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Hydrosounding as a method of study of the critical parameters of the geyser
Journal of Volcanology and Geothermal Research, 3(1978)99--119 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
99
H Y D R O S O U N D I N G AS A M E T H O D O F S T U D Y O F T H E C R I T I C A L PARAMETERS OF THE GEYSER
G.S. STEINBERG', A.G. MERZHANOV2 and A.S. STEINBERG2
'MKB Geographical Society, U.S.S.R. Academy of Sciences, Telmana 2B-47, PetropavloskKamchatsky 683019 (U.S.S.R.) 2Branch of the Institute of Chemical Physics, U.S.S.R.:Academy of Sciences, Chernogolovka, Noginsk District, Moscow 142432 (U.S.S.R.) (Received and accepted July 11, 1977)
ABSTRACT Steinberg, G.S., Merzhanov, A.G. and Steinberg, A.S., 1978. Hydrosounding as a method of study of the critical parameters of the geyser. J. Volcanol. Geotherm. Res., 3: 99--119. A new method of hydrosounding has been devised for clarifying the geyser regime and for determining critical conditions that are essential for geysers to erupt. The method consists of pouring known quantities of water into the geyser system and then measuring changes in the main characteristics of the geyser, i.e., the duration of the eruptive stages and the temperature and quantity of the added and erupted water. The temperature and mass of the added sounding water can be varied and used to provide a series of equations that give average enthalpy of heat-carrying fluids, their natural rate of inflow to the local geyser reservoir, and variations in the process of filling the system, the free volume after eruption and other factors. Experiments were carried out in 1970--1974 in Quathegey and Prince Buratino geysers of Geyser Valley, Kamchatka. The average enthalpies of the heat-carrying fluids are calculated to be 164--174 kcal/kg and 180--195 kcal/kg, respectively.
INTRODUCTION In previous papers we have p r o p o s e d a t h e o r y f o r geyser processes ( M e r z h a n o v et al., 1 9 7 8 a ) a n d have devised a l a b o r a t o r y m o d e l f o r a geyser ( M e r z h a n o v et al., 1 9 7 8 b ) w h i c h has s h o w n a g o o d a g r e e m e n t b e t w e e n t h e t h e o r y and e x p e r i m e n t . C o m p a r i s o n o f t h e p r o p o s e d m e c h a n i s m with t h a t observed in n a t u r e was c o m p l i c a t e d b y t h e impossibility o f influencing t h e eruptive processes in n a t u r a l geysers. Previous studies have p r o v i d e d d a t a o n t e m p e r a t u r e , discharge, c h e m i c a l and i s o t o p i c c o m p o s i t i o n a l changes o r c o r r e l a t i o n s o f t h e s e changes with the n a t u r a l causes, such as tides, a t m o s p h e r i c pressure, f l u c t u a t i o n s of g r o u n d w a t e r levels and precipitations, a n d seismic activity ( R i n e h a r t , 1 9 7 2 ; White, 1 9 6 7 , 1 9 6 8 ; Marler, 1 9 6 9 ) . We have used a n e w m e t h o d t o s t u d y the influence o f various f a c t o r s o n the
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~ Pulsing hot springs ~ ~'4ud
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20c.
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m
Fig. 1. Map of the central Geyser Valley, Kamchatka, showing location of Quathegey and Prince Buratino geysers. (Quathegey = QUAntity THEory GEYsers.)
geyser regime -- a method of hydrosounding (Merzhanov et al., 1973). The hydrosounding experiments were carried out in 1970--1975 in the Geyser Valley of Kamchatka (Fig. 1) on the geysers Quathegey and Prince Buratino. The Quathegey and Prince Buratino geysers are situated on the flanks of the narrow V-shaped valley of the Geysernaya River (Fig. 1) at elevations of 25 m and 5 m respectively above the river level. Both geysers are of a cone type. The pools are rather small (surface area ~ 0.035 m 2 ; volume ~ 3--8 1). Most erupted water does not return to the geysers. Both geysers are characterized by a distinct preliminary discharge stage and by a very constant period (+4% variation). The channel of Quathegey geyser is vertical and chimney-like to a depth of 1.5 m; its diameter is about 10 cm. The orientation of the channel changes at a depth of 1.5 m where there may be a small reservoir or distension of the channel. In its natural regime the preliminary discharge stage of Quathegey is of short duration (Fig. 2a) and displays intensive boiling in the channel and pool. Hence, the natural outflow can be overestimated if boiling is not taken into account. When no boiling is seen {e.g. during sounding), the natural outflow at preliminary discharge is not nearly so large {Figs. 6, 10). The channel of Prince Buratino geyser is fissure-like, with a width of 2--4 cm, a length of about 20 cm, and an inclination of 50--60 °. A stock equipped with temperature sensors was inserted to a depth of 0.7 m. Prince Buratino acted as a pulsating hot spring before 1973. It transformed into a geyser of very stable regime (8 m 35 s) after clearing its vent. The rim of the pool was heightened in August 1974 and hence the level of water in the pool became 10--12 cm higher and the full period of the geyser increased to 9 m 20 s. The preliminary
101
2_.0
lQuathegey geyser
/o\
15
\
0.5
t,
sec
Prince Burotinogeyser
fee/
b
30
20
d 10
•
9
o °-6
•
•
•
150 t,
180
210
SeC
Fig. 2. Water discharge during the full period of Quathegey and Prince Buratino geysers in natural regime.
discharge stage showed no disturbances; intense boiling began 10--15 seconds before the beginning of an eruption (Fig. 2b). Principal characteristics of the geysers in normal regime are shown in Table I
102
TABLE1 Principal c h a r a c t e r i s t i c s o f Q u a t h e g e y a n d Prince B u r a t i n o geysers in n o r m a l regime Quathegey
Prince B u r a t i n o
Full p e r i o d o f the geyser, f r o m start 12m35 s o f o n e e r u p t i o n u n t i l s t a r t of t h e n e x t e r u p t i o n , tf
9m20 s
D u r a t i o n of t h e filling of t h e geyser f r o m end of e r u p t i o n u n t i l t h e beginning of the next preliminary discharge, t d
10m00 s
6m05 s
D u r a t i o n of p r e l i m i n a r y discharge stage
0 TM 45 s
1 m 30 s
D u r a t i o n of t h e e r u p t i o n
1 m 50 s
l m 45 s
V o l u m e of t h e w a t e r t h r o w n o u t d u r i n g t h e e r u p t i o n (liters) M a x i m u m height o f e r u p t e d w a t e r ( m )
120 1.5
120--150 2.5--3
The purpose of this paper is to demonstrate the ability of the method of hydrosounding to establish important parameters characterizing the dynamics of the geyser mechanism. NOTATION Time, t (rain, s) tf td tsd ts to tse At s
full p e r i o d o f t h e geyser ( t h e interval b e t w e e n t w o e r u p t i o n s ) t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l t h e b e g i n n i n g o f t h e p r e l i m i n a r y discharge ( w h i c h c h a r a c t e r i z e s t h e n a t u r a l regime o f s o m e b u t n o t all geysers) t i m e interval f r o m t h e e n d o f s o u n d i n g u n t i l t h e b e g i n n i n g of t h e n e x t p r e l i m i n a r y discharge t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l t h e b e g i n n i n g of s o u n d i n g h y d r a u l i c c o n s t a n t of a geyser (see t e x t ) t i m e interval f r o m t h e e n d of e r u p t i o n u n t i l t h e e n d of s o u n d i n g = tse - ts, t i m e interval f r o m t h e b e g i n n i n g of s o u n d i n g u n t i l t h e e n d of s o u n d i n g
Volume, V (liters) V0
" f r e e " v o l u m e - - t h e p a r t o f t h e geyser c h a n n e l or reservoir f o r m e r l y filled w i t h water, b u t w i t h o n l y s t e a m ( a n d air) a f t e r e r u p t i o n V s t o t a l v o l u m e o f w a t e r a d d e d in s o u n d i n g e x p e r i m e n t Vs the p a r t of t h e free v o l u m e filled a f t e r t h e t i m e interval (t s) f r o m t h e e n d o f e r u p t i o n till t h e b e g i n n i n g o f s o u n d i n g Vse = V s + ~ Vs, t h e p a r t o f t h e free v o l u m e filled at t h e e n d o f s o u n d i n g Vt v o l u m e filled at t h e t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l s o m e m o m e n t t, where 0 < t < td
103
Mass, M (kg)
AM s total mass of water added in sounding mass of water discharged during t i m e interval f r o m the beginning preliminary disMI charge stage until s o m e m o m e n t t natural (feeding) water mass inflow into a geyser during the t i m e interval f r o m the M2 beginning preliminary discharge stage until s o m e m o m e n t t Mtm = V0-~, total mass of water filling the free v o l u m e of a geyser after e r u p t i o n Me mass of water discharged during e r u p t i o n stage of the geyser mass c o n s t a n t of a geyser - - see e q u a t i o n (9) Mo mass of natural water inflow during the time interval (ts) f r o m the end of e r u p t i o n till Ms the beginning of sounding Mt = Vt~ , mass filled during the time interval f r o m the end of e r u p t i o n until s o m e m o m e n t t, where 0 <: t < t d Discharge, G (kg/s)
GO G1 Gt
Gs Gse
natural water inflow i m m e d i a t e l y after e r u p t i o n water discharge during preliminary discharge stage natural water inflow at the m o m e n t t, where 0 < t < t d natural water inflow at the beginning of sounding natural water inflow at the end of sounding
Temperature, T (°C)
Ts Tin Td Ti
t e m p e r a t u r e of water added during sounding mean t e m p e r a t u r e of water discharged during the stage of preliminary discharge t e m p e r a t u r e o f the water discharged during the preliminary stage and during sounding instantaneous t e m p e r a t u r e at a geyser during sounding
Other para meters
i', i" I* I0 A c
e n t h a l p y of saturated water and steam, respectively (kcal/kg) average e n t h a l p y of heating fluid (liquid water or water-steam m i x t u r e ; kcal/kg) heat c o n s t a n t of a geyser (kcal/kg) } see equations (9) to (11) heat c o n s t a n t of a geyser (kcal) heat capacity (calg-~ °C-I ) specific gravity (g/cm 3 )
CRITICAL
CONDITION
FOR A GEYSER
SYSTEM
The critical state of a geyser system occurs when heat supplied to it can no longer be balanced b y additional heating of the water, b y water outflow, and b y surface boiling and evaporation. At the m o m e n t when the critical state is attained, the water in the channel is very close to the boiling temperature. Steam bubbles originating in the b o t t o m parts of the system rise with little or no condensation. The absence of condensation and the expansion o f the bubbles due to the upward decrease of hydrostatic pressure are responsible for the qualitative change in the regime of liquid and steam upflow. The bubbles occupy more and more area of the horizontal section of the channel. The resuiting regime of steam "plugs" is referred to as the "missile regime" of the motion (Fig. 3). The water is pushed up and o u t of the upper part of the
104
~°~
o
i'll
e o o
Fig. 3. T w o - p h a s e (liquid + s t e a m ) regime o f the f l o w in a vertical cha~nel (after Sorokin, 1963). 1 = b u b b l e regime; 2 = missile regime; 3 = dispersive regime; 4 = emulsive regime.
channel by the vapor plugs. "The rates of boiling and upflow increase further as pressuredeclines throughout the system and as the chain reaction extends out to payts of the reservoir previously filled entirely with water" {White, 1967). An eruption then begins. The critical state of a geyser can also be defined as that in which the excessive heat (Qcritical), accumulated in the effective parts of the system (the immediate reservoir, the channel), is so considerable that any further increase brings about an eruption. This definition is identical to the "loading system" of White (1967). Qcritical is energy loading or the heat supplied from the feeding area less the heat dissipated with evaporation and outflow during the interval from the end of one eruption until the beginning of the next. Thus, the critical state of a geyser system can be qualified as the limit of loading the system. Finally, the critical condition for a geyser can be essentially determined as that with a critical enthalpy that somehow must be attained before an eruption. The critical state can be expressed in the form of an equation (equation 9), derived from hydrosounding experiments. A geyser system differs in principle from any other hot spring in that its condition periodically becomes unstable and the process of boiling is triggered as a chain reaction through the system {White, 1967). Such conditions are usually designated by physicists as critical. THE P R O C E D U R E OF H Y D R O S O U N D I N G
The hydrosounding technique consists of rapidly adding known quantities of water to the geyser system through the vent and then measuring changes in characteristic features of the eruptive process, such as the duration of its full period of eruption and its various stages, including changes in temperature, rate of preliminary discharge, and quantity of water erupted with time. The mass and temperature of added water and the time interval between the end of the previous eruption and the m o m e n t of adding the water can be changed from one experiment to another and are also parameters of hydrosounding. At geysers Quathegey and Prince Buratino some 300 runs have been carried out with volumes (AVs) of 1 8 0 , 1 5 0 , 120, 100, 80, 60, 50, 40, 20 a n d l 0 liters and under the temperature (Ts) of 80, 60, 50, 40, 20, and 10°C. The sound-
105
ings began immediately after eruptions. The duration of adding the water varied from as short as 5 seconds (AVs = 10 l) up to as long as 1.5 minutes (A Vs = 180 1), so Ats ~< 8% of the full period of the geyser (under sounding). The authors have assumed the addition to have been instantaneous (ts = tse or Ats = 0), because this assumption greatly simplifies the calculations. The control calculations, when the duration of adding had been taken into account, showed the discrepancy to be less than 5%. Inasmuch as the full-period fluctuations of geysers (by hydrosounding) are -+8%, this assumption seems to be within the limits of experimental accuracy. Considering that the area of the surface pool of b o t h geysers is less than 0.04 m 2 and that neither intensive nor prolonged pre-eruption boiling has taken place, further assumptions have been that: (1) Loss of heat in steam escaping at the surface between eruptions is negligible. (2) Loss of heat in water vapor by evaporation from surface pools is negligible. (3) Exchange of heat between fluids and rocks of the reservoir is negligible or gains and losses are balanced over an eruption cycle. In order to justify the third assumption, the geyser was allowed to erupt 2 or 3 times in its natural regime after every sounding. The next sounding was carried out when the full period of a geyser regained a normal value of tf = 12 m 35 s. In most cases (especially when Ts <~ 60°C), the full period of a geyser in its natural regime became a bit longer, probably due to cooling of the walls of its channel during sounding. The resulting data (Figs. 4--10, 12) for different sets of runs may differ somewhat in their range of accuracy (+ 8%). FREE VOLUME AND SOME MINOR CHARACTERISTICPROPERTIES OF THE GEYSERS The free volume of a system, i.e. a volume filled by water and steam before an eruption and by steam and air after an eruption, can be determined by hydrosounding. It appeared to be 180 1 for both geysers. If this quantity of water is poured into a vent, it should fill the system to the surface. The Quathegey geyser gives about 120 1 of water in each natural eruption. It follows that the portion of the volume of the geyser system that was filled with steam during an eruption is about 60 1 (180 - 120 = 60). The relation of the full period of Quathegey geyser and the period of preliminary discharge to sounding parameters (Figs. 4, 5) illustrates several details of the geyser structure. Three sections can be seen in all the curves of Figs. 4 and 5. They are shown best in Fig. 4 where relation of the full period (tf) to the volume (4 Vs) and temperature (Ts) of the sounding for Quathegey geyser are shown to be as follows: (1) Section a, 0 < AVs < 40 1. The full period decreases as the system is
106
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o ~:o~o°
, !
v T~=60 ° o ,;.~o °
I
/////.
+ T~=4o °
./ J/ f.
2oF
i
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/// natural ~:~
period " ~
E~o
ir
i
~
/ I fv~-'~-v
I',/
o
I
/
/,,
s
°
I /
d \'~,
Fig. 4. Duration o f the full period o f Q u a t h e g e y geyser as related to the parameters o f s o u n d i n g (AVs; Ts).
i
3O k '!
/ 20
z/V s , L
Fig. 5. D u r a t i o n of the p r e l i m i ~ r ] disch~ge stage of Quathegey geyser as related to the parameters of sounding ( A V s, T s).
filled. The duration of the full period does not depend upon the temperature of the added water (Fig. 4). The duration of the preliminary discharge stage does not depend upon either the temperature or volume of the added water (Fig. 5). (2) Section b, 40 1 < A Vs < 80 1. The full period severely increases al~host
107 up to the natural value (12 m 35s), it decreases slightly when sounding at Ts = 80°C, it essentially does not change when Ts = 40--60°C and increases slightly when Ts = 20°C (Fig. 4). The duration of the preliminary discharge stage does not change materially and displays almost no dependence upon the sounding volume (A Vs) at temperatures of Ts = 40 °, 60 °, 80°C, b u t it has a slight tendency to increase with time. The duration of the stage distinctly increases at a temperature of 20°C (Fig. 5). (3) Section c, 80 1 < AVs < 180 1. The full period of a geyser increases linearly as the system is filled and as the temperature (Ts) increases (Fig. 4). One can assume that section a (Fig. 4) is to be explained b y a widened reservoir in the upper part of the system; the filling of the small reservoir affects only the mass balance of the system, not its heat balance. Section b corresponds to the filling of the free volume of the main reservoir of a geyser. The decrease of Vt at Ts = 80°C, stability at Ts = 60°C, and a slight increase at Ts = 20°C suggest that the initial equilibrium temperature of water filling the free volume of the main reservoir is about 60°C. Consequently, it suggests that rather cold water (40°C < T < 80°C) enters the reservoir at the initial stage of the filling. Section c corresponds to the filling of the channel. The lower the value of Ts, the longer are the periods in which steam bubbles condense in the channel. The same is true of the duration of the preliminary discharge stage, and the full period of a geyser. The linear dependence of the full period (tf) and the discharge stage on AV s and T s (Figs. 4, 5) can be explained by a strong deterioration in the convection in the channel compared with that of the convection in the reservoir. CALCULATION OF THE ENTHALPY OF FLUID FEEDING A GEYSER F r o m the corresponding curves for temperature changes during t w o eruptive cycles and for discharge from Quathegey geyser at full sounding (AMs = 180 kg and Ts = 20°C, 40°C) it follows that dTd/dt is constant, in the temperature range of 20--60°C (Fig. 6), because after adding water at 20°C the discharge is nearly the same as that observed for hydrosounding water at 40°C. Taking into account the fact that, for temperatures of preliminary discharge between 20 ° and 60°C, the rate of discharge of water is also constant (GI = 0.08 kg/s), it is possible to calculate a heat balance and to determine the enthalpy of the natural heat-carrying water feeding the geyser. During the sounding, 180 kg (AMs) of water w i t h Ts = 20°C is poured into the geyser instantly. In the following 5 minutes, 25 kg (MI) of water heated from 20 ° to 40°C was discharged from the geyser; so we assume for this period that Tra = 30°C. Meanwhile, the remaining volume of water added to the geyser during the sounding (AMs - M~ = 155 kg) was heated to Ti = 40°C. During this time 25 kg (M2 = M~ ) of water with enthalpy I entered the system. Supposing the heat capacity of water, c = 1 calg -1 °C -1 , we can equate the enthalpy before and after mixing:
108
c[(AMs
-
MI)Ti
+
MI T m + M2 Ti
-
AMsTs]
=
IM2
All values on the left-hand side of this equation were determined from the experiment, so the heat content of the mixture feeding Quathegey geyser is easy to obtain: I = 174 kcal/kg. The enthalpy of a heat-carrier can also be determined from hydrosounding experimental data when Td varies non-linearly and without the assumption that T i = Td. The single assumption used in the calculation has been formulated below as that of a critical state. This assumption for determination of the enthalpy of the heat-carrier by hydrosounding can be written as follows: (1) An eruption begins when an excess heat Qcriticat is accumulated in the effective parts of the geyser (the immediate reservoir and channel). (2) Qcritical is constant for any geyser and does not depend on the sounding parameters (A Vs, Ts). The second assumption is confirmed by the fact that the volume of erupted water and the height of eruption are constant at Prince Buratino geyser both in the natural regime and in different sounding runs. The heat balance equation of a geyser for the period from the end of one
22
Quathegey geyser
~ ~2r d
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100°
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00
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area 2
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400
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~
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800 t, 5ec
,o
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1200
i
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1600
l___J 0
temperature and discharge of Qua~hegey g e y s e r d u r i n g the hydrosounding:
'~'/s = 180 kg; T s = 20°C; 40°C.
109
eruption until the beginning of the next one can be written as follows: Qcritical = Qfeed + Qsound- Qoutflow
(2)
or:
Qcritical = MfeedI* + c A M s T s
- ' Qoutflow
(3)
where: n
Qoutflow = c ~_j M l i T d i
n
= Atc
i=l
~ GliTdi i=l
Mfeed = M2 = M1 + ( M t m - 5Ms)
(4) (5)
- AMs) = mass of a heat-carrier which fills the geyser, if the system has not been filled completely during a sounding (i.e. if A Vs < V0 ). When a sounding is complete (i.e. if h Vs = V0 ), A M s = Vo~/ = M t m a n d M a n - A M s = O. One can easily calculate Qoutflow, when measuring preliminary discharge G, and the temperature of the discharge water. Thus only Qcritical and I* are left u n k n o w n in equation (3). We have used equation (3) for two sounding runs (Fig. 7). Run 151 gives (Fig. 7a): (Mtm
Q c r i t ~ = 428•* - 33968
(6)
and run 112 gives(Fig. 7b): Qcntical = 3741" - 24611
(7)
Considering t h a t Qcritical = constant, we can combine equations (6) and (7)and find I * = 173 kcal/kg and Qcritical = 40150 kcal. One can note, however, that an enthalpy calculated by this method is somewhat less than the true value, because equation (3) does not take account of steam generation when boiling. Since intensive boiling is observed for 10--15 seconds immediately before an eruption of the Prince Buratino geyser, I* can be determined with an error no more than 5%. So, the actual value of I * is 180--185 kcal/kg. Knowing the enthalpy we can estimate the upper limit of steam pressure and the quality of the steam-water mixture (heat-carrier). The m a x i m u m equilibrium pressure of saturated steam at I = 174--185 kcal/kg is 8.4--10.8 atm (Vucalovich and Novikov, 1962). The steam content in the mixture is obtained from: 174 = i " X + i(1 - X ) 6 5 0 X + c T ( 1 - X )
(8)
in which: X = (174 - cT)/(650 - cT) Here X is the weight percentage of the steam, in the total mass. The tempera-
110
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/"
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6o
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50 L
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z~t~ ÷ tsd
5
10 Time,
15
20
rain
F
F
20[-
100
o °.°~°_°.°_°_• ~
k
1O,
i F
80
6O 5() i
/
4o I ,.,,~.v.~._~°.°_._..°. i
ol
. .°. .° ° Q~-°-•_•~•-°°-°-•-°-,
~
go
b zt
± 5
G °.
10 Time,
•-°---. •
•_•~°
15
20
mln
F i g . 7. C u r v e s o f t e m p e r a t u r e and discharge of Prince (a) Experiment No. 151: AV s = 150 l; T s = 20°C. (b) Experiment No. 112: AV s = 180 l; T s = 50°C.
Buratino
geyser
during
hydrosounding,
ture of a heat-carrier must be known for a strict solution of (8); however, the upper limit of the weight percentage of the steam can be estimated if T is taken equal to 100°C. When the temperature of the water is more than 100°C, the weight percentage of the water in the heat-carrier decreases proportionally with increasing temperature up to the condition of dry steam at T = 174°C. CALCULATION
OF THE CRITICAL
CONDITION
The dependence of the full period of the geyser (the interval between initiation of two eruptions) on the mass and enthalpy of the water added to the geyser during hydrosounding is shown in Fig. 8. The linearity of these dependences suggests that we can determine the critical conditions of natural eruptions by extrapolating the lines to their intersection with the enthalpy axis,
III
30 o z ~ M s = 1 8 0 kg
o
20 a
c_ E &
=50
,.J
10
I, k c a l / k g
30
o
k
I - z1[vls = 1 8 0 kg
A 1
2-
= 120
3
= 80
-
o~
o~
55
\'15o\
~6o [,
~o ""~-zso
-
kcQI/kg
Fig. 8. Determination of the critical conditions of the geyser eruption: (a) Prince Buratino geyser, (b) Quathegey geyser. The full period of the geyser depends on the enthalpy and quantity of added water.
assuming the indicated critical heat content I* of water with mass AMs used in the hydrosounding corresponds to the eruption of the geyser just after input of water. For geyser Quathegey, the corresponding enthalpy values for &Ms = 180, 120, and 80 kg are I* = 147, 163, and 263 kcal/kg. The curves showing the dependence of the critical enthalpy value I t upon the mass of water M in Fig. 8 shows that they are related by the equation: I t - I o ~- A / ( M
- Mo)
(9)
i.e. the critical condition for the geyser system can be defined as the condition when a water-steam mixture with mass M and average enthalpy I t , which corresponds to equation (9), occurs in the natural system as a result of simultaneous processes of heat and mass transport. The parameters A and I* in equation (9) are the heat constants but M0 is the mass constant of this source and
112 reflects the peculiarities of the geometry of the system as well as the specific heat and h y d r o d y n a m i c processes in the geyser. These parameters can not be defined in physical terms because they are obtained by the least squares method from equation (9). We hope to determine the physical nature of this term by performing hydrosounding experiments on models or drill-holes that function as geysers. For these geysers one knows the parameters of the channel, the immediate reservoir, the enthalpy of the inflowing fluid, the relations between the input and o u t p u t (dissipation) of energy, and so on. In our laboratory model of a geyser (Merzhanov et al., 1978b), it is observed that during the period prior to eruption, steam bubbles originating in the b o t t o m parts of the channel cool and condense on their way up through water where T < Tsteam, i.e. boiling of the water in the lower parts of the geyser does not yet lead to eruption. Only when the water high in the channel is heated to temperatures close to that of the steam, does condensation cease and allow the steam plugs to force their way to the surface ejecting water from the near-surface vent (the so-called missile regime; Sorokin, 1963); this then leads to an abrupt decrease in pressure in the b o t t o m parts of the system and results in extensive boiling and eruption. The calculated data for the critical conditions of both geysers are shown in Fig. 9 in I and M coordinates. A least squares treatment of these results in accordance with (9) gives us the following expressions: I* - 131 = 1570/(M - 67) I*
-
137 = 5500/(M - 6)
Quathegey
(10)
Prince Buratino
(11)
However, one can ask whether the linear extrapolations of the experimental data (Fig. 8) are meaningful and whether equations (10) and (11) obtained from the extrapolated quantities of I* are reliable for soundings at Ts > 100°C There is another way to verify the equations in question. When we know the mass and the volume of the water erupted by a geyser under natural conditions, we can obtain the enthalpy of heat-carrier from equations (10) and (11).
o ~
240
©uathegey P Burat~no
~ 2ooi 160 i"
"~"~"~'~- o 60
100 140 M kg
1B0
Fig. 9. Relationship of enthalpy and mass of water (or water-steam mixture) in the geyser
for the critical conditions.
113 Comparing those enthalpies with the quantities obtained from the heat-balance equations (1--7), we can verify equations (10) and (11) (Fig. 9) and consequently, the validity of the linear extrapolation (Fig. 8). For Quathegey geyser: Ve = 118--120 l, I = 174 kcal/kg. From equation (10): I =
1570 120 - 67
+ 131 = 161 kcal/kg
For Prince Buratino geyser: Ve = 120--150 1, I = 180--185 kcal/kg. From equation (11): I =
5500 (150 or 120) - 6
+ 137 = 175--185 kcal/kg
The convergence is consistent, so the extrapolation, made above, appears to be acceptable and the derivation of equations (9), (10), and (11) is probably reliable. CALCULATION OF THE RATE OF WATER RECHARGE AND THE CHANGE OF THIS RATE WITH TIME DURING THE ERUPTION CYCLE It is known that high-enthalpy geysers are fed by water under pressure much above hydrostatic conditions and the rate of discharge must be almost constant throughout the geyser cycle. Examples are found among t h e Yellowstone geysers (White et al., 1975) and in the Velikan geyser in Geyser Valley, Kamchatka. In other geysers the fluid pressure depends on various causes, especially the hydrostatic pressure in the reservoir. In this case the rate of discharge must change greatly (White, 1967; Rinehart, 1972). The Quathegey and Prince Buratino geysers belong to the latter type. It was shown in our laboratory model experiments that the inflow of water into the geyser system immediately after the eruption is distinctly higher than that when the geyser system is completely filled (Merzhanov et al., 1978b). This conclusion has been supported b y our field observations on Quathegey and Prince Buratino geysers. It appears that the model principle is rather similar to the natural inechanism in the t w o geysers. The water inflow has been estimated in the experiments at A Vs = 180 1 when the immediate geyser reservoir, the channel, and the pool are completely filled. When no boiling is taking place, the preliminary discharge is equal to the inflow. During the sounding of Quathegey geyser no boiling was registered during the previous 5--10 minutes, and the discharge was constant (G~ = 0.08 l/s (Figs. 6, 10). A similar experiment on Prince Buratino geyser showed GI = 0.4 1/s (Fig. 7). The water discharge of Quathegey geyser later became higher (Figs. 6 , 10). One can distinguish t w o stages of preliminary discharge: (1) a constant-rate stage (Fig. 6, area 1); and (2) an accelerating-rate stage (Fig. 6, area 2). The beginning of the second stage is connected with the onset of boiling.
114
0
+
=40°
/
~1 12~
v
=6o°
|1
I al
o
J_l
, 0
400
800 T~me, sec
1200
1600
Fig. 10. C u r v e s o f d i s c h a r g e o f Q u a t h e g e y g e y s e r d u r i n g h y d r o s o u n d i n g . 1 8 0 1.
AVs = constant =
It is evident that in a geyser being sounded (A Vs = 180 1) the duration of the accelerating-rate stage of preliminary discharge does not depend on the temperature of the sounding (Ts) (Fig. 10). This fact demonstrates that the second stage is related to the time interval from the beginning of boiling until the eruption. The Prince Buratino geyser has a very short boiling duration and the second stage of preliminary discharge is practically absent (Figs. 2b, 7). A simple calculation shows that the water inflow after eruption is considerably higher than that when the geyser system is completely filled. The overall water (without steam), taken in and discharged during a cycle, has been estimated for Quathegey geyser as follows: V = 120 1 + 0.4 1/s x 35 s = 134 l Should the water inflow into the geyser system be constant, the inflow per cycle would be: V = 0.08 1/sec x 745 s = 60 1. That means that V = 134 - 60 = 74 1. A similar q u a n t i t y of 85 1 has been measured during sounding. The discrepancy between the calculated and experimental data for the geysers studied suggests that water inflow varies during the course of filling the system. The time-dependent changes of this discharge may be determined in two ways. The first is a direct m e t h o d consisting of filling the free volume of the geyser in a fixed time interval after eruptions and measuring the M (t) dependence by taking the time differential of this dependence and obtaining G(t) (Fig. 11). This m e t h o d is convenient for investigations of small geysers {Fig. 12). For large geysers it is technically difficult to pour a sufficiently large volume of water rapidly into their vents. It must be noted that the free volume of large geysers may exceed 5--10 m 3 . The second method requires the assumption of an approximate constancy
115
G~V Go
V(t)o~
\
\
/ ° f
/o
~"------ o G 1
LU
U", U v', B v', ~v,, Uv,. ~o
vt-- Vo- .~vs., vt, : vo - ~ & , vt = vo - zlvs,
Fig. 11. Scheme of determination of water inflow to the geyser system from the end of eruption until the beginning of the following preliminary discharge stage.
150
,°°
--. L
2 0 Time,
300
360
sec
Fig. 12. The change in the flow of the feeding fluid in relation to the filling of the geyser system (a small nameless geyser). The inflow was determined by hydrosounding (see Fig. 11).
The geyser was filling under pressure much above hydrostatic, so the rate of inflow did not depend on the extent of the filling of the system. of cross-section in the major part o f the geyser. This a s s u m p t i o n is s e l d o m justified, because t h e cross-sectional areas o f m a n y geysers are clearly n o t constant. For example, t h e probe data from Seismic geyser in Y e l l o w s t o n e and its observed history o f origin and d e v e l o p m e n t provide reasons for believing that its cross-sectional area c a n n o t be c o n s t a n t (Marler and White, 1 9 7 5 ) . However, taking into a c c o u n t t h e linear increase o f t h e full period of
116 Q u a t h e g e y and Prince B u r a t i n o geysers with v o l u m e o f w a t e r a d d e d during the soundings, this a s s u m p t i o n is p r o b a b l y acceptable for t h e geysers we have studied. In this case the water discharge changes as follows ( M e r z h a n o v et ai.. 1 9 7 8a) : Gt
G0exp (-t/t,~
=
t12t
Physically, e q u a t i o n (12) represents a process t h a t can be t h o u g h t o f as one in which water at c o n s t a n t pressure at some distance f r o m t h e geyser t u b e in the p o r o u s r o c k feeds into the geyser tube. T h e rate of flow is p r o p o r t i o n a l to the d i f f e r e n c e in pressure b e t w e e n w a t e r in the geyser t u b e and in the p o r o u s rock. so t h a t the flow decreases as the geyser t u b e fills. The free v o l u m e o f the s y s t e m t h a t fills after an e r u p t i o n is:
ld V,, =
f
td f exp(-t/to)dt
Gdt=Go
0
=
0
= Go to [1 - exp t t d / t o ) ] = Goto - G~ to
(13)
and the c u r r e n t filled v o l u m e is: (14)
Vt = Go to - G t t o
F r o m m e a s u r e m e n t s o f the v o l u m e ( w a t e r level) at various times as the geyser t u b e fills, t h e constants Go and to could be o b t a i n e d f r o m e q u a t i o n s (13) and (14). The m e t h o d of h y d r o s o u n d i n g permits us t o infer these c o n s t a n t s b y measuring the change in the t i m e n e e d e d for t h e geyser t u b e to fill w h e n k n o w n a m o u n t s o f w a t e r are added. At t h e beginning o f h y d r o s o u n d i n g , the p a r a m e t e r s o f the s y s t e m are as follows: G.~ = Go exp ( - t s / t o )
(15)
Vs = to (Go - Gs)
(16)
Taking into a c c o u n t t h e fact t h a t the t i m e required f o r adding t h e v o l u m e A Vs (with mass AMs) is s h o r t c o m p a r e d with t h e filling period and w i t h t h e full period o f t h e geyser, we can consider t h e m o m e n t of beginning t h e h y d r o sounding ts as being c o i n c i d e n t a l w i t h the m o m e n t of its c o m p l e t i o n , t s = tse. After t h e A Vs is a d d e d , we o b t a i n a new discharge in the system, Vse, and a new filled v o l u m e Vse:
Yse
= Ys
Gse = Gs
+ AYs
=
~Ys
--to
t o ( G o - Gs) + AVs
(17)
~ys
Goexp (-ts/to) . . . . to
(18)
C o r r e s p o n d i n g l y , t h e new free v o l u m e o f t h e s y s t e m f r o m t h e e q u a t i o n is: Y = Vo - Vse = Vo - [to(Go - Vs) + AVs]
(19)
117 During the filling period after hydrosounding the inflow is governed b y the relation: G
(-t'/to)
Gse exp
=
(20)
where t' = t - ts and the flow when the tube is filled is given by:
(21)
G1 = Gse exp ( - t s d / t o )
The free volume (19) after hydrosounding can also be calculated b y integrating equation (20) to give: /'sd
V = Gse
;
exp ( - t ' / t o ) dt '=
0
= Gset0 [1 - e x p ( - t s d / t o ) ]
(22)
Equating (19) and (22) and dividing by equation (21) we obtain: Vo
AVs
G1
G1
to Go -
-
G1
[1 - e x p ( - t s / t o ) ] = [ e x p ( t s d / t o ) - 1] to
(23)
and: V0 - AVs = Go to [1 - e x p ( - t s / t o ) ] + G, to [ e x p ( t s d / t o ) - 1]
(24)
We can write t w o equations of the form of (24) for two hydrosoundings carried o u t with identical times ts b u t with different masses of added water (AVs, AVs') and, consequently, with various times for the beginning of preliminary discharge (t'sd , tsd). Subtracting one from the other and carrying out simple modifications, we obtain: 8 Vs = A Vs - A Vs' = G, to [exp ( t'sd /to ) - e x p ( t~d /to) ]
(25)
or:
~Vs/G, to = exp(t'sd/to) -
e x -
l.ll Pt~sd/to)
(26)
As far as GI is experimentally determined, equation (26) can be easily solved relative to to. Go can be found from (12) into which O, expressed in the terms of (26) has been substituted: Go
= G, exp(td/to)
-
8 Vsexp ( td /to ) t tt to [exp(tsd/to) - exp(tsd/to) ]
(27)
The other parameters of the system (G1, AVs, t'sd, ted) are determined directly from the hydrosounding experiments. It is easy to show that for other modifications of soundings we can obtain an equation analogous to equation (25) rela~tive to to if we suppose A Vs = constant and the time of the beginning of the sounding to be variable. Two
118
TABLE 2 The results of the hydrosounding experiments
Full free volume of the system after the eruption, V0 (liters)
Quathegey
Prince Buratino
180
180
Initial rate of discharge of water during preliminary overflow stage, G~ (kg/s)
0.08
0.4
Natural rate of inflow of hot water immediately after the eruption, G O (kg/s)
0.53
0.61
Hydraulic constant, t o (min)
6.7
Average enthalpy of inflowing hot water and steam, I* (kcal/kg)
164--174
Upper limit of steam pressure during the eruption (atm) Parameters of the critical condition (equation 9) A (kcal) I 0 (kcal/kg) M o (kg)
t
8.4
1570 131 67
tl
14.3 180--185 10.8
5500 137 6
t
It
different values of ts and ts will correspond to two values of tsd and tsd. The final equation in this case is: 1 +
vo G1 to
-
exp(t'sd/to) - exp(t'~d/to 1 ,
exp(-ts/to) - exp(-ts/to)
(28)
If we cannot determine V0 directly by means of filling of the free volume of the geyser because its volume is too large, we can calculate this value using equation (13) where to is found from equation (26) and Go from equation (27). The results of our experiments on hydrosounding of Quathegey and Prince Buratino geysers are summarized in Table 2. ACKNOWLEDGEMENTS
The authors are especially grateful to Donald E. White for constructive criticism and editorial advice. We wish to express our thanks to A.T. Naumenko and V.A. Nikolajenko from the Kronotski National Park for their support and help in carrying o u t the experiments, and also to L.J.P. Muffler, N. Nathenson, J. Rinehart and G.R. Robson for critical reviews and to Mrs. O.G. She,vchenko for help in preparing the manuscript. Derek Bostok made extensive editorial revisions of the text.
119
REFERENCES
Marler, G.D., 1969. The story of Old Faithful. Yellowstone Libr. Mus. Assoc. Yellowstone National Park, Wyo., p. 49. Marler, G.D. and White, D.E., 1975. Seismic Geyser and its bearing on the origin and evolution of geysers and hot springs of Yellowstone National Park. Bull. Geol. Soc. Am., 86: 749--759. Merzhanov, A.G., Steinberg, A.S. and Steinberg, G.S., 1978a. To the theory of geyser process. Modern Geol. (in press). Merzhanov, A.G., Steinberg, A.S. and Steinberg, G.S., 1978b. The laboratory model of the geyser. Modern Geology (in press). Merzhanov, A.G., Rasina, A.A., Steinberg, A.S., Steinberg, G.S. and Fundamenski, V.S., 1973. The study of geyser systems by the method of hydrosounding. Bull. Volcanol. Stn., 49 (in Russian). Rinehart, J.S., 1972. Fluctuation in geyser activity caused by variations in earth tidal forces, barometric pressure and tectonic stress. J. Geophys. Res., 77. Sorokin, Ju.L., 1963. A b o u t stability motion water-steam mixture in vertical tubes. J. Appl. Math. Tech. Phys., 6 (in Russian). Vukalovich, M.M. and Novikov, V.A., 1963. Technical Thermodynamics. Mashgiz, Moscow (in Russian). White, D., 1967. Some principles of geyser activity, mainly from Steamboat Springs, Nevada. Am. J. Sci., 265:.641--684. White, D.E., 1968. Hydrology, activity, and heat flow of the Steamboat Springs thermal system, Washoe County, Nevada. U.S. Geol. Surv. Prof. Paper, 458-C. White, D.E., Fournier, R.O., Muffler, L.J.P. and Truesdell, A.H., 1975. Physical results on research drilling in thermal areas of Yellowstone National Park, Wyoming. U.S. Geol. Surv. Prof. Paper, 892.
99
H Y D R O S O U N D I N G AS A M E T H O D O F S T U D Y O F T H E C R I T I C A L PARAMETERS OF THE GEYSER
G.S. STEINBERG', A.G. MERZHANOV2 and A.S. STEINBERG2
'MKB Geographical Society, U.S.S.R. Academy of Sciences, Telmana 2B-47, PetropavloskKamchatsky 683019 (U.S.S.R.) 2Branch of the Institute of Chemical Physics, U.S.S.R.:Academy of Sciences, Chernogolovka, Noginsk District, Moscow 142432 (U.S.S.R.) (Received and accepted July 11, 1977)
ABSTRACT Steinberg, G.S., Merzhanov, A.G. and Steinberg, A.S., 1978. Hydrosounding as a method of study of the critical parameters of the geyser. J. Volcanol. Geotherm. Res., 3: 99--119. A new method of hydrosounding has been devised for clarifying the geyser regime and for determining critical conditions that are essential for geysers to erupt. The method consists of pouring known quantities of water into the geyser system and then measuring changes in the main characteristics of the geyser, i.e., the duration of the eruptive stages and the temperature and quantity of the added and erupted water. The temperature and mass of the added sounding water can be varied and used to provide a series of equations that give average enthalpy of heat-carrying fluids, their natural rate of inflow to the local geyser reservoir, and variations in the process of filling the system, the free volume after eruption and other factors. Experiments were carried out in 1970--1974 in Quathegey and Prince Buratino geysers of Geyser Valley, Kamchatka. The average enthalpies of the heat-carrying fluids are calculated to be 164--174 kcal/kg and 180--195 kcal/kg, respectively.
INTRODUCTION In previous papers we have p r o p o s e d a t h e o r y f o r geyser processes ( M e r z h a n o v et al., 1 9 7 8 a ) a n d have devised a l a b o r a t o r y m o d e l f o r a geyser ( M e r z h a n o v et al., 1 9 7 8 b ) w h i c h has s h o w n a g o o d a g r e e m e n t b e t w e e n t h e t h e o r y and e x p e r i m e n t . C o m p a r i s o n o f t h e p r o p o s e d m e c h a n i s m with t h a t observed in n a t u r e was c o m p l i c a t e d b y t h e impossibility o f influencing t h e eruptive processes in n a t u r a l geysers. Previous studies have p r o v i d e d d a t a o n t e m p e r a t u r e , discharge, c h e m i c a l and i s o t o p i c c o m p o s i t i o n a l changes o r c o r r e l a t i o n s o f t h e s e changes with the n a t u r a l causes, such as tides, a t m o s p h e r i c pressure, f l u c t u a t i o n s of g r o u n d w a t e r levels and precipitations, a n d seismic activity ( R i n e h a r t , 1 9 7 2 ; White, 1 9 6 7 , 1 9 6 8 ; Marler, 1 9 6 9 ) . We have used a n e w m e t h o d t o s t u d y the influence o f various f a c t o r s o n the
100 .
.
.
.
.
.
r
•
x o° _
)~
~
/
(
/ Kamchatka :.~ t
l
7~.,-'
.
t
k:/
.'/
,~_
^
~:~Vo(
~o,~
~z~K,k~r,y(,, o\ Geyse~ ~a:/,a t
t,\
~
! t
~
, ,
~
e
Inn~kov
,~o,~
~/, Kronotzk~,
COilok'
S't¢
(['~
k3~rr~:t ir",c
.
\,~
j
o o o Geysers
. J ~' km
~ Pulsing hot springs ~ ~'4ud
-
pO0
~, ~ t e o n
!
I)
20c.
40C
m
Fig. 1. Map of the central Geyser Valley, Kamchatka, showing location of Quathegey and Prince Buratino geysers. (Quathegey = QUAntity THEory GEYsers.)
geyser regime -- a method of hydrosounding (Merzhanov et al., 1973). The hydrosounding experiments were carried out in 1970--1975 in the Geyser Valley of Kamchatka (Fig. 1) on the geysers Quathegey and Prince Buratino. The Quathegey and Prince Buratino geysers are situated on the flanks of the narrow V-shaped valley of the Geysernaya River (Fig. 1) at elevations of 25 m and 5 m respectively above the river level. Both geysers are of a cone type. The pools are rather small (surface area ~ 0.035 m 2 ; volume ~ 3--8 1). Most erupted water does not return to the geysers. Both geysers are characterized by a distinct preliminary discharge stage and by a very constant period (+4% variation). The channel of Quathegey geyser is vertical and chimney-like to a depth of 1.5 m; its diameter is about 10 cm. The orientation of the channel changes at a depth of 1.5 m where there may be a small reservoir or distension of the channel. In its natural regime the preliminary discharge stage of Quathegey is of short duration (Fig. 2a) and displays intensive boiling in the channel and pool. Hence, the natural outflow can be overestimated if boiling is not taken into account. When no boiling is seen {e.g. during sounding), the natural outflow at preliminary discharge is not nearly so large {Figs. 6, 10). The channel of Prince Buratino geyser is fissure-like, with a width of 2--4 cm, a length of about 20 cm, and an inclination of 50--60 °. A stock equipped with temperature sensors was inserted to a depth of 0.7 m. Prince Buratino acted as a pulsating hot spring before 1973. It transformed into a geyser of very stable regime (8 m 35 s) after clearing its vent. The rim of the pool was heightened in August 1974 and hence the level of water in the pool became 10--12 cm higher and the full period of the geyser increased to 9 m 20 s. The preliminary
101
2_.0
lQuathegey geyser
/o\
15
\
0.5
t,
sec
Prince Burotinogeyser
fee/
b
30
20
d 10
•
9
o °-6
•
•
•
150 t,
180
210
SeC
Fig. 2. Water discharge during the full period of Quathegey and Prince Buratino geysers in natural regime.
discharge stage showed no disturbances; intense boiling began 10--15 seconds before the beginning of an eruption (Fig. 2b). Principal characteristics of the geysers in normal regime are shown in Table I
102
TABLE1 Principal c h a r a c t e r i s t i c s o f Q u a t h e g e y a n d Prince B u r a t i n o geysers in n o r m a l regime Quathegey
Prince B u r a t i n o
Full p e r i o d o f the geyser, f r o m start 12m35 s o f o n e e r u p t i o n u n t i l s t a r t of t h e n e x t e r u p t i o n , tf
9m20 s
D u r a t i o n of t h e filling of t h e geyser f r o m end of e r u p t i o n u n t i l t h e beginning of the next preliminary discharge, t d
10m00 s
6m05 s
D u r a t i o n of p r e l i m i n a r y discharge stage
0 TM 45 s
1 m 30 s
D u r a t i o n of t h e e r u p t i o n
1 m 50 s
l m 45 s
V o l u m e of t h e w a t e r t h r o w n o u t d u r i n g t h e e r u p t i o n (liters) M a x i m u m height o f e r u p t e d w a t e r ( m )
120 1.5
120--150 2.5--3
The purpose of this paper is to demonstrate the ability of the method of hydrosounding to establish important parameters characterizing the dynamics of the geyser mechanism. NOTATION Time, t (rain, s) tf td tsd ts to tse At s
full p e r i o d o f t h e geyser ( t h e interval b e t w e e n t w o e r u p t i o n s ) t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l t h e b e g i n n i n g o f t h e p r e l i m i n a r y discharge ( w h i c h c h a r a c t e r i z e s t h e n a t u r a l regime o f s o m e b u t n o t all geysers) t i m e interval f r o m t h e e n d o f s o u n d i n g u n t i l t h e b e g i n n i n g of t h e n e x t p r e l i m i n a r y discharge t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l t h e b e g i n n i n g of s o u n d i n g h y d r a u l i c c o n s t a n t of a geyser (see t e x t ) t i m e interval f r o m t h e e n d of e r u p t i o n u n t i l t h e e n d of s o u n d i n g = tse - ts, t i m e interval f r o m t h e b e g i n n i n g of s o u n d i n g u n t i l t h e e n d of s o u n d i n g
Volume, V (liters) V0
" f r e e " v o l u m e - - t h e p a r t o f t h e geyser c h a n n e l or reservoir f o r m e r l y filled w i t h water, b u t w i t h o n l y s t e a m ( a n d air) a f t e r e r u p t i o n V s t o t a l v o l u m e o f w a t e r a d d e d in s o u n d i n g e x p e r i m e n t Vs the p a r t of t h e free v o l u m e filled a f t e r t h e t i m e interval (t s) f r o m t h e e n d o f e r u p t i o n till t h e b e g i n n i n g o f s o u n d i n g Vse = V s + ~ Vs, t h e p a r t o f t h e free v o l u m e filled at t h e e n d o f s o u n d i n g Vt v o l u m e filled at t h e t i m e interval f r o m t h e e n d o f e r u p t i o n u n t i l s o m e m o m e n t t, where 0 < t < td
103
Mass, M (kg)
AM s total mass of water added in sounding mass of water discharged during t i m e interval f r o m the beginning preliminary disMI charge stage until s o m e m o m e n t t natural (feeding) water mass inflow into a geyser during the t i m e interval f r o m the M2 beginning preliminary discharge stage until s o m e m o m e n t t Mtm = V0-~, total mass of water filling the free v o l u m e of a geyser after e r u p t i o n Me mass of water discharged during e r u p t i o n stage of the geyser mass c o n s t a n t of a geyser - - see e q u a t i o n (9) Mo mass of natural water inflow during the time interval (ts) f r o m the end of e r u p t i o n till Ms the beginning of sounding Mt = Vt~ , mass filled during the time interval f r o m the end of e r u p t i o n until s o m e m o m e n t t, where 0 <: t < t d Discharge, G (kg/s)
GO G1 Gt
Gs Gse
natural water inflow i m m e d i a t e l y after e r u p t i o n water discharge during preliminary discharge stage natural water inflow at the m o m e n t t, where 0 < t < t d natural water inflow at the beginning of sounding natural water inflow at the end of sounding
Temperature, T (°C)
Ts Tin Td Ti
t e m p e r a t u r e of water added during sounding mean t e m p e r a t u r e of water discharged during the stage of preliminary discharge t e m p e r a t u r e o f the water discharged during the preliminary stage and during sounding instantaneous t e m p e r a t u r e at a geyser during sounding
Other para meters
i', i" I* I0 A c
e n t h a l p y of saturated water and steam, respectively (kcal/kg) average e n t h a l p y of heating fluid (liquid water or water-steam m i x t u r e ; kcal/kg) heat c o n s t a n t of a geyser (kcal/kg) } see equations (9) to (11) heat c o n s t a n t of a geyser (kcal) heat capacity (calg-~ °C-I ) specific gravity (g/cm 3 )
CRITICAL
CONDITION
FOR A GEYSER
SYSTEM
The critical state of a geyser system occurs when heat supplied to it can no longer be balanced b y additional heating of the water, b y water outflow, and b y surface boiling and evaporation. At the m o m e n t when the critical state is attained, the water in the channel is very close to the boiling temperature. Steam bubbles originating in the b o t t o m parts of the system rise with little or no condensation. The absence of condensation and the expansion o f the bubbles due to the upward decrease of hydrostatic pressure are responsible for the qualitative change in the regime of liquid and steam upflow. The bubbles occupy more and more area of the horizontal section of the channel. The resuiting regime of steam "plugs" is referred to as the "missile regime" of the motion (Fig. 3). The water is pushed up and o u t of the upper part of the
104
~°~
o
i'll
e o o
Fig. 3. T w o - p h a s e (liquid + s t e a m ) regime o f the f l o w in a vertical cha~nel (after Sorokin, 1963). 1 = b u b b l e regime; 2 = missile regime; 3 = dispersive regime; 4 = emulsive regime.
channel by the vapor plugs. "The rates of boiling and upflow increase further as pressuredeclines throughout the system and as the chain reaction extends out to payts of the reservoir previously filled entirely with water" {White, 1967). An eruption then begins. The critical state of a geyser can also be defined as that in which the excessive heat (Qcritical), accumulated in the effective parts of the system (the immediate reservoir, the channel), is so considerable that any further increase brings about an eruption. This definition is identical to the "loading system" of White (1967). Qcritical is energy loading or the heat supplied from the feeding area less the heat dissipated with evaporation and outflow during the interval from the end of one eruption until the beginning of the next. Thus, the critical state of a geyser system can be qualified as the limit of loading the system. Finally, the critical condition for a geyser can be essentially determined as that with a critical enthalpy that somehow must be attained before an eruption. The critical state can be expressed in the form of an equation (equation 9), derived from hydrosounding experiments. A geyser system differs in principle from any other hot spring in that its condition periodically becomes unstable and the process of boiling is triggered as a chain reaction through the system {White, 1967). Such conditions are usually designated by physicists as critical. THE P R O C E D U R E OF H Y D R O S O U N D I N G
The hydrosounding technique consists of rapidly adding known quantities of water to the geyser system through the vent and then measuring changes in characteristic features of the eruptive process, such as the duration of its full period of eruption and its various stages, including changes in temperature, rate of preliminary discharge, and quantity of water erupted with time. The mass and temperature of added water and the time interval between the end of the previous eruption and the m o m e n t of adding the water can be changed from one experiment to another and are also parameters of hydrosounding. At geysers Quathegey and Prince Buratino some 300 runs have been carried out with volumes (AVs) of 1 8 0 , 1 5 0 , 120, 100, 80, 60, 50, 40, 20 a n d l 0 liters and under the temperature (Ts) of 80, 60, 50, 40, 20, and 10°C. The sound-
105
ings began immediately after eruptions. The duration of adding the water varied from as short as 5 seconds (AVs = 10 l) up to as long as 1.5 minutes (A Vs = 180 1), so Ats ~< 8% of the full period of the geyser (under sounding). The authors have assumed the addition to have been instantaneous (ts = tse or Ats = 0), because this assumption greatly simplifies the calculations. The control calculations, when the duration of adding had been taken into account, showed the discrepancy to be less than 5%. Inasmuch as the full-period fluctuations of geysers (by hydrosounding) are -+8%, this assumption seems to be within the limits of experimental accuracy. Considering that the area of the surface pool of b o t h geysers is less than 0.04 m 2 and that neither intensive nor prolonged pre-eruption boiling has taken place, further assumptions have been that: (1) Loss of heat in steam escaping at the surface between eruptions is negligible. (2) Loss of heat in water vapor by evaporation from surface pools is negligible. (3) Exchange of heat between fluids and rocks of the reservoir is negligible or gains and losses are balanced over an eruption cycle. In order to justify the third assumption, the geyser was allowed to erupt 2 or 3 times in its natural regime after every sounding. The next sounding was carried out when the full period of a geyser regained a normal value of tf = 12 m 35 s. In most cases (especially when Ts <~ 60°C), the full period of a geyser in its natural regime became a bit longer, probably due to cooling of the walls of its channel during sounding. The resulting data (Figs. 4--10, 12) for different sets of runs may differ somewhat in their range of accuracy (+ 8%). FREE VOLUME AND SOME MINOR CHARACTERISTICPROPERTIES OF THE GEYSERS The free volume of a system, i.e. a volume filled by water and steam before an eruption and by steam and air after an eruption, can be determined by hydrosounding. It appeared to be 180 1 for both geysers. If this quantity of water is poured into a vent, it should fill the system to the surface. The Quathegey geyser gives about 120 1 of water in each natural eruption. It follows that the portion of the volume of the geyser system that was filled with steam during an eruption is about 60 1 (180 - 120 = 60). The relation of the full period of Quathegey geyser and the period of preliminary discharge to sounding parameters (Figs. 4, 5) illustrates several details of the geyser structure. Three sections can be seen in all the curves of Figs. 4 and 5. They are shown best in Fig. 4 where relation of the full period (tf) to the volume (4 Vs) and temperature (Ts) of the sounding for Quathegey geyser are shown to be as follows: (1) Section a, 0 < AVs < 40 1. The full period decreases as the system is
106
! i i 30 l-
o ~:o~o°
, !
v T~=60 ° o ,;.~o °
I
/////.
+ T~=4o °
./ J/ f.
2oF
i
,/
/// natural ~:~
period " ~
E~o
ir
i
~
/ I fv~-'~-v
I',/
o
I
/
/,,
s
°
I /
d \'~,
Fig. 4. Duration o f the full period o f Q u a t h e g e y geyser as related to the parameters o f s o u n d i n g (AVs; Ts).
i
3O k '!
/ 20
z/V s , L
Fig. 5. D u r a t i o n of the p r e l i m i ~ r ] disch~ge stage of Quathegey geyser as related to the parameters of sounding ( A V s, T s).
filled. The duration of the full period does not depend upon the temperature of the added water (Fig. 4). The duration of the preliminary discharge stage does not depend upon either the temperature or volume of the added water (Fig. 5). (2) Section b, 40 1 < A Vs < 80 1. The full period severely increases al~host
107 up to the natural value (12 m 35s), it decreases slightly when sounding at Ts = 80°C, it essentially does not change when Ts = 40--60°C and increases slightly when Ts = 20°C (Fig. 4). The duration of the preliminary discharge stage does not change materially and displays almost no dependence upon the sounding volume (A Vs) at temperatures of Ts = 40 °, 60 °, 80°C, b u t it has a slight tendency to increase with time. The duration of the stage distinctly increases at a temperature of 20°C (Fig. 5). (3) Section c, 80 1 < AVs < 180 1. The full period of a geyser increases linearly as the system is filled and as the temperature (Ts) increases (Fig. 4). One can assume that section a (Fig. 4) is to be explained b y a widened reservoir in the upper part of the system; the filling of the small reservoir affects only the mass balance of the system, not its heat balance. Section b corresponds to the filling of the free volume of the main reservoir of a geyser. The decrease of Vt at Ts = 80°C, stability at Ts = 60°C, and a slight increase at Ts = 20°C suggest that the initial equilibrium temperature of water filling the free volume of the main reservoir is about 60°C. Consequently, it suggests that rather cold water (40°C < T < 80°C) enters the reservoir at the initial stage of the filling. Section c corresponds to the filling of the channel. The lower the value of Ts, the longer are the periods in which steam bubbles condense in the channel. The same is true of the duration of the preliminary discharge stage, and the full period of a geyser. The linear dependence of the full period (tf) and the discharge stage on AV s and T s (Figs. 4, 5) can be explained by a strong deterioration in the convection in the channel compared with that of the convection in the reservoir. CALCULATION OF THE ENTHALPY OF FLUID FEEDING A GEYSER F r o m the corresponding curves for temperature changes during t w o eruptive cycles and for discharge from Quathegey geyser at full sounding (AMs = 180 kg and Ts = 20°C, 40°C) it follows that dTd/dt is constant, in the temperature range of 20--60°C (Fig. 6), because after adding water at 20°C the discharge is nearly the same as that observed for hydrosounding water at 40°C. Taking into account the fact that, for temperatures of preliminary discharge between 20 ° and 60°C, the rate of discharge of water is also constant (GI = 0.08 kg/s), it is possible to calculate a heat balance and to determine the enthalpy of the natural heat-carrying water feeding the geyser. During the sounding, 180 kg (AMs) of water w i t h Ts = 20°C is poured into the geyser instantly. In the following 5 minutes, 25 kg (MI) of water heated from 20 ° to 40°C was discharged from the geyser; so we assume for this period that Tra = 30°C. Meanwhile, the remaining volume of water added to the geyser during the sounding (AMs - M~ = 155 kg) was heated to Ti = 40°C. During this time 25 kg (M2 = M~ ) of water with enthalpy I entered the system. Supposing the heat capacity of water, c = 1 calg -1 °C -1 , we can equate the enthalpy before and after mixing:
108
c[(AMs
-
MI)Ti
+
MI T m + M2 Ti
-
AMsTs]
=
IM2
All values on the left-hand side of this equation were determined from the experiment, so the heat content of the mixture feeding Quathegey geyser is easy to obtain: I = 174 kcal/kg. The enthalpy of a heat-carrier can also be determined from hydrosounding experimental data when Td varies non-linearly and without the assumption that T i = Td. The single assumption used in the calculation has been formulated below as that of a critical state. This assumption for determination of the enthalpy of the heat-carrier by hydrosounding can be written as follows: (1) An eruption begins when an excess heat Qcriticat is accumulated in the effective parts of the geyser (the immediate reservoir and channel). (2) Qcritical is constant for any geyser and does not depend on the sounding parameters (A Vs, Ts). The second assumption is confirmed by the fact that the volume of erupted water and the height of eruption are constant at Prince Buratino geyser both in the natural regime and in different sounding runs. The heat balance equation of a geyser for the period from the end of one
22
Quathegey geyser
~ ~2r d
"°° i
100°
• r~: 20 °
.~.t. ~'''+J
i
osk
i8o °
06 ~
04k 02
T,d''+
.:l-J + ./"~'" / area 1 ~ G i
~/z
F--'--,+-+=-
L ~
00
I
i 60°
area 2
,J /7~ .~ + ...4 -+
i 40° i20°
,,h't"-- ........... I
400
Fig. 6. C m ' v e ~ o f
~
I
___J
800 t, 5ec
,o
i _.~_
1200
i
_J__
1600
l___J 0
temperature and discharge of Qua~hegey g e y s e r d u r i n g the hydrosounding:
'~'/s = 180 kg; T s = 20°C; 40°C.
109
eruption until the beginning of the next one can be written as follows: Qcritical = Qfeed + Qsound- Qoutflow
(2)
or:
Qcritical = MfeedI* + c A M s T s
- ' Qoutflow
(3)
where: n
Qoutflow = c ~_j M l i T d i
n
= Atc
i=l
~ GliTdi i=l
Mfeed = M2 = M1 + ( M t m - 5Ms)
(4) (5)
- AMs) = mass of a heat-carrier which fills the geyser, if the system has not been filled completely during a sounding (i.e. if A Vs < V0 ). When a sounding is complete (i.e. if h Vs = V0 ), A M s = Vo~/ = M t m a n d M a n - A M s = O. One can easily calculate Qoutflow, when measuring preliminary discharge G, and the temperature of the discharge water. Thus only Qcritical and I* are left u n k n o w n in equation (3). We have used equation (3) for two sounding runs (Fig. 7). Run 151 gives (Fig. 7a): (Mtm
Q c r i t ~ = 428•* - 33968
(6)
and run 112 gives(Fig. 7b): Qcntical = 3741" - 24611
(7)
Considering t h a t Qcritical = constant, we can combine equations (6) and (7)and find I * = 173 kcal/kg and Qcritical = 40150 kcal. One can note, however, that an enthalpy calculated by this method is somewhat less than the true value, because equation (3) does not take account of steam generation when boiling. Since intensive boiling is observed for 10--15 seconds immediately before an eruption of the Prince Buratino geyser, I* can be determined with an error no more than 5%. So, the actual value of I * is 180--185 kcal/kg. Knowing the enthalpy we can estimate the upper limit of steam pressure and the quality of the steam-water mixture (heat-carrier). The m a x i m u m equilibrium pressure of saturated steam at I = 174--185 kcal/kg is 8.4--10.8 atm (Vucalovich and Novikov, 1962). The steam content in the mixture is obtained from: 174 = i " X + i(1 - X ) 6 5 0 X + c T ( 1 - X )
(8)
in which: X = (174 - cT)/(650 - cT) Here X is the weight percentage of the steam, in the total mass. The tempera-
110
20r
100 ~
~9 10~
I
/"
70
i
6o
~ i I
50 L
I
4 ~
!
/
G
r I
0
z~t~ ÷ tsd
5
10 Time,
15
20
rain
F
F
20[-
100
o °.°~°_°.°_°_• ~
k
1O,
i F
80
6O 5() i
/
4o I ,.,,~.v.~._~°.°_._..°. i
ol
. .°. .° ° Q~-°-•_•~•-°°-°-•-°-,
~
go
b zt
± 5
G °.
10 Time,
•-°---. •
•_•~°
15
20
mln
F i g . 7. C u r v e s o f t e m p e r a t u r e and discharge of Prince (a) Experiment No. 151: AV s = 150 l; T s = 20°C. (b) Experiment No. 112: AV s = 180 l; T s = 50°C.
Buratino
geyser
during
hydrosounding,
ture of a heat-carrier must be known for a strict solution of (8); however, the upper limit of the weight percentage of the steam can be estimated if T is taken equal to 100°C. When the temperature of the water is more than 100°C, the weight percentage of the water in the heat-carrier decreases proportionally with increasing temperature up to the condition of dry steam at T = 174°C. CALCULATION
OF THE CRITICAL
CONDITION
The dependence of the full period of the geyser (the interval between initiation of two eruptions) on the mass and enthalpy of the water added to the geyser during hydrosounding is shown in Fig. 8. The linearity of these dependences suggests that we can determine the critical conditions of natural eruptions by extrapolating the lines to their intersection with the enthalpy axis,
III
30 o z ~ M s = 1 8 0 kg
o
20 a
c_ E &
=50
,.J
10
I, k c a l / k g
30
o
k
I - z1[vls = 1 8 0 kg
A 1
2-
= 120
3
= 80
-
o~
o~
55
\'15o\
~6o [,
~o ""~-zso
-
kcQI/kg
Fig. 8. Determination of the critical conditions of the geyser eruption: (a) Prince Buratino geyser, (b) Quathegey geyser. The full period of the geyser depends on the enthalpy and quantity of added water.
assuming the indicated critical heat content I* of water with mass AMs used in the hydrosounding corresponds to the eruption of the geyser just after input of water. For geyser Quathegey, the corresponding enthalpy values for &Ms = 180, 120, and 80 kg are I* = 147, 163, and 263 kcal/kg. The curves showing the dependence of the critical enthalpy value I t upon the mass of water M in Fig. 8 shows that they are related by the equation: I t - I o ~- A / ( M
- Mo)
(9)
i.e. the critical condition for the geyser system can be defined as the condition when a water-steam mixture with mass M and average enthalpy I t , which corresponds to equation (9), occurs in the natural system as a result of simultaneous processes of heat and mass transport. The parameters A and I* in equation (9) are the heat constants but M0 is the mass constant of this source and
112 reflects the peculiarities of the geometry of the system as well as the specific heat and h y d r o d y n a m i c processes in the geyser. These parameters can not be defined in physical terms because they are obtained by the least squares method from equation (9). We hope to determine the physical nature of this term by performing hydrosounding experiments on models or drill-holes that function as geysers. For these geysers one knows the parameters of the channel, the immediate reservoir, the enthalpy of the inflowing fluid, the relations between the input and o u t p u t (dissipation) of energy, and so on. In our laboratory model of a geyser (Merzhanov et al., 1978b), it is observed that during the period prior to eruption, steam bubbles originating in the b o t t o m parts of the channel cool and condense on their way up through water where T < Tsteam, i.e. boiling of the water in the lower parts of the geyser does not yet lead to eruption. Only when the water high in the channel is heated to temperatures close to that of the steam, does condensation cease and allow the steam plugs to force their way to the surface ejecting water from the near-surface vent (the so-called missile regime; Sorokin, 1963); this then leads to an abrupt decrease in pressure in the b o t t o m parts of the system and results in extensive boiling and eruption. The calculated data for the critical conditions of both geysers are shown in Fig. 9 in I and M coordinates. A least squares treatment of these results in accordance with (9) gives us the following expressions: I* - 131 = 1570/(M - 67) I*
-
137 = 5500/(M - 6)
Quathegey
(10)
Prince Buratino
(11)
However, one can ask whether the linear extrapolations of the experimental data (Fig. 8) are meaningful and whether equations (10) and (11) obtained from the extrapolated quantities of I* are reliable for soundings at Ts > 100°C There is another way to verify the equations in question. When we know the mass and the volume of the water erupted by a geyser under natural conditions, we can obtain the enthalpy of heat-carrier from equations (10) and (11).
o ~
240
©uathegey P Burat~no
~ 2ooi 160 i"
"~"~"~'~- o 60
100 140 M kg
1B0
Fig. 9. Relationship of enthalpy and mass of water (or water-steam mixture) in the geyser
for the critical conditions.
113 Comparing those enthalpies with the quantities obtained from the heat-balance equations (1--7), we can verify equations (10) and (11) (Fig. 9) and consequently, the validity of the linear extrapolation (Fig. 8). For Quathegey geyser: Ve = 118--120 l, I = 174 kcal/kg. From equation (10): I =
1570 120 - 67
+ 131 = 161 kcal/kg
For Prince Buratino geyser: Ve = 120--150 1, I = 180--185 kcal/kg. From equation (11): I =
5500 (150 or 120) - 6
+ 137 = 175--185 kcal/kg
The convergence is consistent, so the extrapolation, made above, appears to be acceptable and the derivation of equations (9), (10), and (11) is probably reliable. CALCULATION OF THE RATE OF WATER RECHARGE AND THE CHANGE OF THIS RATE WITH TIME DURING THE ERUPTION CYCLE It is known that high-enthalpy geysers are fed by water under pressure much above hydrostatic conditions and the rate of discharge must be almost constant throughout the geyser cycle. Examples are found among t h e Yellowstone geysers (White et al., 1975) and in the Velikan geyser in Geyser Valley, Kamchatka. In other geysers the fluid pressure depends on various causes, especially the hydrostatic pressure in the reservoir. In this case the rate of discharge must change greatly (White, 1967; Rinehart, 1972). The Quathegey and Prince Buratino geysers belong to the latter type. It was shown in our laboratory model experiments that the inflow of water into the geyser system immediately after the eruption is distinctly higher than that when the geyser system is completely filled (Merzhanov et al., 1978b). This conclusion has been supported b y our field observations on Quathegey and Prince Buratino geysers. It appears that the model principle is rather similar to the natural inechanism in the t w o geysers. The water inflow has been estimated in the experiments at A Vs = 180 1 when the immediate geyser reservoir, the channel, and the pool are completely filled. When no boiling is taking place, the preliminary discharge is equal to the inflow. During the sounding of Quathegey geyser no boiling was registered during the previous 5--10 minutes, and the discharge was constant (G~ = 0.08 l/s (Figs. 6, 10). A similar experiment on Prince Buratino geyser showed GI = 0.4 1/s (Fig. 7). The water discharge of Quathegey geyser later became higher (Figs. 6 , 10). One can distinguish t w o stages of preliminary discharge: (1) a constant-rate stage (Fig. 6, area 1); and (2) an accelerating-rate stage (Fig. 6, area 2). The beginning of the second stage is connected with the onset of boiling.
114
0
+
=40°
/
~1 12~
v
=6o°
|1
I al
o
J_l
, 0
400
800 T~me, sec
1200
1600
Fig. 10. C u r v e s o f d i s c h a r g e o f Q u a t h e g e y g e y s e r d u r i n g h y d r o s o u n d i n g . 1 8 0 1.
AVs = constant =
It is evident that in a geyser being sounded (A Vs = 180 1) the duration of the accelerating-rate stage of preliminary discharge does not depend on the temperature of the sounding (Ts) (Fig. 10). This fact demonstrates that the second stage is related to the time interval from the beginning of boiling until the eruption. The Prince Buratino geyser has a very short boiling duration and the second stage of preliminary discharge is practically absent (Figs. 2b, 7). A simple calculation shows that the water inflow after eruption is considerably higher than that when the geyser system is completely filled. The overall water (without steam), taken in and discharged during a cycle, has been estimated for Quathegey geyser as follows: V = 120 1 + 0.4 1/s x 35 s = 134 l Should the water inflow into the geyser system be constant, the inflow per cycle would be: V = 0.08 1/sec x 745 s = 60 1. That means that V = 134 - 60 = 74 1. A similar q u a n t i t y of 85 1 has been measured during sounding. The discrepancy between the calculated and experimental data for the geysers studied suggests that water inflow varies during the course of filling the system. The time-dependent changes of this discharge may be determined in two ways. The first is a direct m e t h o d consisting of filling the free volume of the geyser in a fixed time interval after eruptions and measuring the M (t) dependence by taking the time differential of this dependence and obtaining G(t) (Fig. 11). This m e t h o d is convenient for investigations of small geysers {Fig. 12). For large geysers it is technically difficult to pour a sufficiently large volume of water rapidly into their vents. It must be noted that the free volume of large geysers may exceed 5--10 m 3 . The second method requires the assumption of an approximate constancy
115
G~V Go
V(t)o~
\
\
/ ° f
/o
~"------ o G 1
LU
U", U v', B v', ~v,, Uv,. ~o
vt-- Vo- .~vs., vt, : vo - ~ & , vt = vo - zlvs,
Fig. 11. Scheme of determination of water inflow to the geyser system from the end of eruption until the beginning of the following preliminary discharge stage.
150
,°°
--. L
2 0 Time,
300
360
sec
Fig. 12. The change in the flow of the feeding fluid in relation to the filling of the geyser system (a small nameless geyser). The inflow was determined by hydrosounding (see Fig. 11).
The geyser was filling under pressure much above hydrostatic, so the rate of inflow did not depend on the extent of the filling of the system. of cross-section in the major part o f the geyser. This a s s u m p t i o n is s e l d o m justified, because t h e cross-sectional areas o f m a n y geysers are clearly n o t constant. For example, t h e probe data from Seismic geyser in Y e l l o w s t o n e and its observed history o f origin and d e v e l o p m e n t provide reasons for believing that its cross-sectional area c a n n o t be c o n s t a n t (Marler and White, 1 9 7 5 ) . However, taking into a c c o u n t t h e linear increase o f t h e full period of
116 Q u a t h e g e y and Prince B u r a t i n o geysers with v o l u m e o f w a t e r a d d e d during the soundings, this a s s u m p t i o n is p r o b a b l y acceptable for t h e geysers we have studied. In this case the water discharge changes as follows ( M e r z h a n o v et ai.. 1 9 7 8a) : Gt
G0exp (-t/t,~
=
t12t
Physically, e q u a t i o n (12) represents a process t h a t can be t h o u g h t o f as one in which water at c o n s t a n t pressure at some distance f r o m t h e geyser t u b e in the p o r o u s r o c k feeds into the geyser tube. T h e rate of flow is p r o p o r t i o n a l to the d i f f e r e n c e in pressure b e t w e e n w a t e r in the geyser t u b e and in the p o r o u s rock. so t h a t the flow decreases as the geyser t u b e fills. The free v o l u m e o f the s y s t e m t h a t fills after an e r u p t i o n is:
ld V,, =
f
td f exp(-t/to)dt
Gdt=Go
0
=
0
= Go to [1 - exp t t d / t o ) ] = Goto - G~ to
(13)
and the c u r r e n t filled v o l u m e is: (14)
Vt = Go to - G t t o
F r o m m e a s u r e m e n t s o f the v o l u m e ( w a t e r level) at various times as the geyser t u b e fills, t h e constants Go and to could be o b t a i n e d f r o m e q u a t i o n s (13) and (14). The m e t h o d of h y d r o s o u n d i n g permits us t o infer these c o n s t a n t s b y measuring the change in the t i m e n e e d e d for t h e geyser t u b e to fill w h e n k n o w n a m o u n t s o f w a t e r are added. At t h e beginning o f h y d r o s o u n d i n g , the p a r a m e t e r s o f the s y s t e m are as follows: G.~ = Go exp ( - t s / t o )
(15)
Vs = to (Go - Gs)
(16)
Taking into a c c o u n t t h e fact t h a t the t i m e required f o r adding t h e v o l u m e A Vs (with mass AMs) is s h o r t c o m p a r e d with t h e filling period and w i t h t h e full period o f t h e geyser, we can consider t h e m o m e n t of beginning t h e h y d r o sounding ts as being c o i n c i d e n t a l w i t h the m o m e n t of its c o m p l e t i o n , t s = tse. After t h e A Vs is a d d e d , we o b t a i n a new discharge in the system, Vse, and a new filled v o l u m e Vse:
Yse
= Ys
Gse = Gs
+ AYs
=
~Ys
--to
t o ( G o - Gs) + AVs
(17)
~ys
Goexp (-ts/to) . . . . to
(18)
C o r r e s p o n d i n g l y , t h e new free v o l u m e o f t h e s y s t e m f r o m t h e e q u a t i o n is: Y = Vo - Vse = Vo - [to(Go - Vs) + AVs]
(19)
117 During the filling period after hydrosounding the inflow is governed b y the relation: G
(-t'/to)
Gse exp
=
(20)
where t' = t - ts and the flow when the tube is filled is given by:
(21)
G1 = Gse exp ( - t s d / t o )
The free volume (19) after hydrosounding can also be calculated b y integrating equation (20) to give: /'sd
V = Gse
;
exp ( - t ' / t o ) dt '=
0
= Gset0 [1 - e x p ( - t s d / t o ) ]
(22)
Equating (19) and (22) and dividing by equation (21) we obtain: Vo
AVs
G1
G1
to Go -
-
G1
[1 - e x p ( - t s / t o ) ] = [ e x p ( t s d / t o ) - 1] to
(23)
and: V0 - AVs = Go to [1 - e x p ( - t s / t o ) ] + G, to [ e x p ( t s d / t o ) - 1]
(24)
We can write t w o equations of the form of (24) for two hydrosoundings carried o u t with identical times ts b u t with different masses of added water (AVs, AVs') and, consequently, with various times for the beginning of preliminary discharge (t'sd , tsd). Subtracting one from the other and carrying out simple modifications, we obtain: 8 Vs = A Vs - A Vs' = G, to [exp ( t'sd /to ) - e x p ( t~d /to) ]
(25)
or:
~Vs/G, to = exp(t'sd/to) -
e x -
l.ll Pt~sd/to)
(26)
As far as GI is experimentally determined, equation (26) can be easily solved relative to to. Go can be found from (12) into which O, expressed in the terms of (26) has been substituted: Go
= G, exp(td/to)
-
8 Vsexp ( td /to ) t tt to [exp(tsd/to) - exp(tsd/to) ]
(27)
The other parameters of the system (G1, AVs, t'sd, ted) are determined directly from the hydrosounding experiments. It is easy to show that for other modifications of soundings we can obtain an equation analogous to equation (25) rela~tive to to if we suppose A Vs = constant and the time of the beginning of the sounding to be variable. Two
118
TABLE 2 The results of the hydrosounding experiments
Full free volume of the system after the eruption, V0 (liters)
Quathegey
Prince Buratino
180
180
Initial rate of discharge of water during preliminary overflow stage, G~ (kg/s)
0.08
0.4
Natural rate of inflow of hot water immediately after the eruption, G O (kg/s)
0.53
0.61
Hydraulic constant, t o (min)
6.7
Average enthalpy of inflowing hot water and steam, I* (kcal/kg)
164--174
Upper limit of steam pressure during the eruption (atm) Parameters of the critical condition (equation 9) A (kcal) I 0 (kcal/kg) M o (kg)
t
8.4
1570 131 67
tl
14.3 180--185 10.8
5500 137 6
t
It
different values of ts and ts will correspond to two values of tsd and tsd. The final equation in this case is: 1 +
vo G1 to
-
exp(t'sd/to) - exp(t'~d/to 1 ,
exp(-ts/to) - exp(-ts/to)
(28)
If we cannot determine V0 directly by means of filling of the free volume of the geyser because its volume is too large, we can calculate this value using equation (13) where to is found from equation (26) and Go from equation (27). The results of our experiments on hydrosounding of Quathegey and Prince Buratino geysers are summarized in Table 2. ACKNOWLEDGEMENTS
The authors are especially grateful to Donald E. White for constructive criticism and editorial advice. We wish to express our thanks to A.T. Naumenko and V.A. Nikolajenko from the Kronotski National Park for their support and help in carrying o u t the experiments, and also to L.J.P. Muffler, N. Nathenson, J. Rinehart and G.R. Robson for critical reviews and to Mrs. O.G. She,vchenko for help in preparing the manuscript. Derek Bostok made extensive editorial revisions of the text.
119
REFERENCES
Marler, G.D., 1969. The story of Old Faithful. Yellowstone Libr. Mus. Assoc. Yellowstone National Park, Wyo., p. 49. Marler, G.D. and White, D.E., 1975. Seismic Geyser and its bearing on the origin and evolution of geysers and hot springs of Yellowstone National Park. Bull. Geol. Soc. Am., 86: 749--759. Merzhanov, A.G., Steinberg, A.S. and Steinberg, G.S., 1978a. To the theory of geyser process. Modern Geol. (in press). Merzhanov, A.G., Steinberg, A.S. and Steinberg, G.S., 1978b. The laboratory model of the geyser. Modern Geology (in press). Merzhanov, A.G., Rasina, A.A., Steinberg, A.S., Steinberg, G.S. and Fundamenski, V.S., 1973. The study of geyser systems by the method of hydrosounding. Bull. Volcanol. Stn., 49 (in Russian). Rinehart, J.S., 1972. Fluctuation in geyser activity caused by variations in earth tidal forces, barometric pressure and tectonic stress. J. Geophys. Res., 77. Sorokin, Ju.L., 1963. A b o u t stability motion water-steam mixture in vertical tubes. J. Appl. Math. Tech. Phys., 6 (in Russian). Vukalovich, M.M. and Novikov, V.A., 1963. Technical Thermodynamics. Mashgiz, Moscow (in Russian). White, D., 1967. Some principles of geyser activity, mainly from Steamboat Springs, Nevada. Am. J. Sci., 265:.641--684. White, D.E., 1968. Hydrology, activity, and heat flow of the Steamboat Springs thermal system, Washoe County, Nevada. U.S. Geol. Surv. Prof. Paper, 458-C. White, D.E., Fournier, R.O., Muffler, L.J.P. and Truesdell, A.H., 1975. Physical results on research drilling in thermal areas of Yellowstone National Park, Wyoming. U.S. Geol. Surv. Prof. Paper, 892.