we’re concentrating on generating biogas from coffee grounds in this research. Anaerobic digestion of organic matter-laden effluents occurs in a digester. We made the digester’s biological characterisation using a mathematical model that describes the digester's actual behaviour, El-Fadel’s model. The modeling was carried out using step-by-step method, the Rang-Kutta method, this phenomenon is solved by biological equations. The results obtained satisfactorily reflect the output that explains the difference in the amount of biogas produced that varies from day to day, though linked to the liquid effluent's carbon content