A mathematical approach investigating the production of effective water during coalbed methane well drainage

Drainage of formation water controls pressure dropping behavior of coalbed methane wells. Different behaviors indicate that formation water can be classified into two types. The first type is ineffective water, representing the water from aquifers of strong, extremely strong water yield property, or phreatic water. It is difficult to generate pressure dropping when this type of water is pumped. The other type is effective water, representing the water from aquifers of middle or weak water yield property. Pressure decline will occur if this type of water is pumped. Based on the modified Duipt equation, the production of effective water and the production percentage of ineffective water for well QNPN01 are calculated considering the variations of influence radius, absolute permeability, and relative water permeability. The results show that in the single water flow stage, the production of effective water and the production percentage of ineffective water drop in the zigzag way at first and then keep stable roughly. In the water–gas flow stage, the production of effective water decreases firstly and then keeps stable, while the production percentage of ineffective water increases firstly and then keeps stable. Furthermore, the production of effective water in unit pressure decline indicates that the process of pressure dropping can be divided into four stages. The first one is a single water flow stage in which pressure dropping completely depends on effective water. The second one refers to the beginning of a water–gas flow stage. In the stage, pressure dropping strongly depends on effective water. Pressure dropping caused by effective water drainage starts to be replaced by gas desorbing in the third stage, and completely replaced in the fourth stage.