| time and space corrdinates , -axis is orientated towards the Earth centre, define transversal plane to the -axis |
| LaTeX Math Inline |
|---|
| body | \mathbf{r} = (x, \ y, \ z) |
|---|
|
| position vector at which the flow equations are set |
| LaTeX Math Inline |
|---|
| body | q_{mW} = \frac{d m_W}{dt} |
|---|
|
| speed of water-component mass change in wellbore draining points |
| LaTeX Math Inline |
|---|
| body | q_{mO} = \frac{d m_O}{dt} |
|---|
|
| speed of oil-component mass change in wellbore draining points
|
| LaTeX Math Inline |
|---|
| body | q_{mG} = \frac{d m_G}{dt} |
|---|
|
| speed of gas-component mass change in wellbore draining points
|
| LaTeX Math Inline |
|---|
| 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 |
|---|
|
| volumetric water-component flow rate in wellbore draining points recalculated to standard surface conditions
|
| LaTeX Math Inline |
|---|
| 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 |
|---|
|
| volumetric oil-component flow rate in wellbore draining points recalculated to standard surface conditions
|
| LaTeX Math Inline |
|---|
| 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 |
|---|
|
| volumetric gas-component flow rate in wellbore draining points recalculated to standard surface conditions
|
| LaTeX Math Inline |
|---|
| body | q_w = \frac{d V_w}{dt} |
|---|
|
| volumetric water-phase flow rate in wellbore draining points
|
| LaTeX Math Inline |
|---|
| body | q_o = \frac{d V_o}{dt} |
|---|
|
| volumetric oil-phase flow rate in wellbore draining points
|
| LaTeX Math Inline |
|---|
| body | q_g = \frac{d V_g}{dt} |
|---|
|
| volumetric gas-phase flow rate in wellbore draining points
|
| LaTeX Math Inline |
|---|
| body | q^S_W =\frac{dV_{Ww}^S}{dt} |
|---|
|
| total well volumetric water-component flow rate
|
| LaTeX Math Inline |
|---|
| body | q^S_O = \frac{d (V_{Oo}^S + V_{Og}^S )}{dt} |
|---|
|
| total well volumetric oil-component flow rate
|
| LaTeX Math Inline |
|---|
| body | q^S_G = \frac{d (V_{Gg}^S + V_{Go}^S )}{dt} |
|---|
|
| total well volumetric gas-component flow rate
|
| LaTeX Math Inline |
|---|
| body | q^S_L = q^S_W + q^S_O |
|---|
|
| total well volumetric liquid-component flow rate
|
| LaTeX Math Inline |
|---|
| body | P_w = P_w (t, \vec r) |
|---|
|
| water-phase pressure pressure distribution and dynamics |
| LaTeX Math Inline |
|---|
| body | P_o = P_o (t, \vec r) |
|---|
|
| oil-phase pressure pressure distribution and dynamics |
| LaTeX Math Inline |
|---|
| body | P_g = P_g (t, \vec r) |
|---|
|
| gas-phase pressure pressure distribution and dynamics |
| LaTeX Math Inline |
|---|
| body | \vec u_w = \vec u_w (t, \vec r) |
|---|
|
| water-phase flow speed distribution and dynamics
|
| LaTeX Math Inline |
|---|
| body | \vec u_o = \vec u_o (t, \vec r) |
|---|
|
| oil-phase flow speed distribution and dynamics
|
| LaTeX Math Inline |
|---|
| body | \vec u_g = \vec u_g (t, \vec r) |
|---|
|
| gas-phase flow speed distribution and dynamics
|
| LaTeX Math Inline |
|---|
| body | P_{cow} = P_{cow} (s_w) |
|---|
|
| capillary pressure at the oil-water phase contact as function of water saturation
|
| LaTeX Math Inline |
|---|
| body | P_{cog} = P_{cog} (s_ g) |
|---|
|
| capillary pressure at the oil-gas phase contact as function of gas saturation
|
| LaTeX Math Inline |
|---|
| body | k_{rw} = k_{rw}(s_w, \ s_g) |
|---|
|
| relative formation permeability to water flow as function of water and gas saturation |
| LaTeX Math Inline |
|---|
| body | k_{ro} = k_{ro}(s_w, \ s_g) |
|---|
|
| relative formation permeability to oil flow as function of water and gas saturation
|
| LaTeX Math Inline |
|---|
| body | k_{rg} = k_{rg}(s_w, \ s_g) |
|---|
|
| relative formation permeability to gas flow as function of water and gas saturation
|
| porosity as function of formation pressure |
| absolute formation permeability to air |
| LaTeX Math Inline |
|---|
| body | \vec g = (0, \ 0, \ g) |
|---|
|
| gravitational acceleration vector |
| gravitational acceleration constant
|
| mass density of -phase fluid |
| viscosity of -phase fluid
|
| LaTeX Math Inline |
|---|
| body | \lambda_t(P,T,s_w, s_o, s_g) |
|---|
|
| 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 |
| LaTeX Math Inline |
|---|
| body | \epsilon_\alpha (P, T) |
|---|
|
| differential Joule–Thomson coefficient of -phase fluidдифференциальный коэффициент Джоуля-Томсона фазы |
