New Productivity Calculation Method Considering No Constant Starting Pressure Drop and High Velocity Non-Darcy Flow

Starting pressure drop connected with productivity is not constant and high velocity non-Darcy flow only occurs in the immediate vicinity of well bore,both of which influence productivity.In order to research their effects on productivity,based on gas steady percolation differential equation,the calculation formula for starting pressure drop and additional high velocity non-Darcy flow pressure drop have been revised,and new deliverability equation have been derived which consider both no constant starting pressure drop and high velocity non-Darcy flow drop in the near well bore area.The conventional productivity equation is just a simplified form from it.In addition,we simulated the impact of starting pressure gradient and high velocity non-Darcy flow variations on productivity,finding out that the formation percolation can be divided into three stages:A stage when the starting pressure gradient controls the flow;B stage when both the starting pressure gradient and non-Darcy flow control the flow;and C stage when non-Darcy flow controls the flow.In the study,the changes of deliverability equation coefficients and productivity at the three stages were analyzed,and the range of open flow capacity and the law of deliverability equation coefficients and productivity were figured out.