The invention relates to an exhaust gas after treatment apparatus having a hollow cylindrical casing shell. Transducers are inside the casing and in communication with its own port. The first plurality of teeth is capable of intermeshing with the second plurality of teeth. A gap between the first and second wall surfaces and a gap between the third and fourth wall surfaces become narrower from the discharge port inlet to the discharge port outlet. It also includes the phases of measuring the quantity of given gas in the gases extracted from an analysis sample of the drilling mud in an extraction stage, under the predetermined conditions; and computing the given gas content of the drilling mud on the basis of the measured quantity of given gas and of a curve of said family. Relatively rapid-setting and slower-setting consumable gels form one preferred thickening composition.