Abstract
We have developed a method and computational algorithms for implementing the method, which can generate unstructured Voronoi grids for its use in TOUGH2 simulations of geothermal heat pump systems. An adaptive gridding technique, known as Voronoi tessellation, not only is flexible to include detailed shapes of the cross-sections of pipes at any position inside the geothermal wells, but also always satisfies the orthogonal condition of the TOUGH2 grid, which is that connections between two adjacent grid blocks in a TOUGH2 grid should be orthogonal to their connection interface. A series of newly developed or already existing codes are used to create Voronoi seeds that are placed at specific positions for the geothermal wells, to calculate the x- and y-coordinates of the Voronoi vertices from the Voronoi seeds, to generate 3-D grids and TOUGH2 input files from Voronoi vertices, and to visualize the generated grid and simulation results with ParaView. We show the desired form of the grid generated from the developed method and computational algorithm and perform an example simulation to demonstrate the use of the developed grid that includes four different kinds of geothermal well systems.
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References
Alcott, A., Swenson, D., and Hardeman, B., 2006, Using PetraSim to create, execute, and post-process TOUGH2 models. TOUGH Symposium 2006, Berkeley, May 15–17, p. 1–6.
Aurenhammer, F. and Klein, R., 2000, Voronoi diagrams. Handbook of computational geometry, 5, 201–290.
Berry, P., Bonduá, S., Bortolotti, V., Cormio, C., and Vasini, E.M., 2014, A GIS-based open source pre-processor for georesources numerical modeling. Environmental Modelling and Software, 62, 52–64.
Croucher, A.E. and O’sullivan, M.J., 2013, Approaches to local grid refinement in TOUGH2 models. 35th New Zealand Geothermal Workshop, Rotorua, Nov. 17–20, p. 1–7.
Dirichlet, L.G., 1850, Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. Journal für die Reine und Angewandte Mathematik, 40, 209–227.
Du, Q., Faber, V., and Gunzburger, M., 1999, Centroidal Voronoi tessellations: applications and algorithms. Society for Industrial and Applied Mathematics review, 41, 637–676.
Edwards, A.L., 1972, TRUMP: A computer program for transient and steady state temperature distributions in multidimensional systems. National Technical Information Service, Springfield, 259 p.
Fortune, S., 1987, A sweepline algorithm for Voronoi diagrams. Algorithmica, 2, 153–174.
Freeman, C.M., Boyle, K.L., Reagan, M., Johnson, J., Rycroft, C., and Moridis, G.J., 2014, MeshVoro: A three-dimensional Voronoi mesh building tool for the TOUGH family of codes. Computers and Geosciences, 70, 26–34.
Green, P. and Sibson, R., 1978, Computing Dirichlet tessellations in the plane. The Computer Journal, 21, 168–173.
Haukwa, C., 1998, AMESH A mesh creating program for the integrated finite difference method: A User’s Manual. Lawrence Berkeley National Laboratory, Berkeley, 54 p.
Kim, S.K., Bae, G.O., Lee, K.K., and Song, Y., 2010, Field-scale evaluation of the design of borehole heat exchangers for the use of shallow geothermal energy. Energy, 35, 491–500.
Narasimhan, T.N. and Witherspoon, P.A., 1976, An integrated finite difference method for analyzing fluid flow in porous media. Water Resources Research, 12, 57–64.
Palagi, C.L. and Aziz, K., 1994, Use of Voronoi grid in reservoir simulation. Society of Petroleum Engineers Advanced Technology Series, 2, 69–77.
Pan, L., 2003, Wingridder - an interactive grid generator for TOUGH2. TOUGH Symposium 2003, Berkeley, May 12–14, p. 1–7.
Persson, P.O. and Strang, G., 2004, A simple mesh generator in MATLAB. Society for Industrial and Applied Mathematics review, 46, 329–345.
Pruess, K., 2004, The TOUGH codes - a family of simulation tools for multiphase flow and transport processes in permeable media. Vadose Zone Journal, 3, 738–746.
Pruess, K., Oldenburg, C.M., and Moridis, G.J., 1999, TOUGH2 User’s Guide Version 2. Lawrence Berkeley National Laboratory, Berkeley, 197 p.
Sieger, D., Alliez, P., and Botsch, M., 2010, Optimizing voronoi diagrams for polygonal finite element computations. Proceedings of the 19th international meshing roundtable, Chattanooga, Oct. 3–6, p. 335–350.
Verma, S. and Aziz, K., 1996, Two-and three-dimensional flexible grids for reservoir simulation. 5th European Conference on the Mathematics of Oil Recovery, Leoben, Sep. 3–6, p. 143–156.
Voronoi, G., 1908, Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Journal für die Reine und Angewandte Mathematik. 133, 97–178.
Weatherill, N.P., 1988, A method for generating irregular computational grids in multiply connected planar domains. International Journal for Numerical Methods in Fluids, 8, 181–197.
Xu, T., Spycher, N., Sonnenthal, E., Zhang, G., Zheng, L., and Pruess, K., 2011, TOUGHREACT Version 2.0: A simulator for subsurface reactive transport under non-isothermal multiphase flow conditions. Computers & Geosciences, 37, 763–774.
Zhang, K., Wu, Y.S., and Pruess, K., 2008, User’s guide for TOUGH2-MP - a massively parallel version of the TOUGH2 code. Lawrence Berkeley National Laboratory, Berkeley, 108 p.
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Kim, SK., Bae, GO. & Lee, KK. Improving accuracy and flexibility of numerical simulation of geothermal heat pump systems using Voronoi grid refinement approach. Geosci J 19, 527–535 (2015). https://doi.org/10.1007/s12303-014-0061-3
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DOI: https://doi.org/10.1007/s12303-014-0061-3