Vertical Models

Introduction

The following is a list of equations for Pseudo-Steady-State (PSS) flow for vertical wells, as well as the general scenario where a well is off-centred. These models are used in both the conventional and unconventional tank models including Coal Seam Gas (CSG) .

In terms of shape factor (for a more general scenario), the equations for oil and gas are recast as shown below:

Where for oil, gas and water:

k = absolute permeability, md

h = net pay, ft

P_r = reservoir pressure, psia

r_e = Drainage radius, ft

r_w = Wellbore radius, ft

C_A=shape factor

A = Area, ft2

Where for oil:

B_o = Oil formation volume factor at Pr, dim

u_o = Oil viscosity at Pr, cp

q_o = oil rate, bbl/d

k_ro = relative permeability to oil, dimensionless

Where for gas:

B_w = Water formation volume factor at Pr, dim

u_w = Water viscosity at Pr, cp

q_w = water rate, bbl/d

k_rw = relative permeability to water, dim

Where for gas:

Ψ_r = Reservoir Pseudo Pressure , psia²/cp

Ψ_wf = Flowing Pseudo Pressure , psia²/cp

k_rg = relative permeability to gas, dim

D = Turbulence factor, 1/Mscf

q_g = Gas Rate, Mscf/d

T = Formation Temperature, ^oR

It is important to note that permeability values can be multiplied by a variety of productivity multipliers such as relative permeability, but also geo-mechanical effects.

See Also:

horizontal wells.