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 reservoir inhomogeneities (like boundary and faults and composite areas) but still:
- the dominant part of wellbore and reservoir pressure variation is usually radial-flow or linear-flow and the two represent the basis for Pressure diffusion analysis
- in most practical cases the long-term correlation between the flowrate and bottom-hole pressure response can be approximated by a radial flow pressure model
Formation pressure {p_i}, skin-factor S, transmissibility \sigma and pressure diffusivity \chi are called basic diffusion model parameters as they are essential components of all diffusion models.
Inputs & Outputs
Inputs | Outputs | ||
---|---|---|---|
q_t | total sandface rate | p(t,r) | reservoir pressure |
{p_i} | initial formation pressure | {p_{wf}(t)} | well bottomhole pressure |
\sigma | transmissibility | ||
\chi | pressure diffusivity | ||
S | skin-factor |
Physical Model
Radial fluid flow | Homogenous reservoir | Infinite boundary | Zero wellbore radius | Slightly compressible fluid flow | Constant rate | Constant skin |
---|---|---|---|---|---|---|
p(t, r) | 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 \infty | r_w = 0 | c_t(r,p) = \rm const | q_t = \rm const | S = \rm const |
Mathematical Model
Applications
Equations (5) and (6) show how the basic diffusion model parameters impact the pressure response while other diffusion parameters are encoded in F function and play important methodological role as they are used in many algorithms and express-methods of Pressure Testing.
See also
Physics / Fluid Dynamics / Radial fluid flow
[ Line Source Solution (LSS) @model ]
[ Linear Flow Pressure Diffusion @model ]