Topic: Pressure Loss in Production Tubing
Consider a producer well with TVD of 6250 ft. (Depth of completed zone from the surface). in a formation that has pore pressure gradient of 0.48 psi/ft. (assumed linear for simplicity). Flowing bottom hole pressure is maintained at 2000 psi where the fluid density is 0.001 ppg. The well index for this specific producer is estimated to be 4 bbl/day/psi. Assume that the fully turbulent, single-phase compressible flow of produced fluid inside the production tubing (ID = 2.5") to the wellhead would result in linear gradient in the fluid density of 1.6 x 10-4 ppg/ft (density decreases due to fluid compressibility at lower pressures) while the fluid viscosity remains constant (= 3 cP). The governing equation for the pressure loss per unit length of the production tubing has two main contributions: hydrostatic pressure head (due to gravity) and frictional pressure loss (due to fluid viscosity):
dp/dx = ρg + ƒρV2/2D
Use the following Blasius correlation for friction factor: ?? = 0.0791Re-0.25; Re = ρVD/μ
HINT: Production rate = Well Index *(Pressure Drawdown). Maintain same "mass" flow rate throughout the production tubing.
Task 1: Write a general program that performs numerical integration for N given data points using Newton-Cotes formulae.
Task 2: Write a main subroutine that reads in the given data from the input deck on the spreadsheet, call the general numerical integration subroutine, and output the pressure gradient along the tubing using 25 and 50 nodes to determine the flowing wellhead pressure.
Plot the pressure vs. depth to show the pressure traverse curves at different discretizations.
Break the Main code into several subroutines:
Sub Wellbore
Dim rhs_1(n), rhs_2(n)
Dim dt, dx, mu, ct as double
...
Call Initialize
Call friction factor
...
Call NumericalIntegration(dx, rhs_1, rhs_2, integration, Pwh)
... Call Output
End