Determining Hydraulic Resistance with the Binomial Law of Filtration of Hydrocarbons in a Porous Medium with Allowance f
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 6, November, 2020
DETERMINING HYDRAULIC RESISTANCE WITH THE BINOMIAL LAW OF FILTRATION OF HYDROCARBONS IN A POROUS MEDIUM WITH ALLOWANCE FOR THE INFLUENCE OF THE INITIAL GRADIENT T. Sh. Salavatova and I. R. Gasanovb
UDC 66.023
Hydraulic resistance and the Reynolds number are important parameters of flow, because of which determining them is necessary when hydrodynamic flow is calculated and modeled. In the present work, the authors give formulas for determining the Reynolds number and hydraulic resistance with the binomial law of filtration of hydrocarbons in a porous medium with allowance for the influence of the initial gradient, and also obtain a formula for the velocity as a function of these parameters. Keywords: hydraulic resistance, Reynolds number, binomial filtration law, initial gradient. It is common knowledge that the filtration of hydrocarbons in a porous medium often occurs nonlinearly. Deviations appear for the following reasons: 1) turbulent flow that may result from both great velocities and the random position of elementary channels in the stratum (e.g., rocks with varying number, dimensions, and orientation of cracks); 2) non-onedimensional filtration; 3) boundaries of the stratum are moving; 4) the presence of solid particles of asphaltenes and resinous substances playing an important role in the structure formation of a dispersed medium with rheological properties inherent in this structure. The models for describing the behavior of structured oil disperse systems do not always satisfy physical laws, except the behavior of single particles. They represent empirical or semiempirical approximations to a true picture, which is explained by random interactions between the particles and the stochastic nature of their behavior. The rheological equations of state insufficiently accurately describe actual fluids or rocks; 5) no account is taken of the inertia of the fluid, the temperature field, phase transitions, etc. N. N. Pavlovskii was the first to hydrodynamically substantiate the problem on the limits of applicability of the linear filtration law [1]. He proposed the formula vd ρ Re = . (1) (0.75m + 0.23)μ N. N. Pavlovskii established that the critical value of the Re number ranges within Recr = 7.5–9. V. N. Shchelkachev [2] presented the expression for the Re number in the form Re =
10 v k ρ , μ
m 2.3
(2)
and Recr = 1–12. The authors of [3–6] propose different modifications of formulas for determining the Re number. In the proposed paper, the Reynolds number and hydraulic resistance with the binomial law of filtration of hydrocarbons in a porous medium are determined with allowance for the influence of the initial gradient, which may be written in the form μ μ dp ⎛ dp ⎞ bv 2 + v = ⎜ − γ 0 ⎟ or bv 2 + v + γ 0 = . (3) k k dr ⎝ dr ⎠ a
Azerbaijan State Oil and Industry University, 34 Azadlyg Ave., Baku, AZ 1010, Azerbaijan, email: petrotech@ asoiu.az; bSOCAR–NIPI "Neftegaz," 88a G. Zardabi Ave., Baku, AZ1112, Azerbaijan, email: i
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