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The basic concepts essential to using MinFrac and implementing the
results are discussed below for each type of analysis:
Step Rate Analysis
 A step rate test is used to
determine the fracture extension pressure. This is typically considered the
upper bound for the minimum horizontal stress or closure pressure.
After breakdown, fluid is pumped at increasing flow rates in a
stair-step fashion. Ideally, each flow rate is maintained until a
stabilized pressure is achieved. In lieu of achieving a stabilized
pressure, it has been proposed periods of equal time for each flow rate can
be used. Regardless, the bottomhole pressure at the end of each rate
interval is then plotted versus rate to identify a change in slope. This
change or “break” indicates the start of fracture extension that is
theoretically equal to the magnitude of the closure pressure plus the
fracture friction and propagation resistance.
Step Down Analysis
 The step
down analysis is used to calculate perforation and near wellbore friction
losses. If the step down analysis is performed using surface treating
pressure, the pipe friction needs to be entered for analysis credibility.
This analysis is used to determine near wellbore pressure loss effects
(i.e., problems with anomaly high pressures which may cause a near wellbore
screen-out).
This analysis is performed after fracture propagation has been
established. Then during shut down the rate is decreased in a stair-step
fashion for a short period of time while the pressure stabilizes. As the
injection rate decreases, the pressure will also decrease as a result of
perforation and near wellbore pressure losses. The relationship between the
decreasing rate and pressure results in a determination of near wellbore
pressure losses.
Horner Analysis
 The Horner plot is used to
determine if pseudo-radial flow developed during pressure decline. If a
semi-log straight line is observed and the line can be extrapolated to a
reasonable value of reservoir pressure, radial or pseudo-radial flow may be
affecting the decline behavior. This suggests that the fracture is already
closed and that data beyond the point of influence need not be considered
in the evaluation of closure.
The Horner plot provides a lower bound, first estimate of closure
pressure.
Regression Analysis
 Regression
Analysis is the procedure where treatment events are identified and
parametric effects evaluated. The specific methodology is as follows:
- Graphically identify the major events that occurred during the
treatment cycle (e.g., Initiation, ISIP, Closure etc.). Diagnostic plots
can be generated using a variety of time functions. These plots are used
in the determination of closure. In addition, a statistical procedure can
be invoked to automatically determine closure.
- Once the events, including closure time, have been identified,
parameters can be selected and history matches performed comparing the
theoretical response to the actual measured data for each fracture model
contained in the program. A regression technique is used to minimize the
difference between the model results and the measured data. This process
can be repeated as many times as desired.
- When satisfied with the combination of history-matched responses and
parameter optimization for the fracture geometry models, calculation of
the fracture geometry and associated fluid loss parameters can be
made.
The following information can be determined from a properly conducted
Regression Analysis:
- Instantaneous shut-in pressure, ISIP.
- Closure pressure, PC.
- Closure time, tC.
- Fracture efficiency, η =
G (tC)/(2 + G (tC)).
- Fraction of PAD, fmin ≈ (1-η)2 and
fmax ≈ (1-η)/(1+η).
- Fracture net pressure, ΔP =
ISIP - PC.
- Parametric uncertainly (history match).
- Applicable fracture model (history match and net pressure).
- Fracture area based on the best-fit geometry model.
- Leakoff coefficient, C, if the fracture area is known.
Derivative Method
The Derivative Method is one of the methodologies for determining
inflection points (i.e. fracture closure). Analyzing the derivative, dP/dt,
as a function of time is a method of determining closure. The resulting
trend represents the rate-of-change of pressure with respect to time.
Depending on the type of data (i.e., flowback or natural decline), the
derivative plot can be used to identify the closure by observing a
characteristic change in the shape of this relationship.
Nolte was the first to implement this concept. In simple terms, if one
can find a time function where the rate of pressure decline with respect to
a time function is a constant during fracture closure, the closure time
would be indicated by a deviation from the measured and theoretical
pressure declines. This concept is formulated below:
ISIP - p(Ψ) = Ψd(ISIP - p)/dΨ =
ΨdP / dΨ
or
p(Ψ) = ISIP - ΨdP / dΨ
Where p is the pressure, p = ISIP - p and Ψ is a time
function.
The time function Nolte purposed was the Nolte G time (i.e., P =
G dP/dG).
During closure the user may perform a minifrac analysis with a time
function that gives the best fit pressure decline match with an inflection
point at closure. Although this time function may give the best fit, it may
not be the "unique solution" in the sense that there could be other
solutions that match equally well.
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