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220 Part III Underbalanced Drilling Systems

formation damage due to the pressure surge inside the reservoir that
mobilizes the formation fines and plugs reservoir pores.
The pressure fluctuation can be characterized with the term instability
factor, which is defined as the ratio of the change in bottomhole pressure
to the change in surface pressure ðΔP BH /ΔP S Þ. Figure 10.9 plots the
pressure instability factor for the conditions in Figure 10.8. The highest
3
instability factor occurs for gas injection rates between 5 m /min and
3
10 m /min for the examined cases. Beyond this gas injection range,
increasing the gas injection rate lowers the instability factor. It is generally
believed that instability factors below 1.5 are manageable in UBD
operations.
Guo and Ghalambor (2006) presented the following mathematical
model for estimating the instability factor:

ð1 − 2bmÞðP S + mÞ − ðm + bn − bm Þ
2
b + c
2
ðP S + mÞ + n
≈ = (10.1)
ΔP BH dP BH
ð1 − 2bmÞðP BH + mÞ − ðm + − bm Þ
ΔP S dP S bn 2
b + c
2
ðP BH + mÞ + n

3.0
3
Liquid Injection Rate=0.1m /min
2.5

2.0
Δ P BH / Δ P S 1.5

1.0

0.5
3
Liquid Injection Rate=0.9m /min
0.0
0 10 20 30 40 50 60
3
N Injection Rate (m /min)
2
Figure 10.9 Pressure instability factor for the conditions in Figure 10.8.