Method for detecting and quantifying leaks in a gas network under pressure or vacuum, the gas network comprising: - one or more sources of compressed gas or vacuum; - one or more consumers or consumer areas of compressed gas or vacuum applications; - pipelines or a network of pipelines to transport the gas or vacuum from the sources to the consumers, consumer areas or applications; - a plurality of sensors (9a, 9b) which determine one or a plurality of physical parameters of the gas at different times and locations in the gas network; characterized in that the gas network is further provided with a number of controllable or adjustable relief valves and that the method comprises the following steps: - a training phase in which a mathematical model is established between the measurements of a first group of sensors (9a, 9b) and a second group of sensors (9a, 9b) comprising a plurality of pressure sensors, possibly a number of flow sensors and possibly number of state sensors at different locations in the gas network, based on different measurements of these sensors (9a, 9b), the second group of sensors comprising a plurality of state sensors at different locations in the gas network, wherein a sensor from the first group is not in the second group and vice versa, in which the adjustable relief valves are controlled in a predetermined order and according to well-designed scenarios to generate leaks; - an operational phase, in which the mathematical model established between the measurements of the first group of sensors (9a, 9b) and the second group of sensors (9a, 9b) is used to detect, locate and quantify leaks in the gas network; wherein the operational phase comprises the following steps: - controlling the relief valves in a predetermined order and according to well-designed scenarios; - reading out the first group of sensors (9a, 9b); - based on these readout measurements, calculating or determining the value of the second group of sensors (9a, 9b) with the help of the mathematical model; - comparing the calculated or determined values of the second group of sensors (9a, 9b) with the read values of the second group of sensors (9a, 9b) and determining the difference between them; - determining whether there is a leak in the gas network on the basis of the aforementioned difference and any of its derivatives comprising a mathematical quantity extractable from the difference; - generating an alarm if a leak is detected and/or; generating a leakage rate and/or generating the corresponding leakage cost as well as any location if a leak is detected. - one or more sources of compressed gas or vacuum; - one or more consumers or consumer areas of compressed gas or vacuum applications; - pipelines or a network of pipelines to transport the gas or vacuum from the sources to the consumers, consumer areas or applications; - a plurality of sensors (9a, 9b) which determine one or a plurality of physical parameters of the gas at different times and locations in the gas network; - a training phase in which a mathematical model is established between the measurements of a first group of sensors (9a, 9b) and a second group of sensors (9a, 9b) comprising a plurality of pressure sensors, possibly a number of flow sensors and possibly number of state sensors at different locations in the gas network, based on different measurements of these sensors (9a, 9b), the second group of sensors comprising a plurality of state sensors at different locations in the gas network, wherein a sensor from the first group is not in the second group and vice versa, in which the adjustable relief valves are controlled in a predetermined order and according to well-designed scenarios to generate leaks; - an operational phase, in which the mathematical model established between the measurements of the first group of sensors (9a, 9b) and the second group of sensors (9a, 9b) is used to detect, locate and quantify leaks in the gas network; wherein the operational phase comprises the following steps: - controlling the relief valves in a predetermined order and according to well-designed scenarios; - reading out the first group of sensors (9a, 9b); - based on these readout measurements, calculating or determining the value of the second group of sensors (9a, 9b) with the help of the mathematical model; - comparing the calculated or determined values of the second group of sensors (9a, 9b) with the read values of the second group of sensors (9a, 9b) and determining the difference between them; - determining whether there is a leak in the gas network on the basis of the aforementioned difference and any of its derivatives comprising a mathematical quantity extractable from the difference; - generating an alarm if a leak is detected and/or; generating a leakage rate and/or generating the corresponding leakage cost as well as any location if a leak is detected.