Page 470 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

426 Production

Solving the above equation for the values of Z at the maximum and mini-
mum gives

a a, p
-
-2 - f 4 - 4-
zl,* = 3 9 3 (6-58)
2
If the algebraic expression under the square root sign is negative or zero,
only one real value of the compressibility factor will satisfy the equation of state
(Figure 63% or d). If, however, the value of the expression under the radical
is positive, three real roots exist and limits for the vapor and liquid phase
compressibility factors can be determined from Equation 6-58. The solutions of
Equation 6-58 represent the value of Z at the maximum and minimum points
of Figure 6-33b. The value of the maximum will represent the largest possible
value for the liquid compressibility factor and the value at the minimum
represents the smallest possible value of the vapor compressibility factor. These
limits can then be used with arbitrary values for the other limit to assure that
the root obtained is the valid one. The limits thus set up are adjusted at the
end of each iteration to narrow the interval of search.
FLOW OF FLUIDS

Fluid is defined as a single phase of gas or liquid or both. Each sort of flow
results in a pressure drop. Three categories of fluid flow: vertical, inclined and
horizontal are shown in Figure 6-34. The engineer involved in petroleum
production operations has one principal objective to move the fluid from some
location in an underground reservoir to a pipeline that may be used to transport
it or storage. Possible pressure losses in complete production system and produc-
tion pressure profile are shown in Figures 6-35 and 636, respectively. On the
way from reservoir to pipeline or storage tank, fluid is changing its temperature,
pressure and, consequently, composition of each phase. In case of dry gas
reservoir a change in pressure and temperature does not create two-phase flow;
also in case of black oil with very small GOR, it could be assumed that two-
phase flow does not occur.
Based on the law of conservation of energy, the total energy of a fluid at
any particular point above datum plane is the sum of the deviation head, the
pressure head and velocity head as follows:

144p v*
H=Zd+-+- (6-59)
Y 2g

In reality, whenever fluid is moving there is friction loss (hJ. This loss describes
the difference in total energy at two points in the system. Expressing the energy
levels at point 1 versus point 2 then becomes

144p v, 144p ve
+
+
+
Z,,
Z,, + 2 1 + 2 h,
=
2
Y1 2g YS 2g
All practical formulas for fluid flow are derived from the abe, where H = total
energy of fluid; Z, = pipeline vertical elevation rise (ft); pl, pp = inlet and outlet