field-average pressure within the 9-cell area

p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l}

p_{e9, \ i,j} = \frac{1}{9} ( p_{i,j}
+ p_{i, \, j+1} + p_{i, \, j-1}
+ p_{i-1, \, j} + p_{i-1, \, j}
+ p_{i-1 \, j-1} + p_{i+1, \, j+1}
+ p_{i-1 \, j+1} + p_{i+1, \, j-1} )

phase flowrate at sandface:

(each fluid phase separately)

phase productivity index:

, ,

field-average pressure within the drainage area

p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS

surface component flowrate

(each fluid component separately)

and sometimes liquid flowrate

fluid component productivity index:

, ,

and sometimes liquid productivity index:

average pressure value along the boudary of drainage area

p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl

where is the boundary of drainage area

total flowrate at sandface:

– for Black Oil

– for Volatile Oil

or pseudo-components of Compositional Model

total multiphase productivity index: