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Short-term correction using the cylindrical heat source

Open MassimoCimmino opened this issue 5 years ago • 4 comments

This issue concerns the implementation of the infinite line source and cylindrical heat source solutions to correct the short-term response of geothermal bore fields.

MassimoCimmino avatar Dec 10 '19 15:12 MassimoCimmino

Is this something that could be implemented as a method? I saw this issue and it reminded me of this piece of code from our previous works

def shortTermCorrection(time, gFunc, r_b, aSoi):
    
    def _CHS(u, Fo, p):
        CHS_integrand = 1./(u**2*pi**2)*(np.exp(-u**2*Fo) - 1.0) / (j1(u)**2 + y1(u)**2) * (j0(p*u)*y1(u) - j1(u)*y0(p*2))
        return CHS_integrand
    
    def _ILS(t, aSoi, dis):
        ILS = exp1(dis**2/(4*aSoi*t))
        return ILS
    
    for i in range(len(time)):
        ILS = _ILS(time[i], aSoi, r_b)
        CHS, err = quad(
            _CHS, 1e-12, 100., args=(aSoi*time[i]/r_b**2, 1.))
        gFunc[i] = gFunc[i] + 2*pi*CHS - 0.5*ILS

    return gFunc

icupeiro avatar Feb 19 '21 09:02 icupeiro

I tend to remember that the code presently in the branch issue44 is indeed from our previous work.

The development of the common interface for #33 will be a good opportunity to re-implement this into a method for the (still in development) g-function class.

MassimoCimmino avatar Feb 20 '21 19:02 MassimoCimmino

Could the MIFT solution be applied to short-time steps, or is it still not applicable until the breaking time, t_b = 5*r_b**2/alpha?

Is there a specific reference that is going to be utilized to address this issue?

j-c-cook avatar Nov 12 '21 02:11 j-c-cook

The validity range of the MIFT solution is the same as for the uniform temperature condition. The breaking time t_b is related to the difference between heat emitted by a line source (at the center of the borehole) and heat emitted at the borehole wall. It is an estimation of the time it takes for the two source geometries to have matching temperatures at r=r_b.

The methodology in the above comments is inspired by Li et al. (2014) [1].

There is a distinction to make on the validity range of the g-function between the prediction of borehole wall temperatures (T_b) due to heat extracted at the borehole wall (Q_b), and the prediction of fluid temperatures (T_f) due to heat extracted from the fluid loop (Q_f). The correction using the CHS applies to the first case. The second case requires some transient heat transfer model for the inside of the boreholes.


[1] Li, M., Li, P., Chan, V. and Lai, A.C., 2014. Full-scale temperature response function (G-function) for heat transfer by borehole ground heat exchangers (GHEs) from sub-hour to decades. Applied Energy, 136, pp.197-205.

MassimoCimmino avatar Nov 12 '21 14:11 MassimoCimmino