The article relates to heat-recovery (HR)/non-recovery (NR) coke ovens. A one-dimensional home-made mathematical model of a horizontal oven has been developed and it includes a series of sub-models. The heart of the model is a hydraulic network sub-model which is used to calculate both the amount of air entrained from surroundings and the flow rates in the oven's channels/ducts. This paper, which focuses both on the hydraulic network model and on the methods of obtaining its coefficients, is the first publication (Part I) describing the whole HR/NR oven model. In the associated publications (Parts II, III) the other sub-models are described whilst in Part IV the model is used to predict the performance of an industrial HR plant located in South America. (C) 2016 Elsevier Ltd. All rights reserved.