Jökull - 01.12.1966, Page 32

for the discrepancy in the vapour data is not
known with certainty, but it is believed that
there are two contributing causes.
(a) There is a failure to attain complete se-
paration and some entrained and subdivid-
ed liquid is being discharged through the
vapour orifices. The entrained liquid in-
creases the flow resistance and the pressure
drop through the orifice.
(b) The pressure ratio across tlie orifices for
large well-head valve openings was smaller
than is usually recommended and approach-
ed the critical value. Compressibility factors
are not available for low pressure ratios,
and values were obtained by linear extra-
polation of the curve of existing values.
It is believed that minor modifications to
this plant would rnake its performance more
accurate, but in view of its great size and
weight, the question arises as to whether a
simpler rnethod of flow assessment might not
be devised.
Summing up, therefore, one may say that the
flow measurement methods used to date both
in Iceland and New Zealand are based mainly
on traditional and well-tried ideas. In view,
however, of the great efflux quantities to be
handled and the inconvenience of orthodox
plants, an accurate simplified method of flow
prediction would be welcome. The most promis-
ing approach would seem to be one which
exploits recently acquired knowledge concern-
ing the manner of association of the phases
within the flow.
THE PRESENT STATUS OF TWO-PHASE
CRITICAL ELOW STUDIES
The present decade has seen an intense and
widespread research effort directed towards
understanding the flow behaviour of water/
steam mixture in pipes. Much of this work has
been on vertical upward flow and has been
directed towards the understanding of heat
transfer, critical flow and “burn-out” pheno-
mena in the context of the nuclear reactor. In
many cases attention has been focussed upon
the exit regime in the flow from the open ends
of a cyclindrical pipe. Is has been found, as
in the case of a perfect gas, that if the back
pressure is progressively lowered, the mixed
flow attains a maximum discharge at a given
pressure ratio, and becomes independent of the
back pressure for smaller values of this ratio.
The conditions governing this critical flow are
much more complex than those operative in
the single phase perfect gas case, and depend,
among other things, upon the physical mode
of association between the liquid and the
vapour as the exit is approached and passed.
Investigators have observed and classified a
number of modes of association ("models”) be-
tween the phases. Briefly they comprise bubble
flow, slug flow, annular flow, annular flow
with core entrainment and mist. flow, the list
being in order of increasing dryness fraction.
It is clear that laboratory studies made of two-
phase critical flow from open-ended vertical
ducts are applicable to the geothermal well,
since it is readily possible to surmount any
bore by a straight vertical extension pipe. It
is also tempting to entertain the possibilitv that,
in such case, suitable measurements, e.g. bore
diameter, static pressure profile at exit and
base temperature in the hydrothermal flow,
might enable the mass discharge to be found
directly. In such a case, flow measurement from
a given well would merelv necessitate the trans-
port, fitting and use of a portable “instrument
pipe extension”.
APPLICATION OF TWO-PHASE
CRITICAL FLOW STUDIES
TO THE GEOTHERMAL WELL
(a) Flow Regime
There is as yet no unanimity concerning the
groups of physical factors which promote a
given type of phase association. A number of
investigators have, however, suggested flow pat-
tern diagrams. Two such may be mentioned
here; those due respectively to Kozlov (1954)
and Baker (1954). Kozlov plotted the instant-
aneous volumetric dryness fraction (“void frac-
tion”), xv, against the Froude Number Fr =
Vm2/gD where Vm is the effective homogeneous
equilibriunr mixture velocity, and D is the pipe
diameter. On the basis of experimental results
available for slug flow he divided the diagram
into regions defining slug flow, bubble flow
and annular/mist flow.
Baker presented a much nrore sophisticated
186 JÖKULL