A reverse circulation is another way to circulate by circulating into annulus up to a bit and drill string. The fluid outlet is at stand pipe side. For drilling operation, we almost use forward circulation; however, in completion operation, the reverse circulation is utilized more often. For more understanding, I would like to shoe an image below which demonstrates a flow path of the reverse circulation.
For the topic today, I would like to show the effect of frictional pressure on the bottom hole pressure and equivalent circulating density while the reverse circulation is performed.
Under a static condition: The bottom hole pressure is equal to hydrostatic pressure from the drilling fluid.
BHP = Hydrostatic Pressure
Under a dynamic condition: Stand pipe pressure equates to summation of pressure loss of whole system. See the diagram below.
Stand pipe pressure = Pressure loss in the annulus Pressure + Pressure loss across the bit + Pressure loss in BHA + Press loss in drill string
Please remember that the pressure loss acts opposite way while fluid is being moved.
For this case we can write the relationship of bottom hole pressure as shown in the following equation.
Bottom hole pressure = Hydrostatic Pressure + pressure loss across the bit + pressure loss across the BHA + pressure loss in drill string.
The bottom hole pressure can be expressed in terms of the equivalent circulating density:
ECD = Current Mud Weight + [(pressure loss across the bit + pressure loss across the BHA + pressure loss in drill string) ÷ (0.052 x TVD of the well)]