No abstract

Previous models of the gas-production rate of hydraulic fracturing horizontal wells were by assuming permeability heterogeneity, which is unrealistic in water-bearing tight gas reservoirs because of sandstone-mudstone crossover. Therefore, we develop an analytical model to describe the gas-production dynamics of hydraulic fracturing horizontal wells that considers permeability heterogeneity. In addition, threshold pressure gradient, stress sensitivity, and slippage are incorporated into the model. To solve this model analytically, the elliptical flow is transformed to radial flow by conformal transformation. The gas-production rate, reservoir pressure distribution, and average formation pressure are obtained by superposition principle, boundary pressures are calculated by material balance method, and the dynamic supply boundary propagation is modeled by steady-state sequential replacement. Actual field production data from Ordos Basin, China is used to verify the new model, which increases accuracy by 11.3% over previous models (98.6% versus 87.3%). The propagation distance of the dynamic supply boundary is predicted (in the fracture direction it is 109.3 m and in the vertical fracture direction it is 44.2 m). We analyze how stress sensitivity, the dynamic threshold pressure gradient, matrix permeability, pressure difference, and initial water saturation affect gas production rate and dynamic supply boundary. Based on orthogonal experimentation, the factors affecting the gas production rate and dynamic supply boundary of tight gas reservoirs can ranked in the following order: pressure difference > permeability > initial water saturation. This analytical model can accurately characterize gas production and pressure response, it is easy to use and rapid to calculate.

The fluid flow is closely related to the reservoir microstructure. And the pore throat is small, and the pore structure is complex of tight reservoirs, so the fluid flow mechanism is different from the conventional sandstones. In this paper, the sample size and scanning accuracy are determined by mercury-pressure experiments, and the gray-scale images of core samples are enhanced, filtered, and noise reduced, segmented by Avizo software, and finally 3D digital cores are constructed to realize quantitative characterization of pore throat parameters. The results show the following: (i) It is highly accurate to determine 3D digital core by comparing porosity measurement and calculating porosity; (ii) the average pore radius of the three samples is more than 7 μm, the pore number is less than 651, the average throat length is greater than 159 μm, and the percentage of connected pore volume is above 95%; (iii) large pores are mainly developed in the reservoir, while a certain number of isolated pores exist, and the connected pores are distributed in sheets and strips; (iv) the pores of tight reservoir are mainly micron pores, and the distribution frequency histogram of pore radius is single peak; (v) porosity is related to connectivity, pore radius, and pore number; and (vi) the influence of throat on porosity and permeability is greater than that of pore. This paper is helpful for quantitative evaluation of reservoir microscopic parameters and provides technical support for visualization and quantitative characterization of rock microstructure.