PETE 325 PETROLEUM PRODUCTION SYSTEMS LAB
Lab Week 10: Stimulation Design and Materials
Note: All references to PPS book (your text for the course) are for the second edition.
Objectives:
 Understand how to compute skin for different types of stimulation scenarios.
 Understand how to compute productivity ratios for undamaged/damaged reservoirs.
 Have a basic understanding of stimulation design criteria.
Equipment: Computer, PPS book
Discussion:
 Discuss Hawkin’s formula
 Discuss the effect of closure stress on conductivity.
Derivation of Hawkin’s formula
1. Let us say we have a well with a radius rw and a damaged zone radius, rs. The
undamaged permeability is k and the damaged permeability is ks. Derive
Hawkins’ formula.
2. Assume we are discussing a carbonate reservoir. Also, assume that this reservoir
has been acidized, and wormholes with average radii of penetration of rwh were
created.
 Will the definition of skin be different when rwh > rs and rwh < rs?
 Using Hawkins’ reasoning, derive an expression for skin factor for the
following scenarios:
o rwh < rs
o rwh > rs
Note: Refer to page 538 of PPS book.
3. Diversion is sometimes necessary when acid is to be pumped into large intervals
or intervals with large permeability contrasts. This is to ensure uniform
distribution of acid across the treatment interval.
 What are some methods used for diversion during matrix acidizing
treatments?
o Refer to relevant sections of the PPS book (pages 496-509).
 One mechanism used for uniform distribution of acid into treatment intervals
is viscous diversion. In this method, flow resistance is increased in higher
permeability regions as a result of the injection of viscous fluid. This process
can be modeled as viscous skin effect defined by the following equation:
  gel
  rgel
s vis  
 1 ln 
 
  rw




rgel is the radius penetrated by the gel. Using Hawkin’s reasoning, derive the above
expression.
Effect of skin improvement on PI-ratio
4. We have shown in your class notes (Week 8) that if an undamaged well in a
sandstone reservoir is acidized, the resultant productivity increase is marginal. If
however, an undamaged well in a carbonate reservoir is stimulated, the resultant
productivity increase is substantial.
 Illustrate these two observations by re-producing Figure 14-2 of the PPS
book (Page 446)
 In this context, summarize the contrast between sandstone and carbonate
matrix acidizing in your own words.
Acidizing volumes example
5. In a well 7000 ft deep, an engineer decided to perforate in the overbalanced
condition. As a result of this operation, debris is displaced into the reservoir 3.9ft
in the radial direction from the wellbore. It was determined by laboratory tests
that acid can be used to remove this damage. The engineer wants to design the
acidizing operation. Answer the following questions to help the engineer with the
design (Note: reservoir / perforation thickness = 100ft).
 What is the volume in barrels of the 3.5” OD, 12.95 #/ft tubing?
 What is the volume of acid, in barrels, needed to contact the 3.9 feet of
damage in the reservoir (porosity=0.3)?
 What is the cost of the acid if acid costs $100/barrel? Assume mobilization
fee is $10,000 and a one-time service charge for pumping the acid of
$20,000.
 Let us say the production tubing is partially plugged with calcium
carbonate scale. A caliper run was made and it was determined that the
cross-sectional flow ID was reduced by 0.75”. We can further assume that
this restriction continues for 1000ft. We know 1 cubic feet of acid will
remove 12.2 cubic feet of calcium carbonate scale. How much acid would
the engineer have to pump to remove all these scale from the tubing
assuming instant dissolution?
Fracturing
6. Answer the following questions:
 Name 10 fluid additives used in gelled fracture fluids and describe their
functions (include FracFocus.Org in your study).
o In addition to the above, using your class notes and literature,
determine the most important components of a cross-linked
fracturing fluid.

In the fracturing of shales, slickwater is used as the fracturing fluid. List
the most important component(s) of slickwater.

Name 3 different types of proppant.
o What are their strength ranges?
o How are they obtained (mined, manufactured) and what are the
steps of getting from raw material to finished product

Liquified propane as base fluid is being used in some fracturing
applicatons. Discuss where it has been used and several advantages and
disadvantages of using this base fluid. List any literature citations you can
find on use of propane as a frac fluid.

Explain in your own words what these terms mean in the context of
hydraulic fracturing. For each of the terms, use a maximum of 5 lines.
o
o
o
o
o
o
o
o
o

Fracture conductivity
In-situ stress
Closure stress
Blender
Fracturing fluid
Bottomhole treating pressure
Tortuosity
Perforation friction
Net Pressure
The Nierode and Kruk model for conductivity estimation at zero closure
stress in acid fracturing is as follows:
k w
f
0
 1.47 x10 7 wi2.47
(1)
(The width is in inches)
o Make a plot of conductivity at zero closure stress versus the width
(vary the width values from 0.01 to 0.35 inches).
o Assume the fracture is now subjected to a given level of closure stress.
Is the fracture conductivity expected to increase or decrease? Why?
o If you were an engineer and you wanted to modify equation (1) above
to include the effect of closure stress, how would you do it?
Hint: Multiply the existing equation by a function that is dependent on
closure stress. There are multiple answers to this part of the question.
7. It has been determined via experiments using rock from a given province and
using a particular proppant that fracture conductivity (md-ft) varies with closure
stress according to the following relationship:
wk f  3.4 1013 1.5 ,  is the effective closure stress expressed in N/m2.
The drainage radius is 745 ft, width of the fracture is 0.1 inch, fracture half-length=500ft,
fracture height=100ft, reservoir permeability=0.1md, effective closure stress is 6000psi.



What is the dimensionless fracture conductivity?
What is the equivalent skin effect due to the presence of the hydraulic fracture?
What is the post-fracturing dimensionless productivity index for this scenario?