The general form of objective function for production targets optimisation is given by:
(1) | G(t) = \sum_{p=1}^{N^{\uparrow}} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot q^{\uparrow}_{G, p} \right] - \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_L \cdot q^{\uparrow}_{L, p} - \sum_{p=1}^{N^{\uparrow}} C_O \cdot q^{\uparrow}_{O, p} - \sum_{p=1}^{N^{\uparrow}} C_G \cdot q^{\uparrow}_{G, p} - \sum_{p=1}^{N^{\uparrow}} C_W \cdot q^{\uparrow}_{W, p} - \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_W \cdot q^{\downarrow}_{W, i} - \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_G \cdot q^{\downarrow}_{G, i} \rightarrow \rm max |
where
q^{\uparrow}_{O, p} | volume/day | oil production rate for p-th producer, | C_O | cash/volume | cost of oil treatment at surface, | R_O | cash/volume | oil price, |
---|---|---|---|---|---|---|---|---|
q^{\uparrow}_{G, p} | volume/day | gas production rate for p-th producer, | C_G | cash/volume | cost of gas treatment at surface | R_G | cash/volume | gas price |
q^{\uparrow}_{W, p} | volume/day | water production rate for p-th producer | C_W | cash/volume | cost of water treatment at surface | N^{\uparrow} | cash/volume | number of producers |
q^{\uparrow}_{L, p} | volume/day | liquid production rate for p-th producer | C^{\uparrow}_L | cash/volume | cost of fluid lift, cash/volume | N^{\downarrow}_W | cash/volume | number of water injectors |
q^{\downarrow}_{W, i} | volume/day | water injection rate for i-th water injector | C^{\downarrow}_W | cash/volume | cost of water injection, including purchase, treatment, transportation and pumping | N^{\downarrow}_G | cash/volume | number of gas injectors |
q^{\downarrow}_{G, i} | volume/day | gas injection rate for i-th gas injector | C^{\downarrow}_G | cash/volume | cost of gas injection, including purchase, treatment, transportation and pumping | t | months | time |
This can be rewritten in terms of sandface flowrates:
(2) | G = \sum_{p=1}^{N_{\rm prod}} G^{\uparrow}_{ut,p} \cdot q^{\uparrow}_{t, p} - \sum_{i=1}^{N_{W, \rm inj}} G^{\downarrow}_w \cdot q^{\downarrow}_{w, i} - \sum_{j=1}^{N_{G, \rm inj}} G^{\downarrow}_g \cdot q^{\downarrow}_{g, i} \rightarrow \rm max |
where
\displaystyle G^{\uparrow}_{t,p} |
\displaystyle G^{\downarrow}_w = B_w \cdot C_{W, \rm inj} |
\displaystyle G^{\downarrow}_g = B_g \cdot C_{G, \rm inj} |
See Also
Petroleum Industry / Upstream / Production / Field Development Plan
Subsurface Production / Well & Reservoir Management / [ Production Targets ]
Subsurface E&P Disciplines / Production Technology