The production rate of a well depends on how easily fluids can flow through the reservoir toward the wellbore. This behavior can be described using Darcy’s law. For radial flow under steady-state conditions, the relationship between production rate and reservoir properties is given by the steady-state inflow equation:
Where:
- \(\boldsymbol{q}\): production rate
- \(\boldsymbol{k}\): reservoir permeability
- \(\boldsymbol{h}\): reservoir thickness
- \(\boldsymbol{\Delta P}\): pressure gradient
- \(\boldsymbol{\mu}\): fluid viscosity
- \(\boldsymbol{P_D}\): dimensionless pressure term
For steady-state radial flow toward a vertical well, the dimensionless pressure term is
Where:
- \(\boldsymbol{r_e}\): drainage radius
- \(\boldsymbol{r_w}\): wellbore radius
Substituting this expression gives the familiar steady-state inflow equation:
This equation shows that the production rate depends on reservoir properties, fluid properties, and the geometry of flow toward the well.
In many reservoirs, particularly unconventional formations such as shale or tight sandstones, the permeability is extremely low. Under these conditions, fluid movement through the rock is highly restricted, and the ability of the reservoir to deliver fluids to the wellbore is limited.
Hydraulic fracturing is used to address this limitation. By creating fractures that extend outward from the wellbore, highly conductive pathways are introduced into the formation. These fractures provide more efficient flow channels, improving the connectivity between the reservoir and the well. As a result, the reservoir is able to deliver fluids to the wellbore more effectively.
