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

G(t) = \sum_{p=1}^{N^{\uparrow}_P} \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^{\uparrow}_O \cdot q^{\uparrow}_{O, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_G \cdot q^{\uparrow}_{G, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_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

volume/day	oil production rate for -th producer,	cash/volume	cost of produced oil treatment and transportation from wellhead to CMS	cash/volume	oil selling price
volume/day	gas production rate for -th producer,	cash/volume	cost of produced gas treatment and transportation from wellhead to CMS	cash/volume	gas selling price
volume/day	water production rate for -th producer	cash/volume	cost of produced water treatment and transportation from wellhead to CMS	counts	number of producers at
volume/day	liquid production rate for -th producer	cash/volume	cost of fluid lift, cash/volume	counts	number of water injectors at
volume/day	water injection rate for -th water injector	cash/volume	cost of water injection, including purchase, treatment, transportation and pumping	counts	number of gas injectors at
volume/day	gas injection rate for -th gas injector	cash/volume	cost of gas injection, including purchase, treatment, transportation and pumping	months	time

This can be rewritten in terms of sandface flowrates:

G = \sum_{p=1}^{N^{\uparrow}_P}} G^{\uparrow}_{ut,p} \cdot q^{\uparrow}_{t, p}
- \sum_{i=1}^{N^{\downarrow_W} G^{\downarrow}_w  \cdot q^{\downarrow}_{w, i}
- \sum_{j=1}^{N^{\downarrow_G} 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