The general form of objective function for production targets optimisation is given by:

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_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max

where

oil production rate for -th producer, volume/day	cost of oil treatment, cash/volume	oil price, cash/volume
gas production rate for -th producer, volume/day	cost of gas treatment, cash/volume	gas price, cash/volume
water production rate for -th producer, volume/day	cost of water treatment, cash/volume	number of producers
liquid production rate for -th producer, volume/day	cost of fluid lift, cash/volume	number of water injectors
water injection rate for -th water injector, volume/day	cost of water injection, cash/volume	number of gas injectors
gas injection rate for -th gas injector, volume/day	cost of gas injection, cash/volume	time

This can be rewritten in terms of sandface flowrates:

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

G = \sum_{p=1}^{N_{\rm prod}} \left[ (R_O -C_O) \cdot q^{\uparrow}_{O, p} + (R_G-C_G) \cdot  q^{\uparrow}_{G, p}
- C_L  \cdot q^{\uparrow}_{L, p} - C_W  \cdot q^{\uparrow}_{W, p} \right] 
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj}  \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj}  \cdot q^{\downarrow}_{G, i} \rightarrow \rm max

G = \sum_{p=1}^{N_{\rm prod}} \left[ \left[ (R_O -C_O) + (R_G-C_G) \cdot GOR \right] \cdot  q^{\uparrow}_{O, p}
- (C_L + C_W \cdot Y_w)  \cdot q^{\uparrow}_{L, p}  \right] 
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj}  \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj}  \cdot q^{\downarrow}_{G, i} \rightarrow \rm max

G = \sum_{p=1}^{N_{\rm prod}} \left[ \left[ (R_O -C_O) + (R_G-C_G) \cdot GOR \right] \cdot  (1-Y_w)
- (C_L + C_W \cdot Y_w)    \right] \cdot q^{\uparrow}_{L, p}
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj}  \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj}  \cdot q^{\downarrow}_{G, i} \rightarrow \rm max

See Also