| indicates a mixture of fluid phases | | time and space corrdinates , -axis is orientated towards the Earth centre, define transversal plane to the -axis |
| water, oil, gas phase indicator | | LaTeX Math Inline |
|---|
| body | l | \mathbf{r} = (x, \ y, \ z) |
|---|
|
| position vector at which the flow equations are set |
| measured depth along wellbore trajectory | LaTeX Math Inline |
|---|
| body | dl^2 = dx^2 + dy^2 + dz^2 |
|---|
|
starting from tubing head | LaTeX Math Inline |
|---|
| body | l (x = x_0, \ y=y_0, \ z = z_{THP}) = 0 |
|---|
|
| | LaTeX Math Inline |
|---|
| body | q_\alpha(t, l) = \frac{d V_\alpha}{dt} |
|---|
|
| volumetric flow rate -phase fluid at wellbore depth |
| in-situ velocity of -phase fluid flow | | gravitational acceleration constant |
| -phase fluid density at pressure and temperature | | |
| cross-sectional average fluid density | |
|
| wellbore trajectory inclination to horizon | |
|
| cross-sectional average pipe flow diameter | | |
| in-situ cross-sectional area | LaTeX Math Inline |
|---|
| body | A(l) = 0.25 \, \pi \, d^2(l) |
|---|
|
| | |
| Darci flow friction coefficient at fluid velocity | | 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 saturationmeasure length along wellbore trajectory |
| in-situ velocity kinematic viscosity of -phase fluid flow | | rock matrix thermal conductivity |
| temperature of -phase fluid densityflowing from reservoir into a wellbore | | rho | m(l) cross-sectional average fluid density | thermal conductivity of -phase fluid |
| LaTeX Math Inline |
|---|
| body | \theta(l)mu_\alpha(p,T) |
|---|
|
| wellbore trajectory inclination to horizoncross-sectional average pipe flow diameter | | A(l) | in-situ cross-sectional area | rock matrix mass density |
|
| | A(l) = 0.25 \, \pi \, d^2(l) | differential adiabatic coefficient of -phase fluid |
|
| | specific isobaric heat capacity of the rock matrix Darci flow friction coefficient |
|
| | \nu | | specific isobaric heat capacity | kinematic viscosity |
|
| | T | l | temperature differential Joule–Thomson coefficient of -phase fluid | flowing from reservoir into a wellbore |
