okamoto, 1980). Other parameters of steaming ground have apparently not been studied. At a few selected sites we therefore measured T-profiles and constructed temperaturegradient (T/z)z profiles. In addition, core samples were taken in sequence over small depth intervals at several sites down to depth zBP ; their dry (σ d ), wet (σ w ), and particle

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Fig. 9. Temperature sections (observations repeated during one year): (a) temperature gradient vs. depth plots (site KP06); (b) temperature vs. depth plots (site KP06).

density (σ p ) were measured in the laboratory. To check for reproducibility and seasonal effects, measurements and sampling were repeated several times during the year. It was found that the T–z profiles can be linearized by using an empirical function of the type: z = exp[C1 (TBP − Tz )] + C2

(12)

where Tz is the temperature at depth z, TBP the boiling temperature (given by the atmospheric pressure), and C1 , C2 a set of best-fit constants. T-depth curves for site KP06 are shown in Fig. 9b, the corresponding gradient (T/z)z -depth curve in Fig. 9a. It can be seen that the gradient reaches a maximum value at the surface, where the scatter of the data is large (influence of the solar heat) and decreases with depth, attaining zero value close to zBP . The conductive flux qcond is therefore always a maximum at the surface. Subsequent analysis of the KP06 site showed that the boiling depth shifted during the year (0.55 m < zBP < 0.75 m).1 The variation in the level of zBP with time at KP06 points to seasonal variations of the vapour flux at depth, reflecting the influence of the seasonal component qyr . The scatter in the T–z profiles is less on a plot of dimensionless temperature (T/TBP ) versus normalized depth (z/zBP ) (Fig. 10). The residual scatter in this figure probably reflects inhomogeneities in the temperature field beneath this site. 1

A more recent survey showed that during the summer of 2003/4 the boiling depth at KP06 was again at 0.53 m (on 15 February 2004).

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Fig. 10. Normalized temperature (T/TBP ) vs. normalized depth (z/zBP ) plot (site KP06).

The parameters ‘wet’ density σ w , specific moisture content Φ, and (partial) liquid saturation S1 are affected by condensation (Fig. 11b). ‘Dry’ parameters, such as dry density σ d , particle density σ p , and porosity φ, are shown in Fig. 11a. The two figures show that for a small depth interval the magnitude of most soil parameters is quite reproducible. Information about the likely fluid movement is given by the liquid saturation (S1 ) versus depth (z) profile (Fig. 11b), which shows a well-defined condensation maximum at shallow depth (here at about 0.1 m). The S1 values decrease upwards (for z < 0.1 m), presumably reflecting evaporation, and decline slightly below boiling depth. The ‘Corey-relations’ can be used to interpret the fluid movement close to boiling temperatures in terms of a natural two-phase flow (where 0.3 < S1 < 0.7). The S1 profile indicates that heat-and-mass transfer involves movement of a natural two-phase fluid with vapour rising and liquid droplets descending from the shallow level, where S1 attains a maximum. The two-phase flow regimen extends below zBP where S1 is between 0.5 and 0.6. The Hipaua steaming ground near Tokaanu (Severne and Hochstein, 1994) also exhibits natural two-phase flow. The liquid saturation profiles (S1 versus z) and volumetric moisture profiles (S1 φ versus z) at five other steaming ground sites with zBP between 0.1 and 0.25 m are shown in Fig. 12. Their saturation characteristics are similar to those beneath site KP06. Maximum condensation occurs at shallow depth (usually 0.05–0.1 m). Latent heat at this level maintains the steep temperature gradient, which causes heat to transfer by conduction to the surface (qcond ). Liquid droplets also form at this depth and slowly descend into the two-phase layer, where some re-evaporation occurs (extending to depths z > zBP ). This upflow of vapour and counterflow of liquid droplets constitutes a ‘heat pipe’ setting, as has

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Fig. 11. Soil parameters: (a) plots of dry density σ d , particle density σ p , and porosity φ of core samples vs. depth z (site KP06); (b) plots of specific moisture content Φ, liquid saturation S1 , and wet density σ w of core samples vs. depth z (site KP06).

been observed in the laboratory (Bau and Torrance, 1982). The decrease in liquid saturation close to the surface can only be caused by evaporation at the free ground surface. It is likely that a significant portion of the condensate collected at the bottom of the calorimeter, i.e. a significant portion of qconv , derives from the evaporation of condensates. A few physical models have been put forward to explain the heat transfer in steaming ground. The first was that by Elder (1966), who assumed that all vapour originated from a saturated sub-surface layer at boiling temperature with the ascending vapour flux being controlled by Darcy’s Law. A similar model, but including conductive transfer, was proposed by Ehara and Okamoto (1980). Our liquid saturation profiles do not support these simple models. Numerical modelling (TOUGH 2 geothermal simulator) was used recently by Newson and O’Sullivan (2002) to model heat and mass transfer at one of our colder sites (KP03), where detailed ground temperatures had been recorded and a few saturation data are known down to 0.2 m. Allowing for capillary forces and a small net (upward) mass flux, their model reproduces the quasi-exponential shape of the temperature–depth profile.

7. Predicting heat loss from steaming ground Our methods described here are time-consuming and are not practical for any rapid assessment of heat losses of large areas of steaming ground. For this it is more practical to

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Fig. 12. Liquid saturation (S1 ) and volumetric moisture content (S1 φ) vs. depth (z) at six different steaming ground sites in the greater Wairakei area (see Fig. 3 for locality).

use empirical functions, which relate heat flux data, qtot , to controlling parameters such as ground temperatures Tz at a reference depth z. Benseman (1959a) was the first to introduce a plot of qtot data versus ground temperatures at 0.35 m depth to predict steaming ground losses (Benseman, 1959b). Thompson et al. (1964) used the same approach but for temperatures Tz at 0.15 m depth. Because of the large uncertainty of their data, based on few observations at Karapiti, the predictive power of their empirical functions was low. However, in the absence of a better alternative, the relationship between qtot and shallow temperatures (at 0.15 m or 0.01 m depth), proposed by Thompson et al. and recast by Dawson (1964), has been used by many authors (Sorey and Colvard, 1994; Mongillo and Graham, 1999; Allis et al., 1999) to assess heat loss of steaming ground. Daily surface temperature variations cause changes in the near-surface temperature gradient which, in turn, cause periodic variations of the conductive flux component qcond (λ). That effect is reduced by using values at a depth, for example the boiling depth zBP , where the variations have decayed. Functions of the type: qtot = f(zBP ) were investigated. Appropriate zBP values were obtained by using Eq. (12). A plot of zBP /z0 versus qtot , using data from all sites covered by this study, is shown in Fig. 13a. This points to a power-law relationship

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Fig. 13. Plots of boiling point depth (zBP ) vs. fluxes (qtot and qcond ).

of the form:  qtot = a

zBP z0

−b (13)

with a = 185 W/m2 , b = 0.757, zBP in metres, and z0 denoting unit depth (1 m). A similar relationship is found when zBP /z0 data are plotted versus conductive flux q  cond (λ ), yielding constants of a = 97.3 (W/m2 ) and b = 0.709 in Eq. (13). The plot of zBP /z0 versus q  cond (λ ) is shown in Fig. 13b. For most values of zBP , the resulting value of q  cond (λ ) is about half that of qtot using the equations listed in Fig. 13a and b. This proportionality agrees with that indicated by earlier experimental results (Fig. 6). A relationship similar to that in Fig. 13b had previously been proposed (Hochstein and Bromley, 2002, Fig. 6). However, the constants in that empirical function contain an error caused by uncertainties in the thermal conductivity data (see previous Section 6). Applying Eq. (13) to, say, gridded field sites within sub-areas of similar thermally stressed vegetation allows assessment of the total heat discharge of any large area of steaming ground. Additional studies, however, are required to find out whether calorimeter studies, as described here, are necessary to establish empirical relations of the type listed in Eq. (13) for each new steaming ground area.

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8. Summary Total heat flux qtot at the surface of steaming ground is the sum of convective (qconv ) and conductive (qcond ) flux components. The conductive heat transfer includes a timevariable component (qdy ), which is mainly controlled by the time-variable (daily), nearsurface temperature gradient in the top soil layer. The effect of other time-variable components, such as an episodic component qfilt and the seasonal component qyr , is small and can be neglected if qtot measurements are made during long dry periods and during the summer. Most of the conductive heat flux is driven by the condensation of rising vapour, which occurs within a thin near-surface layer, and the subsequent liberation of latent heat, which heats this layer. This process maintains a steep temperature gradient within the near-surface layer above the condensate layer. The liquid saturation of the pores of the shallow condensate layer rarely exceeds 70%, thus indicating that some vapour can pass through this layer to the free surface. The escaping vapour constitutes the convective flux component. Evaporation within the near-surface layer also contributes to the vapour flux and increases the convective component. Our study began with an assessment of the conductive flux component qcond (λ) using shallow temperature data and computing a value for the thermal conductivity λ from measured soil parameters in the top layer. A mean value for the thermal diffusivity was obtained from an analysis of daily temperature variations. It was assumed that the diffusivity is almost constant, with small random variations between sites. Without any independent control, however, the error of the conductive flux data could not be assessed. The total flux qtot was later measured by employing a ground calorimeter. The condensation rate at the bottom of the calorimeter was used to estimate the convective flux qconv . Both components show small short- and long-term flux variations. The heat transfer processes at the bottom of the calorimeter and in the surface soil layer are complex. This is indicated by the observed decrease in the convective flux and a small decrease in the near-surface soil temperatures (small increase in conductive flux) at almost 70% of all sites during site occupation. Other effects that impede maximum heat transfer, such as the thermal resistance of the bottom plate and storage of heat in the calorimeter casing, are small and can be neglected. The reproducibility of the calorimeter measurements was good (on average <7% error when repeated in the summer months a year later). The advantage of using a ground calorimeter with a fixed bottom is that it allows an independent estimate of the actual conductive flux qcond given by the observed flux difference [qtot − qconv ]. An auto-correlation plot showed that the previously computed values of qcond (λ) were on average about 30% greater than those given by the difference of the two measured fluxes. The error was due to the incorrect assumption that the thermal diffusivity α can be treated as a constant, since it also varies with the volumetric moisture content (S1 φ). An appropriate empirical diffusivity function α = f (S1 φ) was found, which reduces the difference between the qcond (λ) and the [qtot − qconv ] values to a minimum. A new set of conductive flux data q  cond (λ ) were obtained, derived from revised thermal conductivities λ . The measured qtot and computed q  cond (λ ) flux data vary systematically with ground temperature. The boiling depth zBP at different sites correlates well with both fluxes, point-

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Fig. 14. Schematic diagram showing inferred fluid movement and inferred phase changes in steaming ground based on results of this study.

ing to a power-law relationship. For most zBP values the magnitude of the conductive flux q  cond (λ ) is about half that of the total flux qtot . Measurements of soil parameters were extended, at a few sites, beyond boiling depth. The liquid saturation and volumetric moisture–depth profiles show how a convective mode of heat transfer can develop in steaming ground. A natural two-phase zone located beneath the thin surface layer is marked by enhanced condensation (S1 up to 0.7, but not reaching full saturation). The bottom of the two-phase zone lies below the depth zBP where vaporization of descending droplets occurs. The resultant ‘heat-pipe’ effect is driven by phase changes at the top and bottom of the two-phase zone. A model that illustrates the heat-and-mass transfer processes in steaming ground is shown in Fig. 14.

Acknowledgements Equipment of the Soil Laboratory at the School of Engineering (University of Auckland; UofA) and of IGNS Wairakei was used for measurement of soil parameters and for field studies. The calorimeter was built in the Workshop of the School of Engineering (UofA). Financial support for materials and fieldwork was provided by the Geothermal Institute (UofA), grants from Environment Waikato (for MPH), and the NZ Foundation of Research Science and Technology (for CJB). Dr. C. Werner (IGNS, Wairakei) checked the CO2 flux at most calorimeter sites; Ms L. Cotterall (Geology Dept., UofA) draughted the figures.

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