Page 263 - Petroleum Production Engineering, A Computer-Assisted Approach

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17/262 PRODUCTION ENHANCEMENT
of the selected fracture half-length x f and the calculated but this operation is quite time consuming and is not
fracture width w, together with formation permeability the goal of the exercise. Perfect matches are sometimes
(k) and fracture permeability (k f ), can be used to predict proposed by manually changing the number of fractures
the dimensionless fracture conductivity F CD with Eq. during the propagation. Unfortunately, there is no inde-
(17.10). The equivalent skin factor S f can be estimated pendent source that can be used to correlate a variation of
based on Fig. 17.7. Then the productivity index of the the number of fractures. The option of multiple fractures
fractured well can be calculated using Eq. (17.11). Produc- is not available to all simulators. Nevertheless, much pres-
tion forecast can be performed using the method presented sure adjustment can be obtained by changing parameters
in Chapter 7. controlling the near-wellbore effect. Example parameters
Comparison of the production forecast for the fractured are the number of perforations, the relative erosion rate
well and the predicted production decline for the unstimu- of perforation with proppant, and the characteristics
lated well allows for calculations of the annual incremental of fracture tortuosity. These parameters have a major
cumulative production for year n for an oil well: impact on the bottom-hole response but have nothing
DN p,n ¼ N f N nf , (17:36) to do with the net pressure to be matched for fracture
p,n p,n geometry estimate.
where
DN p,n ¼ predicted annual incremental cumulative Matching the Net Pressure during Calibration Treat-
production for year n ment and the Pad. The calibration treatment match is part
N f p,n ¼ forecasted annual cumulative production of the set of analysis performed on-site for redesign of the
of fractured well for year n injection schedule. This match should be reviewed before
N nf ¼ predicted annual cumulative production proceeding with the analysis of the main treatment itself.
p,n
of nonfractured well for year n. Consistency between the parameters obtained from both
matches should be maintained and deviation recognized.
If Eq. (17.36) is used for a gas well, the notations DN p,n , The first part of the treatment-match process focusing
f
nf
N f p,n ,and N nf should be replaced by DN p,n , N p,n ,and N p,n , on the pad is identical to a match performed on the cali-
p,n
respectively.
bration treatment. The shut-in net pressure obtained from
The annual incremental revenue above the one that the a minifrac (calibration treatment decline) gives the magni-
unstimulated well would deliver is expressed as tude of the net pressure. The pad net pressure history (and
DR n ¼ $ðÞDN p,n , (17:37) low prop concentration in the first few stages) is adjusted
by changing either the compliance or the tip pressure. The
where ($) is oil price. The present value of the future Nolte–Smith Plot (Nolte and Smith, 1981) provides indi-
revenue is then cation of the degree of confinement of the fracture.
m
X A positive slope is an indication of confinement, a negative
NPV R ¼ DR n n , (17:38) slope an indication of height growth, and a zero slope an
ð 1 þ iÞ
n¼1 indication of toughness-dominated short fracture or mod-
where m is the remaining life of the well in years and i is the erate height growth.
discount rate. The NPV of the hydraulic fracture project is
Using 2D Models. In general, when the fracture is
NPV ¼ NPV R cost: (17:39) confined (PKN model) and viscous dominated, we either
decrease the height of the zone or increase the Young’s
The cost should include the expenses for fracturing fluid,
proppant, pumping, and the fixed cost for the treatment modulus to obtain higher net pressure (compliance is
job. To predict the pumping cost, the required hydraulic h=E). For a radial fracture (KGD model), we adjust the
horsepower needs to be calculated by tip pressure effect to achieve net pressure match. If the
fractured formation is a clean sand section and the fracture
q i p si
HHP ¼ : (17:40) is confined or with moderate height growth, the fracture
40:8 height should be fixed to the pay zone. In a layered forma-
tion/dirty sandstone, the fracture height could be adjusted
because any of the intercalated layers may or may not have
17.6 Post-Frac Evaluation been broken down. The fracture could still be confined, but
the height cannot a priori be set as easily as in the case of a
Post-frac evaluation can be performed by pressure match-
ing, pressure transient data analysis, and other techniques clean sand zone section. Unconsolidated sands show low
5
Young’s modulus ( 5 10 psi), this should not be
including pumping radioactive materials stages and run-
changed to match the pressure. A low Young modulus
ning tracer logs, running production logging tools, and
value often gives insufficient order of magnitude of net
conducting back-pressure and performing Nodal analysis.
pressure because the viscous force is not the dominating
factor. The best way to adjust a fracture elastic model to
17.6.1 Pressure Matching match the behavior of a loosely consolidated sand is to
Pressure matching with a computer software is the first increase the ‘‘apparent toughness’’ that controls the tip
step to evaluate the fracturing job. It is understood that the effect propagating pressure.
more refined the design model is, the more optional Using Pseudo-3D Models. Height constraint is adjusted
parameters we have available for pressure matching and by increasing the stress difference between the pay-zone
the more possible solutions we will get. The importance of and the bounding layer. Stiffness can be increased with an
capturing the main trend with the simplest model possible increase of the Young modulus of all the layers that are
can only be beneficial. Attention should be paid to those fractured or to some extent by adding a small shale layer
critical issues in pressure matching such as fracture con- with high stress in the middle of the zone (pinch-point
finement. Therefore, all the lumped pseudo-3D models effect). Very few commercial fracturing simulators actually
developed for processing speed of pressure-matching ap- use a layer description of the modulus. All of the lumped
plications are widely used. 3D models use an average value. Tip effect can also be
The final result of the net pressure-matching process adjusted by changing toughness (Meyer et al., 1990). For
should ideally be an exact superposition of the simulation some simulators, the users have no direct control of this
on the pumping record. A perfect match is obtainable by effect, as an apparent toughness is recalculated from the
adjusting controlling parameter of a fracture simulator, rock toughness and fluid-lag effect.