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

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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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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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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GEORG Geothermal Workshop 2016 – Reykjavik, Iceland

Digital Elevation Map

Contour Map Digital Elevation MapDEM Resolution: 1 m

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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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GEORG Geothermal Workshop 2016 – Reykjavik, Iceland

Distance Transform:

Distance Transform DT

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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, and slope, , are user defined.

A DEM is a 2-D matrix where each element , represents the height in the corresponding surface location

GEORG Geothermal Workshop 2016 – Reykjavik, Iceland

Variable Topography Distance Transform VTDT

Distance Transform VTDT

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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) pointsand optimum placement of the sample point.

Distance Transform MWDT

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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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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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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 thePower Plant

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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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GEORG Geothermal Workshop 2016 – Reykjavik, Iceland

Conclustion

Thank you!

Questions?

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