| time and space corrdinates , -axis is orientated towards the Earth centre, define transversal plane to the -axis |
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| body | \mathbf{r} = (x, \ y, \ z) |
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| position vector at which the flow equations are set |
| measured depth along borehole wellbore trajectory | LaTeX Math Inline |
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| body | dl^2 = dx^2 + dy^2 + dz^2 |
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starting from tubing head | LaTeX Math Inline |
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| body | l (x = x_0, \ y=y_0, \ z = z_{THP}) = 0 |
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| body | q_{mW} \alpha(t, l) = \frac{d m_W}{dt} |
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| speed of water-component mass change in wellbore draining points |
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| body | q_{mO} = \frac{d m_O}{dt} |
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| speed of oil-component mass change in wellbore draining points |
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| body | q_{mG} = \frac{d m_G}{dt} |
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| speed of gas-component mass change in wellbore draining points |
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| body | q_W = \frac{1}{\rho_W^{\LARGE \circ}} \frac{d m_W}{dt} = \frac{d V_{Ww}^{\LARGE \circ}}{dt} = \frac{1}{B_w} q_w |
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| volumetric water-component flow rate in wellbore draining points recalculated to standard surface conditions
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| body | q_O = \frac{1}{\rho_O^{\LARGE \circ}} \frac{d m_O}{dt} = \frac{d V_{Oo}^{\LARGE \circ}}{dt} + \frac{d V_{Og}^{\LARGE \circ}}{dt} = \frac{1}{B_o} q_o + \frac{R_v}{B_g} q_g |
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| | volumetric flow rate -phase fluid at wellbore depth |
| -phase flow speed at wellbore depth |
volumetric oil-component flow rate in wellbore draining points recalculated to standard surface conditions
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| body | q_G = \frac{1}{\rho_G^{\LARGE \circ}} \frac{d m_G}{dt} = \frac{d V_{Gg}^{\LARGE \circ}}{dt} + \frac{d V_{Go}^{\LARGE \circ}}{dt} = \frac{1}{B_g} q_g + \frac{R_s}{B_o} q_o |
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| volumetric gas-component flow rate in wellbore draining points recalculated to standard surface conditions
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| body | q_w = \frac{d V_w}{dt} |
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| volumetric water-phase flow rate in wellbore draining points
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| body | q_o = \frac{d V_o}{dt} |
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| volumetric oil-phase flow rate in wellbore draining points
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| body | q_g = \frac{d V_g}{dt} |
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| volumetric gas-phase flow rate in wellbore draining points
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| body | q^S_W =\frac{dV_{Ww}^S}{dt} |
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| total well volumetric water-component flow rate |
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| body | q^S_O = \frac{d (V_{Oo}^S + V_{Og}^S )}{dt} |
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| total well volumetric oil-component flow rate
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| body | q^S_G = \frac{d (V_{Gg}^S + V_{Go}^S )}{dt} |
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| total well volumetric gas-component flow rate
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| body | q^S_L = q^S_W + q^S_O |
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| total well volumetric liquid-component flow rate
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| body | \vec u_w = \vec u_w (t, \vec r) |
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| water-phase flow speed distribution and dynamics
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| body | \vec u_o = \vec u_o (t, \vec r) |
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| oil-phase flow speed distribution and dynamics
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| body | \vec u_g = \vec u_g (t, \vec r) |
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| gas-phase flow speed distribution and dynamics |
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| body | \vec g = (0, \ 0, \ g) |
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| gravitational acceleration vector |
| gravitational acceleration constant
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| mass density of -phase fluid |
| viscosity of -phase fluid |
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| body | \lambda_t(Pp,T,s_w, s_o, s_g) |
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| effective thermal conductivity of the rocks with account for multiphase fluid saturation |
| rock matrix thermal conductivity |
| thermal conductivity of -phase fluid |
| rock matrix mass density |
| differential adiabatic coefficient of -phase fluid |
| specific isobaric heat capacity of the rock matrix |
| specific isobaric heat capacity of -phase fluid |
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| body | \epsilon_\alpha (P, T) |
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| differential Joule–Thomson coefficient of -phase fluid дифференциальный коэффициент Джоуля-Томсона фазы |
