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HF2D06.doc - Harold Vance Department of Petroleum Engineering

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HF2D06.doc - Harold Vance Department of Petroleum Engineering

    HF2D FRAC DESIGN SPREADSHEET RAC ESIGN PREADSHEETHF2DFDS

    April 2001

    (Updated May 30, 2006)

Dr Peter P. Valkó

    Associate professor

    Harold Vance Department Petroleum Engineering

    Texas A&M University

    HF2D Page 1

    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 2

     EXECUTIVE SUMMARY XECUTIVE UMMARYES 1 1

    The HF2D Excel spreadsheet is a fast 2D design package for the 2D design of traditional (moderate permeability 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 optimum 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.

HF2D Page 3

     DATA REQUIREMENT DATAREQUIREMENT 2 2

    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

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

    proppant 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

    calculation 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.

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

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

    modulus, because the Poisson ratio has little effect on it. For hard rock it might be 6510 psi, for soft rock 10 psi or less.

    HF2D Page 4

    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

    0.5Leakoff coefficient in pay layer, ft/min 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.

    2Spurt loss coefficient, Sp, gal/ft 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, The most important equipment constraint. Some current mixers can provide lbm/gallon fluid (ppga) 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

    design. The program adjusts the proppant schedule accordingly, to ensure the

    required amount of proppant is injected.

HF2D Page 5

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

    (dynamically 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 6

     CALCULATED RESULTS CALCULATEDRESULTS 3 3

    The results contain the optimum fracture dimensions, followed by the fracture dimensions achieved taking 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 optimum 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 7

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

    x, ft half-length of the fracture at time t f

    w, in. average width of the fracture at time t ave

    w/ D the ratio of average width of the fracture to the maximum proppant diameter, should be at least 3 ave pmx

    w/ w the ratio of dry to wet width. dry wet

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

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

    prescribed 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 8

    THEORETICAL FRACTURE PERFORMANCE HEORETICAL RACTURE ERFORMANCETFP 4 4

    The fracture design should be based on sound principles of fluid flow in porous media. We start the description of the fractured well performance with the pseudo-steady state Productivity Index. It is well understood that in tight gas the transient regime might last for a considerable time therefore well produc-tion 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.

     2x f2xf

    h

    w w

     x2r ee

Fig. 1. Notation for fracture performance

Note that in reality the drainage area is neither circular nor rectangular. Using r or x is only a matter of ee

    convenience. The relation between r and x is given by ef

    22 Ar?x ................................................................ (1) ee

    HF2D Page 9

where A is the drainage area.

    Productivity Index

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

    ?2qkhJJ ........................................................ (2) DppBwf1

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

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

    for a coherent system).

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

    1 J ........................................................... (3) Dr3elnsr4w

    In the case of a propped fracture there are several ways to incorporate the stimulation effect into the productivity index. One can use the pseudo-skin concept:

    1J .......................................................... (4) Dr3elnsfr4w

    or the equivalent wellbore radius concept:

    1J ............................................................. (5) Dr3elnr'4w

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

     J= function(drainage-volume geometry, fracture parameters ) D

    HF2D Page 10

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