Heat Transfer Through the Wairakei‐Tauhara Geothermal System Quantified by Multi‐Channel Data Modeling

The problem

A geothermal well sited on a misinterpreted survey can encounter only dry, cool rock. Such a well costs about 10 million US dollars. Because geothermal reservoirs are buried, finding and characterising them relies on surveys made from above (Cumming, 2009). A reservoir is usually overlain by rock of low permeability, often clay formed where hot water has altered the rock. This clay cap separates hot reservoir fluid from cold groundwater near the surface. Its shape can constrain the models used to explore and manage a field.

Clay of this kind conducts electricity well. Magnetotelluric (MT) surveys are now the preferred way to map the resulting electrical structure (Johnston et al., 1992). However, conductive clays also form outside active hydrothermal systems. In the Taupō Volcanic Zone, ignimbrites held at low temperatures for a long time have altered to conductive clays and zeolites. This has led to misinterpretation of resistivity surveys (Bibby et al., 2005).

The Wairakei-Tauhara field lies on the northeast shore of Lake Taupō. Its heat output was previously estimated at about 530 MW from its chloride flux, the rate at which dissolved chloride flows out of the field (Bibby et al., 1995; Fisher, 1964). This method has large uncertainties. Our goal in this study was to map the clay cap across the field, test what temperatures it formed at, and estimate how much heat passes through it.

What we did

We used data from a 2010 MT survey of 250 stations (Sepulveda et al., 2012). At each station, a Bayesian inversion (Ardid et al., 2021) produced many three-layer models consistent with the data, with the middle layer limited to a resistivity of 1 to 5 ohm metres, typical of conductive clays. We also used methylene blue (MeB) tests on drill cuttings from 50 wells, which measure clay content (Gunderson et al., 2000). These gave starting ranges, or priors, for the depths of the top and bottom of the conductor. This is because MT data alone resolve the lower boundary poorly.

Next, we read temperatures at the top and bottom of the cap from logs in 122 wells. Finally, we fitted a one-dimensional model of heat conduction plus upward water flow (Bredehoeft and Papadopulos, 1965) to each well's temperatures within the cap.

What we found

In the centre of the field, the clay cap largely follows the Huka Falls Formation, a sequence of low-permeability lake sediments. The cap averages about 316 m thick. Across the 4 km of the main upflow, its top and bottom roughly follow the 100°C and 180 to 200°C isotherms. However, outside the upflow the 180°C isotherm dips more steeply than the clay.

Temperatures at the top and bottom of the cap averaged 58°C and 199°C. This is consistent with the 50 to 200°C range over which smectite clays form (Browne, 1978). However, the ranges containing 95% of the values were about 20 to 120°C at the top and 130 to 250°C at the bottom. We therefore caution against inferring temperature from clay alone, particularly where no well confirms the clay.

At Aratiatia Flats, MT shows a conductor deeper than 400 m outside the usual field boundary. Wells there are cold, and the conductor lies in the Wairakei ignimbrite. We suggest it formed by diagenesis, slow alteration at low temperature.

Using a typical thermal conductivity of 2.2 W/m/°C, the median temperature gradient through the cap of 476°C/km corresponds to a conductive heat flux of about 1.05 W/m². Summed over the field, conduction accounts for 153 ± 18 MW.

In the model, faster upflow of hot water steepens the temperature gradient near the top of the cap and flattens it below. In a calculation of our own, not reported in the paper, a value of about 1.6 for β, a number comparing heat carried by rising water with heat conducted through rock, doubles the heat flux at the top and raises the temperature halfway down the cap from 129°C to 155°C. Fitted to the wells, conduction plus upflow gives a median heat flux of 2.15 W/m², or a total of 380 ± 21 MW when summed over the field. The fits imply water rising through the cap at roughly 53 mm a year, with a 95% range of about 4 to 230 mm.

We interpret 380 MW as a lower bound on the heat output of the system. This is because it omits heat that leaves the reservoir sideways beneath the cap, or through narrow permeable paths that wells have not sampled (Hunt et al., 2009). For scale, 380 MW is the output of about 190,000 two-kilowatt heaters running continuously. The earlier estimate of 530 MW is about 40% higher than ours. The difference may arise because our estimate is a lower bound and because chloride-based estimates have uncertainties of about 25% (Bibby et al., 1995).

Limitations

Our model assumes that temperatures in the cap are still those of the natural state before development began in the 1950s. About 60 years of production and reinjection have probably disturbed temperatures, particularly in the reservoir below. By conduction alone, such a disturbance would reach about 43 m into the cap, or 14% of its average thickness. We therefore expect its effect on our heat fluxes to be second-order at most.

The one-dimensional model gives only an average flow rate for each well, and the conductive estimate ignores variations in rock properties. In early exploration, before MT and temperature data exist, chloride-based methods may still be preferred.

Glossary

A geothermal reservoir is a body of permeable rock holding hot water that can be produced through wells.

The clay cap is a layer of low-permeability clay, formed by hot water altering rock, that overlies a geothermal reservoir.

Permeability is a measure of how easily water flows through rock.

Magnetotellurics (MT) is a surface electromagnetic survey that estimates how electrical resistivity varies with depth.

Methylene blue (MeB) is a dye whose uptake by drill cuttings measures their content of conductive clay.

A Bayesian inversion returns a range of models consistent with both the data and prior information.

Smectite is a clay mineral, formed by hot water at about 50 to 200°C, that conducts electricity well.

An ignimbrite is a rock formed from the deposits of an explosive volcanic eruption.

Diagenesis is the slow alteration of rock at low temperature after it is deposited.

An isotherm is a line joining points of equal temperature.

Resistivity is how strongly a material resists an electric current, measured in ohm metres. A low resistivity marks a good electrical conductor.

The upflow is the zone where hot water rises from the reservoir towards the surface.

Heat flux is the rate of heat flow through a unit area, in watts per square metre (W/m²). Summed over an area it gives heat flow in megawatts (MW).

Zeolites are minerals formed when volcanic rock is altered by water at low temperature.

A prior is the range of values a parameter is allowed to take before the data are considered.