Depth of Valve using Taylor Series Approximation

Estimate gas injection depth is the important factor to be known because it’s data can be used for tubing design to improve oil production. Special thanks go to Arif Pranoto (122060…), my classmate who introduced Taylor Series method to find estimate depth of valve gas injection.

Now, let see the problem. All Vogel assumption applied to this example.

At point of gas injection,

At point of balance,

We can use Cullender and Smith method to calculate surface injection pressure. Because of the large cross-sectional area of the annular space, the frictional pressure losses are often negligible. Then the average temperature and compressibility factor model degenerates to (Economides et al., 1994)

Modification of calculation

Using definition of Taylor Series,


Assume that


Has small value and negligible, thus


Back to equation point of balance,


Subtitute ....


Now, we can estimate depth of valve by this equation

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