Deliverability equation in pseudo-steady state for fractured vertical well in tight gas

Based on non-Darcy flow theory in tight gas reservoirs, a new deliverability equation of fractured vertical gas well in pseudo-steady state is presented with the consideration of the stress-sensitive effect, and the open flow capacity calculation formula of gas well has been also derived. With the new deliverability equation, the effects of stress-sensitive coefficient, fracture parameters and matrix permeability on the productivity of gas well have been analyzed. The computation across an instance shows that due to the stress-sensitive effect, the IPR curves bend over to the pressure axis and the productivity of gas well is lower than that derived from the equation without consideration of stress-sensitive effect under the same pressure drop. As the stress-sensitive coefficient increasing, the well productivity becomes lower, the decline rate of production is higher and the IPR curve bends over in earlier stage with a greater bending. Besides, the productivity is affected by and has a positive correlation with the length and conductivity of fracture, namely that it becomes lower as the length and conductivity of fracture decreasing. Matrix permeability has an apparent impact on the productivity. If matrix permeability is extremely low, gas well cannot achieve the industrial production even after fracturing. As the matrix permeability increasing, stimulation results are significant.