The Minimum Herd for a Cooking Household: A Collectable-Dung Bound and Digester Sizing Rule

A household cannot cook on biogas if the dung it can actually collect does not contain enough volatile solids, regardless of digester size. This simulated study, not a measurement, states a cooking demand of 1.6 m3 of biogas per day and computes, from stated per-animal dung production, volatile-solids fractions, collectable fractions and biogas yields, the smallest herd that meets that demand: 8 cattle, 15 pigs, or 198 poultry birds, considered separately. A single cattle animal contributes 0.2184 m3 per day under the stated assumptions, so two cattle supply only 0.4368 m3 per day, 27.3 percent of cooking demand. At a stated hydraulic retention time of 40 days and a 1-to-1 dilution with water, the cattle case requires a total digester volume of 4.8 m3. The central result is a threshold, not a recommendation to build larger: below 5.714 kg of collectable cattle volatile solids per day, no digester volume produces 1.6 m3 per day from cattle dung alone at the stated yield.