SPE 142389

Does Rock Really Weaken During Acid Fracturing Operations? E.O. Joel and M. Pournik, University of Oklahoma

Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Production and Operations Symposium held in Oklahoma City, Oklahoma, USA, 27–29 March 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessar ily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Acid fracturing is a stimulation process in which the dissolution of the fracture faces creates conductivity after fracture closure. The

resulting fracture conductivity depends highly on the amount and pattern of etching in addition to the strength of asperities. While there has

been significant amount of studies on enhancing fluid systems to generate more optimum etching pattern, etched width, and etched length,

there has been minimal work on understanding how the acid systems influence rock strength and affect closure of fracture under stress.

A systematic review of all available data on rock strength used in acid fracture modeling was conducted with emphasis on

determining errors involved in each measurement. Furthermore, a detailed review of documented effect of acid on rock strength was also

undertaken to understand how acid changes fracture face strength. Finally, the impact of errors in rock strength values used in conductivity

correlations was studied in order to determine the importance of using correct values for rock strength.

Based on analysis of measured rock strength measurements, an average of 20% has been observed in data with greater errors for

dolomite formations. Furthermore, there are great variations among rock strength values among different studies, with variations up to six

times. In terms of effect of acid on rock strength, the measured weakening of rock of an average of 15% is within the measurement error

limits and hence no conclusion can be made on acid weakening rock strength. Effect of errors in rock strength values used in conductivity

correlations suggests significant errors in conductivity estimation, especially for softer rocks and higher closure stresses.

There have been many developments in enhancing the performance of acid fractured wells. However one major reason for the

lack of success is limited understanding of the effect of acid on rock strength and incorrect estimation of rock strength. In order to

understand the effect of acid fracturing on rock strength and resulting fracture conductivity under closure stress, a better method of

measuring rock strength is needed in addition to detailed study on the effect of treatment parameters including acid type and contact time

on rock strength variation.

Introduction Acid fracturing is a common well stimulation practice used to enhance the performance of carbonate reservoirs. The process involves

pumping an acid fluid at high rate and pressure to create and/or extend a fracture in the formation. The acid injected into the facture reacts

with the formation to create uneven fracture surfaces which is the basis for the fracture conductivity. The importance of rock strength in

maintaining sufficient fracture conductivity has been emphasized in previous studies (Greenwood & Williamson 1966; Walsh 1981; Gong

1997; Abass et al. 2006; Jaeger et al. 2007). After the acid treatment, closure stress is attempting to close the fracture, while the strength of

fracture face asperities is holding the fracture open. Contact ratio, asperity distribution, and mechanical properties of the asperities are three

important parameters that control the change in fracture width with closure stress. Abass et al. (2006) expressed that the asperities act as

support for the conduits created from the etching process. They also highlighted how mechanical properties and processes (compressive

strength, creep, and elastic response) determine the closure of the conduit created. The strength of the rock and the asperities created by the

acid fracturing process determine the stress-strain behavior under closure stress. Under closure stress conditions, the elastic response and

compressive strength of the rock work to keep the effective aparture open and retain fracture conductivity. The different strength properties

detailed by Gangi (1978), Walsh (1981), Gong (1997), and Abass et al. (2006) in their various models attempt to describe how the strength

of the rock in addition to distribution of asperities interact in keeping the fracture open under closure stress.

Acid fracture conductivity has been modeled using different approaches. There have been theoretical models and experimental

correlations used to model the behavior of acid fracture under closure stress. The models attempt to directly or indirectly determine some

parameters that can be used to express the behavior of fracture conductivity under closure stress. Although not all approaches were

designed with acid fracture conductivity in mind, it is apparent that rock strength is a very important factor.

Experimentally, Neirode and Kruk (1973) created a correlation that estimates the fracture conductivity solely as a function of the

volume of rock removed during the etching process and the rock embedment strength. The correlation is based on exponential relationship

between fracture conductivity and rock strength as follows:

, ………………………………………………………………………………………………........................................ (1)

where kfw is the fracture conductivity, A is a variable dependent on the amount of rock removed, B is solely function of the formation rock

embedment strength, and σ is the closure stress.

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Gangi (1978) developed a theoretical model of fracture conductivity where fracture conductivity is a function of asperity

distribution assuming that the asperities are a bed of nails with the same radius at different heights. In his model, a power equation is used

to relate the fracture conductivity and the asperity effective bulk moduli as shown:

- ⁄ , …………………………………………………………………………………………………………...………….. (2)

where k is the fracture permeability, ki is the initial fracture permeability, m is the asperity distribution factor, and M is the asperity moduli

estimated to be in the order of one-tenth to one–hundredth of the intact rock moduli.

A detailed theoretical model of fracture conductivity was also developed by Walsh (1981), which expresses fracture conductivity

as a function of the aparture, closure stress, elastic modulus and the fracture configuration in the form of:

, ………………………………………………………………………………………………………...…………. (3)

where A is a variable dependent on the initial fracture conductivity, B is dependent on the elastic moduli, original aparture distribution and

fracture conductivity, and pe is the effective pressure.

Gong (1997) introduced a model with experimental support. This equation related the fracture conductivity to the yield stress as a

power equation as follows:

- ⁄

, ………………………………………………………………………................................................................. (4)

where A is a function of the initial fracture conductivity, B is a variable dependent on the initial fracture conductivity and asperity

distribution of the fracture, σy is the rock yield stress, and C is a function of the asperity distribution only.

Jaeger et al. (2007) discussed a couple of theoretical models that express the transmissivity of a fracture, and they concluded that

stiffness and asperity conditions controlled conductivity of a fracture. All these models have their benefits and short comings, however one

clear outcome from all the models is that rock strength significantly influences fracture conductivity under closure stress and proper

characterization of rock strength is required for accurate prediction of conductivity.

The different models and correlations introduced utilize different mechanical properties to characterize how rock strength

influences behavior of fracture conductivity under closure stress. Each mechanical property expresses a specific mechanical signature.

Properties that have been used in the models are elastic modulus, ultimate compressive strength, yield stress, poisson ratio, surface

hardness values, embedment strength, and shear modulus. Tests used to measure these properties range from destructive to non-destructive

tests. The most commonly used property is the rock embedment strength (RES) as described by Neirode and Kruk (1973). It is the force

required to push a steel ball bearing into a rock surface to a distance equal to the radius of the ball, divided by the projected area of the

bearing. This non destructive test measures the resistance of the rock to plastic deformation. Depending on the correlation, it could also be

used to determine the elastic moduli and the yield strength of the formation because they characterize properties in the elastic zone of

deformation. The problems associated with this measurement are found to be the error encountered due to the presence of uneven sample

surfaces, heterogeneity in rock properties, and variation in pore distribution. Another issue has been that different measurement methods

have been described for measuring the rock embedment strength, such as the Howard and Fast (1970) method which uses indentation equal

to half of the radius of the ball. As a result of this difference, measured values of RES measured by Neirode & Kruk (1973) method are up

to four times smaller than those measured by Howard & Fast (1970) method.

Other similar nondestructive tests that can provide similar information are Schmidt hammer test, Rockwell test, and Brinell test.

The Brinell hardness test method consists of indenting the test material with a 10 mm diameter hardened steel or carbide ball subjected to a

load. The full load is normally applied for 10 to 15 seconds in the case of iron and steel and for at least 30 seconds in the case of other

metals. The diameter of the indentation left in the test material is measured with a low powered microscope. The Brinell harness number is

calculated by dividing the load applied by the surface area of the indentation. While Brinell and Rockwell tests are very similar, Rockwell

test is better suited for softer formations.

The fracture conductivity model by Walsh (1981), Gong (1997), and Abass et al. (2006) require the yield strength, elastic moduli,

ultimate compressive strength, and shear moduli. These values can be derived from a simple compression and shear test. These are

destructive test that measure the maximum strength the rock can carry before it starts experiencing irreversible changes, the ultimate load

the formation can handle, the force required to cause a unit deformation in the rock, and the rock strength properties mentioned earlier.

These devices use LVDT’s, hydraulic load frames, and strain gauges primarily to determine these values. Some of these results could be

determined by sonic measurements.

Anderson et al. (1989), Gong (1997), Pournik (2008), and Nasr-El-Din et al. (2006) have run experiments to observe the effect of

the acidizing process on the rock strength. The most general conclusion is a weakening of the rock. The effect has been discussed to vary

depending on the formation involved, the contact time, and the type of the acid mixture used. There are a lot of errors in measurements and

treatment procedures that can obscure the results of the effects on rock strength. These errors will vary based on the testing procedure and

the machine used to measure the mechanical property. Proper characterization of the rock strength is equivalent to a better characterization

of the fracture conductivity. Experimental study on the effect of the various treatment conditions (contact time, temperature, type of acid,

injection rate, and formation) will advance the proper characterization of the effect of acid treatment on the rock strength. The errors

involved in the measurement of the these mechanical properties have to be properly evaluated to determine how relevant the results derived

from the acidizing process are in characterizing the fracture conductivity.

Results and Discussion Rock Strength Variation. While there are several different rock strength properties used in acid fracture conductivity models and

correlations, rock embedment strength (RES) is the only one that has been measured widely by several different investigators. Table 1 and

Fig. 1 summarize average value of rock embedment strength in addition to errors associated with each average value that have been

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gathered by several studies on three different common formation types. The error was calculated as standard error of the mean, estimated as

standard deviation of samples divided by the square root of the sample size. Results from different studies clearly show significant

variation and error in rock embedment strength measurements for a given formation within one study, among different studies, and also

between the two measurement techniques. Within each study, there are large variations in measured RES values with error in average RES

value ranging from 4% to 49% with an average error of about 20%. The type of formation tested also influences the amount of error in

RES. Most of the studies show more significant error in RES value of dolomite sample compared to limestone, which might be due to

higher RES values of dolomite. In addition, there is also large variation in RES values for the same formation depending on the

measurement method. RES values measured by Neirode & Kruk (1973) method range from 19,500 to 64,200 psi, while the measurements

from Howard & Fast (1970) method range from 34,500 to 205,800 psi for Indiana limestone, which shows variation of almost three times

in average RES between these two methods. Furthermore, the differences in RES values become even more significant among different

studies with average RES values ranging from two to six times each other. The error in average RES values among different studies for the

same formation measured using the same method range from 30% to 70% with an average error of 50%. While the difference in RES

values for the same formation might be due to compositional, crystalline structure, and heterogeneity differences, the error is significant

and cannot be ignored and must be considered when utilized in for estimating fracture conductivity. There is a reduced variation in RES

values reported by Pournik (2008) as the average value was based on 28 readings across the fracture, while the other studies did not make

such extensive measurements. This suggests that measurement errors can be reduced if significantly large numbers of data points are taken.

TABLE 1-AVERAGE AND STANDARD ERROR OF ROCK EMBEDMENT STRENGTH MEASUREMENTS ON

UNACIDIZED FORMATIONS FROM DIFFERENT STUDIES.

Method Study Austin Chalk Indiana Limestone San Andres Dolomite

Average RES (psi)

Error (psi)

Error (%)

Average RES (psi)

Error (psi)

Error (%)

Average RES (psi)

Error (psi)

Error (%)

Neirode & Kruk

Neirode & Kruk (1973) 9,967 2,266 23 19,500 2,623 13 57,233 83,812 15

Beg et al. (1996) - - - 64,200 - - - - -

Gong (1997) 64,231 28,878 45 - - -

Howard & Fast

Gong (1997) - - - 205,792 1,510 10 - - -

Howard & Fast (1970) - - - - - - 202,310 99,510 49

Pournik (2008) 22,803 1,035 4.5 34,509 1,414 4 58,036 3,368 5.8

Nasr-El-Din et al.

(2006) - - - 68,038 8,453 12 228,725 78,212 34

Fig. 1- Comparison of rock embedment strength values and measurement errors for unacidized formations among different studies

using two different measurement methods.

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

Indiana Limestone(Neirode&Kruk)

Indiana Limestone(Howard&Fast)

San Andres Dolomite(Neirode&Kruk)

San Andres Dolomite(Howard&Fast)

RE

S (

psi)

Neirode & Kruk (1973) Beg et al. (1996)Gong (1997) Pournik (2008)Gong (1997) Howard&Fast (1970)

SPE 142389

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Effect of Acid on Rock Strength. The effect of acid on rock strength has been discussed and experimentally tested with the general

consensus that acid reduces the rock strength. Average percentage of change in rock embedment strength due to acid etching from different

studies are shown in Fig. 2 with positive changes representing a decrease in RES with acidizing. While some of the studies have

investigated the effect of different treatment parameters like acid type, contact time, temperature, and rock saturation condition on rock

weakening with acid etching, average values of changes in RES with acidizing are shown in the Fig. 2 without differentiating among

experimental conditions. Also, while Nasr-El-Din et al. (2008) do not mention the formation type and only describes rocks as limestone or

dolomite, their results are included in the specific type of each rock type mentioned in Fig. 2. The results show a decrease in RES ranging

from 8 to 30% with an average decrease of about 15% for Indiana limestone, while the change in RES ranges from 5 to 55% with an

average RES decrease of 30% for San Andres dolomite. As the changes in RES values due to acid etching are within the measurement error

limits of actual RES values for unacidized samples (about 18% for Indiana limestone and about 25% for San Andres dolomite), no

conclusive remark can be made about the effect of acid etching on rock strength. Even though all the results show an average decrease in

rock strength with acid etching, several studies have observed increase in rock strength after acid etching, which are within the

measurement errors (Pournik 2008; Gong 1997). In terms of Brinell hardness, Gong (1997) measured an average of 11% decrease;

however the change ranged from 8% increase to 33% decrease. The studies that have focused on the effect of treatment conditions on rock

weakening have observed that acid type and contact time affect the rock weakening measured, however the measured changes are within

the measurement error limits (Nasr-El-Din et al. 2008; Pournik 2008).

Fig. 2- Comparison of changes in rock embedment strength due to acid etching among different studies.

Sensitivity of Fracture Conductivity on Rock Strength. The effect of errors in measurement of the rock strength and short comings of

the rock strength measurement process can affect the estimated fracture conductivity. This can be evaluated by estimating the change in the

fracture conductivity due only to the change in rock strength parameter. To achieve this, both Nierode and Kruk (1973) and Gong (1997)

model that characterize fracture conductivity based on a rock strength parameter are evaluated in terms of the effect of errors in rock

strength parameter measurement on fracture conductivity at different closure stresses as shown in Fig. 3 and Fig. 4, respectively. A typical

error of 20% in value of RES and yield stress, which was observed in Table 1, is used in calculating the errors in conductivity based on the

two models. In order to determine the influence of the type of formation on errors in estimating conductivity, three different cases are

presented as follows:

Case1: low rock strength

Case 2: medium rock strength

Case 3: high rock strength

The results clearly show that both formation type (expressed in terms of initial rock strength) and closure stress significantly

influence the amount of errors in estimating conductivity from above two models for a given error in initial rock strength value. The error

in conductivity estimation ranges from 5% up to greater than 180%, depending on formation strength, closure stress and model used in

estimating conductivity. There is about two to five times increase in errors with conductivity estimation as formation’s initial rock strength

becomes smaller. In addition, as closure stress increases, the errors in conductivity estimation also increase with significant errors at larger

closure stresses, while errors at very low closure stresses (below 1,000 psi) are relatively small for stronger formations. Furthermore, there

is much greater effect of errors in rock strength values on conductivity estimation for Gong (1997) model. These results clearly confirm the

importance of proper characterization of rock strength with minimal measurement error in order to have accurate estimation of

conductivity. It is important to note that these errors in conductivity estimation are based on initial rock strength values and has not taken

into consideration the effect of acid on rock strength, which would magnify the errors.

0

10

20

30

40

50

60

Indiana Limestone San Andres Dolomite

Perc

enta

ge c

hange in R

ES

Pournik (2008) Gong (1997) Nasr-El-Din et al. (2006)

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Fig. 3- Effect of rock embedment strength on conductivity at different closure stresses for Neirode and Kruk model.

Fig. 4- Effect of rock yield strength on conductivity at different closure stresses for Gong model.

Conclusions Based on analysis of published rock strength measurements used in different acid fracture conductivity models, it has been shown that:

1. There are significant errors in measurement of rock embedment strength with an average error of 20% based on each specific

study, which also varies depending on formation type and measurement methodology.

2. There is even greater error in average values of rock embedment strength (average error of 50%) with consideration of values

from different studies, even though the same measurement method was used.

3. While most studies have shown reduction in rock strength with acid etching, the values reported for rock embedment strength are

within the measurement error limits and hence there is no conclusive finding on the effect of acid on rock weakening.

4. Furthermore, analysis on the effect of a typical 20% error in rock strength measurement on conductivity estimation has shown

conductivity errors can range from 5% to over 180%, with the error depending on formation type, closure stress, and conductivity

model.

Based on the analysis, there is a need for a better method to characterize rock strength to be used in acid fracture conductivity models, in

addition to providing conclusive findings on the effect of acid etching on rock strength.

0

10

20

30

40

50

60

1000 2000 3000 4000 5000

Perc

enta

ge C

hange in C

onductivity

Closure stress (psi)

Low RES Medium RES High RES

0

20

40

60

80

100

120

140

160

180

200

1000 2000 3000 4000 5000

Perc

enta

ge C

hange

in C

onductivity

Closure Stress (psi)

Low Yield Stress Medium Yield Stress High Yield Stress

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Nomenclature RES = Rock Embedment Strength, m/Lt2, Pa [psi]

σy = Yield Stress, m/Lt2, Pa [psi]

kfw = Fracture Conductivity, L3, [md-ft]

M = Elastic Moduli of Asperities, m/Lt2, Pa [psi]

σ = Closure Stress, m/Lt2, Pa [psi]

k = Fracture Permeability, L2, m2 [md]

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SPE 142389