Geothermal reservoir modelling: sustainability
and renewability
Mike O’Sullivan, Engineering Science
University of Auckland, New Zealand
2
Basic ideas on sustainability of geothermal projects
The amount of thermal energy extracted in most
(perhaps all) geothermal projects compared with
the natural through-flow of energy is large.
Therefore “heat mining” is going on and the
projects are not indefinitely sustainable
But if the projects are shut down, then after
sometime the geothermal systems will return to
close to their pre-exploitation state
I will illustrate these ideas by using Wairakei as
an example
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“Production ratio”
I like to talk about the “production ratio,” or PR,
defined as follows:
PR = (produced energy flow)/(natural energy flow)
For Wairakei the natural energy flow was
estimated by Allis to be ~400MWth. The current
take is ~1900MWth giving a PR for Wairakei of
4.75
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Taupo Volcanic Zone (New Zealand)
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History of Wairakei
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The issues for Wairakei
Computer modeling studies show that the
present rate of steam production at Wairakei-
Tauhara can be sustained for at least fifty years
But questions arise as to what happens after
that:
(i) How long will it take for Wairakei-Tauhara to
fully recover to its original state after shut-down
at sometime in the future?
(ii) What changes will occur during the recovery
process?
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Approaches to resolving the issues about Wairakei
Simple lumped parameter model
Large, complex, 3D computer model
More details in 2010 paper: Geothermics, 39(4),
314-320.
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Lumped parameter model
Geothermal system
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A convective geothermal system
heat
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Energy balance for lumped parameter model
Natural state
During exploitation.
deepsurf QQ =
rechdeepsurfprodextr QQQQQ −−′+=
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Approximate energy balance equation
Assume heat flow at surface is small after
exploitation begins
Assume extra recharge is small
If deep induced recharge is included as a
fraction f of the original deep upflow then
deepdeepprodextr QPRQQQ )1( −≈−≈
deeprechdeepprodextr QfPRQQQQ )1( −−≈−−≈
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Recovery
If after a time, the power plant is shut down, thenatural energy flow will slowly replenish thegeothermal system and it will again be availablefor production.
The rate of energy recovery will be given by:
rechdeepsurfreco QQQQ ++′′−=
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Recovery (continued)
Again if we assume that the surface flow and
the induced recharge are small and can be
ignored then
Now we can balance the total heat extracted with
the total heat recovered to determine the
recovery time
deepreco QQ ≈
extrextrrecoreco tQtQ ≈
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Recovery (continued)
Here trecov is the recovery time and t extr is the
duration of past production
Some rearrangement gives
For Wairakei (PR=4.75) this means that 100
years of production will require 375 years of
recovery
extrreco tPRt )1( −≈
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3D model of Wairakei
Wairakei
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Model grid
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More recent model grid
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Pressure response at Wairakei
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Comments on pressures
The rapid decline in pressure after production
began in 1953 is clearly shown
A rapid pressure recovery is predicted after shut-
down in 2053.
Most of the current production is from the
Western borefield and Te Mihi, but after shut-
down the pressure recovery is very rapid in both
the Western and Eastern borefields.
This is a consequence of the high permeabilities
in the Wairakei-Tauhara system.
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Temperature response
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Comments on temperatures
The temperature plot shows a slower decline
followed by the expected slower recovery than
for pressure.
The recovery is slower in the Eastern borefield,
which is further away from the deep recharge.
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Temperatures on slice AA
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Comments on temperature profiles
The 2006 temperatures show the effects of the
gradual “mining” of heat during the production
phase.
The temperatures in the Eastern borefield area
have declined significantly between 1953 and
2006. This effect is confirmed by field data.
Similarly, the temperatures in the Western
borefield and Te Mihi have declined.
The plot shows that further mining of heat from
the top of the upflow plume will occur by 2056.
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Comments on temperature profiles (continued)
After shut-down the slow recovery begins; and
by 2156 the hot plume has started to rise in the
Western Borefield and Te Mihi.
This process has proceeded further by 2256
when some recovery in the Eastern Borefield
can be seen.
After an additional 200 years, by 2456, the
system has almost recovered to its pre-
production state
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Boiling
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Comments on boiling
There was only a low level of boiling in the pre-
production state in 1953
But there was a large expansion of the boiling
zone during production up to 2006
The slow cooling of the system between 2006
and 2056 causes the boiling zone to contract
slightly although pressures continue to fall
slowly.
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Comments on boiling (continued)
The pressure build-up after shut-down causes
the rapid collapse of the steam zone.
By 2156, there is very little boiling
However, a very slow return of a very low level of
shallow boiling occurs by 2256 and increases
further by 2456
The boiling zone has still not returned to the
natural state conditions by 2456.
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Vapor saturation vs. time for two steam zone blocks
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Surface mass and heat flows at Geyser Valley
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Comments on heat and mass flows
These plots show the rapid decline of activity at
Geyser valley resulting from production (as was
observed)
There is a rapid return of surface flows after field
shut-down.
However, the surface flows at Geyser Valley
after 2053 will be initially cool and it will take a
long time for the original thermal activity to re-
develop.
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Conclusions from 3D modelling
The model results show that the pressure at
Wairakei will recover very fast - on a time scale
of years.
But the temperature recovery will be much
slower, occurring on a time scale of centuries.
Thus, Wairakei is indefinitely sustainable on a
cycle of 100 years of production (at 170MWe)
followed by ~400 years of recovery.
Whether this strategy is optimal is an interesting
question that is left to a future study.
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Parameters for several geothermal systems
Name Type Area (km2)
Natural heat flow (MW)
Heat flux
(W/m2)
Electricity Production
(MW)
Production heat flow
(MW)
PR Recovery time
(years)
East Mesa Hot water 215 32 0.149 50 2000 63 6200
Wairakei-Tauhara
Liquid-dominated2-phase
30 400 13.3 190 1900 4.8 380
Darajat Vapour-dominated2-phase
16 80 5.0 150 1500 19 1800
Cooper Basin
EGS (hotdry rock)
40 4.2 0.105 280 5600 1300 130000
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Observations from similar studies
Pritchett (1998):
“Accordingly, it seems reasonable to conclude
that geothermal systems which have been
thermally depleted in this way will not recover
after abandonment on time-scales comparable to
lifetimes of typical electrical power development
projects. They will, however, recover on time-
scales typical of lifetimes of civilizations”
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Observations from similar studies (continued)
Rybach et al.:
“the recuperation period equals nearly the
operation period”.
“(T)hus, geothermal resources can be
considered renewable on time-scales of
technological/societal systems and do not need
geological times as fossil fuel reserves do (coal,
oil, gas)”
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Observations from similar studies (continued)
Stefansson:
“… that the natural recharge of energy to most
natural geothermal systems takes place on a
similar time-scale as the exploitation of these
resources…”
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Analysis of the Pritchett model
A generic geothermal reservoir
High permeability upflow leading into a reservoir
zone with horizontal and vertical permeability of
10 md
Natural state inflows are 100kg/s and 133MWth
(330oC water)
The reservoir was produced for 50 years at an
average rate of 60MWe.
This corresponds to 166.7kg/s of separated
steam (5.5bars well head pressure)
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Analysis of the Pritchett model (continued)
Pritchett does not provide the average fluid
enthalpy, but if we use a typical value from
Wairakei of 1150kJ/kg then the total mass flow is
708kg/s and the energy flow is 814MWth
This gives a PR value of 6.1
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Analysis of the Pritchett model (continued)
After production ceased at 50 years, Pritchett ran
his model for a further 1000 years and calculated
a 90% energy recovery at this time
He also gave a 57.9% energy recovery at 250
years
Using my formula, with a PR=6.1, gives a
recovery time of 255 years which is of the right
order of magnitude