Page 321 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 256

3
109
8
7
6
5
4
3
2

10 2
9
8 7
k (md) 6 5 4
3
2

10
9
8
7
6
5
4
3
2

1 2 3 4 5 7 89 2 3 4 5 789 2 3 4 5 789 2 3 4 5 789
10 5 10 6 10 7 10 8 10 9
β - FACTOR (1/cm)

Fig. 8.8 Laboratory determined relationship between β ββ β and the absolute permeability
A relationship is usually derived of the form

constant
β = (8.28)
k α

in which the exponent α is a constant. For the experimental results shown in fig. 8.8 the
specific relationship is

2.73 × 10 10
β =
k 1.1045

-1
where k is in mD and β in ft . Providing that the range of porosity variation in the
samples is not too great, the variation of β with φ can be neglected in comparison with
the variation of β with the absolute permeability.

The experimental value of β so determined is applicable to the flow of gas at 100%
saturation. In the presence of a liquid saturation, e.g. connate water and immobile
7,8
liquid condensate, Gewers, Nichol and Wong have experimentally determined that
the permeability term in equ. (8.28) should be replaced by the effective permeability to
gas at the particular liquid saturation S L, thus

constant
β = α (8.29)
(kk rg )

It should be noted that the experimental work of Gewers, Nichol and Wong, in directly
measuring β in the presence of a liquid saturation, was conducted on microvugular
carbonate rock samples for which the dry core β values are at least an order of