Jökull - 01.12.1987, Page 40

concentration of N2 in the parent hot water was taken to
be 0.71 mmoles/kg which corresponds to saturation in
water at 5°C in contact with the atmosphere (the mean
annual temperature in Krísuvík) using solubility data
from Weiss (1970). N2 saturation at 25°C gives the fol-
lowing expression:
t = 135.9 + 63.14 • Qcn +
6.241 • Qcn- - 1.813 • Qcn' (2a)
Equations (2) and (2a) can be used as a gas geother-
mometer. Steam condensation in the upflow, if it occurs
by conductive heat loss, does not affect the C02/N2 ratio
significantly unless well over 95% of the steam condens-
es. Therefore, discrepancy between the N2 c concentra-
tions according to equation (1) and the C02/N2 geother-
mometry estimates can be used to evaluate condensa-
tion in the upflow, if it is assumed that this condensation
occurs by conductive heat loss. For each C02/N2 temper-
ature there is a corresponding value for N2 c (see equa-
tion 1). From conservation of mass of nitrogen we have:
N| = N: m(l—Zc) (3)
and
Zc = (N: m - N: C)/N: m (3a)
where Zc is the fraction of steam which condensed (1—Zc
is, therefore, the remaining steam fraction), N2 m is the
measured N: concentration in the steam and equation
(1) defines N2 c. The temperature which is to be inserted
into equation (1) is derived from the CO:/N2 ratio (equa-
tion 2).
When steam condensation occurs by mixing with cold
water the situation is more complicated than is the case
with conductive heat loss. The cold water will contain
dissolved N2 that will be transferred to the remaining
steam and the N2 content of the initial steam will depend
on the temperature of the parent water as well as on the
temperature of the steam when the mixing occurs.
Fet us assume that condensation occurs by mixing
steam with cooler water under adiabatic conditions, that
the masses of H20, CO: and N: are conserved, that
negligible fraction of the CO: dissolves in the steam
heated water and that the cold water is quantitatively
degassed with respect to N:. Expressing the mass of
water and steam as fractions gives:
Xs, + Xw2 = 1
and
X,.f = xs„ - Xc. (5)
xw, = xw, + Xc (6)
for the steam and water phases, respectively. The sub-
scrips s and w note steam and water phases, respectively;
i and f indicate the initial and final mass fractions and Xc
is the mass fraction of steam of the total mass which
condenses. The fraction of steam which has condensed,
Zb, out of the initial steam fraction is thus defined as
zb = Xjxs, (7)
From conservation of heat, C02 and N2 we have:
hs • Xs, + hw • Xw, = hs • Xs, + hf • Xw, (8)
CO: c • Xs i = CO, m • Xs f (9)
N2.c • Xs, + N2 k • Xw, = N: m • Xs, (10)
h is the enthalpy of the steam and water phases. The
subscripts s, w, i and f have the same notation as in
equations (4) to (6); k indicates the N2 concentration in
the cold water and m indicates the measured gas concen-
tration in the steam; c designates calculated gas concen-
trations from equation (1) in the case of N2. For CO: the
CO: gas geothermometry function of Arnórsson and
Gunnlaugsson (1985) was used:
t = -44.1 + 269.25 • Qc - 76.88 • Qc2 + 9.52 • Qc3(U)
t is in °C and Qc = logCO: in mmoles/kg. From equa-
tions (4), (6) and (8) it is seen that C02 c = CO: m(l-Zb).
Combining equations (4) to (7) into equation (10) and
eliminiation of Xc, Xw, and Xs, yields:
XS,(N2, + N: m(l—Zb) - N: c) = N:, (12)
Similarly combination of equations (4) to (7) into equa-
tion (8) gives:
Xs,(Zb(hs-hf) + h, - hw) = h, - hw (13)
or
Zb = (N:.m - N2 c)/(N2 m + F) (14)
(4) where F = N2, • (hs—hf)/(hf—hw). If condensation of
100°C steam occurs in 5°C water and N2, = 0.71 mmoles/
kg (the amount of N2 dissolved in water at 5°C — the
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