Modelling facility for field-average formation pressure p(t) at any time moment t as response to production flowrates history:
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where
p_i | initial formation pressure: p_i = p(0) | Q^{\uparrow}_O(t) | Cumulative oil production by the time moment t |
V_e | initial oil+gas pay drainage volume (excluding the aquifer and gas cap) | Q^{\uparrow}_G(t) | Cumulative gas production by the time moment t |
c_\phi | pore compressibility | Q^{\uparrow}_W(t) | Cumulative water production by the time moment t |
s_{wi} | initial water saturation | Q^{\downarrow}_W(t) | Cumulative water injection by the time moment t |
s_{gi} | initial gas saturation | Q^{\downarrow}_G(t) | Cumulative gas injection by the time moment t |
s_{oi} | initial oil saturation: s_{oi} = 1 - s_{wi} - s_{gi} | Q^{\downarrow}_{WAQ}(t) | Cumulative water influx from Aquifer Expansion by the time moment t |
B_o(p) | Oil formation volume factor as functions of reservoir pressure p | Q^{\downarrow}_{GCAP}t) | Cumulative gas influx from Gas Cap expansion by the time moment t |
B_g(p) | Gas formation volume factor as functions of reservoir pressure p | ||
B_w(p) | Water formation volume factor as functions of reservoir pressure p | ||
R_s(p), \, R_v(p) | Solution GOR and Vaporized Oil Ratio as functions of reservoir pressure p |
The MatBal equation (1) is often complemented by constant PI model of Bottom-Hole Pressure ( p^{\uparrow}_{wf}(t) for producers and p^{\downarrow}_{wf}(t) for injectors):
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where | where | ||||||
p^{\uparrow}_{wf, \, k}(t) | p^{\downarrow}_{wf, \, j}(t) | ||||||
Q^{\uparrow}_k(t) | cumulative offtakes from k-th producer by the time moment t | Q^{\downarrow}_j(t) | cumulative intakes to j-th injector by the time moment t | ||||
J^{\uparrow}_k | productivity index of k-th producer | J^{\downarrow}_j | injectivity Index of j-th injector |
In practice there is no way to measure the external influx Q^{\downarrow}_{GC}(t) and Q^{\downarrow}_{AQ}(t) so that one need to model them and calibrate model parameters to fit available data on production flowrates history and formation pressure data records.
There is a list of various analytical Aquifer Drive and Gas Cap Drive models which are normally related to pressure dynamics p(t):
Gas Cap Drive @model | Aquifer Drive @model | ||||
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which closes equation (1) for the pressure p(t).
Variations
In some specific cases equation (1) can be explicitly integrated:
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\{ \phi_e = {\rm const}, \ c_t = {\rm const} \} | c_t = c_r + \frac{1}{p} \sim \frac{1}{p} | ||||
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where
V_e = A_e \, h_e \, \phi_e | drainage volume |
This allows using simple graphical methods for estimating drainage volume V_e.
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Material Balance Analysis (MatBal)
[ Material Balance Pressure Plot ][ FMB Pressure @model]
[ Derivation of Material Balance Pressure @model ]