absorption_chillers.rst

Absorption chiller

Calculations for absorption chillers based on the characteristic equation method.

Scope

This module was developed to provide cooling capacity and COP calculations based on temperatures for energy system optimizations with oemof.solph.

Concept

A characteristic equation model to describe the performance of absorption chillers.

Fig.1: Absorption cooling (or heating) process.

The cooling capacity (Q̇_E) is determined by a function of the characteristic temperature difference (ΔΔt′) that combines the external mean temperatures of the heat exchangers.

Various approaches of the characteristic equation method exists. Here we use the approach described by Kühn and Ziegler [1]:

ΔΔt′ = t_G − a ⋅ t_AC + e ⋅ t_E

with the assumption

t_A = t_C = t_AC

where t is the external mean fluid temperature of the heat exchangers (G: Generator, AC: Absorber and Condenser, E: Evaporator) and a and e are characteristic parameters.

The cooling capacity (Q̇_E) and the driving heat (Q̇_G) can be expressed as linear functions of ΔΔt′:

Q̇_E = s_E ⋅ ΔΔt′ + r_E

Q̇_G = s_G ⋅ ΔΔt′ + r_G

with the characteristic parameters s_E, r_E, s_G, and r_G.

The COP can then be calculated from Q̇_E and Q̇_G:

$$COP = \frac{\dot{Q}_{E}}{\dot{Q}_{G}}$$

These arguments are used in the formulas of the function:

symbol	argument	explanation
ΔΔt′	:pyddt	Characteristic temperature difference
tG	:pyt_hot	External mean fluid temperature of generator
tAC	:pyt_cool	External mean fluid temperature of absorber and condenser
tE	:pyt_chill	External mean fluid temperature of evaporator
a	:pycoef_a	Characteristic parameter
e	:pycoef_e	Characteristic parameter
s	:pycoef_s	Characteristic parameter
r	:pycoef_r	Characteristic parameter
Q̇	:pyQ_dots	Heat flux
Q̇E	:pyQ_dots_evap	Cooling capacity (heat flux at evaporator)
Q̇G	:pyQ_dots_gen	Driving heat (heat flux at generator)
COP	:pyCOP	Coefficient of performance

Usage

The following example shows how to calculate the COP of a small absorption chiller. The characteristic coefficients used in this examples belong to a 10 kW absorption chiller developed and tested at the Technische Universität Berlin [1].

import oemof.thermal.absorption_heatpumps_and_chillers as abs_chiller

# Characteristic temperature difference
ddt = abs_chiller.calc_characteristic_temp(
    t_hot=[85],  # in °C
    t_cool=[26],  # in °C
    t_chill=[15],  # in °C
    coef_a=10,
    coef_e=2.5,
    method='kuehn_and_ziegler')

# Cooling capacity
Q_dots_evap = abs_chiller.calc_heat_flux(
    ddts=ddt,
    coef_s=0.42,
    coef_r=0.9,
    method='kuehn_and_ziegler')

# Driving heat
Q_dots_gen = abs_chiller.calc_heat_flux(
    ddts=ddt,
    coef_s=0.51,
    coef_r=2,
    method='kuehn_and_ziegler')

COPs = Q_dots_evap / Q_dots_gen

Fig.2 illustrates how the cooling capacity and the COP of an absorption chiller (here the 10 kW absorption chiller mentioned above) depend on the cooling water temperature, i.e. the mean external fluid temperature at absorber and condenser.

Fig.2: Dependency of the cooling capacity and the COP of a 10 kW absorption chiller on the cooling water temperature.

You find the code that is behind Fig.2 in our examples: https://github.com/oemof/oemof-thermal/tree/master/examples

You can run the calculations for any other absorption heat pump or chiller by entering the specific parameters (a, e, s, r) belonging to that specific machine. The specific parameters are determined by a numerical fit of the four parameters with testing data or data from the fact sheet (technical specifications from the manufacturer) if temperatures for at least two points of operation are given. You find detailed information in the referenced papers.

This package comes with characteristic parameters for five absorption chillers. Four published by Puig-Arnavat et al. [3]: 'Rotartica', 'Safarik', 'Broad_01' and 'Broad_02' and one published by Kühn and Ziegler [1]: 'Kuehn'. If you like to contribute parameters for other machines, please feel free to contact us or to contribute directly via github.

To model one of the machines provided by this package you can adapt the code above in the following way.

import oemof.thermal.absorption_heatpumps_and_chillers as abs_chiller
import pandas as pd
import os

filename_charpara = os.path.join(os.path.dirname(__file__), 'data/characteristic_parameters.csv')
charpara = pd.read_csv(filename_charpara)

chiller_name = 'Kuehn'  # 'Rotartica', 'Safarik', 'Broad_01', 'Broad_02'

 # Characteristic temperature difference
ddt = abs_chiller.calc_characteristic_temp(
    t_hot=[85],  # in °C
    t_cool=[26],  # in °C
    t_chill=[15],  # in °C
    coef_a=charpara[(charpara['name'] == chiller_name)]['a'].values[0],
    coef_e=charpara[(charpara['name'] == chiller_name)]['e'].values[0],
    method='kuehn_and_ziegler')

# Cooling capacity
Q_dots_evap = abs_chiller.calc_heat_flux(
    ddts=ddt,
    coef_s=charpara[(charpara['name'] == chiller_name)]['s_E'].values[0],
    coef_r=charpara[(charpara['name'] == chiller_name)]['r_E'].values[0],
    method='kuehn_and_ziegler')

# Driving heat
Q_dots_gen = abs_chiller.calc_heat_flux(
    ddts=ddt,
    coef_s=charpara[(charpara['name'] == chiller_name)]['s_G'].values[0],
    coef_r=charpara[(charpara['name'] == chiller_name)]['r_G'].values[0],
    method='kuehn_and_ziegler')

COPs = [Qevap / Qgen for Qgen, Qevap in zip(Q_dots_gen, Q_dots_evap)]

You find information on the machines in [1], [2] and [3]. Please be aware that [2] introduces a slightly different approach (using an improved characteristic equation with ΔΔt″ instead of ΔΔt′). The characteristic parameters that we use are derived from [1] and therefore differ from those in [2].

References