The document describes a method for optimizing the placement of separators and routes for two-phase geothermal fluid pipelines between well sites and separators. It uses weighted variable topography distance transforms to account for terrain constraints and find the shortest pipeline routes. The transforms are applied to find the optimum placement of separators that minimize the total pipeline length between wells. The results demonstrate how the method facilitates optimal route design and placement of separators and power plants.

1. Optimizing placement of separators using weighted
virtual topography distance transfrom
Magnús Þór Jónsson and Lilja Magnúsdóttir
Harrison Kiplimo Keter and Daniel Wanga Odongo
GEORG Geothermal Workshop 2016 – Reykjavik, Iceland 1

2. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Outline:
- Introduction
- Digital Elevation Map DEM
- Distance Transform (DT – VTDT - MWDT)
- Route Selection – Optimum Placement
- Conclusion
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3. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Introduction
Objective:
To find the optimum placement of the separator station and the
optimum routes for the two phase flow pipelines from each
well site to the separator station.
The objective function
includes the capital
investment and the
operational cost.
The constraints are the landscape, steam and water velocity
and the upward slope of the two phase flow pipelines.
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4. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Introduction
Motivation:
The location of the well platforms is based on geological and
hydrological surveys and they are scattered around the
reservoir area often with long distances between sites.
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5. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Digital Elevation Map
Contour Map Digital Elevation Map
DEM Resolution: 1 m
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6. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Distance Transform
Chamfer mask
The central function in a distance
transfer algorithm is the following
(Bellman’s equation):
Value at central point
Value at the cell
Local distance, mask
Distance Transform DT
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7. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Distance Transform:
Distance Transform DT
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8. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Variable Topography Distance Transform VTDT
The gradient constraint is implemented :
Distance Transform VTDT
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The critical values of height difference, Δ𝐻 𝑐 and slope,
𝛼 𝑐 , are user defined.
A DEM is a 2-D matrix where each element 𝐻𝑖𝑗, represents
the height in the corresponding surface location (𝑖, 𝑗).

9. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Variable Topography Distance Transform VTDT
Distance Transform VTDT
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10. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Multiple Weight Distance Transforms (MWDT)
An algorithm that utilizes many distance transforms, each
with weighted distance to relative importance:
The MWDT matrix becomes,
D = ∑k wk DTi{Ak}
where DTi{Ak} is a distance transform of type i to an
object set {Ak} and wk is the weight factor.
Shortest route from End (E) points to Sample (S) points
and optimum placement of the sample point.
Distance Transform MWDT
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11. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Route Selection
Multiple Weight Distance Map
Pipe routes from wells (E)
to a separator (S)
with shortest length.
No access is through
the white area with a
monotonic pipeline,
considering all wells.
Total length of the pipe
system is 10301 m.
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12. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Route Selection
Multiple Weight Distance Map – Optimum Location
Route selection for an
optimum location of the
separator based on
weighted variable
topography distance
transform.
Total length of the
pipe system is 9864 m.
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13. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Route Selection
Multiple Weight Distance Map – Optimum Location
Pipe routes from separators (E)
to a power plant (S) based
on weighted variable
topography distance
transform.
Optimum location of the
Power Plant
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14. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Conclustion
Summary:
The results shows how the Multiple Weight Distance
Transform method can facilitate the route design process
for pipes carrying two-phase geothermal fluid.
Results show how the method can be used for optimum
placement of separators and power plant site
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15. GEORG Geothermal Workshop 2016 – Reykjavik, Iceland
Conclustion
Thank you!
Questions?
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