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HF2D FHF2D FRACRAC D DESIGNESIGN SSPREADSHEETPREADSHEET

April 2001

(Updated May 30, 2006)

Dr Peter P. Valkó

Associate professor

Harold Vance Department Petroleum Engineering

HF2D Page 11

Texas A&M University

HF2D Page 22

TABLE OF CONTENTS

1 EXECUTIVE SUMMARY...........................................................................................4

2 DATA REQUIREMENT.............................................................................................5

3 CALCULATED RESULTS........................................................................................8

4 THEORETICAL FRACTURE PERFORMANCE.....................................................10

5 SUGGESTED DESIGN PROCEDURE BASED ON OPTIMAL PSEUDO-STEADY STATE PERFORMANCE........................................................................................20

6 SAMPLE RUNS......................................................................................................27

NOMENCLATURE..................................................................................................36

CASE STUDIES......................................................................................................38

HF2D Page 33

11 EEXECUTIVEXECUTIVE SSUMMARYUMMARY

The HF2D Excel spreadsheet is a fast 2D design package for the 2D design of traditional (moderate per-

meability and hard rock) and frac&pack (higher permeability and soft rock) fracture treatments.

Currently it contains the following worksheets:

Traditional design with PKN (Perkins-Kern-Nordgren) model

TSO (tip screen-out) design with PKN model

Design with CDM (Continuum Damage Mechanics) version of the PKN model

The unique feature of this design package is the logic it is based on. The design starts from the amount of

proppant available. Then the optimum dimensions of the fracture are determined. Finally, the treatment

schedule is found which will realize the optimum proppant placement. If the constraints do not allow opti-

mum placement, a sub-optimal placement is designed.

The results include fluid and proppant requirements, injection rates, added proppant concentrations (that

is the proppant schedule) and additional information on the evolution of the fracture dimensions.

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22 DATADATA REQUIREMENTREQUIREMENT

The following table contains the description of the input parameters.

Input Parameter Remark

Proppant mass for (two wings), lab This is the single most important decision variable of the design procedure

Sp grav of proppant material (water=1) For instance, 2.65 for sand

Porosity of proppant pack The porosity of the pack might vary with closure stress, a typical value is 0.3

Proppant pack permeability, md Retained permeability including fluid residue and closure stress effects, might be re-

duced by a factor as large as 10 in case of non-Darcy flow in the frac Realistic prop-

pant pack permeability would be in the range from 10,000 to 100,000 md for in-situ flow

conditions. Values provided by manufacturers such, as 500,000 md for a “high strength”

proppant should be considered with caution.

Max prop diameter, Dpmax, inch From mesh size, for 20/40 mesh sand it is 0.035 in.

Formation permeability, md Effective permeability of the formation

Permeable (leakoff) thickness, ft This parameter is used for Productivity Index calculation (as net thickness) and in calcu-

lation of the apparent leakoff coefficient, because it is assumed there is no leakoff (and

spurt loss) outside the permeable thickness.

Well Radius, ft Needed for pseudo skin factor calculation

Well drainage radius, ft Needed for optimum design. (Do not underestimate the importance of this parameter!)

Pre-treatment skin factor Can be set zero, it does not influence the design. It affects only the "folds of increase" in

productivity, because it is used as basis.

Fracture height, ft Usually greater than the permeable height. One of the most critical design parameters.

Might come from lithology information, or can be adjusted iteratively by the user, to be

on the order of the frac length.

Plane strain modulus, E' (psi) Defined as Young modulus divided by one minus squared Poisson ratio. E’=E/(1-2) It

is almost the same as Young modulus, and it is about twice as much as the shear modu-

lus, because the Poisson ratio has little effect on it. For hard rock it might be 106 psi, for

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soft rock 105 psi or less.

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Slurry injection rate (two wings, liq+ prop), bpm The injection rate is considered constant. It includes both the fracturing fluid and

the proppant. The more proppant is added, the less the calculated liquid injection

rate will be. A typical value is 30 bpm.

Rheology, K' (lbf/ft^2)*s^n' Power law consistency of the fracturing fluid (slurry, in fact)

Rheology, n' Power law flow behavior index

Leakoff coefficient in pay layer, ft/min0.5 In general, the leakoff coefficient outside the pay layer may be less, than in the

pay. Hence a multiplier is used outside the pay, see below.

Spurt loss coefficient, Sp, gal/ft2 The spurt loss in the pay layer. Outside the permeable layer the spurt loss for

out of pay is considered zero. See the remark above.

Fluid loss multiplier for out of pay layer If this multiplier is set zero, there is no leakoff and spurt loss outside the pay

layer. It is more realistic to use a multiplier between zero and one, say 0.5.

Max possible added proppant concentration,

lbm/gallon fluid (ppga)

The most important equipment constraint. Some current mixers can provide

more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maxi-

mum technically possible concentration.

Multiply opt length by factor This design parameter can be used for sub-optimal design. If the optimum length

is too small (and the fracture width is too large), a value greater than the one

used. If the optimum length is too large (and the fracture width is too small) , a

fractional value might be useful. This possibility of user intervention is advanta-

geous to investigate the pros and contras of departing from the technical opti-

mum. The default value should be 1. See more on this issue in the text.

Multiply pad by factor In accordance with Nolte's suggestion, the exponent of the proppant concentra-

tion schedule and the pad fraction (relative to the total injected volume) are taken

to be equal. This happens if this design parameter is at its default value, which is

at 1. The user may experiment with other values. It will have the effect of short-

ening or elongating the pad period that is having less or more conservative de-

sign. The program adjusts the proppant schedule accordingly, to ensure the re-

quired amount of proppant is injected.

HF2D Page 77

Additional input parameters

TSO criterion Wdry/Wwet This design parameter appears only for TSO design. It specifies the ratio of dry

width (assuming only the "dry" proppant is left in the fracture) to wet width (dy-

namically achieved during pumping). According to our assumptions, the screen-

out happens when the ratio of dry to wet width reaches the user specified value.

We suggest a number between 0.5 and 0.75., but the best method is gradually

calibrate this parameter in the field by evaluating successful TSO treatments.

HF2D Page 88

33 CALCULATEDCALCULATED RESULTSRESULTS

The results contain the optimum fracture dimensions, followed by the fracture dimensions achieved tak-

ing into account the constraints (max possible added proppant concentration.) The constraints may or may

not allow to achieve the technical optimum fracture dimensions. A red message will tell whether the opti-

mum dimensions could be achieved.

The main fracture dimensions, such as half-length, average width, areal proppant concentration determine

the performance of the fractured well, which is given in terms of dimensionless productivity index and

also as pseudo-skin factor.

The fluid and proppant requirements are given in cumulative terms and the injection rate of the fluid and

the added proppant concentration are presented as functions of time.

HF2D Page 99

The results include:

t, min time elapsed from start of pumping

qi_liq, bpm liquid injection rate (for two wings)

cum liq, gal cumulative liquid injected up to time t

cadd, lbm/gal added proppant to one gallon of liquid, in other words ppga

cum prop, lbm cumulative proppant injected up to time t

xf, ft half-length of the fracture at time t

wave, in. average width of the fracture at time t

wave / Dpmx the ratio of average width of the fracture to the maximum proppant diameter, should be at least 3

wdry / wwet the ratio of dry to wet width.

During pumping the actual wet width is 2 to 10 times larger than the dry width, that would be necessary to con-

tain the same amount of proppant without any fluid and packed densely. Usually it should be less than a pre-

scribed number, such as 0.2 for avoiding screen-out during the job.

The TSO criterion in the TSO version of the design spreadsheet is formulated in terms of this output variable.

HF2D Page 1010

44 TTHEORETICALHEORETICAL F FRACTURERACTURE P PERFORMANCEERFORMANCE

The fracture design should be based on sound principles of fluid flow in porous media. We start the de-

scription of the fractured well performance with the pseudo-steady state Productivity Index. It is well un-

derstood that in tight gas the transient regime might last for a considerable time therefore well production

is affected by the transient process. Nevertheless, it is impossible to understand the well behavior without

first considering the pseudo-state flow regime.

We consider a fully penetrating vertical fracture in a pay layer of thickness h, see Fig. 1 for notation.

Fig. 1. Notation for fracture performance

Note that in reality the drainage area is neither circular nor rectangular. Using re or xe is only a matter of

convenience. The relation between re and xf is given by

.................................................(1)

where A is the drainage area.

HF2D Page 1111

2re xe

2xf 2xf

w w

h

Productivity Index

The pseudo-steady state productivity index relates production rate to pressure drawdown:

..........................................(2)

where JD is called the dimensionless productivity index, k is the formation permeability, h is the pay

thickness, B is the formation volume factor, is the fluid viscosity and 1 is a conversion constant (one

for a coherent system).

For a well located in the center of a circular drainage area the dimensionless productivity index reduces

to

.............................................(3)

In the case of a propped fracture there are several ways to incorporate the stimulation effect into the pro -

ductivity index. One can use the pseudo-skin concept:

.............................................(4)

or the equivalent wellbore radius concept:

..............................................(5)

or one can just provide the dimensionless productivity index as a function of the fracture parameters:

JD = function(drainage-volume geometry, fracture parameters )

All three options give exactly the same results (if done coherently). The last option is the most general

and convenient, especially if we wish to consider fractured wells in a rectangular drainage area.

HF2D Page 1212

Many authors have provided charts and correlations in one or another form for special geometries, reser -

voir types, etc. Unfortunately, most of the results are less obvious to apply in high permeability environ-

ment. Also there are quite large discrepancies as shown for instance on Fig. 12-13 of Reservoir Stimula-

tion 3rd edition, 2000. Therefore we provide a fresh look at the partly known results.

Proppant Number

For a vertical well intersecting a rectangular vertical fracture which penetrates fully from the bottom to

the top of the rectangular drainage volume the performance is known to depend on the x-directional pene-

tration ratio:

...................................................(6)

and on the dimensionless fracture conductivity:

..................................................(7)

where xf is the fracture half length, xe is the side length of the square drainage area, k is the formation per-

meability, kf is the proppant pack permeability, and w is the average fracture width.

The key to formulating a meaningful technical optimization problem is to realize that penetration and di-

mensionless fracture conductivity (through width) are competing for the same resource: the propped vol -

ume. Once the reservoir and proppant properties and the amount of proppant are fixed, one has to make

the optimal compromise between width and length. The available propped volume puts a constraint on the

two dimensionless numbers. To handle the constraint easily we introduce the dimensionless proppant

number:

....................................(8)

Note that only that part of the proppant counts into the propped volume, that reaches the pay. If for in -

stance the fracture height is three times the net pay thickness, then the Vprop can be calculated as the bulk

volume of one third of the injected proppant, if it is closely packed.

HF2D Page 1313

The Dimensionless Proppant Number, Nprop, is nothing else but the ratio of two volumes: the propped

volume in the pay divided by the reservoir volume in the pay, both volumes weighted by their permeabil-

ity, respectively. (In addition, a factor of two is used in front of the propped volume.) As we will see, the

proppant number is the most important parameter in fracture design.

A convenient algorithm to calculate JD is available1. Fig. 2 shows JD represented in a traditional manner,

as a function of dimensionless fracture conductivity, CfD, with Ix as a parameter. Similar “productivity in-

crease” graphs are numerous in the published literature2,3.

1 Valkó, P. P. and Economides,M.J.: “Heavy Crude Production from Shallow Formations: Long Horizontal Wells

Versus Horizontal Fractures,” paper SPE 50421, 1998.

2 McGuire, W.J. and Sikora, V.J.: “The Effect of Vertical Fractures on Well Productivity,” Trans. AIME (1960) 219,

401-405.

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

1983) 170-178.

HF2D Page 1414

0

0.5

1

1.5

2

0.01 0.1 1 10 100 1000 10000Dimensionless Fracture Conductivity, CfD

Dim

ensi

onle

ss P

rodu

ctiv

ity in

dex,

JD

I x = 1

0.9 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.01

2xf

xe

ye = xe

Fig. 2. Calculated dimensionless productivity index as a function of dimensionless fracture conductivity and penetration

Fig. 2 is not very helpful to solve the optimization problem involving any fixed amount of proppant. For

this purpose in Figs 3 and 4 we present the same results, but the individual curves correspond to JD at a

fixed value of the proppant number, Nprop.

Fig 3 a and Fig. 3 b emphasize the importance of the proppant number.

HF2D Page 1515

Fig. 3a. Dimensionless productivity index as a function of dimensionless fracture conductivity and proppant number (for Nprop < 0.1)

Fig. 3b. Dimensionless productivity index as a function of dimensionless fracture

conductivity and proppant number (for Nprop > 0.1)

HF2D Page 1616

0.5

0.4

0.3

0.2

Dim

ensio

nles

s Pro

duct

ivity

Inde

x, J

D

10-4 10-3 10-2 10-1 100 101 102

Dimensionless Fracture Conductivity, C fD

Np=0.001

Np=0.003

Np=0.006

Np=0.0001

Np=0.01

Np=0.03

Np=0.06

Np=0.0003Np=0.0006

Ix=1

Xe

2X fY e

Xe=Ye

Np=0.1

2.0

1.5

1.0

0.5Dim

ensio

nles

s Pro

duct

ivity

Inde

x, J

D

0.1 1 10 100 1000Dimensionless Fracture Conductivity, C fD

Np=0.1

Np=0.3

Np=0.6

Np=1

Np=3

Np=6

Np=10

Np=30

Np=60

Np=100

Xe

2X fY e

Xe=Ye

Ix=1

Fig. 4.a Dimensionless productivity index as a function of penetration ratio and proppant number (for Nprop < 0.1)

Fig. 4.b Dimensionless productivity index as a function of penetration ratio and proppant number (for Nprop > 0.1)

HF2D Page 1717

0.45

0.40

0.35

0.30

0.25

0.20

0.15

Dim

ensio

nles

s Pro

duct

ivity

Inde

x, J

D

10-3 10-2 10-1 100

Penetration Rate, I X

Np=0.0001

Np=0.0003

Np=0.0006

Np=0.001

Np=0.003

Np=0.006

Np=0.01

Np=0.03

Np=0.06

Np=0.1

Xe

2X fY e

Xe=Ye

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Dim

ensio

nles

s Pr

oduc

tivity

Inde

x, J

D

0.01 0.1 1

Penetration Rate, I X

Np=0.1

Np=0.3

Np=0.6

Np=1

Np=3

Np=6

Np=10

Np=30

Np=100

Xe

2X fY e

Xe=Ye

As seen from Figs. 3 a and b, for a given value of Nprop , that is for a fixed amount of available proppant,

there exists an optimal dimensionless fracture conductivity, representing the optimal compromise be-

tween the ability of the fracture to conduct the flow into the wellbore and its ability to get inflow from the

formation.

Figs. 4 a and 4 b show the performance as a function of penetration ratio. The large J D values (above

JD = 0.8) correspond to streamlines parallel to the y axis in pseudo-steady state, a highly desirable, but ex-

tremely difficult (if not impossible) to achieve situation.

It is important to understand that Figs 3 a and 4 a are equivalent, and their correct use should lead to the

same results. Similarly, Figures 3 b and 4 b carry equivalent information.

One of the main result seen from the figures is, that at "low" proppant numbers (low proppant volume

and/or high formation permeability), the optimal compromise occurs at CfD = 1.6. The behavior at large

Nprop is as anticipated because we know that the absolute maximum for JD is 6/ = 1.909 (this value is the

productivity index for a perfect linear flow in a square reservoir.

When the propped volume increases, the optimal compromise happens at larger dimensionless fracture

conductivities because the penetration cannot exceed unity. Figure 2.b shows this effect clearly.

In “medium and high” permeability formations, that is above 50 md, it is practically impossible to

achieve a proppant number larger than 0.1. For Frac-and Pack typical proppant numbers range between

0.0001 and 0.01 . Therefore, for medium/high permeability formations the optimum dimensionless frac-

ture conductivity is always CfDopt = 1.6.

In “tight gas” it is possible to achieve large dimensionless proppant numbers, at least in principle. If one

calculates the proppant number with a limited drainage area and does not question whether the proppant

really reached the pay layer, dimensionless proppant number 1 or even 5 can be calculated. However, the

personal belief of this author is that proppant numbers larger than one are impossible to realize. The rea-

son is that for large treatments there is a great uncertainty of where the proppant goes both in horizontal

and in vertical direction. One has to be very optimistic to believe that the proppant injected remains in the

pay layer vertically and also remains contained in the lateral direction with respect to the targeted

drainage area.

For large treatments the drainage area is oftentimes dynamic in the sense that the extreme fracture length

causes increase of the drainage area with respect to the originally targeted or even with respect to the ex-

HF2D Page 1818

isting well spacing.

This author’s opinion is that a dimensionless proppant number larger than 0.5 is rarely realized, be-

cause the proppant can not be contained in the pay and within the drainage area.

Unfortunately, in case of regular well-spacing the proppant extending laterally outside the drainage area

can be totally discounted. It does not contribute to the proppant number and to the performance.

The situation is more complex in case of an individual well in a larger area. Then the large fracture length

tends to increase the drainage area and hence the proppant number decreases. Ultimately, the large frac-

ture is beneficial, but the approximate upper limit (0.5) on the realizable proppant number still remains

valid.

The maximum possible dimensionless Productivity Index for Nprop = 0.5 is JD = 0.75 . The dimension-

less Productivity Index of an undamaged vertical well is between 0.12 and 0.14 depending on the well

spacing and assumed well radius. Therefore, there is a realistic maximum for the “ folds of increase” of

the pseudo-steady state productivity (with respect to the zero skin case) and it is given by 0.75 / 0.13 ~

6 . Any hope to achieve larger folds of increase (raised mostly by the simplicistic view: “equivalent well-

bore radius equals xf/2”) ultimately has to face reality. Of course, much larger folds of increase can be

achieved with respect to an originally damaged well (where the pre treatment skin factor is positive.)

Another common misunderstanding is connected with the existence of the transient regime. In transient

regime the Productivity Index (and hence the production rate) is larger than in pseudo-steady state. With

this qualitative picture in mind it is easy to discard the pseudo-steady state optimization procedure and to

“shoot” for very high dimensionless fracture conductivity and/or to anticipate much more folds of in-

crease in the transient period. In reality, the existence of the transient period does not change the previous

conclusions on optimal dimensions and should not induce too high anticipations. Our calculations show,

that there is no reason to depart from the optimum compromise described above, even if the well will pro-

duce in transient regime for a considerable time (several months or even years.)

HF2D Page 1919

55 SSUGGESTEDUGGESTED D DESIGNESIGN P PROCEDUREROCEDURE B BASEDASED ONON O OPTIMALPTIMAL P PSEUDOSEUDO--STEADYSTEADY S STATETATE PPERFORMANCEERFORMANCE

To exploit the potentials of a given proppant number one has to place the proppant optimally (or near

optimally). Therefore, the optimal design of a fracture treatment consists of two steps. The first one is to

make a decision on size (in fact on proppant number). The second one is to design the treatment in such a

way that we make maximum use of the potential of the realized proppant number. These issues are dis -

cussed in the following section.

Sizing

Specify the goal of the treatment in form of amount of proppant reaching the target layer. (Denote it by

Vprop = 2Vf ). Calculate the proppant number, from that the maximum possible pseudo-steady state Produc-

tivity Index can already be computed.

The target proppant number has to be at least 0.0001, otherwise there is no stimulation effect. It seems

reasonable to select Nprop= 0.0005 - 0.001 as a target for many high permeability formations, because that

would provide a JD about 0.2. Since wells in high permeability formations are often damaged (the pre-

treatment skin is a large positive number) most of the economic benefit comes from bypassing the origi-

nal damage. To increase the JD significantly beyond 0.2, one would need order of magnitude larger prop-

pant numbers, that is economically (and sometimes even technically) not feasible.

It is the experience of this author that for tight gas it seems reasonable to select a target proppant number

in the range between Nprop = 0.1 to 0.5 or sometimes around 1.

The majority of formations are, however, not tight and neither of extreme high permeability. For those

“medium” reservoirs the Nprop = 0.1 seems to be a reasonable target.

HF2D Page 2020

Of course, the above suggestions should be taken only as starting point. The actual sizing process should

consider a whole range of proppant numbers including and evaluate the options by Net Present Value

analysis.

The most important thing to remember about the proppant number is that it has to be calculated with the

proppant placed into the pay layer and with the representative in-situ conductivity of the proppant pack.

The first problem requires the understanding of the layered structure of the reservoir and of the stress situ-

ation controlling fracture height containment (if any). In this respect, fracture propagation (3D or P3D

modeling) plays an important role, but one has to be aware how the fracture dimensions will affect the fi-

nal performance, and oftentimes in reality, this effect is less than that the literature and common belief

suggest. The reason is that once the amount of proppant reaching the pay is already fixed, the actual frac-

ture shape (especially the length) has limited effect on the final performance. To put it in simple words:

the real question is not “what the length would be” but rather how much proppant would be placed into

the target layer”. One of the most important concepts of the design procedure is the percentage of prop-

pant reaching the target layer(s). If, for instance, several shale layers are imbedded between the pay lay -

ers, the actual proppant reaching the target might be less than 50 %, even with perfect height contain-

ment!

The other important issue is the actual proppant pack permeability. The proppant number (and dimen-

sionless fracture conductivity) have to be calculated with the in-situ representative permeability of the

proppant pack. For instance, a proppant manufacturer may report 500 Darcy or even 1000 Darcy nominal

permeability of the proppant at the estimated closure stress. In reality, however, because of the residue

from the fluid, the actual retained permeability can be, for instance, 10 times less. If two phase flow is in-

volved (gas with significant water, for instance) an other effect will dramatically decrease the effective

(or apparent) permeability of the propped fracture. That effect is often referred to as non-Darcy flow. In

the two-phase flow situation the origin of the additional energy loss in the fracture is due to the periodic

acceleration and deceleration of the liquid droplets. This effect may be detrimental and may call for an

additional factor of 5 or 10 to obtain a representative apparent permeability of the proppant pack. The un-

derstanding of the in-situ proppant permeability (conductivity) is therefore another important issue in

fracture design. There is a large amount of information available on the actual in-situ conductivity of the

proppant packs and it should be of primary concern of every design. Any other factor (such as vertical

stress profile and variation of the Poisson ratio, dilatancy and/or apparent fracture toughness, wall build-

ing and/or radial leakoff, shear thickening and/or viscoelasticity, just to mention a few) should be consid-

HF2D Page 2121

ered after the sizing has been done correctly, taking into account the main issues such as: net pay thick -

ness, formation permeability, percentage of proppant reaching the pay, apparent proppant permeability.

In the sizing phase of the fracture design we make a decision on the dimensionless proppant number to re -

alize. This determines the maximum possible Productivity Index and the optimum fracture dimensions are

those realizing this “best” performance.

Optimum fracture dimensions

The optimum design represents the best compromise between width and length. Once we know the vol-

ume of the propped one-wing in the pay layer, Vf (note that this is half of the propped volume in the pay

layer : Vf = Vprop /2 and, naturally, much less than half of the proppant volume injected) then we can use

the definition of dimensionless fracture conductivity to obtain the optimum width and length:

..............................................(9)

...........................................(10)

Once we know the proppant number, the optimum dimensionless fracture conductivity can be read from

Fig. 3 a or b or calculated from suitable correlations built into the HF2D spreadsheet. Most often the op-

timum CfD will be 1.6, but the program can do the optimization for very large proppant numbers as well,

where the optimum dimensionless fracture conductivity will be largergher.

The fracture dimensions obtained from Eqs. 9 and 10 will realize the previously determined maximum

possible Productivity Index.

Of course, the above half-length and width are meant as “equivalent length” and “equivalent average

propped width”, because the performance model represents the vertical fracture by a crude approxima-

tion as a rectangular fracture with constant width.

The actual shape of the fracture might be different but that can bring only minor deviations from the re -

sults presented here. (The most difficult thing in petroleum engineering is the separation of the really im-

portant effects from the lots parameters of secondary importance. )

HF2D Page 2222

Pumping Schedule

Once the target length and width is known, one can proceed with the actual design of the treatment. The

design includes the determination of the injection time, the necessary maximum added proppant concen-

tration and the detailed proppant schedule realizing the optimum dimensions. The basic algorithm is de-

scribed in the Appendix.

If technical constraints do not allow the realization of the “optimum placement”, one has to make a depar-

ture from it, but only to the extent it is really necessary. For instance, in very low permeability formations

the optimum width might be less than two or three proppant diameters. Then we have to put a constraint

on the minimum width and modify the target width and length accordingly (still providing the target

proppant number.) It can be shown with the presented curves that such a departure – if done only to the

necessary extent - causes a loss of productivity that is within reasonable limits and most often not impor-

tant at all.

It is important to note that:

o There is no theoretical difference between low and high permeability fracturing. In both cases

there exists a technically optimal fracture, and in both cases it should have a dimensionless frac-

ture conductivity depending solely on the proppant number. While in a low permeability forma-

tion this requirement results in a long and narrow fracture, in high permeability formations, a

short and wide fracture will provide the same dimensionless conductivity.

o Increasing the volume of proppant or the permeability of the proppant pack by a given factor (for

example, 2 ) has exactly the same effect on the productivity if otherwise the proppant is placed

optimally.

o To achieve the same post-treatment skin factor in a low and a high permeability formation the

volume of proppant placed to the pay layer should be increased by the ratio of the formation per -

meabilities, provided all the other formation and proppant parameters are the same.

o Since not all proppant will be placed into the permeable layer, the optimum length and width

should be calculated with the effective volume, subtracting the proppant placed in the non-pro-

HF2D Page 2323

ductive layers.

o In high permeability formations, the indicated fracture length might not be enough to bypass the

damaged zone, therefore a minimum length should be applied.

o Considerable fracture width can be lost because of proppant embedment into soft formations. For

gas wells, non-Darcy effects may create a dependence of the apparent permeability of the prop-

pant pack on the production rate itself. These issues are best handled by using proper effective

width and effective peremeabilities in the conductivity expression (both in the proppant number

and in the dimensionless proppant conductivity).

Of course it is possible that the technical constraints (first of all maximum possible proppant concentra -

tion in the slurry) does not allow optimal placement. In case of conflict the design engineer has several

options: e.g. choosing another type of fluid and/or equipment, but for higher permeability formations

most likely a tip screenout (TSO) design has to be considered.

The TSO design differs from the above procedure in one basic feature: it uses a TSO criterion to separate

the lateral fracture propagation period from the width inflation period. In our design model this criterion

is based on “dry to wet” average width ratio. The “TSO criterion” specifies the ratio of dry width (assum -

ing only the "dry" proppant is left in the fracture) to wet width (dynamically achieved during pumping).

According to our assumptions, the screen-out happens and fracture propagation stops when the ratio of

dry to wet width reaches the user specified critical value. After the TSO is triggered, only the width is in-

flated, as far as additional slurry is injected. It is possible to schedule the proppant to such that the critical

dry to wet width ratio is reached at that moment when the fracture length arrived at the desired distance.

With TSO design, practically any width can be achieved, at least in principle. We suggest a number be-

tween 0.5 and 0.75. for the “TSO criterion: dry/wet width” parameter, but there is no good theoretical

model behind this suggestion.

(Unfortunately, if the formation does not allow it, it might be impossible to arrest fracture propagation

(the rock is not soft enough, the elasticity modulus is too high, the leakoff is too high, etc.) There is no

clear procedure to predict if a TSO-type width inflation will be possible in the given formation or not. En-

gineering intuition and previous experience are of crucial importance in making that judgment.)

Note that we use the word “optimum” for placing a given amount of proppant the best possible way into

the formation. The determination of the optimum amount of proppant is called sizing. For optimum sizing

one needs to know the costs and revenues. The costs increase with proppant number in a well defined

HF2D Page 2424

manner. The revenues also increase with proppant number, and that can be calculated knowing the tar -

geted Productivity Index. There is no need to do a detailed fracture design in order to size a treatment. (In

fact sizing and detailed design should be separated. Optimum sizing should be done exclusively by the

operator and not by the service company.)

In case of conflict the design engineer may consider using another type of fluid and/or consider using

equipment providing a higher maximum proppant concentration, and/or tip screenout design.

There are several other checks the design engineer has to conduct. For instance, at the end of the pad in -

jection the current hydraulic width should be large enough to accommodate proppant that is wet width per

dry width should be at least 3.

The TSO design differs from the above procedure in one basic feature: it uses the TSO criterion (critical

ratio of wet width per dry width) to separate the lateral fracture propagation period from the width infla-

tion period.

It is possible that the design does not require a tip screenout. This is indicated by a message and then the

user is suggested to run a traditional design without TSO.

If the constraints do not allow the best placement of the proppant, the traditional PKN algorithms still

provides a design, but the created fracture will be suboptimal. Warning messages indicate suboptimality

and possible modification of injected proppant. In modifying the requirements the program takes the easy

road, that is it reduces the amount of proppant placed. Sometimes this is acceptable, but more often you

should explore other options.

The first thing to look at is to use various fluids (that is changing rheology and leakoff), changing the in-

jection rate or assuring larger maximum possible added proppant concentration by selecting a better

equipment.

Often the optimum proppant placement can be realized by a tip-screenout design, and in such case the

user should use the PKN-TSO method. The TSO design is not a well established procedure, because the

prediction of the tip screen-out point is not based on sound physical principles. In our model a TSO crite-

rion is used to trigger TSO and this criterion has to be selected carefully. That design parameter is only

for TSO design. It specifies the ratio of dry width (assuming only the "dry" proppant is left in the fracture)

to wet width (dynamically achieved during pumping). According to our assumptions, the screen-out hap-

HF2D Page 2525

pens when the ratio of dry to wet width reaches the user specified value. We suggest a number between

0.5 and 0.75., but there is no good theoretical model behind this suggestion.

Unfortunately, TSO treatment can be impossible, if the formation does not allow it (the rock is not soft

enough, the leakoff is too high, etc.) There is no clear procedure to predict if a frac&pack type width in -

flation will be possible in the given formation or not. Engineering intuition and previous experience are of

crucial importance in such case.

If the given amount of proppant can not be placed optimally by a traditional design and you can not apply

a TSO design (because the high leakoff, and/or high elastic modulus, and/or consolidated rock make it

impossible) the traditional PKN design procedure should be used with an additional design factor that be-

comes especially important. In the spreadsheet it is called “multiply opt length by a factor”.

Once you see the error message “Optimum placement of proppant is not possible” and you have tried all

other options you have to make a decision on which design goal to relax. If you still want to place the

originally specified amount of proppant, you have to depart from the optimum length. In such case you

specify a factor of 2, 3, or even 10 to multiply the theoretically optimum length. With large enough factor

used, you will be able to place all the proppant into the formation. The resulting suboptimal design will

yield a reduced PI (compared to the optimum one.) At this point you have to decide whether it was a

good idea to stick with the original amount of proppant. (It is possible that the answer is NO. As you will

find, often a fraction of the original amount of proppant, BUT PLACED OPTIMALLY, gives almost the

same PI as the large SUBOPTIMAL treatment while the cost of a small treatment is, of course, consider-

ably less.)

HF2D Page 2626

66 SSAMAM

PLEPLE R RUNSUNS

HF2D Page 2727

1) Traditional PKN design

Input

Proppant mass for (two wings), lbm 150,000

Sp grav of proppant material (water=1) 2.65

Porosity of proppant material 0.38

Proppant pack permeability, md 60,000

Max prop diameter, Dpmax, inch 0.031

Formation permeability, md 0.5

Permeable (leakoff) thickness, ft 45

Well Radius, ft 0.30

Well drainage radius, ft 2100

Pre-treatment skin factor 0.0

Fracture height, ft 120

Plane strain modulus, E' (psi) 2.00E+6

Slurry injection rate (two wings, liq+ prop), bpm 20

Rheology, K' (lbf/ft^2)*s^n' 0.0180

Rheology, n' 0.65

Leakoff coefficient in permeable layer, ft/min^0.5 0.00400

Spurt loss coefficient, Sp, gal/ft^2 0.01000

Fluid loss multiplier outside the pay 0

Max possible added proppant concentration, lbm/gal neat fluid

12

Multiply opt length by factor 1

Multiply Nolte pad by factor 1

HF2D Page 2828

Part of Output

Optimum placement without constraints

Proppant number, Nprop 0.211

Dimensionless PI, JDopt 0.56

Optimal dimensionless fracture cond, CfDopt 1.7

Optimal half length, xfopt, ft 661.1

Optimal propped width, wopt, inch 0.1

Post treatment pseudo skin factor, sf -6.33

Folds of increase of PI 4.57

Constraints allow optimum placement

Actual placement

Proppant mass placed (2 wing) 150,000


Dimensionless PI, JDact 0.56

Dimensionless fracture cond, CfD 1.7

Half length, xf, ft 661.1

Propped width, w, inch 0.11



HF2D Page 2929

Treatment details

Efficiency, eta, % 33.1

Pumping time, te, min 84.5

Pad pumping time, te, min 42.5

Exponent of added proppant concentration, eps 0.5029

Uniform proppant concentration in frac at end, lbm/ft^3 47.8

Areal proppant concentration after closure, lbm/ft^2 0.9

Max added proppant concentration, lb per gal clean fluid 9.0

Net pressure at end of pumping, psi 262.5

HF2D Page 3030

2) PKN-TSO design

Input



Porosity of proppant material 0.38


Max propp diameter, Dpmax, inch 0.031

Formation permeability, md 15



Well drainage radius, ft 2,100


Fracture height, ft 75.0


Slurry injection rate (two wings, liq+ prop), bpm 15.0


Rheology, n' 0.45



Fluid loss multiplier outside the pay 0

Max possible added proppant concentration, lbm/gallon fluid 16


TSO criterion Wwet/Wdry 0.7

Multiply pad by factor 1

HF2D Page 3131

Part of Output









Optimum placement

TSO criterion was achieved

Actual placement









HF2D Page 3232

Treatment details

Pad pumping time, min 0.37

TSO time, min 7.1

Total pumping time, min 16.2

Mass of proppant in frac at TSO, lbm 13,628

Added proppant concentration at TSO, ca, lbm/gal liq 4.0

Half length at TSO, xf, ft 89.1

Average width at TSO, inch 0.6

Net pressure at TSO, psi 30.1

Max added proppant concentration at end, lbm/gal-liq 16.0


Net pressure at end of pumping, psi 79

HF2D Page 3333

NNOMENCLATUREOMENCLATURE

Bo = oil formation volume factor, RB/STB

CfD =dimensionless fracture conductivity

CL =leakoff coefficient, ft/min1/2

h =pay thickness, ft

hp =net pay thickness, permeable thickness, ft

hf =fracture height, ft

Ix =penetration ratio, calculated for a square drainage area

J =productivity index, BOPD/psi

JD =dimensionless productivity index

E' = plain strain modulus, psi

k =effective formation permeability, mD

kf =effective proppant pack permeability, mD

K' =Power law consistency index , lbf/(ft2-sec)

n' =Power law flow behavior index

Nprop = proppant number

=average reservoir pressure, psi

pwf =flowing bottomhole pressure, psi

q =oil flow rate, STB/D

qi =fluid injection rate, bpm

rp = permeable to total area ratio

HF2D Page 3434

rw = wellbore radius, ft

r'w = equivalent wellbore radius due to fracture, ft

Rf = created fracture radius, ft

sf = pseudo skin factor due to fracture

te = pumping time, min

Vi = injected volume, ft3

Vp = propped volume of the two wing contained in the pay layer, ft3

Vr = drainage volume: net height by drainage area, ft3

xf = fracture half length, ft

xe = size of study area in x-direction

ye = size of study area in y-direction

w = propped fracture width, ft

1 = conversion factor (for field units 887.22)

= pad fraction

= Nolte exponent

p = proppant pack porosity, fraction

= opening time distribution factor, dimensionless

= formation fluid viscosity, cp

= fluid (slurry) efficiency, fraction

HF2D Page 3535

AA CASE STUDIESCASE STUDIES

Table 1 Overview

Medium Permeability Formation MPF Standard MPF01

Pushing the limit MPF02

Proppant Embedment MPF03

Non-Darcy

Fracture face skin

High Permeability Formation HPF Standard MPF01

Extreme High MPF02

Low Permeability Formation LPF Low Permeability (tight gas) LPF01

HF2D Page 3636

A.1 A Typical Preliminary Design: Medium Permeability Formation, MPF01

In the remaining part of this chapter we will illustrate the design logic incorporated in the Unified Frac -

ture Design. We will intentionally consider cases, where only limited data are available.

Table 2 shows available data for a “medium” permeability formation (with permeability 1.7 md. and net

pay of 76 ft). The input data contains the well radius and the drainage radius (calculated from 40 acre

spacing). These important reservoir parameters should not be missed.

A preliminary sizing decision is that 90,000 lbm proppant should be injected.

At the closure stress anticipated (5000 psi) the selected resin coated 20/40 mesh sand will have an in-situ

permeability of 60,000 md. In this number we already incorporated the effect of some proppant crushing

and the decrease of proppant pack permeability due to imperfect breaking of the gel. Obviously, this is

one of the key parameters of the design, and the design engineer has to do everything in her/his power to

make this estimate as relevant as possible. (Buying an expensive 3D program with vendor provided prop -

pant data and clicking the name of the proppant is obviously not enough.)

The plane-strain modulus (that is basically the Young modulus) is 2106 psi. Minifrac tests in the same

formation with the same fluid usually result in a leakoff coefficient 0.005 ft/min1/2 and some spurt loss is

also anticipated. (Note that these values are with respect to the pay layer. It is assumed, that outside the

pay there is no leakoff.) The fluid rheology parameters are provided by the service company and (because

of pressure limitations in this case) the injection rate is 20 bpm.

HF2D Page 3737

Table 2. Input Data For MPF01



Porosity of proppant pack 0.38








Fracture height, ft



Rheology, K' (lbf/ft2)sn' 0.07

Rheology, n' 0.45

Leakoff coefficient in permeable layer, ft/min1/2 0.005


The input data are summarized in Table 2. The line of fracture height is still left empty. We know that the

gross pay is 100 ft, that is the distance between the top and bottom perforations is 100 ft. Within this in -

terval, only 76 ft is pay, though. A preliminary estimate of fracture height should be minimum 100 ft, but

the actual height will be related to several other factors.

HF2D Page 3838

A reasonable assumption – in the absence of any reliable data on stress contrast – is, that the aspect ratio

of the created fracture is 2:1 . In other words, we will find the fracture height, hf, by adjusting it to the

target length, according to hf = xf .

At this point we put a starting estimate of hf =100 ft into our design spreadsheet and we specify the fol-

lowing operational constraint/parameters, as shown in Table 3:

Table 3. Additional Input For MPF01

Max possible added proppant concentration, lbm/gal neat fluid 12



The maximum available proppant concentration in ppga (lbm proppant added to 1 gallon of neat fractur-

ing fluid) is 12 according to the service company. The other two parameters are fixed at their default

value.

The output of the first run of our design spreadsheet contains three parts. In the first part a “wish-list” is

shown.

Table 4. Theoretical Optimum for MPF01-1

HF2D Page 3939

Output









It states that the proppant number is 0.35 and with the proppant placed optimally we could achieve a di -

mensionless productivity index of 0.65 that is a skin factor as negative as –5.72. The Folds of increase in

productivity (with respect to the zero skin situation we fixed in line 10 of the input as the basis of compar-

ison ) is 4.74 .

A red warning message is, however, indicating, that our wish-list could not be realized:

Suboptimal placement with constraints satisfied

Mass of proppant reduced

The actual placement, the design program was able to produce is somewhat disappointing, as shown in

Table 5:

HF2D Page 4040

Table 5. Actual placement for MPF01-1

Actual placement









In other words, the design program can assure only the placement of 58,500 lbm proppant. The reason

for this will be discussed later. At this point we should not pay too much attention to it, because our speci -

fied fracture height (100 ft) was not realistic.

To approach our required aspect ratio: hf =xf we increase the fracture height to 200 ft. The calculated the-

oretical optimum target length is now hf = 216 ft. A third adjustment to hf =211 ft will finally establish the

required aspect ratio.

HF2D Page 4141

Table 6. Theoretical Optimum for MPF01-3 ( hf = 211 ft )



Dimensionless PI, Jdopt 0.53






We see that the proppant number is significantly less: 0.168, than previously. Why did this happen? Be-

cause the increase in fracture height decreases the volumetric proppant efficiency, that is the part of prop-

pant “working for us”. The optimum length corresponding to this proppant number is 211 ft, and that

means that our fracture – if it can be realized – will have the desired 2:1 aspect ratio. But can it be real-

ized?

The red message:


shows that yes, the optimum placement can be realized.

HF2D Page 4242

Table 6. Actual Placement MPF01-3 ( hf = 211 ft )

Actual placement









We found that the 90,000 lbm proppant can be safely placed into the well. Not all of the proppant will be

placed into the pay layer, though.

The part of the proppant reaching the pay will represent a proppant number Nprop = 0.168, and the opti-

mum half length corresponding to it is 211 ft. The treatment will establish a dimensionless productivity

index, JDact = 0.53 in other words a negative equivalent skin, sf = -5.37 will be created.

Note that the whole design logic is based on the proppant number concept. We do not specify an arbitrary

length, rather we obtain the optimum length and the design process makes sure that the desired length is

realized and the desired amount of proppant is placed uniformly.

Some details of the treatment are shown in Table 7.

HF2D Page 4343

Table 7. Some Details of the Actual Placement MPF01-3 ( hf = 211 ft )

Treatment details






Areal proppant concentration after closure, lbm/ft2 1.0



More details can be found by running the spreadsheet.

A.2 Pushing the limit: Medium Permeability Formation, MPF02

For illustrative purposes we will consider MPF01 as our base case. In this section we ask the question:

can we place 150,000 lb proppant in a similar manner? If yes, what good will it do for the well productiv-

ity?

The reader is now able to do the design so we will not show the detailed “iteration”, only the main results.

Table 8. Some Details of the Input MPF02-3 ( hf = 248 ft )


…


…

HF2D Page 4444

Table 9. Theoretical optimum for MPF02-3 ( hf = 248 ft )

Output









The first thing we should note that the increase of proppant and corresponding increase of proppant num-

ber will result – even if everything goes well – only a marginal improvement in productivity. This should

make us think whether it is worth “pushing the limit”. Even more food for thought is provided by the

message:



and by the next output:

Table 10. Actual placement for MPF02-3 ( hf = 248 ft )

HF2D Page 4545

Actual placement









Treatment details









As we see the design program had to reduce the amount of proppant placed into the formation. With this

reduction the actual folds of increase is hardly more than what we can achieve with 90,000 lb proppant

and it is obvious that “pushing the limit” in this case is not worth the effort and money.

But is it really obvious? Several service companies would rather suggest a better equipment capable to do

as high proppant concentration as 16 ppga.

Table 11. Actual placement for MPF02-4 ( hf = 248 ft, max possible conc: 16 ppga )

HF2D Page 4646


The message is now encouraging:


Table 12. Actual placement for MPF02-3 ( hf = 248 ft, max possible conc: 16 ppga )

Actual placement









Treatment details









HF2D Page 4747

The increase in the maximum possible proppant concentration did the trick. It is now possible to place the

required quantity of proppant (because larger concentration allows to put more proppant into the same

width). In fact we did not even use all the capabilities of the equipment, a 14 ppga maximum proppant

concentration would be enough.

Also it is clear that our actual design now realizes the “wish-list” originally stated in Table 9. The ques-

tion, whether it is worth doing the larger treatment or not, is however, still open. Only careful economic

calculations can tell if it is worth doing the larger treatment, that will be about 50 % more expensive, but

will realize a post treatment skin of –5.54 instead of the –5.50 calculated for our base case, MPF01-3.

Since the difference is clearly in the “error margin” it is difficult to believe that a manager would decide

on the more expensive (and more risky) larger treatment.

A.3 Proppant Embedment: MPF03

It is well-known, that in softer formations a considerable part of the injected proppant might be “lost” be-

cause it is embedded into the formation wall. Some estimates talk about 30 % loss of width because of

embedment (Lacy, 1994)

Let us assume that the rock mechanics lab measured a 33.3 % embedment for the given formation and

closure stress. How can we incorporate this into the design?

The easiest way is to say that the proppant pack permeability (now 60,000 md) will apparently be reduced

to 40,000 md.

Changing one input line of case MPF01-3, that is putting


HF2D Page 4848










As we see, now the maximum possible dimensionless productivity index is less, only 0.50, but even this

can not be realized as the error message indicates:




Actual placement









HF2D Page 4949

In fact only 65,300 lb proppant can be placed because the width at 185 ft is less than it was at 211 ft and

because we need more width to compensate for the loss of conductivity (due to embedment.)

To make the design possible we will depart from the optimum by multiplying the theoretical optimum

length by a factor. In this case we select the factor to target 250 ft for length, so we change the height to

250 ft (remember, we still use the 2:1 aspect ratio as most probable) and then we have to find a factor re-

sulting in the half length 250 ft. This value is 1.58:

Table 14. Height and Constraint for MPF03-4



Multiply opt length by factor 1.58


Table 15. First Part of Output for MPF03-4

Output









HF2D Page 5050

The message shows that the sub-optimal placement with the required modification can be realized:


Length modified

Table 16. Additional Output for MPF03-4

Actual placement



Dimensionless PI, Jdact 0.44






Now we can place all the 90,000 lb proppant but we have to depart from the theoretical optimum place-

ment. The “success” is, however, questionable, because with all the 90,000 lb proppant placed we still

create only a - 4.98 equivalent skin, while the 65,300 lb – placed according to MPF03-3 – actually cre -

ates a better skin: -5.06.

By now the reader might feel why we call our approach “Unified Fracture Design”. The systematic use of

the proppant number and the optimality criterion makes the decisions more transparent.

A.4 Non-Darcy Flow in the fracture

For high-rate gas wells, where a certain percentage liquid content of the gas is inevitable, the concept of

proppant pack permeability deserves special attention. When the gas-liquid mixture flows in the propped

HF2D Page 5151

fracture with high velocity, the liquid droplets collide with the proppant grains and the result is a signifi-

cant dissipation of energy (loss of pressure). As a result, the nominal permeability contrast (in the fracture

vs in the formation) is not representative for the relative magnitude of pressure losses. The fracture be-

haves, as if its apparent permeability were much less, than the nominal value measured at single phase

flow conditions. There is an extensive literature available describing this non-Darcy flow effect in the

fracture (Jin and Penny, 2000, Cikes, M. 2000, Milton-Tayler, 1993, Gidley, 1990, Guppy et al., 1982).

From our point of view it is enough to understand, that at actual flow conditions the proppant pack can be

described by an apparent permeability – or if we wish – a correction factor multiplying the nominal per -

meability. Depending on the actual velocity of the gas, the liquid content and the droplet size distribution,

in addition to the proppant quality, the correction factor can be as low as 0.1.

The treatment of this phenomenon within the Unified Fracture Design is relatively simple. Using an esti -

mate of the correction factor, the apparent proppant permeability should be reduced, for instance from

60,000 md to 10,000 md. From the calculated maximum productivity index – corresponding to the cor-

rected proppant number – a better estimate of the anticipated gas velocity can be obtained. (For this cal-

culation a drawdown has to be assumed and the properties of the gas – liquid mixture have to be known.)

With the improved estimate of gas velocity, an improved estimate of the non-Darcy flow correction factor

can be obtained and the design can be continued using the corrected proppant number.

For instance, in our previous example the proppant number calculated with a nominal permeability:

60,000 md was obtained as Nprop = 0.095 . In the presence of significant non-Darcy effect, this number

should be reduced to Nprop = 0.05 or – in extreme cases – to Nprop = 0.01. If we want to compensate for the

loss of productivity, we have to increase the amount of proppant placed into the pay by the same factor.

A.5 Compensating for fracture face skin

In a certain reservoir it is suspected that the fracturing fluid filtrate will interact with the formation and an

estimated fracture face skin sff = 1 will be created. What is the effect of this phenomenon on the produc-

tivity of the well and how can we compensate for it? Assume the proppant number of the suggested treat -

ment is about Nprop = 0.1.

We recall, that the maximum of the dimensionless productivity index that can be achieved with Nprop = 0.1

is (see Chapter 3):

HF2D Page 5252

(8)

If there is a fracture face skin sff = 1, (and we assume the simple case of uniform influx) then the actual

productivity will be

(9)

The fracture face skin causes a considerable decrease in productivity. From the equation it is seen that

approximately e2 = 7.4 times more proppant would compensate for the loss of productivity caused by a

fracture face skin of one.

A.6 Fracture Design for High Permeability Formation: HPF01

In high permeability formations the optimality criterion will result in a short and wide fracture. To have a

basis for comparison, we will use the previous data set except for the following variables: permeability,

plane strain modulus, spurt loss and leakoff coefficient.

HF2D Page 5353

Table 17. Input Data For MPF01











Fracture height, ft



Rheology, K' (lbf/ft2)sn' 0.07

Rheology, n' 0.45

Leakoff coefficient in permeable layer, ft/min1/2 0.01


The line of fracture height is still left empty. We know that the gross pay is 100 ft, that is the distance be -

tween the top and bottom perforations is 100 ft. A reasonable assumption for high permeability fracturing

– in the absence of any reliable data on stress contrast – is, that extensive height growth will not occur as

far as the target length is less than half of the height. At this point we put a starting estimate of hf =100 ft

into our design spreadsheet and we specify the following operational constraint/parameters, as shown in

Table 18:

HF2D Page 5454

Table 18. Additional Input For HPF01

Max possible added proppant concentration, lbm/gallon fluid 16


Multiply pad by factor 1

Table 19. Theoretical optimum for HPF01-1



Dimensionless PI, Jdopt 0.31






From the first design attempt we see that the proppant number is Nprop = 0.012 . This is a typical situation

for high permeability formations: not even a considerable amount of proppant and well contained fracture

height will produce large proppant numbers. The message says that



HF2D Page 5555

Table 20. Actual placement without TSO design: HPF01-1

Actual placement









In fact only 10,700 lbm proppant can be placed into the formation, if the target length is 56.7 ft. Such a

treatment would realize a very low proppant number and an equivalent skin of –2.5, that is usually not

satisfactory, especially because other factors can decrease further the stimulation effect.

The problem is, that the width of the fracture (even though this is a relatively “soft” formation) created

during normal fracture propagation is not enough to accept more proppant. (Note that we have already in-

creased the maximum possible proppant concentration to 16 ppga, but that is still not enough.)

The solution to the problem is to design a TSO treatment. Knowing that the formation is “soft” and rela -

tively unconsolidated, we intentionally arrest fracture propagation at the target length (56.7 ft) and inflate

the fracture from there on.

For the TSO design we use exactly the same input as previously, the only additional parameter is:

TSO criterion Wdry/Wwet 0.7

The meaning of this parameter is, that we anticipate the fracture to stop propagating if – because of fluid

loss, in other words dehydration – the “dry width” is already near to the “wet width”. The dry width is de -

HF2D Page 5656

fined as the width of the fracture after all fluid have leaked off, while the wet width is the width during

the treatment when still part of the proppant carrying fluid has not leaked off. We use the critical value

of 0.7, but depending on the actual fracture shape and proppant type the value might vary.

Table 21. Actual placement with TSO design: HPF01-TSO

Actual placement









From the output we see, that with TSO we could place all the proppant into the 57-ft long fracture. This is

achieved by (internally) adjusting the proppant schedule to reach the critical proppant concentration in the

fracture when the lateral extension reaches the target length.

HF2D Page 5757

Table 22. Actual placement with TSO design: HPF01-TSO

Treatment details


TSO time, min 7.9










In fact 11,000 lb proppant is placed into the fracture in a usual manner in less than 8 minutes. After that

the fracture length remains constant and only the width inflated.

Fig. 3 Fluid, proppant schedule and net pressure forecast for the TSO treatment.

The net pressure is considerable, almost 500 psi at the end of the treatment. This is anticipated, because

the optimum placement calls for an almost 1-inch propped fracture width.

HF2D Page 5858

0

5

10

15

20

25

0 5 10 15 20 25 30

Pumping time, min

Liqu

id in

ject

ion

rate

, bpm

024681012141618

ca, l

bm p

rop

adde

d to

ga

llon

liqui

d

0

100

200

300

400

500

600

0 5 10 15 20 25 30

Pumping time, min

Net p

ress

ure,

psi

A.7 Extreme High Permeability: HPF02

In naturally fractured formations several hundred md permeabilities are not uncommon. To investigate

this territory we repeat the design with the same input, except for


Table 23. Theoretical optimum for: HPF02









As we see, the target length is now 18 ft. In fact the design program can produce a TSO design for this

case also:

HF2D Page 5959

Table 24. First attempt for HPF02

Actual placement









but the design cannot be accepted, because it would result in an extremely high net pressure, as seen from

Table 25.

Table 25. First attempt for HPF02

Treatment details


TSO time, min 1.2










HF2D Page 6060

Several parameters have unrealistic values in the results of the first attempt. The extremely short fracture

– even if it could be realized – would not be necessarily useful, because the near wellbore damage might

be still dominating at such distances. A reasonable design would call for longer fracture. From an opera -

tional point of view, net pressure limitation is the most important constraint in high permeability fractur-

ing. A maximum allowable net pressure should be specified from safety considerations. A typical value

would be for instance 1000 psi. Therefore we will modify our design in order to satisfy this limitation.

We have several options.

One possibility is to depart from the optimum length, that is multiplying it by a factor. A realistic design

would try to keep the 1:1 aspect ratio, therefore we select


That would give us a placement

Table 26. HPF02 with modified length

Actual placement









HF2D Page 6161

Treatment details


TSO time, min 7.2










Such a treatment already satisfies the net pressure constraint. The calculated design calls for starting the

addition of proppant almost from the beginning of the treatment. Unfortunately, the design depends heav-

ily on the selected TSO criterion and on the accuracy of the leakoff description. In reality, it is difficult to

predict the TSO with such an accuracy. The art of arresting fracture propagation but still avoiding a near-

wellbore screenout (that would cause us to stop the treatment) often requires the intuition and experience

of the fracturing engineer. The operator company may increase the chance for success by reducing the

risks associated with the treatment. That leads us to another possibility: to reduce the amount of proppant

and multiply the optimum length by a factor, at the same time:



HF2D Page 6262

Table 27. HPF02 with less proppant and modified length


Actual placement









Treatment details


TSO time, min 6.5










HF2D Page 6363

The important thing to note is, that there is little to lose when we reduce the proppant number from

0.0012 to 0.0006. In this proppant number region the dimensionless productivity index is less sensitive to

the amount of proppant or to the departure from the optimum length, as a matter of fact. Only a moder -

ately negative equivalent skin factor can be realized at such low proppant numbers. This explains the

widely accepted view that in extremely high permeability formations the most important issue is “to get

behind the damage” and create a pack (“halo”) around the screen. The actual fracture length has less sig -

nificance. Many high permeability fracturing treatments use only 50,000 lbm or less proppant.

A.8 Low Permeability Fracturing: LPF01

To maintain consistency with our previous examples we consider a low permeability formation with most

of the input parameters similar to our base case:

Table 28. Input for LPF01





Max 64rop diameter, Dpmax, inch 0.031






HF2D Page 6464

Fracture height, ft




Rheology, n' 0.45






Again we will start the design by specifying hf = 100 ft.

Table 29. Theoretical optimum assuming 100 ft fracture height: LPF01









HF2D Page 6565

The proppant number is large, because of the large contrast in permeabilities. At such large proppant

number the indicated fracture half length is already near to the “side length” of the drainage area (this is

why the optimum dimensionless fracture conductivity is significantly more than 1.6).

If such a fracture could be realized, an extremely large dimensionless productivity index would be estab-

lished. Unfortunately, there is little chance that a fracture with aspect ratio 8:1 could be created without

height increase. It is more likely that an aspect ratio of about 2:1 will be obtained.

Therefore we base our design on the assumption of aspect ratio 2:1. Changing the fracture height to

300 ft, the theoretical optimum values become more realistic, because the decrease of volumetric prop-

pant efficiency reduces the proppant number .

Table 29. Theoretical optimum assuming 300 ft fracture height: LPF01-1









HF2D Page 6666

Table 29. Actual placement assuming 300 ft fracture height but unchanged leakoff coefficient:

LPF01-2

Actual placement









Treatment details









While the design is now more realistic, one variable deserves special attention. The fluid efficiency in -

creased to 67 %. Why did this happen? The reason is that, according to our definition, leakoff happens

only in the pay layer (with net thickness 76 ft). Now, that the actual fracture height is taken as 300 ft, only

one quarter of the total surface contributes to leakoff and the efficiency is very high. In reality it is not

likely, that perfectly non-permeable shale is surrounding the pay. Therefore it is wise to reconsider the

leakoff (and spurt loss) parameters once a significant change in fracture height has been introduced.

HF2D Page 6767

Repeating the design with correspondingly adjusted leakoff and spurt loss coefficients:



we obtain the results in Table 30.

Table 30. Actual placement assuming 300 ft fracture height and adjusted leakoff and spurt loss co-

efficients: LPF01-3

Actual placement









HF2D Page 6868

Treatment details









The fluid efficiency is more realistic now, but the final fracture length and propped width is exactly the

same as previously. How is it possible that such a large change in the leakoff parameters does not affect

the final results? The answer to this question reveals the main difference between simulation and design.

In our design procedure the target length and target propped width are derived from the reservoir and

proppant properties. The leakoff parameters (and other variables) determine how we achieve our final

goal, but the goal is the same, whether there is intensive leakoff or not. The change in the leakoff param-

eters shows up in the actual proppant schedule. Now we have to pump for a considerably longer time.

Experienced fracturing engineers would probably not accept the design yet. The point is that the indicated

propped fracture width is only 0.06 inch, that is less than 3 grains of the 20/40 mesh proppant. A good de-

sign ensures a certain minimum width (or a certain minimum areal proppant concentration.)

At this point we either increase the amount of proppant or depart from the indicated optimum length, now

multiplying it by a factor less than one. The advantage of creating a shorter fracture shows up also in the

volumetric proppant efficiency: in other words keeping the aspect ratio 2:1 we will have less proppant

“avoiding” the pay. The relevant lines of the input are shown in Table 31.

Table 31. Final design: LPF01-4

HF2D Page 6969


…

Fracture height, ft 200.0

…




Multiply opt length by factor 0.55


Table 32. Actual placement: LPF01-4

Actual placement









Table 33. Some Details of the Actual placement: LPF01-4

HF2D Page 7070

Treatment details









Note that targeting the smaller fracture allowed us to reduce the assumed height as well. Therefore, the

design can utilize more efficiently the 90,000 lbm proppant. The post-treatment dimensionless productiv-

ity index and equivalent skin factor are basically the same as in the case of LPF01-3. The final design,

LPF01-4, is more practical and certainly easier to carry out.

A.9 Summary

In this Appendix we showed some examples of practical fracture design. The concept of proppant num-

ber and dimensionless productivity index helped us to make important decisions without going into un-

necessary details. The design spreadsheet was used extensively to consider what-if scenarios and investi-

gate options. In hydraulic fracture design, where the reliability of the available input data is always lim-

ited and the process itself is inherently stochastic, it is extremely important to proceed in an evolutionary

manner, continuously improving the design process. The simple spreadsheet does not substitute the so-

phisticated “3D” fracture simulators. Rather, it provides a flexible tool to make the basic decisions before

the final design.

HF2D Page 7171

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