MINI FRAC TEST

DRILLING POSTGRADUATE STUDIES 2013

ROCK MECHANICS

Introduction Well testing has been used for decades to determine essential formation properties and to assess wellbore condition. However, under certain conditions, traditional test methods are not feasible for various reasons. This is especially true for very low permeability formations that require massive stimulation to obtain economic production. For these formations, it is extremely important to establish the formation pressure and permeability prior to the main stimulation. One test that has proved to be convenient for this purpose is commonly referred to as a “Minifrac” test.

A minifrac test is an injection-falloff diagnostic test performed without proppant before a main fracture stimulation treatment. The intent is to break down the formation to create a short fracture during the injection period, and then to observe closure of the fracture system during the ensuing falloff period. Historically, these tests were performed immediately prior to the main fracture treatment to obtain design parameters i.e.:

- fracture closure pressure,

- fracture gradient,

- fluid leakoff coefficient,

- fluid efficiency,

- formation permeability and

- reservoir pressure.

The created fracture can cut through near-wellbore damage and

and near-wellbore stress concentrations and connects wellbore to

a significant portion of the reservoir layer thickness, enabling a

representative investigation of reservoir fluid flow properties by

methods shown below.

Figure1: Idealized View of Induced Fracture

Typical pressure behavior of Minifrac Tests:

Figure 2: Total Test Overview Plot

Figure 3: Typical flow regimes

Key Results From Minifrac Tests:

Following a brief injection period, the wellhead valve is closed, and the pressure falloff is recorded (at the wellhead or downhole) for a few hours to several days, depending on how permeable the formation is. The pressure falloff data are then analyzed using specialized techniques to yield the following information:

• Fracture closure pressure (pc)

• Instantaneous shut-in pressure (ISIP)

ISIP = Final Flow Pressure - Final Flow Friction

Final Flow Friction is the friction component of the bottomhole calculation.

• Fracture gradient

Fracture Gradient = ISIP / Formation Depth

• Net Fracture Pressure (Δpnet)

Net fracture pressure is the additional pressure within the frac above the pressure required to keep the fracture open. It is an indication of the energy available to propagate the fracture.

Δpnet = ISIP - Closure Pressure

• Fluid efficiency

Fluid efficiency is the ratio of the stored volume within the fracture to

the total fluid injected. A high fluid efficiency means low leakoff and

indicates the energy used to inject the fluid was efficiently utilized in

creating and growing the fracture. Unfortunately, low leakoff is also

an indication of low permeability. For minifrac after-closure analysis,

high fluid efficiency is coupled with long closure durations and even

longer identifiable flow regime trends.

• Formation leakoff characteristics and fluid loss coefficients.

• Formation permeability (k)

• Reservoir pressure (pi)

Before Closure Theory

Valko and Economides (1995; 1999) presented a methodology for analysis and simulation of before-closure fracture pressure fall off, based on Carter’s leak-off model, Nolte’s assumption on fracture surface growth, and elastic behavior of the closing fracture walls under the formation in-situ stress. While tip-extension effects may occur in tight formations, we assume that immediately after the shut-in the fracture ceases to propagate. The pressure falloff is governed by the gradual loss of hydraulic fracture width w

pw = pc + Sf w (1)

where pw is wellbore pressure,

pc is the fracture closure pressure and

Sf is the “fracture stiffness”, measured in psi/ft and representing the relationship between fracture net pressure and fracture width according to the linear elasticity theory.

Different analytical expressions have been presented for all based on the assumption that There is no lateral flow in the fracture and the pressure is constant along the fracture at any given shut-in time.

¯ ̄

Table 1: Fracture stiffness and a values for 2D fracture geometry models

Table 1 presents expressions for Sf for the vertical plane strain

assumption (2D PKN-geometry, Perkins and Kern, 1961; Nordgren,

1972), for the horizontal plane strain assumption (2D KGD-geometry,

Geertsma and De Klerk, 1969) and for the simplest radial geometry.

Table 1 Proportionality constant, Sf and suggested for basic fracture geometries

PKN KGD Radial

4/5 2/3 8/9

S f 2E

h f

'

E

x f

'

3

16

E

R f

'

Figure 4. Basic notation for PKN and KGD geometries. hp= permeable height,

hf = fracture height and qL= rate of fluid loss.

Figure 5. Basic notation for radial geometry

The injection time, te, computed in an analogous way to the material

balance time, is used in the dimensionless shut-in time given by

(2)

and the two-variable function: introduced by Nolte

Valko and Economides (1995; 1999) expressed the fracture width at a

given time t after shut-in from a material balance scheme accounting

for leak-off in the formation and fracture propagation of the total injected

fluid, resulting in

(3)

Combining Eqs. 1 and 3 provides the final before-closure fracture

pressure falloff model

(4)

where:

Vi is the volume of fluid injected in one wing of the fracture (i.e. half of

the total injected fluid volume),

Ae is the equivalent surface area of one face of one wing,

Sp is the “spurt loss” that indicates the fraction of fluid loss in formation

at the very early stages of the leak-off process,

CL is the leak-off coefficient.

Valko and Economides (1995) provided an analytical expression for the

dimensionless g-function, g(Δt,α) introduced by Nolte (1979) for this

power law fracture surface growth assumption. This analytical

expression is based on a complicated mathematical function called

Hypergeometric function, available in form of tables (Abramowitz and

Stegun, 1972) and computing algorithms (Wolfram, 1991). A rigorous

calculation of the necessary g-function values requires also using the

proper power law exponent α, whose values for the familiar 2D fracture

geometry models are presented in Table 1.

Equation 4 suggests that the bottomhole pressure decreases linearly

with the g-function until the fracture finally closes, after which the

pressure falloff will depart from this linear trend. The linear nature of

this model is better visualized when Eq. 4 is expressed as equation of a

straight line of intercept bN and slope mN

(5)

Where (6)

and (7)

if plotted against the g-function (i.e., transformed time). The g-function

values should be generated with the exponent, , considered valid for

the given model. The slope of the straight line, mN , is related to the

unknown leak-off coefficient by:

(8)

Valko and Economides (1995; 1999) presented an exhaustive set of

equations for the familiar 2D fracture geometry models, based on the

Shlyapobersky et al. (1998) assumption of negligible spurt loss, to

calculate leak-off coefficient, fracture extent, hydraulic average width (at

end of pumping) and fracture fluid efficiency. All these equations are

presented in Table 2, and we can notice that bN and mN are necessary

input parameters. This technique requires the graph of the recorded

wellbore pressure falloff data versus the values of the g-function shown

on the graph on the in Fig. 6.

Figure 6

Table 2: Fracture-injection/falloff analysis model based on the Shlyapobersky et al.

(1998) assumption

Table 2 Minifrac Analysis by the Nolte-Shlyapobersky method

PKN KGD Radial

Leakoff

coefficient,

CL

N

e

fm

Et

h

'4

N

e

fm

Et

x

'2

N

e

fm

Et

R

'3

8

Fracture

Extent CNf

if

pbh

VEx

2

2

CNf

if

pbh

VEx

3

8

3

CN

i

fpb

VER

Fracture

Width

eL

ff

ie

tC

hx

Vw

830.2

eL

ff

ie

tC

hx

Vw

956.2

eL

f

i

e

tC

R

Vw

754.2

2

2

Fluid

Efficiency i

ffe

eV

hxw

i

ffe

eV

hxw

i

fe

eV

Rw2

2

This table shows that for the PKN geometry the estimated leakoff coefficient does

not depend on unknown quantities since the pumping time, fracture height, and

plain-strain modulus are assumed to be known.

For the other two geometries considered, the procedure results in an estimate of the

leakoff coefficient which is strongly dependent on the fracture extent (xf or Rf ).

From Equation (4) we see that the effect of the spurt loss is concentrated in the

intercept of the straight-line with the g = 0 axis:

(9)

Equation (9) can be used to obtain the unknown fracture extent, if we assume

there is no spurt loss (by Shlyapobersky et al. 1988).

Table 2. shows the estimated fracture extent for the three basic models. Note

that the no-spurt loss assumption results in the estimate of the fracture length

also for the PKN geometry, but this value is not used for obtaining the leakoff

coefficient. For the other two models, the fracture extent is obtained first, and

then the value is used in interpreting the slope.

Once the fracture extent and the leakoff coefficient are known, the lost width

at the end of pumping can be easily obtained from

(10)

and the fracture width for the two rectangular models from

(11)

and for the radial model:

Often the fluid efficiency is also determined

Please note that neither the fracture extent nor the efficiency are model

parameters. Rather, they are state variables and hence, will have different values in

the minifrac and the main treatment. The only parameter that is transferable is the

leakoff coefficient itself, but some caution is needed in its interpretation. The bulk

leakoff coefficient determined from the method above is apparent with respect to

the fracture area. If we have information on the permeable height hp, and it

indicates that only part of the fracture area falls into the permeable layer, the

apparent leakoff coefficient should be converted into a "true value" with respect to

the permeable area only. This is done simply by dividing the apparent value by rp

(ratio of permeable area to total fracture area)

(12)

(13)

While adequate for many low permeability treatments, the outlined procedure

might be misleading for higher permeability reservoirs. The conventional mini-

frac interpretation determines a single effective fluid-loss coefficient, which

usually slightly overestimates the fluid loss when extrapolated to the full job

volume

Figure 7. Fluid Leakoff Extrapolated to Full Job Volume, Low

Permeability (after Dusterhoft et al.,1995)

This overestimation typically provides an extra factor of safety in low-permeability

formations to prevent screenout. However, when this same technique is applied in

high-permeability or high-differential pressure between the fracture and the

formation, it significantly overestimates the fluid loss for wall-building fluids if

extrapolated to the full job volume (Dusterhoft et al., 1995). Figure 8. illustrates the

overestimation of fluid loss which might be detrimental in high-permeability

formations where the objective often is to achieve a tip screenout.

Figure 8.Overestimation of Fluid Leakoff Extrapolated to Full Job

Volume, High Permeability (after Dusterhoft et al., 1995)

Filter-cake plus reservoir pressure drop leakoff model (according to

Mayerhofer et al., 1993) describes the leakoff rate using two parameters

that are physically more discernible than the leakoff coefficient to the

petroleum engineer:

- R0 the reference resistance of the filter cake at a reference time t0 and

- kr the reservoir permeability.

To obtain these parameters from an injection test,;

- the reservoir pressure,

- reservoir fluid viscosity,

- formation porosity and

- total compressibility must be known

Figure 5-8. is a schematic of the Mayerhofer et al. model in which the total

pressure difference between the inside of a created fracture and a far

point in the reservoir is shown with its components. Thus, the total

pressure drop is

∆p(t) = ∆pface (t) + ∆pr (t) (14)

∆pface - pressure drop across the fracture face dominated by the filter

cake,

∆pr - the pressure drop in the reservoir

Figure 9. .Filter-cake plus reservoir pressure drop in the Mayerhofer et al.(1993)

model.

Using the Kelvin-Voigt viscoelastic model for description of the flow through

a continuously depositing fracture filter cake, Mayerhofer et al. (1993) gave

the filter-cake pressure term as

where R0 is the characteristic resistance of the filter cake, which is reached

during reference time t0. The flow rate qL is the leakoff rate from one wing of

the fracture. In Eq. 21-14, it is divided by 2, because only one-half of it flows

through area A.

The pressure drop in the reservoir can be tracked readily by employing a

pressure transient model for injection into a porous medium from an infinite-

con-ductivity fracture. For this purpose, known solutions such as the one by

Gringarten et al. (1974) can be used. The only additional problem is that the

surface area increases during fracture propagation. Therefore, every time

instant has a different fracture

length, which, in turn, affects the computation of dimensionless time. The

transient pressure drop in the reservoir is

(14)

(15)

The Mayerhofer et al.method is based on the fact that it equation

can be written in straight-line form as

(16)

(17)

The coefficients c1 and c2 are geometry dependent. Once the x and y

coordinates are known, the (x,y) pairs can be plotted. The corresponding

plot is referred to as the Mayerhofer plot.

A straight line determined from the Mayerhofer plot results in the estimate

of the two parameters bM and mM. Those parameters are then interpreted in

terms of the reservoir permeability and the reference filter-cake resistance.

(18)

(19)

Table 4. reservoir and well information

Example interpretation of fracture injection test

Table 3. pressure decline data

The closure pressure pc determined independently is 5850 psi.

Figure 10. is a plot of the data in Cartesian coordinates and also shows

the closure pressure.

Figure 10. Example of bottomhole pressure versus shut-in time.

Figure 11. Example Mayerhofer plot with radial

geometry.

The g-function plot in Fig. 11 is created using α= 8 ⁄9, which is considered

characteristic for the radial model.

From the intercept of the straight line is obtained the radial fracture radius Rf

= 27.5 ft. (The straight-line fit also provides the bulk leakoff coefficient CL=

0.033 ft/min1/2 and fluid efficiency η= 17.9%.)

The ratio of permeable to total area is rp= 0.76.

Figure 12 is the Mayerhofer plot. From the slope of the straight line (mM=

9.30 ×107) is obtained the apparent reservoir permeability kr,app= 8.2 md and

the true reservoir permeability kr = 14.2 md.

The resistance of the filter cake at the end of pumping (te = 21.2 min) is

calculated from the intercept (bM= 2.5 ×10–2) as the apparent resistance

R0,app= 1.8 ×104 psi/(ft/min) and the true resistance R0= 1.4 ×104 psi/(ft/min)

Figure 12. Example g-function plot

Literature

1. SPE 144028 Global Model for Fracture Falloff Analysis M. Marongiu-Porcu, C. A. Ehlig-

Economides / Texas A&M University, and M. J. Economides / University of Houston

2. Petroleum Well Construction – Halliburton. Editors: Michael J. Economides, Texas

A&M University, Larry T. Watters, Halliburton Energy Services, Shari Dunn-Norman,

University of Missouri-Rolla, Duncan, Oklahoma July 2, 1997

3. SPE 152019 A Method to Perform Multiple Diagnostic Fracture Injection Tests

Simultaneously in a Single Wellbore A.R. Martin, SPE, D.D. Cramer, SPE, O. Nunez, SPE,

and N.R. Roberts, SPE, ConocoPhillips

4. Mini Frac Spread Sheet Dr Peter P. Valkó, visiting associate professor. Harold Vance

Department Petroleum Engineering, Texas A&M University. April 2000

5. Reservoir Stimulation Third Edition Michael J. Economides Kenneth G. Nolte June, 2000

6. . “Determination of Fracture Parameters from Fracturing Pressure Decline", Nolte, K. G.,

Paper SPE 8341, Presented at the Annual Technical Conference and Exhibition, Las Vegas,

NV, Sept. 23-26, 1979