The general form of objective function for production targets optimisation is given by:
| (1) | G = \sum_{p=1}^{N_{\rm prod}} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot q^{\uparrow}_{G, p} \right] - \sum_{p=1}^{N_{\rm prod}} C_L \cdot q^{\uparrow}_{L, p} - \sum_{p=1}^{N_{\rm prod}} C_O \cdot q^{\uparrow}_{O, p} - \sum_{p=1}^{N_{\rm prod}} C_G \cdot q^{\uparrow}_{G, p} - \sum_{p=1}^{N_{\rm prod}} C_W \cdot q^{\uparrow}_{W, 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 |
where
q^{\uparrow}_{O, p} | oil production rate for p-th producer, volume/day | C_O | cost of oil treatment, cash/volume | R_O | oil price, cash/volume |
|---|---|---|---|---|---|
q^{\uparrow}_{G, p} | gas production rate for p-th producer, volume/day | C_G | cost of gas treatment, cash/volume | R_G | gas price, cash/volume |
q^{\uparrow}_{W, p} | water production rate for p-th producer, volume/day | C_W | cost of water treatment, cash/volume | ||
q^{\uparrow}_{L, p} | liquid production rate for p-th producer, volume/day | C_L | cost of fluid lift, cash/volume | ||
q^{\downarrow}_{W, i} | water injection rate for i-th water injector, volume/day | C_{W, \rm inj} | cost of water injection, cash/volume | ||
q^{\downarrow}_{G, i} | gas injection rate for i-th gas injector, volume/day | C_{G, \rm inj} | cost of gas injection, cash/volume |
| (2) | 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 |
| (3) | 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 |
| (4) | 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
Petroleum Industry / Upstream / Production / Field Development Plan
Subsurface Production / Well & Reservoir Management / [ Production Targets ]
Subsurface E&P Disciplines / Production Technology