...
| LaTeX Math Block |
|---|
| P_{\Psi} \left[ p_{e,n} \ (t) \right] = P_{\Psi} \left[ p_{i,n} \ (0) \right] + \gamma_n^{-1} \cdot \left[
B_{og} \cdot Q^{\uparrow}_{O,nn} + f^{\uparrow}_{W,nn} \cdot B_w \cdot Q^{\uparrow}_{W,n} + \sum_{m \neq n} Q^{\uparrow}_{nm} + \sum_k Q^{\downarrow}_{nk} \right] |
| | LaTeX Math Block |
|---|
| p_{{\rm wf}, n} \ \ \ (t) = p_e \ (t) + 0.5 \cdot J_{On}^{-1} \cdot \left[ q^{\uparrow}_{On}(t) + f^{\uparrow}_{W,nn} \cdot \frac{\mu_W}{\mu_O} \cdot \frac{k_{ro}(s_{w,n})}{k_{rw}(s_{w,n})} \cdot q^{\uparrow}_{Wn}(t) \right] |
|
| LaTeX Math Block |
|---|
| s_{w,n} = \left[ 1 + \frac{B_o}{B_w} \cdot \frac{q^{\uparrow}_{On}}{f^{\uparrow}_{W,nn} \cdot q^{\uparrow}_{Wn}} \right]^{-1} |
| | LaTeX Math Block |
|---|
| Q(t) = \int_0^t q(t) \, dt |
|
| LaTeX Math Block |
|---|
| Q^{\uparrow}_{nm} \ =
\ - \ f^{\uparrow}_{O,nm} \ \cdot B_{ob} \cdot \, Q^{\uparrow}_{O,m}
\ - \ f^{\uparrow}_{G,nm} \ \cdot B_{go} \cdot Q^{\uparrow}_{G,m}
\ - \ f^{\uparrow}_{W,nm} \ \cdot B_w \cdot Q^{\uparrow}_{W,m}
|
| | LaTeX Math Block |
|---|
| Q^{\downarrow}_{nk} \ =
f^{\downarrow}_{G,nk} \ \cdot B_{go} \cdot Q^{\downarrow}_{G,k}
\ + \ f^{\downarrow}_{W,nk} \ \cdot B_w \cdot Q^{\downarrow}_{W,k}
\ + \ B_{go} \cdot Q^{\downarrow}_{GCAP,k} \
\ + \ B_w \cdot Q^{\downarrow}_{WAQ,k}
|
|
| LaTeX Math Block |
|---|
| B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
| | LaTeX Math Block |
|---|
| B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} |
|
...
where
| LaTeX Math Inline |
|---|
| body | B_o, \, B_g, \, B_w, \, R_s, \, R_v |
|---|
|
are
Dynamic fluid properties and | LaTeX Math Inline |
|---|
| body | --uriencoded--P_%7B\Psi%7D [] |
|---|
|
is Normalized Pseudo-Pressure .
The value of cumulative Gas Cap influx
| LaTeX Math Inline |
|---|
| body | --uriencoded--Q%5e%7B\downarrow%7D_%7BGCAP%7D |
|---|
|
is modelled as in
Gas Cap Drive @model.
...
| productivity is a positive number |
| drainage volume is a positive number |
| LaTeX Math Inline |
|---|
| body | --uriencoded--f_%7Bnm%7D \ \geq 0 |
|---|
|
| interference coefficients are all positive numbers |
| LaTeX Math Inline |
|---|
| body | --uriencoded--0 \leq f_%7BW,nn%7D \leq 1 |
|---|
|
| total water production from a given well is a sum of good water and bad water and as such its share of the total water production the good water share is always less or equal to one |
| LaTeX Math Inline |
|---|
| body | --uriencoded--\sum_m f%5e%7B\uparrow%7D_%7BO, nm%7D \ \leq 1 |
|---|
|
|
|
| LaTeX Math Inline |
|---|
| body | --uriencoded--\sum_m f%5e%7B\uparrow%7D_%7BG, nm%7D \ \leq 1 |
|---|
|
|
|
| LaTeX Math Inline |
|---|
| body | --uriencoded--\sum_m f%5e%7B\downarrow%7D_%7BW, nm%7D \ \leq 1 |
|---|
|
|
|
| LaTeX Math Inline |
|---|
| body | --uriencoded--\sum_m f%5e%7B\downarrow%7D_%7BG, nm%7D \ \leq 1 |
|---|
|
|
|
...
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Capacitance Resistance Model (CRM)[ / Capacitance-Resistivity Model (CRM) @model
][ Slightly compressible Material Balance Pressure @model ]
...
