Motivation
In many practical cases the reservoir fluid flow created by well is getting aligned with a radial direction towards or away from well.
This type of reservoir fluid flow is called radial fluid flow and corresponding pressure diffusion models provide a diagnostic basis for pressure-rate base reservoir flow analysis.
The radial flow can be infinite acting or boundary dominated or transiting from one to another.
Although the actual reservoir fluid flow may not have an axial symmetry around the well-reservoir contact or around reservoir inhomogeneities (like boundary and faults and composite areas) but still in many practical cases the long-term correlation between the flowrate and bottom-hole pressure response can be approximated by a radial flow pressure model
Inputs & Outputs
Inputs | Outputs | ||
---|---|---|---|
q_t | total sandface rate | p(r) | reservoir pressure |
{p_i} | initial formation pressure | p_{wf} | well bottomhole pressure |
\sigma | transmissibility, \sigma = \frac{k \, h}{\mu} | ||
S | skin-factor | ||
r_w | wellbore radius |
Physical Model
Radial fluid flow | Homogenous reservoir | Finite reservoir flow boundary | Zero wellbore radius | Slightly compressible fluid flow | Constant rate | Constant skin |
---|---|---|---|---|---|---|
p(t, {\bf r}) \rightarrow p(r) {\bf r} \in ℝ^2 = \{ x, y\} | M(r, p)=M =\rm const \phi(r, p)=\phi =\rm const h(r)=h =\rm const c_r(r)=c_r =\rm const | r \rightarrow r_e | r_w = 0 | c_t(r,p) = \rm const | q_t = \rm const | S = \rm const |
Mathematical Model
Applications
Equation (6) shows how the basic diffusion model parameters impact the relation between drawdown \Delta = p_i - p_{wf}and total sandface flowrate q_t and plays important methodological role as they are used in many algorithms and express-methods of Pressure Testing. It also called Dupuis
See Also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Radial fluid flow
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
[ Well & Reservoir Surveillance ]
[ Pressure diffusion ] [ Pressure Diffusion @model ] [ Dupuit equation @model ]