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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

3

“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

4

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?

7

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 ++′′−=

13

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

29

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.

32

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)”

35

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…”

36

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)

37

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