Model Input/Output
- Input: N↑ , Pwf, qW↓, QW↓, QO↑ , QG↑ , QW↑
- Output: qO , qG , qW , P
Model Parameters
Model Parameters:
- M = { VO , yW , xW , xG , yW , xJ , JW0 } – totally7 constants
Restrictions:
- all constants are positive
Model fitting
Source data corrections:
- one time-array Pwf(t)
Restrictions:
- 0 < Pwf, min < Pwf(t) < Pwf, max
Goal function:
- E[M] = wO ‧ Σ δ[qO] + wW ‧ Σ δ[qW] + wG ‧ Σ δ[qG] + wP ‧ Σ δ[P] + wf ‧ Σ δ[Pwf] → min
δ[A] = [2 ‧ (A-A*)/(A+A*) ] 2
A(t) – model prediction
A*(t) – historical value (if any)
Weights:
- wO + wW + wG + wP + wf = 1 (although it is not necessary)
Default settings: wO = 0.5 , wW = 0.1, wG = 0.1 , wP = 0.2 , wf = 0.1
Model function
qO↑ = qO1↑ ‧ N↑ | qO1↑= JO ‧ ( P - Pwf )
qW↑ = qW1↑ ‧ N↑ | qW1↑ = JW(t) ‧ ( P - Pwf )
qG↑ = JG ‧ N↑ | qG1↑= JG ‧ ( P - Pwf )
P = Pi + ( yW ‧ Bw ‧ ΣQW↓ + Bo ‧ ΣQO↑ + xW ‧ Bw ‧ ΣQW↑ + xG ‧ Bg ‧ ΣQG↑ )‧ Pi ‧ xP /VO
d = DFO = ΣQO↑ / VO
JO = kro(d) ‧ xJ
JW = JW0 + krw(d) ‧ xJ
JG = Rs ‧ JO
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM) / Capacitance-Resistivity Model (CRM) @model
[ Slightly compressible Material Balance Pressure @model ]