Abstract
The application of traditional well test interpretation methods cannot comprehensively consider characteristics of stress sensitivity and non-Darcy flow for low-permeability composite gas reservoirs, which makes it difficult to obtain real reservoir parameters. Based on the micro-mechanism analysis of stress sensitivity and non-Darcy flow in low-permeability gas reservoirs, the flow motion equation was improved. Thus, a mathematical model was established which belongs to the inclined well in the composite gas reservoir with a conventional internal zone and low-permeability external zone. Applying the finite element method to solve the flow model through Matlab programming, the equivalent pressure point was selected to research the pressure distribution of the inclined well. On this basis, the bottom hole pressure dynamic curve was drawn, the flow process was divided into seven stages, and the parameter sensitivity analysis was carried out. Finally, the advanced nature of the new model applied to the interpretation of the well test model is compared by conventional methods. The non-Darcy flow can cause the gradual upward warping of the bottom hole pressure dynamic curve in the later stage, and non-linear enhancement leads to an increase in the upturn through the simulation test. When the inclination angle is greater than 60°, early vertical radial flow and mid-term linear flow gradually appear. A decrease leads to a shorter duration of the pseudo radial flow in the internal zone and the radius of the internal zone. The conduction coefficients ratio of internal and external zones affects the pseudo pressure derivative curve slope in transition phase of pseudo radial flow in the internal and external zones. A comprehensive consideration of the low-permeability composite gas reservoir flow characteristics can improve the fitting degree of the pressure curves. Not only that, but it can also solve the strong diversification of reservoir parameters. Results have a guiding significance for low-permeability composite gas reservoir development and pressure dynamic evaluation in inclined wells.
Highlights
In low-permeability gas reservoirs, measures of acidification are often used to improve the near-wellbore area physical properties, which will lead to aggravated reservoir heterogeneity and show composite gas reservoir flow characteristics
Where bmlD represents the dimensionless pseudo threshold pressure gradient reciprocal; zwD represents the dimensionless inclined well center longitudinal depth; εD represents dimensionless variables; reD represents dimensionless maximum boundary radius; and M1,2 represents the ratio of the internal zone and external zone
The pseudo pressure and its derivative curves of the pseudo threshold pressure gradient model and the nonlinear flow model are all upturned from the pseudo radial flow section in the external zone
Summary
In low-permeability gas reservoirs, measures of acidification are often used to improve the near-wellbore area physical properties, which will lead to aggravated reservoir heterogeneity and show composite gas reservoir flow characteristics. Most of them are characterized by a simplified pseudo threshold pressure gradient model, which does not comprehensively consider reservoir stress sensitivity It cannot fully reflect the low-permeability composite gas reservoir flow characteristics. Where Ki represents initial reservoir permeability, μm; γ represents permeability modulus, MPa−1; and pi represents original formation pressure, MPa. In summary, the equation of motion considering conditions such as stress sensitivity and low-permeability gas reservoir non-Darcy flow is: v=. Based on the physical model assumptions, we combine the non-Darcy equation of motion, mass conservation equation and state equation and introduce the pseudo-pressure function to obtain the dimensionless differential equation of a low-permeability compound gas reservoir inclined well non-Darcy flow:. Where bmlD represents the dimensionless pseudo threshold pressure gradient reciprocal; zwD represents the dimensionless inclined well center longitudinal depth; εD represents dimensionless variables; reD represents dimensionless maximum boundary radius; and M1,2 represents the ratio of the internal zone and external zone. Ctn represents comprehensive compression coefficient of internal and external zone, MPa−1. h represents reservoir thickness, m. zw, ε represent longitudinal depth and micro variables in the center of the inclined shaft, m. γm represents Permeability modulus defined by pseudo pressure, mPa·s/MPa2. bml represents threshold pressure gradient reciprocal, mPa·s·m/MPa2
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