GENG4405 2019 – Assignment 2, Part 1
Flash geothermal power plants work in the following manner:
Liquid water exists in a high temperature reservoir, underground. The water is a saturated liquid or a subcooled liquid close to its saturation temperate and is under ~hydrostatic pressure.
By drilling into the reservoir and pumping, that water can be brought to the surface, still at high pressure. Some pressure drop and consequently phase separation (i.e. flashing) is necessary. Increased pressure drop (that is to say, lower wellhead pressure) usually leads to an increase in flowrate.
The water moves through insulated pipes along the surface from the wellhead to the powerhouse where it goes into a “separator” here the saturated vapor is separated from the saturated liquid.
The steam from the separator goes in to the turbine to generate power and then is condensed, usually in a water-cooled condenser.
The liquid from the separator can either be disposed of by reinjection to the reservoir through an injection well or flashed again at a lower pressure in a second separator, with the steam being fed to a second, low pressure turbine.
Australia has the wrong geology for such power plants but they are common in New Zealand, Indonesia and the Philippines and there is significant potential on New Guinea.
Part 1 of the Assignment: How big is the reservoir?
A layer of highly permeable rock has been identified. Primarily geophysical measurements have led to a network of points, spaced at 500 meter intervals, at which the depth to the top and bottom of the reservoir are approximately known. The data has been passed to your team (as an Excel spread sheet) with the expectation that you’ll be able to estimate the volume of the reservoir. The data consists of the elevation above sea level of the surface of the ground at the point where each measurement was made, the depth below the surface at which the top of the reservoir was detected and the depth below the surface at which the bottom of the reservoir was detected. The measurements were made by seismic reflectance and it’s known that this form of measurement has trouble distinguishing between layers that aren’t at least 10 meters apart.
A geologist has also looked at the data and she notes that the permeable layer appears to have filled in an ancient valley; the base rock has much lower permeability than the reservoir. After deposition the permeable layer was covered by another impermeable layer. The reservoir runs approximately along a north-south axis. Faulting has (conveniently) truncated the reservoir just
south of the first row of data and just north of the ninth row. Less conveniently it appears that the ancient valley branched at the northern end and part of the lesser branch falls outside the grid of data. The geologist has also drawn her interpretation of the shape of the reservoir (fig. 1).
Fig. 1 – Geologist’s interpretation of the shape of the reservoir
Assignment questions:
1. (5%) Write MATLAB code to estimate the reservoir volume via the trapezoid rule
2. (10%) Write MATLAB code to estimate the reservoir volume via Simpson’s rule
3. (15%) Write MATLAB code to estimate the reservoir volume by first creating an interpolating polynomial for each row (you may use more than one function for the rows at the top), then use Gaussian quadrature with a sufficient number of points to exactly match the interpolating polynomial. Integrate between the rows (the north-south direction) using any method you like
This is a case where there is a lot of uncertainty. Some of reservoir appears to fall outside the data grid and some of the data falls within the uncertainty limits of the measurement method (that is the difference in depths is less than 10 meters). Use your best judgement. If you need to interpolate for additional points or even guess at the value at certain points, that’s not necessarily wrong. Because of the degree of uncertainty, there is no canonically correct answer however any assumptions you make must be stated and justified.
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