reservoir base fracture optimization approach

This innovative fracture design methodology has capability to determine appropriate fracture conductivity and an economic optimum fracture length while reconciling these with actual frac

Copyright 2004, Society of Petroleum Engineers Inc

This paper was prepared for presentation at the SPE International Thermal Operations and

Heavy Oil Symposium and Western Regional Meeting held in Bakersfield, California, U.S.A.,

16–18 March 2004

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Abstract

A new methodology to obtain the optimum fracture treatment

design for a wide range of reservoir conditions has been

developed and successfully implemented The approach

discussed here significantly reduces the time required to

evaluate an optimum design and limits the materials considered

to only those that are appropriate for the reservoir conditions

These improvements make it an ideal methodology for

real-time re-design of fracture treatments after feedback from

minifrac data has been implemented

This innovative fracture design methodology has capability

to determine appropriate fracture conductivity and an economic

optimum fracture length while reconciling these with actual

fracture growth behavior in the reservoir The technique

incorporates the following simple, automated steps:

1 Selects the most cost-effective fluid that will meet a

minimum apparent viscosity requirement at a specified shear

rate and temperature condition from a large industry fluid

library to ensure that the proppant will be placed within the

pay zone

2 Selects a proppant that will provide the required fracture

conductivity at the cheapest cost from a large industry library

3 Determines the proppant concentration that is required at

the wellbore to achieve a user-specified dimensionless

conductivity criterion for a range of fracture lengths

4 Evaluates economic criteria such as net present value

(NPV) and return on investment (ROI) for different fracture

lengths by comparing fracture treatment cost and revenues

from production response

5 Determines the optimum fracture conductivity profile that

will have a uniform pressure drop down the fracture The

conductivity is adjusted for potential losses from non-Darcy

and multi-phase flow, gel damage, embedment, and other

proppant damage effects

6 Iterates a fracture treatment schedule that will result in the best fit of the optimum conductivity profile

The methodology can help optimize fracture treatments in any type of environment The technique is simple and can be run quickly in a real-time environment after a minifrac is conducted to make changes to the propped fracture treatment The procedure has been implemented in a commercially available fracture design program

Introduction/Background

During the last two decades, the oil and gas industry has actively been seeking methods to optimize its various processes In the most recent activity, the drive for optimization has focused on operator cost reduction to improve project NPV

In the completion of a well, the fracturing process has the potential to add the most value because of the enormous effect

it can have on overall reservoir performance, and consequently,

on the economic outlook of a project Since production pays for the entire cost of the well construction and completion, fracturing efficiency is a key factor in enabling production to meet economic needs

Another need has also been evidenced in the industry; i.e., transferring the knowledge of the aging workforce in our industry to the younger generation in order to prepare for the needs of the next two decades By developing a computer model that captures the optimization processes that an experienced fracture designer would follow when designing a fracturing treatment, a vast store of knowledge can be transferred to the new workforce to provide the tools needed to design an optimized fracturing treatment

The optimization approach to fracture design given in this paper is new to our industry in that it approaches the problem from the opposite direction than other methods; i.e., it uses the conventional design method in most cases What this approach accomplishes is that it reduces the time to develop an optimized solution and constantly considers economic drivers in order to find the treatment that will provide the greatest value for the given reservoir parameters

Since fracture optimization has been considered critical to economic success for quite some time, several approaches have been devised The oldest attempt at fracture optimization was described by Prats.1 The approach that Prats took was to optimize fracture dimensions based on a pre-determined proppant volume Prats discovered that for a certain fracture volume, the fracture that gives the optimum performance should have a dimensionless conductivity of 1.6 Since then, several other authors have re-confirmed Prats’ findings

SPE 86991

Reservoir-Based Fracture Optimization Approach

M Y Soliman, SPE, Audis Byrd, SPE, Harold Walters, SPE, Halliburton Energy Services, Inc., and Leen Weijers, SPE, Pinnacle Technologies, Inc

Theoretically speaking, this approach is probably the most

effective, but unfortunately, several factors can compromise its

general application

First, the fracture volume is not usually the controlling

parameter unless the reservoir is highly permeable Thus, high

fracture conductivity is required to achieve a dimensionless

fracture conductivity of 1.6 If the formation permeability is

low, then it would be advantageous to design the fracture with

significantly higher dimensionless conductivity than 1.6

Second, fracture conductivity always changes with time;

proppant failure, and embedment would cause conductivity to

decline with stress and time.2 It is easy to see that loss of

conductivity when starting with relatively low conductivity

could seriously compromise the fracture performance

Third, it has been found that the clean up of fracturing fluid

and the associated multi-phase flow in the fracture would

require higher conductivity to be effective.3 This is especially

true for tighter gas-bearing formations

Fourth, the presence of several fluids inside the fracture, as

could be expected in all but dry gas reservoirs, would require

higher fracture conductivity than 1.6 to efficiently produce the

reservoir The potential presence of turbulence would also

dictate the creation of highly conductive fractures

As an example, if the formation permeability is 0.1 md, and

we design a 500-ft fracture with a dimensionless conductivity

of 1.6, the required fracture conductivity is only 80 md-ft This

low conductivity would impair the cleanup of the fracture, and

consequently, would negatively affect the productivity of the

well On the other hand, increasing the conductivity to the level

advocated in reference 3 would be fairly inexpensive

Another optimization technique was presented by Poulsen

and Soliman.4 In their approach, Poulsen and Soliman

optimized the proppant distribution inside a fracture in order to

achieve an equivalent fracture with uniform conductivity.5

Although the approach did consider some of the reservoir

properties, it did not optimize the total process In other words,

the designed fracture was not necessarily the optimum fracture

that had the best economical return In addition, the process

used a two-dimensional reservoir simulator approach

The technique considered state-of-the-art in today’s oilfield

is to run a simulator and develop a matrix of possible solutions

for the design parameters Then, the NPV is evaluated for each

design This process is very tedious because of the many

variables that come into play There are different fluids, fluid

concentrations, chemical additives, proppants, proppant

concentrations, and pump rates that can make this a tedious

task The most significant problem with this approach is that

the designer has to select the materials for the design matrix,

and because of the numerous possibilities available, the

designer may not select the best combination of fluids, fluid

concentrations, proppant type, proppant size, etc to produce

the optimum solution for reservoir This approach only picks

the best option in the matrix and is not a true optimization

process For this reason, many people give up on the

optimization process

This process may be also considered a simulation process,

and therefore, needs to be differentiated from the design

process A design process consists of assembling the building

blocks one after another to eventually build the best

fracture design

After the optimization has been done, it is common to perform a pump-in shut-in test to verify the reservoir inputs prior to the treatment on the day of the treatment At this point, there is not enough time on location to re-do the design matrix for the optimization process prior to pumping the treatment It

is for this reason that most of the changes on the day of the treatment are limited to adjusting the PAD volume only and not the proppant pumping schedule

Some of the new 3-D geometry models have a design tool

to speed the process The software integrates the desired proppant concentration into a pumping schedule to provide the desired proppant concentration in the fracture from the tip to the wellbore This approach provides the speed to do the computation on location but only provides a change in the PAD volume and the pumping schedule

A true design model would use the rock mechanics and stress layers to evaluate the fracture-growth profile predicted

by the model, and then, would create an optimized conductivity profile for the permeability of the reservoir It would also create the needed geometry to develop a treatment that may deliver the selected conductivity profile using the best combinations of all the design-material options based on a cost-versus-results basis In this way, the design model can iterate all the variables available to the fracture designer This process can be accomplished successfully if the material criteria limits are defined in a database that the design program can use In cases where no real data base exists, a rule-based system is developed by experts and used to fill in the gaps The criteria can be established by testing, or in other cases, by expert opinion on the appropriate application ranges This allows the developed technique to iterate or make selections on the rule-based system during the process to prioritize the materials appropriate for the design criteria These criteria would include temperature, closure stress, conductivity, two-phase flow, and any other parameters that an expert would deem appropriate

By developing a design process as described above, a consistent design philosophy can be deployed to transfer best practices and enable the novice to design fracture treatments based on the latest technology Using a consistent approach will help prove new technology and any new design philosophies developed as result of applying the new concept

This approach will ensure that the new philosophies will be transferred to everyone using this optimization approach, and thus, reduce the learning curve and training requirements

In this paper, the authors will present a methodology for designing a fracture that results in optimum return from the reservoir This approach relies not only on theoretical considerations, but also on practical experience and considerations Field examples illustrating the application of this methodology will be presented and discussed later in this paper

Fractured Well Productivity Ratio

Fractured-well productivity has been extensively studied, and several production-increase curves have been developed and presented in literature.6-8 These production-increase curves varied in complexity, but all predicted increase in well productivity as a result of fracturing treatments The curves presented by Tinsley, et al6 and Soliman7 are probably the most comprehensive They consider not only the effect of fracture

conductivity and length relative to the reservoir radius, they

consider the effect of fracture height to the total formation

height However, most of the production increase curves and

ratios are given in terms of dimensionless parameters Using

this type of presentation, it is often difficult to translate to

practical values This is the motivation for determining a new

dimensional approach to presenting production increase

concepts to average users

A transient pressure analysis of a vertical fractured well in

pseudo-radial flow, as described by Cinco-Ley and

Samaniego-V.9, forms the basis for the new technique Pseudo-radial flow

is appropriate for evaluating long-term production trends,

which is our area of interest The basic idea was to present the

production increase contours as a function of fracture half

length and fracture conductivity, both of which are widely

understood variables The process is as follows:

For a given reservoir, wellbore conditions and production

increase ratio contours are used to calculate the infinitely

conductive fracture half length

⎜⎜

⎛

−

=

PI

r r r

L f exp ln2d ln d / w (1)

Then, for the finite conductivity fracture half

lengths, calculate

⎜⎜

⎛

−

=

PI

r r r

r w' exp ln d ln d / w (2)

Using the dimensionless curves in Cinco-Ley and

Samaniego-V,9 calculate the dimensionless fracture

conductivity, and finally, the fracture conductivity

f fD

fw C kL

k = (3)

An example of this new type of production increase ratio

curve presentation is given in Figure 1 The figure is for a well

spacing of 320 acres and a wellbore diameter of 7.875 in

Reproducing the figure with a formation permeability of 0.1

md yields Figure 2 Assuming that for an efficient fracture

cleanup a CfDof approximately 30 is required, if a production

increase ratio of 4 is desired, then a fracture conductivity of

about 1300 md-ft would be required

The relationship between the parameters that can be

changed by fracture design, which include fracture half length

and conductivity, are now easily related in a dimensional

fashion to production increase ratios and dimensionless fracture

conductivity The average user is now able to easily examine

the tradeoffs between these variables and make informed

decisionsconcerning their use

Other production increase curves could be plotted easily in

the fashion that would make them more valuable to the

practicing engineer

Outline of the Optimization Process

The integrated computer-aided design and completion approach

presented in this paper includes at least three steps, and

possibly, a fourth step as well The goal of the first step is to

calculate the parameters of an approximately optimized fracture using a simple graphical approach This step includes selecting initial fracture parameters This step also provides an initial completion design to be further optimized in the next steps The second step involves a comprehensive approach to optimizing fracture design based on economics The initial design of step one is the starting point of the optimization process of step two Step three includes adjusting the model parameters on location using real data from the subject well to create an optimized treatment schedule for the fluid and proppant available on location at the time of treatment The fourth step is the inclusion of risk analysis in this optimization process The fourth step is optional, but it will provide another quantitative measure to the optimized design, and while not required for generating the optimum fracture design, does add

an important analysis to the process

The four steps may be based on computational algorithms

or may be based on neural network algorithms The neural network algorithm accurately mimics the behavior of various computational algorithms such as fracture geometry calculation Each of these steps will be described in more detail in the following sections

Initial Design

1 Run logs to determine physical and mechanical properties

of the formation The physical properties may include, for example, permeability, porosity, type of the fluid and fluid saturation The physical properties are usually obtained from a combination of logs such as gamma ray, density, sonic, electric, and pulse neutron logs The mechanical properties include Young’s Modulus and Poisson’s Ratio The stress field, including in-situ stresses at different height locations, can also be determined Logs such as long-spaced sonic and dipole sonic may be used for this task If a magnetic resonance imaging (MRI) tool is used, the list of parameters may also include irreducible fluid saturation, hydrocarbon, and water permeability The MRI log gives a strong indication of the grain size and distribution, and in some cases, clay content Whatever parameters are selected should be digitally encoded

2 Divide the measured and calculated formation parameters into zones from a fracturing point of view Usually, this is done based on the calculated or measured in-situ stress

3 Develop a limit on fracture-design parameters using the physical properties of the formation and a production increase curve such as the one discussed in the previous section It is possible to use other production increase curves described in literature.6-8 Unsteady-state production increase calculations may be also used

For illustration of this concept using steady-state conditions, the production increase curves discussed in the previous section and Figure 1 are used The production-increase curves are dependent on formation permeability, fracture length, fracture conductivity, drainage area, and wellbore diameter For example, if one is to stimulate a formation with a permeability of only 0.1 millidarcy (md), the

graph of Figure 2 reveals that a fairly long fracture with

conductivity in excess of 1,000 md-ft would be beneficial This is shown more clearly in the expanded section shown in

Figure 3 The graph of Figure 3 indicates that a production

increase (PI) ratio of 7.5 is attainable with a fracture

conductivity of 2,000 md-ft and a fracture length of 667 feet

shown as intersection point A

To allow for an efficient fracture clean up in a fairly tight

formation, a dimensionless fracture conductivity approaching

30 is usually recommended.3 The line for a dimensionless

fracture conductivity of 30 is shown in Figure 3

If the formation permeability is 100 md and the curve for

dimensionless conductivity of 30 is again considered, creating

a fracture length of 33 feet requires a fracture conductivity of

100,000 md-ft as shown in Figure 4 at point A Such

conductivity would be difficult to attain if not impossible In

addition, this high dimensionless conductivity is no longer

required for clean up Thus, the design should be only

considering the well productivity In this case, the program

then may opt to use a dimensionless conductivity of 3, yielding

a required fracture conductivity of 10,000 md-ft (see point B in

Figure 4) Such fracture conductivity may be attainable using

special fracture design procedures (tip screen out) In a

high-conductivity fracture such as this, the use of an optimum

dimensionless conductivity of 1.6 (discussed earlier in the

paper) may be acceptable provided degradation of conductivity

is taken into consideration

If turbulent flow is expected to take place inside the fracture

(from calculated flow rate), adjustment of designed

conductivity should be considered as the effective fracture

conductivity is lower than the actual fracture conductivity

First, the potential for turbulence using established techniques

should be calculated A factor based on degree of turbulence

and the effective fracture conductivity should be determined

The actual flow rate is then calculated In case of steady state,

the calculation can be done once; however, in the case of

unsteady state, the calculation of the turbulent factor is done in

steps at different times

4 Calculate an approximate fracture width using the

mechanical properties of rock (Young’s Modulus and Poisson’s

Ratio) For example, a two-dimensional model equation such

as those developed by Perkins and Kern can be used

5 Calculate the required proppant deposition (such as in

pounds per square feet) given the conductivity that has been

determined using published tables or equations Such

determination should account for stress carried by the proppant

type(s) and size of the proppant(s) Allow for possible

proppant embedment, especially in soft formations, and any

effect of proppant embedment in filtercake

Referring to Figure 5, the graphs show that different

proppants have different disposition requirements at a

conductivity of 10,000 md-ft, for example The one requiring

the least amount per square foot for this condition is a

resin-coated proppant indicated at point A of Figure 5 (slightly less

than four lbm per square foot) This material is suitable for a

stress characteristic of approximately 3,000 psi at a

conductivity of 10,000 md-ft shown as point A in Figure 6

Thus, given a calculated desired conductivity, a desired

concentration, and a stress parameter, the list of available

proppants may be quickly narrowed

6 Calculate the required sand concentration in pounds per

gallon (lbm/gal or ppg) for a given width and desired

conductivity using digitally encoded published equations or

graphs such as those illustrated in Figure 7 For the above

example of a proppant deposition of about four pounds per

square foot and a calculated width of 0.875 inch Figure 7 shows that the proppant concentration in the fracturing fluid should be 10 lbm/gal; point A

7 Calculate downhole temperature at each fluid stage using a temperature calculation model/correlation

8 Define the best fluid to carry the proppant and keep the majority of the proppants in suspension (70%) using the calculated temperature Factors that may be considered include leak-off coefficient, closure time, and degradation of fluid viscosity with time

9 If it is found that the designed proppant concentration is higher than could be normally achieved, a tip-screen-out (TSO) design should be considered In tip screen out, the fracture is designed so that the proppant reaches the tip of the fracture at the time the fracture reaches the desired length When the proppant reaches the tip of the fracture, the fracture will stop growing in length Then, by continuing to inject sand-laden fluid, the fracture will grow in width (balloon) After the fracture is allowed to close, the sand concentration will be significantly higher than would otherwise be achieved

Steps 6 through 9 may be reiterated to conclude the best proppant, average proppant concentration, and fluid system for the treatment Preferably, the foregoing will be performed using a suitable software that includes digital implementations

or representations of computational and materials information (for example, suitable programming to permit use of the information and relationships as represented in Figures 5-10)

Refined Design

The above is done more for materials selection, whereas the following fine tunes the design using the lowest cost materials

The initial run uses more generic information to limit the materials list, and in this stage of selection, the various chosen materials are run in one or more models provided in commercially available simulators

One may have noted from the above discussion that a specialized approach is needed to obtain the desired conductivity and that this phase is where that process will be optimized The following steps should be followed:

1 Generate a desired fracture conductivity using the initial design given above and the determined desired fracture conductivity This fracture conductivity is the fracture

conductivity at the wellbore; therefore, a conductivity profile that creates a fracture with constant pressure drop down the fracture is generated.10

2 Run a fracture simulation using the mechanical properties

of rock (Young’s Modulus and Poisson’s Ratio), physical properties, zoning of the formation, and calculated in-situ stresses The simulator uses the fluid and proppant type or

types that were determined in the initial design

3 Calculate downhole temperature using a temperature calculation model/correlation This temperature profile is used

to determine the fluid degradation, and thus, proppant transport and settling to develop the in-situ proppant conductivity

4 Define the best fluid needed to carry the proppant and keep the majority (for example, 70%) of the proppants in suspension using the calculated temperature Factors that should be

considered include leak-off coefficient, closure time, and degradation of fluid viscosity with time and temperature If the original fluid mixture is insufficient, then more polymer or less

breaker will be adjusted to achieve the desired proppant

suspension Determine the feasibility of propped fracture

length and width by running a fracturing model using selected

fluid/fluids to determine the effect on the fracture geometry

This process examines whether the fracture geometry (length,

height, and width profile) would significantly change from the

original design

6 Calculate the proppant profile inside the fracture, both

settled or in suspension These calculations take into

consideration fluid rheology, proppant size, density and

concentration This is needed in the event that all the proppant

is not perfectly transported to the designed location within the

fracture (which it will not be but it should be close if the fluids

are adjusted correctly), the ideal conductivity will be affected

7 Determine proppant concentration needed at each location

to produce the non-uniform fracture conductivity This could

be based on the theoretical curve developed by Soliman,5 who

developed a set of curves describing the change in conductivity

with distance inside the fracture As described by Soliman, if

the conductivity inside the fracture changes, then the fracture

will behave as if it has a uniform conductivity

8 Determine initial proppant in slurry and fluid for each

location This is done by dividing the fracture into segments

and adding the fluid that was lost during its transport down the

fracture to give the needed concentration at the surface This

calculation considers the physical properties of the rock, the

rheological properties of the fluid, and the concentration of the

proppant in the fluid

9 Adjust for settled proppant and determine proppant

schedule The fluid degradation may cause some settling, and

this is where the final fluid mixture is adjusted to achieve the

proppant transport needed for the conductivity profile Steps 4

through 9 may be reiterated to conclude the best proppant,

average proppant concentration, and fluid system for

the treatment

10 Run a reservoir simulation to predict well performance

using the optimum fracture designs with and without fracturing

and for the different designs that will result from the material

selections The reservoir simulator produces a profile of well

productivity for each local optimum fracture design Based on

the chosen economic drivers (see next item) a global optimum

is determined

11 Run an economics model and plot a selected economic

parameter such as NPV, Benefit/Cost Ratio, ROI, etc., versus

fracture length

If working with a 3-D design, only concentration against

the pay zone is considered The above design was essentially

for a two-dimensional model It may be expanded to a

three-dimensional situation by considering that the formation

consists of a contributing formation and non contributing

formation The proppant concentration against the contributing

formation is the critical factor

Real Time Modification to Design

After the desired fluid and proppant have been determined

using the above steps, those materials in suitable quantities are

delivered to the actual well site (if they are not already there)

Before the fracturing job is performed, however, a pumping or

treatment schedule must be determined This is accomplished

by conducting the following steps:

1 Pump mini-frac job with step-down test to perform a fluid efficiency test

2 Determine if and how much near-wellbore friction exists

3 Determine closure, net pressure, and fluid efficiency for formation

4 Adjust fracture-design program-model parameters to match net-pressure and leak-off rate from mini-frac

5 Use fracture-design program model design mode to optimize fluid and proppant on location for new model parameters matched

in step 4 of this section

6 Pump treatments as per new optimized design in step 5 of this section

7 Monitor treatment with fracture-design program in real time model to predict fracture growth during treatment

8 Make adjustments to treatment based on model prediction

as required

Real-Time Application

Implementation of this design methodology in a commercial simulator allows the design strategy to be revisited many different times as the amount of knowledge about a reservoir increases during the development cycle of a well or a field

An initial design based on log-based reservoir information can be created using this methodology and can be redone in real time once additional data from breakdown injections and/or minifracs (fluid efficiency test) becomes available These injection tests provide necessary information about fracture-closure stress, level of net pressure, and fracture-fluid efficiency (or leakoff behavior) These simple and direct measurements can have a big impact on fracture designs and should be incorporated in the final treatment design For example, leakoff behavior observed during a minifrac has a big impact on sizing the pad to obtain a TSO in a high-permeability reservoir

In a field development situation, once a single fracture treatment is conducted, fracture design work is not finished Instead, fracture design is a continuous task that slowly evolves

as more data become available, for example, from net pressure matching of the propped fracture treatment data, from direct measurements of fracture growth using direct fracture diagnostics (such as tiltmeter or microseismic fracture mapping), or from longer-term production data

Implementation into Fracturing Simulator

This methodology was recently implemented into a commercial hydraulic-fracture-growth system to 1) make the methodology widely available, and 2), to come to a more uniform design approach throughout the company This method is illustrated

in the chart in Figure 8

Once the most applicable and cheapest proppant and fluids are selected, the simulator will approximate how much proppant and fluid will be required to obtain a certain fracture length, given a user-defined dimensionless conductivity criterion

As shown in Figure 9, the simulator will determine the

fracture height, conductivity, net pressure, etc for every length

the user wants, Figure 10 shows a fracture profile as a function

of all the fracture lengths for which the model has been run

Once the fracture dimensions are known as well as how the actual reservoir impacts fracture growth, it also becomes

possible to estimate a theoretical production response using the

PI-conductivity plot in Figure 11 The black dots in this figure

provide the solution from the simulator that is closest to a

desired dimensionless conductivity criterion that is specified by

the user

If the required fracture width at closure time is smaller than

the width during the fracture opening in the baseline design, we

do not have to go into a TSO The required width at the

wellbore at closure on proppant is a function of the width at the

end of pumping and the actual proppant concentration in the

fracture (close to the wellbore) at that time:

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

−

=

max

max

1

) 1 /(

C X

C X w

w

propvol

prop propvol

pumping end proppant

on

closed

φ

(4)

where Cmax is the maximum proppant concentration, φprop

is the proppant porosity and Xpropvol is the proppant volume

factor in gal/lbs (which equals 1/ (SG*8.345404)) with SG

being the proppant’s Specific Gravity in kg/l

The desired width to obtain a certain CfD goal is

calculated by

embedment f

f fD goal

k

kL C

w

where kis the average height-weighted permeability for all

pay zones combined, Lf is the fracture half-length, and kf is the

permeability (after damage) of the proppant pack M is the

number of conductive multiples and dembedment is the embedment

thickness of one fracture wall

Now, we can determine the maximum proppant

concentration that needs to be pumped to obtain the required

propped width by setting

proppant on closed goal

C w

w

If wC goal wclosed on proppant

fD > with 15 ppg is being set at

the default proppant concentration, then the simulator will

automatically consider a TSO design To do this, we will keep

the maximum proppant concentration at 15 ppg (or anything

else the user has defined in the screen above) and keep the tip

screen-out net pressure increase within user-defined limits

The net pressure increase to reach the CfDgoal can be

estimated as follows:

( max) ,

,

C w

w p

p

proppant on closure

goal C pumping

of end net goal

C

net

fD

The net pressure at the end of pumping would be the net

pressure taken at the required fracture half-length in the

baseline calculation

When conducting a design, it could very well be possible (as shown in Figure 11) that the CfD

goal cannot be achieved,

in which case the only other available alternative is to pump better proppant or a higher proppant concentration

Economic Analysis

The simulator contains a large library with fluid and proppant properties as well as pricing Up to date pricing information is obtained from the service company’s price book The simulator has calculated how much fluid and proppant is required for every fracture half-length, how long it will take to pump the job, and what the required horsepower will be With this information, it is possible to calculate the approximate cost

of each job as a function of the obtained propped fracture

half-length as shown in Figure 12

Figure 13 shows results when a single-layer single-phase

finite difference simulator is used to forecast production response of the stimulated fracture

To do a proper economic analysis, both treatment cost and expected revenues from production should be evaluated The simulator can then be used to select the treatment with the best NPV or ROI for a user-specified time period as shown in

Figure 14

Determine Treatment Schedule

The proppant distribution is provided by the following equations4:

8 8 2 2 1

⎠

⎞

⎜

⎜

⎝

⎛ + +

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

f f

f f

fD

L

x a L

x a L

x a a L

x

with

( ) ( ( ) )2

2 , 1

, 0

,

0

j fD

j j

j

C

A C

A A

f L

x being the distance in the fracture away from the

wellbore divided by the fracture half-length, and CfD (0) is the CfD goal at the wellbore

The simulator will iterate on the proppant profile within the fracture and minimize a weighted, least-squares error of the difference between the ideal proppant profile and the actual proppant profile

The error is weighted by distance away from the wellbore

to allow the profile at the wellbore to be more important than if matching it far away into the fracture The following error is minimized while using a constant of approximately 1:

) 9 ( ) )

/ 1

((

) )

/ 1

((

)

constant fraclength

distance ideal

constant fraclength

distance ideal

model error i i

+

−

+

−

−

Example Application 1 - Moderate permeability oil

well in Venezuela

Figures 9-14 show fracture design and optimization results for

an oil reservoir at a depth of 6100 ft in the Lagunillas field in

Venezuela The horizontal section has moderate permeability

of about 60 md and requires a TSO design strategy in order to

obtain CfD’s within a reasonable range

Fracture growth is believed to be somewhat confined based

on anecdotal evidence that certain fracture treatment sizes do

not penetrate specific layers The stress profile is not well

known – the stress in the producing sand comes from

pressure-decline analysis of breakdown injections, while the sand-shale

stress contrast is “guesstimated,” based on pore-pressure

differences To mimic the slight fracture confinement, a

composite layering effect was used The permeability, the

driving parameter for the type of design, was determined from

pressure buildup tests in nearby wells, and therefore, is

relatively well known

Two selection criteria dominated the analysis:

1 What treatment can maximize economic benefits? The

economic analysis resulted in a maximum NPV for a fracture

half-length of about 240 ft

2 What treatment can avoid growth in a water-bearing zone

approximately 100 ft above the top perforation? Since the

fracture profile for a fracture with a 240-ft half length is clearly

penetrating the water-bearing zone above, a smaller half length

of 150 ft was selected to avoid growth into this unfavorable

zone

Example Application 2 - Low permeability Gas well in

the Rockies

This application is in a sandstone reservoir bounded by

shale layers, all with moderate to high Young's modulus of

about 3,500,000 psi which is typical for the US Rockies The

closure stress gradients are modest at about 0.55 - 0.60 psi/ft,

and reservoir permeability is of order 0.1 md A Borate Guar

fluid with relative low gel loading was used to stimulate

these wells

Many times, when people design a fracture, they usually do

not incorporate any feedback from real data Engineers could

use what they have learned from indirect measurements such as

net-pressure history matching and production data analysis to

estimate what they are achieving with their propped fracture

treatments Although this type of analysis can be very

beneficial to obtain a basic understanding of what is achieved,

a problem with these types of analyses is that solutions can be

non-unique As a result, economic optimization may not

provide a true design optimum

To address this shortcoming, the capability to calibrate

fracture models with directly measured fracture dimensions, for

example, using tiltmeter fracture mapping or microseismic

fracture mapping is now possible

Figure 15 shows the net pressure history match The

uncalibrated net pressure inferred geometry in Figure 16 (top)

shows significant out-of-zone growth This match was

conducted using the “classical” assumption that confinement

was only caused by fracture closure stress contrast

However, microseismic mapping showed an actual fracture

height of only 130 ft and a fracture half-length of 700 ft – very

different from the uncalibrated pressure-matching result Net pressure history matching was redone to match the actual geometry First, we determined that a closure stress gradient in excess of 1 psi/ft was required in the shale to obtain the observed confinement, and this was considered unrealistic Therefore, a composite layering effect was introduced Most fracture-growth models in the industry assume that there is perfect coupling of the fracture walls along its height As a fracture tip grows through layer interfaces, some of these interfaces may become partially de-bonded, and the fracture may start growing again at a local weakness offset from the

original path, slowing vertical fracture growth Figure 16 (bottom) shows the final fracture geometry from the

calibrated model

Now that a calibrated model has been obtained by matching net pressure response AND directly measured fracture dimensions, the fracture model can be run in predictive mode

to evaluate alternative designs In this particular example, production data showed that effective propped half-length was far shorter than the 700-ft hydraulic fracture half-length, most likely due to insufficient cleanup farther away in the fracture Significant cost savings have been achieved by pumping smaller treatments on subsequent jobs, reducing hydraulic fracture half-length while maintaining effective propped fracture half-length and production response

Figure 17 shows the fracture treatment cost for typical

fracture treatments in this area These treatment costs incorporate variable costs dictated by horsepower, level of surface pressure and rate, job duration, quantity of fluid and proppant used, and fixed costs such as mobilization The dashed curve shows the dramatic increase in costs for the near-radial fracture growth anticipated in the initial design, which was not calibrated using direct fracture growth measurements The solid curve shows the modest increase in costs for the confined fracture growth that was measured using direct fracture growth measurements

Figure 18 shows the differences in NPV for a 1-year period

following the propped fracture treatments, assuming the following facts:

1) monthly production maintenance cost of about $500 2) average cost for fracture job with 500,000 lbs Ottawa and about 5000 bbl fluid of approximately $100,000

3) expected IP at 500 to 700 Mscfd, 35 ft pay, 0.1 mD permeability and 200 ft half-length

4) approximately 75% decline

Due to the differences in height/length growth, NPV estimates for both designs are very different Due to dramatically increasing cost when assuming near-radial fracture growth, the NPV maximizes for a much shorter propped half-length of about 280 ft This requires a treatment volume of about 800 bbl The calibrated design, which incorporates the measurement of significant fracture confinement, provides a maximum NPV at a fracture half-length of more than 600 ft, and will require a fracture treatment volume of about 1500 bbl This calibrated design and larger optimum length also requires the use of a larger amount

of proppant

Conclusions

A comprehensive methodology that equally considers both

theoretical and practical aspects has been developed to

optimize fracture design

1 The procedure can help to effectively optimize fracture

treatments in any type of environment and can be done quickly

in real-time after a minifrac is conducted to make changes to

the propped fracture treatment

2 The methodology has been successfully implemented in

fracture design software

3 The presented field examples illustrate the validity of the

presented methodology

Acknowledgments

The authors of this paper would like to express their thanks to

Halliburton Energy Services, Inc and Pinnacle Technology for

allowing this work to be published They would also like to

thank Nancy Woods, Carolyn Williams, and Sam Moore for

their efforts in preparing the manuscript

Nomenclature

,

0

a

= constants

,

, j

i

A

= constants

fD

C

= dimensionless fracture conductivity

max

C

= the maximum proppant concentration

embedment

d

= the embedment thickness of fracture wall

w

kf

= fracture conductivity, md-ft

k= reservoir permeability, md

f

k

= fracture permeability, md

f

L

= fracture half length, ft

M = the number of conductive multiples

p= pressure

net

p

= pressure above closure pressure (net pressure)

PI = production increase ratio

d

r

= drainage radius, ft

w

r

= wellbore radius, ft

'

w

r

= effective wellbore radius, ft

w= fracture width

proppvol

X

= the proppant volume factor, gal/lbs

propp

φ

= the proppant porosity

References

1 Prats, M.: “Effect of Vertical Fracture on Reservoir Behavior – Incompressible Fluid Case,” JPT (June, 1961) 105-118

2 McDaniel, B W.: “Conductivity Testing of Proppants at High Temperature and Stress,” SPE 15067 presented at the 56th California Regional Meeting, held in Oakland, California, April 2-4, 1986

3 Soliman, M.Y and Hunt, J.: “Effect of Fracturing Fluid and Its Clean-up on Well Performance,” SPE 14514, presented at the Eastern Regional Meeting held in Morgantown, West Virginia, Nov 6-8, 1985

4 Poulsen, D., and Soliman, M Y.: "A Procedure for Optimal Fracturing Treatment Design," SPE 15940, presented at the Eastern Regional Meeting held in Columbus, Ohio, November 12-14, 1986

5 Soliman, M Y.: "Fracture Conductivity Distribution Studied,” Oil

& Gas Journal, February 10, 1986

6 Tinsley, J M., Tiner, R., Williams, J and Malone, W T.: “Vertical Fracture Height — Its effect on Steady State Production Increase,” JPT, May 1969, 633-638

7 Soliman,M.Y.:“Modifications to Production Increase Calculations for a Hydraulically Fractured Well,” JPT, Jan 1983

8 McGuire, W.J, and Sikora, V J.: “The Effect of Vertical Fracture

on Well Productivity,” Trans AIME, (1960) 219, 401-405

9 Cinco-Ley, H and Samaniego-V., F.:“Transient Pressure Analysis for Fractured Wells,” JPT, Sept 1981, 1749-1758

10 Perkins, T K and Kern, L R.: “Width of Hydraulic Fractures,”

JPT (Sept 1961) 937-49

SI Metric Conversion Factors

bbl x 1.589 873 E - 01 = m3 gal x 3.785 412 E - 03 = m3 bbl/min x 2.649 788 E - 02 = m3/h

ft x 2.831 685 E - 02 = m3

in x 2.54* E + 01 = mm

md x 9.869 233 E - 04 = m3 psi x 6.894 757 E + 00 = kPa

*Conversion factor is exact

Figure 1 - Fractured Well

Production Increase Curves

1E3 1E4 1E5 1E6 1E7

Fracture Half Length

Well Diameter 7.875 (in) Spacing 80 (acre)

8 7 6 5 4 3 2

1 10 100 1E3 1E4

0.1 1 10 100 1E3

10 100 1E3 1E4 1E5

100 1E3 1E4 1E5

1E6

Permeability 0.1

Production Increase

Figure 2 Fractured Well Production Increase Example

Figure 3 - Expanded view of

Production Increase Curve

Figure 4 Production Increase curves

1

Permeability 0.1 md Well Spacing 320 acre Hole Diameter 7.875 in

Fracture Half Length (ft)

2

3

4

6

8

2

3

4

6

8

2

3

4

6

8

10

100

1000

10000

C fD 10

5

PI6

Fracture Half Length (ft)

2000

1000

30

A

B

PI

C fd

7 7.5