DFIT

Brief

Stimulated well drainage

DFIT is the diagnostic fracture injection test or the fracture calibration injection falloff test performed to estimate fluid efficiency, leak off coefficient, formation permeability and pressure before the main hydraulic fracture treatment.

Math & Physics

Steady state flow boundary conditions:

$P |_{x=x_e/2} = P |_{x=-x_e/2} = P_i$

$\frac{dP}{dt} =0\ for \ \forall x$

From Darcy's law:

$\frac{q}{2}=\frac{kA}{\mu}\ \frac{dP}{dx}$

$A =y_e*h$

$dP=\frac{q \mu}{2ky_eh} dx$

Integration gives: $P-P_{wf}=\frac{q \mu}{2ky_eh} x$

Since average pressure is: $\bar P = \frac{\int P dx}{\int dx}$

$\bar P = \frac{ \int \limits_{0}^{x_e/2} \left ( \frac{q \mu}{2ky_eh} x + P_{wf} \right ) dx}{\int dx} = \left. \frac{q \mu}{2ky_eh} \frac{x}{2} \right|_{x=0}^{x=x_e/2} + P_{wf} = \frac{q \mu x_e}{8ky_eh} + P_{wf}$

$J_D=\frac{q \mu}{2 \pi k h} \frac{1}{( \bar P - P_{wf})} =\frac{q \mu}{2 \pi k h} \frac{8ky_eh}{q \mu x_e} = \frac{4y_e}{\pi x_e}=\frac{4}{\pi}$

See also

6/π stimulated well potential
JD
optiFrac
fracDesign
Production Potential

Nomenclature

$A$ = cross-sectional area, cm2

$h$ = thickness, m

$J_D$ = dimensionless productivity index, dimensionless

$k$ = permeability, d

$P$ = pressure, atm

$P_i$ = initial pressure, atm

$\bar P$ = average pressure, atm

$q$ = flow rate, cm³/sec

$x$ = length, m

$x_e$ = drinage area length, m

$y_e$ = drinage area width, m

Greek symbols

$\mu$ =viscosity, cp