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Inputs

Outputs

LaTeX Math Inline

body	q_t

total sandface rate

LaTeX Math Inline

body	p(t,r)

reservoir pressure

LaTeX Math Inline

body	p_i

initial formation pressure

LaTeX Math Inline

body	p_{wf}(t)

well bottomhole pressure

LaTeX Math Inline

body	d

reservoir channel width

LaTeX Math Inline

body	\sigma

transmissibility

LaTeX Math Inline

body	\chi

pressure diffusivity

Expand

title	Detailing

LaTeX Math Inline

body	\sigma = \frac{k \, h}{\mu}

transmissibility

LaTeX Math Inline

body	\mu

dynamic fluid viscosity

LaTeX Math Inline

body	\chi = \frac{k}{\mu} \, \frac{1}{\phi \, c_t}

pressure diffusivity

LaTeX Math Inline

body	c_t = c_r + c

total compressibility

LaTeX Math Inline

body	k

absolute permeability

LaTeX Math Inline

body	{c_r}

pore compressibility

LaTeX Math Inline

body	{\phi}

LaTeX Math Inline

body	c

fluid compressibility

Physical Model

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Constant rate production

LaTeX Math Inline

body	q_t = \rm const

Linear fluid flow

LaTeX Math Inline

body	p(t, {\bf r})

Slightly compressible fluid flow

LaTeX Math Inline

body	c_t(p) = c_r +c = \rm const

Homogeneous reservoir

LaTeX Math Inline

body	M({\bf r}, p)=M =\rm const

LaTeX Math Inline

body	\phi({\bf r}, p)=\phi =\rm const

LaTeX Math Inline

body	h({\bf r})=h =\rm const

Infinite boundary

LaTeX Math Inline

body	r \rightarrow \infty

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