To ensure the smooth transition from historical data
| LaTeX Math Inline |
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| body | [(t_1,q_1)... (t_N, q_N)] |
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to the production forecasts in future time moments
| LaTeX Math Inline |
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| body | --uriencoded--[(t_%7BN+1%7D,q_%7BN+1%7D), ...] |
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one may wish to constrain the model by firm matching the production at the last historical moment
which leads to the following form of
Arp's model:
| Exponential Production Decline | Hyperbolic Production Decline | Harmonic Production Decline |
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| | |
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| q(t)=q_N \cdot \exp \big[ -D_0 \cdot (t-t_N) \big] |
| | LaTeX Math Block |
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| q(t) = q_N \cdot \left[ \frac{1+b \cdot D_0 \cdot t_N }
{ 1+b \cdot D_0 \cdot t } \right]^{1/b} |
| | LaTeX Math Block |
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| q(t) = q_N \cdot \left[ \frac{1+D_0 \cdot t_N }
{ 1+ D_0 \cdot t } \right] |
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| LaTeX Math Block |
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| Q(t) - Q_N = [ q_N - q(t)] \, \tau_0 |
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| Q(t) - Q_N = \frac{q_N^b \, (\tau_0 + b \, t_N)}{1-b} \left[ q_N^{1-b} - q^{1-b}(t) \right] |
| | LaTeX Math Block |
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| Q(t) - Q_N = q_N \, (\tau_0 + t_N) \cdot \ln \frac{q_N}{q(t)} |
|
See Also
...
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Decline Curve Analysis / DCA Arps @model
