A novel steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs

It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional（3-D） flow into two-dimensions（2-D）.This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs.Firstly,the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir.Then,using the fundamental solution and the Simpson integral formula,the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section.Two case-studies are given in the paper,the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data,indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.

Inter-layer interference for multi-layered tight gas reservoir in the absence and presence of movable water

Due to the dissimilarity among different producing layers,the influences of inter-layer interference on the production performance of a multi-layer gas reservoir are possible.However,systematic studies of inter-layer interference for tight gas reservoirs are really limited,especially for those reservoirs in the presence of water.In this work,five types of possible inter-layer interferences,including both absence and presence of water,are identified for commingled production of tight gas reservoirs.Subsequently,a series of reservoir-scale and pore-scale numerical simulations are conducted to quantify the degree of influence of each type of interference.Consistent field evidence from the Yan'an tight gas reservoir(Ordos Basin,China)is found to support the simulation results.Additionally,suggestions are proposed to mitigate the potential inter-layer interferences.The results indicate that,in the absence of water,commingled production is favorable in two situations:when there is a difference in physical properties and when there is a difference in the pressure system of each layer.For reservoirs with a multi-pressure system,the backflow phenomenon,which significantly influences the production performance,only occurs under extreme conditions(such as very low production rates or well shut-in periods).When water is introduced into the multi-layer system,inter-layer interference becomes nearly inevitable.Perforating both the gas-rich layer and water-rich layer for commingled production is not desirable,as it can trigger water invasion from the water-rich layer into the gas-rich layer.The gas-rich layer might also be interfered with by water from the neighboring unperforated water-rich layer,where the water might break the barrier(eg weak joint surface,cement in fractures)between the two layers and migrate into the gas-rich layer.Additionally,the gas-rich layer could possibly be interfered with by water that accumulates at the bottom of the wellbore due to gravitational differentiation during shut-in operations.