Motivation

In many practical cases the reservoir flow created by well is getting aligned with a radial direction towards or away from well.

This type of flow is called radial fluid flow and a type library model provides a reference for radial fluid flow diagnostics.

Inputs & Outputs

Inputs		Outputs
	total sandface rate		reservoir pressure
	initial formation pressure
	transmissibility
	pressure diffusivity

	transmissibility			dynamic fluid viscosity
	pressure diffusivity			total compressibility
	absolute permeability			pore compressibility
	porosity			fluid compressibility

Mathematical Model

\frac{\partial p}{\partial t} = \chi \, \left[  \frac{\partial^2 p}{\partial t^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right]

p(t=0,r) = p_i

p(t, r=\infty) = p_i

\left[ r \frac{\partial p}{\partial r} \right]_{r=0} = - \frac{q_t}{2 \pi \sigma}

Computational Model

p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} {\rm Ei} \left(-\frac{r^2}{4 \chi t} \right)

Approximations

Late-time response

p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} \left[  
\gamma + \ln \left(\frac{r^2}{4 \chi t} \right) \right] 

= p_i - \frac{q_t}{4 \pi \sigma} \ln \left(\frac{2.24585 \, t}{r^2} \right)

Motivation

Inputs & Outputs

Mathematical Model

Computational Model

Approximations

See also