The general form of objective function for production targets optimisation is given by:
(1) | 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}_P} C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{O,p} \cdot q^{\uparrow}_{O, p} - \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{G,p} \cdot q^{\uparrow}_{G, p} - \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,p} \cdot q^{\uparrow}_{W, p} - \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i} - \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j} \rightarrow \rm max |
where
q^{\uparrow}_{O, p} | volume/day | oil production rate for p-th producer, | C^{\uparrow}_{O,p} | cash/volume | cost of produced oil treatment and transportation from wellhead to CMS | R_O | cash/volume | oil selling price |
---|---|---|---|---|---|---|---|---|
q^{\uparrow}_{G, p} | volume/day | gas production rate for p-th producer, | C^{\uparrow}_{G,p} | cash/volume | cost of produced gas treatment and transportation from wellhead to CMS | R_G | cash/volume | gas selling price |
q^{\uparrow}_{W, p} | volume/day | water production rate for p-th producer | C^{\uparrow}_{W,p} | cash/volume | cost of produced water treatment and transportation from wellhead to CMS | N^{\uparrow}_P | counts | number of producers at t |
q^{\uparrow}_{L, p} | volume/day | liquid production rate for p-th producer | C^{\uparrow}_{L, p} | cash/volume | cost of fluid lift to the wellhead, cash/volume | N^{\downarrow}_W | counts | number of water injectors at t |
q^{\downarrow}_{W, i} | volume/day | water injection rate for i-th water injector | C^{\downarrow}_{W,i} | cash/volume | cost of water injection, including purchase, treatment, transportation and pumping | N^{\downarrow}_G | counts | number of gas injectors at t |
q^{\downarrow}_{G, i} | volume/day | gas injection rate for i-th gas injector | C^{\downarrow}_{G,j} | cash/volume | cost of gas injection, including purchase, treatment, transportation and pumping | t | months | time |
Left part of equation (1) can be rewritten in terms of Sandface flowrates:
(2) | G = \sum_{p=1}^{N^{\uparrow}_P} G^{\uparrow}_{t,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, j} \rightarrow \rm max |
(3) | G^{\uparrow}_{t,p} = \frac{\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{g,p} \right] \cdot (1- Y_{w,p}) - C^{\uparrow}_{L,p} \cdot q^{\uparrow}_{L, p} - C^{\uparrow}_{W,p} \cdot Y_{w,p} } {B_w Y_{w,p} + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_{g,p} \right] \cdot (1-Y_{w,p})} |
(4) | G^{\downarrow}_w = B_w \cdot C^{\downarrow}_W |
(5) | G^{\downarrow}_g = B_g \cdot C^{\downarrow}_G |
where
Bo, Bg, Bw | |
Yg,p | |
Yw,p |
See Also
Petroleum Industry / Upstream / Production / Field Development Plan
Subsurface Production / Well & Reservoir Management / [ Production Targets ]
Subsurface E&P Disciplines / Production Technology