Utilities Module¶

pygfunction.utilities.cardinal_point(direction)¶

pygfunction.utilities.erfint(x)¶

Integral of the error function.

Parameters

xfloat or array: Argument.

Returns

float or array: Integral of the error function.

pygfunction.utilities.exp1(x)¶

Exponential integral E1.

Parameters

xfloat or array: Argument.

Returns

E1float or array: Exponential integral.

References

1: Barry, D.A., Parlange, J.-Y. & Li, L. (2000). Approximation for the exponential integral (Theis well function). Journal of Hydrology, 227 (1-4): 287-291.

pygfunction.utilities.segment_ratios(nSegments, end_length_ratio=0.02)¶

Discretize a borehole into segments of different lengths using a geometrically expanding mesh from the provided end-length-ratio towards the middle of the borehole. Eskilson (1987) 2 proposed that segment lengths increase with a factor of sqrt(2) towards the middle of the borehole. Here, the expansion factor is inferred from the provided number of segments and end-length-ratio.

Parameters

nSegmentsint: Number of line segments along the borehole.
end_length_ratio: float, optional: The ratio of the height of the borehole that accounts for the end segment lengths. Default is 0.02.

Returns

segment_ratiosarray: The segment ratios along the borehole, from top to bottom.

References

2: Eskilson, P. (1987). Thermal analysis of heat extraction boreholes. PhD Thesis. University of Lund, Department of Mathematical Physics. Lund, Sweden.

Examples

>>> gt.utilities.segment_ratios(5)
array([0.02, 0.12, 0.72, 0.12, 0.02])

pygfunction.utilities.time_ClaessonJaved(dt, tmax, cells_per_level=5)¶

Build a time vector of expanding cell width following the method of Claesson and Javed 3.

Parameters

dtfloat: Simulation time step (in seconds).
tmaxfloat: Maximum simulation time (in seconds).
cells_per_levelint, optional: Number of time steps cells per level. Cell widths double every cells_per_level cells. Default is 5.

Returns

timearray: Time vector.

References

3: Claesson, J., & Javed, S. (2012). A load-aggregation method to calculate extraction temperatures of borehole heat exchangers. ASHRAE Transactions, 118 (1): 530-539.

Examples

>>> time = gt.utilities.time_ClaessonJaved(3600., 12*3600.)
array([3600.0, 7200.0, 10800.0, 14400.0, 18000.0, 25200.0, 32400.0,
       39600.0, 46800.0])

pygfunction.utilities.time_MarcottePasquier(dt, tmax, non_expanding_cells=48)¶

Build a time vector of expanding cell width following the method of Marcotte and Pasquier 4.

Parameters

dtfloat: Simulation time step (in seconds).
tmaxfloat: Maximum simulation time (in seconds).
non_expanding_cellsint, optional: Number of cells before geomteric expansion starts. Default is 48.

Returns

timearray: Time vector.

References

4: Marcotte, D., & Pasquier, P. (2008). Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems. Geothermics, 37: 651-665.

Examples

>>> time = gt.utilities.time_MarcottePasquier(3600., 13*3600.,
                                              non_expanding_cells=6)
array([3600., 7200., 10800., 14400., 18000., 21600., 28800., 43200.,
       72000.])

pygfunction.utilities.time_geometric(dt, tmax, Nt)¶

Build a time vector of geometrically expanding cell width.

Parameters

dtfloat: Simulation time step (in seconds).
tmaxfloat: Maximum simulation time (in seconds).
Ntint: Total number of time steps.

Returns

timearray: Time vector.

Examples

>>> time = gt.utilities.time_geometric(3600., 13*3600., 5)
array([3600., 8971.99474335, 16988.19683297, 28950.14002383, 46800.])