### Inflow Performance Relationship of Vertical & Slanted Solution Gas-Drive Wells

This Excel spreadsheet calculates the Inflow Performance Relationship, or IPR, for vertical and slanted solution-gas drive wells.

The IPR of a well determines the relationship between its flowing bottom pressure, and the well production rate (or deliverability). IPR also helps engineers investigate the economics of a well, and is critical in optimizing the well, artificial lift design and determining the nature of the surface equipment.

For single-phase fluids, the IPR relationship is linear. However, when two-phase liquid and gas below its bubble-point pressure are produced, the relationship is non-linear.

Several researchers have studied this process, most notably Vogal (1968) and Cheng (1990). Cheng's semi-empirical correlation is applied to slanted wells, while Vogal's work applies to vertical wells.

Vogel and Cheng's equations are

where
• q0 is the flow rate in bbl/day
• q0,max is the oil flow rate at a flowing bottom hole pressure of 0 in bbl/day
• pwf is the flowing bottom hole pressure in psi
• pr is the reservoir pressure in psi
• a0, a1 and a2 are empirical parameters that vary with the slant angle. In the spreadsheet these parameters are listed again several values of the slant angle. Intermediate values are linearly interpolated.

### Ergun Equation Calculator

This Excel spreadsheet helps you calculate the pressure drop through packed and fluidizeds bed with the Ergun equation.

Fluidized beds are a commonly unit operation in the process industries. Their nature makes them particularly suitable venues for gas-solid catalyzed reaction, often in the petroleum industry to produce gasoline and other chenicals. They have also found use in the polymer industry, and bioreactors (in the form of liquid fluidized beds)

In 1952, Sabri Ergun derived the following equation to predict the pressure drop in packed beds.

• ΔP is the pressure drop
• L is the height of the bed
• Dp is the particle diameter
• ε is the porosity of the bed
• μ is the gas viscosity
• V0 is the superficial velocity (the volumetric gas flowrate divided by the cross-sectional area of the bed)
• ρg is the gas density
The pressure drop required for minimum fluidization is given by

• ρp is the particle density
• εM is the porosity of the bed at minimum fluidization
By comparing the pressure drop given by the Ergun equation to the pressure drop for minimum fluidization, you can calculate the superficial velocity necessary for fluidization. At this point, bubbles of gas form and rise through the bed. This increases the effective volume of the bed.

### Liquid Volume in Partially Filled Horizontal Tanks

This Excel spreadsheet helps you calculate the liquid volume in partially filled horizontal tanks.

Tanks are often used in storing chemicals. Often, only the liquid height from a level indicator is known. This means you need a method of calculating the liquid volume based on the liquid height and the tank dimensions.

The tank ends can be

• flat (so the tank is just a horizontal cylinder)#
• dished (ASME F&D, or Flanged & Dished)
• 2:1 elliptical
• hemispherical
The liquid volumes in a horizontal cylinder, and ASME F&D, 2:1 elliptical and hemispherical ends are given by these equations.

where
• D is the diameter of the cylinder and the heads
• L is the length of the cylindrical shell
• h is the height of liquid in the tank
The diagram at the top illustrates the notation.

Hence the total volume of liquid in the tank is simply the liquid volume in the cylinder plus 2 times the liquid volume in the heads.

The dimensions can be specified in any length unit. The unit of the volumes will simply be the length unit cubed.

This spreadsheet can be easily modified to created a Dip chart (i.e. a chart giving the liquid volume as a function of liquid height).