A microporous membrane is used in combination with rectangular microchannels in the absorber of an absorption chiller with the aim of reducing the size of this cooling technology. The simulation of the heat and mass transfer between the solution and the vapour phase in a H2O&-LiBr absorber using porous fibres is considered. Heat and mass transfer processes are modelled by means of selected correlations and data gathered from the open literature. This new model is applied for the simulation of the absorber under typical operating conditions of absorption cooling chillers. Absorption rate, heat and mass transfer coefficients, solution concentration, temperatures of the working fluids and pressure potential along the absorption channels are calculated. For the case considered in this study, the absorber channels are of 5 cm length, offering a maximum ratio between cooling capacity of the chiller and absorber volume of 1090 kW/m3. This ratio is higher than twice the usual values found in falling film absorbers using conventional circular tubes. The mean absolute error between the model results and the experimental data gathered from the open literature is 8.5%, showing the capability of the model to predict the performance of membrane-based absorbers. The financial support of this study by the Ministerio de Economía y Competitividad of Spain through the research grant ENE2013-43131-R is greatly appreciated.