The general form of objective function for production targets optimisation is given by:
G(t) = \sum_{k=1}^{N^{\uparrow}_P} \left[ R_O \cdot q^{\uparrow}_{O, k} + R_G \cdot q^{\uparrow}_{G, k} \right] - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{L,k} \cdot q^{\uparrow}_{L, k} - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{O,k} \cdot q^{\uparrow}_{O, k} - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{G,k} \cdot q^{\uparrow}_{G, k} - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{W, k} - \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
volume/day | oil production rate for | cash/volume | cash/volume | oil selling price | ||||
---|---|---|---|---|---|---|---|---|
volume/day | gas production rate for | cash/volume | cash/volume | gas selling price | ||||
volume/day | water production rate for | cash/volume | counts | number of producers at | ||||
volume/day | liquid production rate for | cash/volume | cost of fluid lift from reservoir to the | counts | number of water injectors at | |||
volume/day | water injection rate for | cash/volume | cost of water injection, including purchase, treatment, transportation and pumping into | counts | number of gas injectors at | |||
volume/day | gas injection rate for | cash/volume | cost of gas injection, including purchase, treatment, transportation and pumping into | months | time |
The objective function can be rewritten in terms of Surface flowrates
:
G(t) = \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{OGW} \cdot q^{\uparrow}_{L, 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} |
C^{\uparrow}_{OGW}(t) = \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} - C^{\uparrow}_{W,p} \cdot Y_{w,p} |
where
Watercut in | |
Gas-Oil Ratio in |
Usually, each well has a fixed range of its rate variations:
q^{\uparrow}_{LMIN, p} \leq q^{\uparrow}_{L, p} \leq q^{\uparrow}_{LMAX, p}, \ q^{\downarrow}_{WMIN, i} \leq q^{\downarrow}_{W, i} \leq q^{\downarrow}_{WMAX, i}, \q^{\downarrow}_{GMIN, j} \leq q^{\downarrow}_{G, j} \leq q^{\downarrow}_{GMAX, j} |
The objective function can be further rewritten in terms of Sandface flowrates
:
G = \sum_{k=1}^{N^{\uparrow}_P} G^{\uparrow}_{t,k} \cdot q^{\uparrow}_{t, k} - \sum_{i=1}^{N^{\downarrow}_W} G^{\downarrow}_{w,i} \cdot q^{\downarrow}_{w, i} - \sum_{j=1}^{N^{\downarrow}_G} G^{\downarrow}_{g,j} \cdot q^{\downarrow}_{g, j} \rightarrow \rm max |
G^{\uparrow}_{t,k} = \frac{\left[ (R_O - C^{\uparrow}_{O,k}) + (R_G - C^{\uparrow}_{G,k}) \cdot Y_{g,k} \right] \cdot (1- Y_{w,k}) - C^{\uparrow}_{L,k} - C^{\uparrow}_{W,k} \cdot Y_{w,k} } {B_{w,k} Y_{w,k} + \left[ (B_{o,k} - R_{s,k} B_{g,k}) + (B_{g,k} - R_{v,k} B_{o,k}) \, Y_{g,k} \right] \cdot (1-Y_{w,k})} |
G^{\downarrow}_{w,i} = B_{w,i} C^{\downarrow}_{W,i} |
G^{\downarrow}_{g,i} = B_{g,i} \cdot C^{\downarrow}_{G,i} |
where
Water FVF for | BHPin | ||
Oil FVF for | Solution GOR in | ||
Gas FVF for | Vaporized Oil Ratio in |
|
Depending on Lift mechanism the rates in equation may be set directly or calculated from THP and formation pressure
(which is a usual case in injection wells):
q^{\uparrow}_{t, k} = J_{t,k} \cdot ( p_{e,k} - p_{wf,k} ) |
G^{\downarrow}_{w,i} = J_{w,i} \cdot ( p_{wf,i} - p_{e,i} ) |
G^{\downarrow}_{g,i} = J_{g,i} \cdot ( p_{wf,i} - p_{e,i} ) |
Producing wells may spontaneously vary between Constant rate production: qL = const and Constant pressure production: pwf = const (see Constant rate production: qL = const for alternation details).
Petroleum Industry / Upstream / Production / Field Development Plan
Subsurface Production / Well & Reservoir Management / [ Production Targets ]
Subsurface E&P Disciplines / Production Technology
[ Constant rate production: qL = const ] [ Constant pressure production: pwf = const ]