لخّصلي

If the assumed aquifer and dimensionless time are correct, the plot will be a straight line with N being the Y-intercept and C being the slope.In addition, statistical methods could be used in the consistency test to determine for a preassigned degree of probability the confidence band for the calculated values of N and C. In many large fields, it is often found that an infinite linear water drive satisfactorily describes the production pressure behavior of the said fields, it is suggested to try first the infinite linear case to determine if a successful solution could be obtained.As it is evident from the foregoing, there are two basic sources of errors, systematic and random, which could prevent the obtention of a straight line when Eq. 3a is applied.A systematically upward or downward curved line suggests that the ??p Q (?td) is too small or too large, respectively.After satisfactory values for r e r a / and for (?tD) are chosen, the results can be refined by applying the standard deviation test suggested by van Everdingen, et al.'The slopes of the N and C straight lines are then calculated and plotted vs their corresponding (?tD ), values on a common graph paper.These are a complete scatter, a line curved upward, a line curved downward, and an S-shaped curve (Fig.In some reservoirs, the standard deviation plotted vs log ?td will not give a sharp minimum but will be "dish-shaped".Proper statistical analysis could indicate which source causes the linearity of the plot predicted by Eg. 3a not to be satisfied.An S-shaped curve indicates that a better fit could be obtained if a linear water influx is assumed.The sequence of the plotted points as indicated by the arrow of Fig.Complete random scatter of the individual points indicates that the calculations and/or the basic data are in error. 3a).However.

If the assumed aquifer and dimensionless time are correct, the plot will be a
straight line with N being the Y-intercept and C being the slope.
Four other different plots beside the straight line may result. These are a complete
scatter, a line curved upward, a line curved downward, and an S-shaped curve (Fig.
3a). Complete random scatter of the individual points indicates that the
calculations and/or the basic data are in error. A systematically upward or
downward curved line suggests that the Σ∆𝑝 Q (∆td) is too small or too large,
respectively. This means that the assumed re/rw and/or the ∆td are, respectively,
too small or too large. An S-shaped curve indicates that a better fit could be
obtained if a linear water influx is assumed. The sequence of the plotted points as
indicated by the arrow of Fig. 3a will persist as long as the aquifer behaves like an
infinite one. This is particularly applicable for infinite or fairly large aquifers. In this
case, non-steady state water influx calculations are a must. On the other hand, if
one suspects the presence of a small aquifer, in which steady-state depletion type
flow would obtain in a short time after production commences, then, it is better to
start with the case shown in Eq. 3b.
After satisfactory values for 𝑟 𝑒 𝑟 𝑎
⁄ and for (∆𝑡𝐷) are chosen, the results can be refined
by applying the standard deviation test suggested by van Everdingen, et al.' The
most probable values for N and C will be those corresponding to the dimensionless
time which gives the minimum standard deviation min. In some reservoirs, the
standard deviation plotted vs log ∆td will not give a sharp minimum but will be
"dish-shaped". This phenomenon usually results from the fact that the particular
reservoir is insensitive to the changes of (∆𝑡𝐷 ). The establishment of the most
probable value of (∆𝑡𝐷), becomes, in such a case, only of academic interest.
An additional criterion used to judge the most probable values for N and C is called
the consistency test, which is described in the following. Several (∆𝑡𝐷), values
around the minimum point of the standard deviation plot are read. For every
chosen (∆𝑡𝐷 ), N and C as functions of real-time are calculated. Plots of N vs real-
time and C vs real-time are constructed, and by means of the least square method,
the best straight line is drawn through the points of every plot. The slopes of the N
and C straight lines are then calculated and plotted vs their corresponding (∆𝑡𝐷 ),
values on a common graph paper. The intersection of the two plots gives the most
probable value for the (∆𝑡𝐷). Theoretically, the two plots should intersect at a value
of zero slope.
This is true because if the correct 𝑟 𝑒 𝑟 𝑎
⁄ and (∆𝑡𝐷), are
chosen, and if the field data are correct, then N and C should not vary with time,
i.e., the N-time plot as well as the C-time plot should result in a zero slope.
As it is evident from the foregoing, there are two basic sources of errors, systematic
and random, which could prevent the obtention of a straight line when Eq. 3a is
applied. Proper statistical analysis could indicate which source causes the linearity
of the plot predicted by Eg. 3a not to be satisfied. In addition, statistical methods
could be used in the consistency test to determine for a preassigned degree of
probability the confidence band for the calculated values of N and C.
In many large fields, it is often found that an infinite linear water drive
satisfactorily describes the production pressure behavior of the said fields, it is
suggested to try first the infinite linear case to determine if a successful solution
could be obtained. However. even in such a case, the confidence band should be
evaluated as a numerical aid in judging the acceptability of N and C.