Difference between revisions of "DFIT"

Latest revision as of 18:57, 8 July 2023

Brief

Stimulated well drainage

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

Math & Physics

in progress

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

@@ Line 7: / Line 7: @@
 in progress
-Steady state flow boundary conditions:
-:<math>P |_{x=x_e/2} = P |_{x=-x_e/2} = P_i</math>
-:<math> \frac{dP}{dt} =0\ for \ \forall x </math>
-From [[Darcy's law]]:
-:<math>\frac{q}{2}=\frac{kA}{\mu}\ \frac{dP}{dx}</math>
-:<math> A =y_e*h</math>
-:<math>dP=\frac{q \mu}{2ky_eh} dx</math>
-Integration gives: <math>P-P_{wf}=\frac{q \mu}{2ky_eh} x</math>
-Since average pressure is: <math>\bar P = \frac{\int P dx}{\int dx}</math>
-:<math> \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}</math>
-:<math>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}</math>
 ==See also==

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