SummaryAcid fracturing and matrix acidizing are used as well-stimulationprocesses for carbonated reservoirs. In matrix acidizing, a deeppenetration of wormholes around the well is required; in the acid-fracturing process, fluid leak-off must be limited and wormholesare prohibited. Laboratory tests are necessary to improve thedesign of these operations.

Specific laboratory equipment was designed to reproducedownhole flow conditions. Matrix acidizing is a constant flow rateprocess, whereas acid in fracture is forced from the fracture wall tothe formation, a process occurring at a constant pressure drop. Thisprocess was represented in the laboratory and a new tangential cell,aiming at working with straight acids in reservoir temperature andpressure conditions, was specially designed to handle this applica-tion. The first part of the paper presents a methodology for theevaluation of acid/rock properties. Results of acid injections atconstant flow rates are compared to results obtained from injec-tions at constant pressure drop. Experiments have been conductedwith limestone core samples of different petrophysical properties.Performance of different acid formulations including straightacids, emulsions, and gels was evaluated.

Results are discussed in terms of acid propagation rates and dis-solution patterns. They are analyzed using x-ray computed tomog-raphy. They are classified into wormholes, i.e., branched patternsof large extension, and compact ones. Finally, recommendationsare made concerning operating conditions favorable for matrixacidizing. On the opposite, conditions are given to limit dissolutionand to restrict fluid loss for the acid fracturing application.

IntroductionHCl is injected into carbonate formation routinely to improve oilproduction. The porous medium is not etched uniformly; unstabledissolution channels are formed. Control of the formation of thesechannels, commonly called wormholes, is the key to the success ofthe treatments. In matrix acidizing, deep, highly ramified worm-holes are required whereas in acid fracturing, compact patterns atthe fracture walls are preferred. This paper has several aims. Theprimary objective is to set up an experimental methodology forcomparing different acid fluids for two acidizing applications. Forthe matrix acidizing process, we provide a methodology and aframe of reference for the interpretation of wormhole propagationrates. This framework provides possible guidelines for evaluationof new products. For acid fracturing, new equipment is designed toreproduce representative downhole conditions. They are used forevaluation of basic properties of gelled acids: fluid leak-off andwormhole propagation rate.

Dissolution patterns in limestone are classified as compact,wormholes, or uniform, depending on the relative influence offlow rate with respect to the overall reaction rate. For highly reac-tive fluids like HCl in limestone, the effect of flow rate on the dis-solution pattern is dominant. Experiments supported by analysis ofdissolution mechanisms at the pore level give the following corre-spondence between flow regimes and dissolution patterns.1

• At low flow rate, the convection-limited regime leads tocompact pattern.

• At intermediate flow rate, mass-transport-limited kinetics pro-duces wormhole patterns.

• At high flow rate, the surface-reaction-limited regime yields auniform dissolution pattern.

Most laboratory studies dealing with matrix acidizing show thatthe efficiency of treatments goes through a maximum. This obser-vation leads to the concept of “optimum injection rate:”2 it is theacid injection rate corresponding to the minimum volume of acidrequired for wormhole breakthrough. Microscopic descriptions arenot sufficient to describe overall propagation of wormholes inporous medium and “optimum flow rate.” Because the geometry ofthe system changes with time, transitions from the wormhole tocompact or the uniform regime are likely to occur. As a result,wormhole propagation may stop. Two mechanisms at the origin ofwormhole growth termination have been proposed:3,4 (1) high con-sumption at wormhole walls, which limits acid concentration at thewormhole tip for extension and (2) filtration losses through thewormhole. In the first case, extinction is linked to a transition frommass-transport-limited kinetics to the convection-limited regimeoccurring at the wormhole tip; in the second case, it is the transitionfrom mass-transport-limited kinetics to the surface-reaction-limitedregime. These transitions are difficult to predict theoretically.Validation of the modeling is difficult because most experimentalstudies address a limited range and number of parameters. On theother hand, new products5-7 are proposed and there is a lack of dataproviding a frame of reference for comparing their properties tocommonly used acids. In this paper, we present results relating opti-mum injection rate to acid concentration, temperature, core length,and permeability. The methodology and the results obtained withstraight acids then are used for evaluation of an acid in emulsion.

In acid fracturing applications, the rate of fluid leak-off throughthe formation is one of the most critical factors affecting fracturegeometry and conductivity. It is believed that acid leak-off is themajor factor limiting fracture length and etching. Gelled acids areused commonly in acid fracturing operations to reduce fluid leak-off. However, they do not perform correctly and there is a lack ofexperimental data regarding the effectiveness of these products.Experiments performed in a Hassler cell at constant flow rate arenot representative of fluid flow in the fracture geometry. Otherequipment has been designed for leak-off studies.8-10 Their maindrawback is the small core length allowed to acid filtration. Veryrecently, a tangential cell previously developed to test fluid-loss-control additives in conventional hydraulic fracturing11 has beenused for evaluation of wormhole-breakthrough times of gelledacids.12 However, leak-off rates are not measured. In this paper, wepresent specific equipment designed to reproduce downhole flowconditions for evaluation of leak-off. This experimental device isused to give an overall evaluation of acid fracturing fluids inporous medium in terms of wormhole propagation rate, wormholedistance, and leak-off rates. Moreover, we use x-ray tomography tovisualize dissolution patterns and to give information on conditionsleading to compact dissolution figures at the fracture wall.

The primary objective of the paper is to give a laboratorymethodology representative of fluid flow conditions for the matrixand the acid-fracturing processes. In the first part, we focus on thematrix acidizing process. We discuss acid propagation rates, worm-hole patterns, and optimal injection rates depending on acid con-centration, acid injection rate, and temperature. In the second part,

22 February 2001 SPE Production & Facilities

Copyright © 2001 Society of Petroleum Engineers

This paper (SPE 66566) was revised for publication from paper SPE 49491 presented atthe 8th Abu Dhabi Intl. Petroleum Exhibition and Conference, Abu Dhabi, U.A.E., 11–14October 1998. Original manuscript received for review 22 June 1999. Revised manuscriptreceived 23 March 2000. Paper peer approved 22 June 2000.

From Matrix Acidizing to Acid Fracturing: A Laboratory Evaluation

of Acid/Rock InteractionsB. Bazin, SPE, Inst. Français du Pétrole

we present the experimental device used for the evaluation of acidfracturing fluids. Fluid properties are discussed in terms of leak-off rates and dissolution figures at the core face. Finally, we giverecommendations for using acid in well treatments.

Matrix AcidizingOptimum flow rate is the dominant concept in matrix acidizing.After a rapid background on the optimum injection rate, the exper-iments give results on the variation of the optimum flow rate withcore length, concentration, and temperature. Analysis of the resultsfocuses on an understanding of the optimum flow rate. Based onthis study, recommendations are made in terms of laboratorymethodology to improve evaluation of new products. We point outproperties of an acid-diesel emulsion.

Experimental Procedure and Data Analysis. Linear corefloodexperiments are performed using a Hassler cell. Limestone cores 5cm in diameter and 5, 10, 20, or 40 cm in length are studied. Twolimestones are used: Lavoux limestone has a permeability of 5 md,and Estaillades limestone has a permeability of approximately 200md (Table 1). Acid fluid is injected axially through the core at aconstant flow rate. A pressure transducer monitors the pressure dropalong the length of the core. Pressure data are recorded every sec-ond in a computer file. A valve arrangement starts and ends theexperiment automatically. The CO2 reaction product is kept in solu-tion by maintaining a minimum pressure with a pressure regulator.As an example, pressure as high as 180 bar is required when using15% HCl at 50°C. The experiment is terminated when acid breaksthrough the core, as evidenced by a negligible pressure drop.

Wormhole propagation rate is calculated from the volume ofacid injected expressed in pore volume. Dissolution patterns areobtained by subtracting the initial x-ray image from the final one.Experiments are performed at temperatures of 20, 50, and 80°C.HCl concentrations vary from 0.7 to 17-wt %.

Background on the Optimum Injection Rate. Previous studieshave shown the determinant effect of acid injection rate on thewormhole propagation rate. The wormhole propagation rate isreported as a function of the injection rate in Fig. 1. Curves of thistype have been reported in a large number of studies. We havedivided Fig. 1 schematically in three domains, depending on theacid injection rate:

• Region I: acid injection rate is low. The wormhole may formbut does not break through the core.

• Region II: acid volume required to break through the coredecreases as injection rate increases.

• Region III: acid volume injected increases with injection rate.Wang2 defined the optimum injection rate as the acid injection

rate at the transition between regions II and III. At the optimum,flow rate corresponds to the minimum volume of acid required forwormhole breakthrough.

A previous study by x-ray tomography13 gives some insight intothe mechanisms of wormhole propagation and wormhole geometryin Regions II and III. Wormhole formation and propagation werevisualized as acid injection proceeds. In an experiment at a lowinjection rate (Region II), a rapid growth of the wormhole tip at thebeginning of acid injection was shown. Then, as acid injection con-tinues, the wormhole extension in length occurs step by step withstops and starts. At the same time, sever-branching occurs at thewormhole tip with an increase of wormhole diameter. It is sup-posed that the wormhole growth process shifts from mass-transfer-limited regime to convection or surface-reaction-limited growth.The same experiment was made with an injection rate higher thanthe optimum injection rate (Region III). In that case, a dominantchannel quickly forms and continues to propagate at a high rate.

Very fine ramifications around the main wormhole are formed; it issupposed that wormhole growth occurs in the surface or fluid-loss-limited regime. From these experiments it may be concluded thatthe optimum flow rate is the minimum injection rate required todevelop the wormhole continuously, i.e., with maximum efficien-cy, in the mass-transfer-limited regime. At this optimum flow ratecorresponds a minimum volume of acid injected.

Optimum Flow Rate, Pore Volume to Breakthrough, andWormhole Propagation Length. Our purpose is to give more under-standing on the optimum flow rate by studying the effect of corelength on the optimum flow rate. We performed experiments withcores from 5 to 40 cm in length. Fig. 2 shows the value of the opti-mum flow rate increases with the core length in Lavoux limestone at20°C and HCl 7%. This means that propagation of a wormhole alonga 20-cm core length with minimum acid loss requires a higher acidinjection rate and a higher volume of acid in terms of pore volume.When flow rate exceeds the optimum flow rate for the core of 20 cmin length, the volume of acid for breakthrough, in normalized porevolume, is no longer dependent on core length. Note that this is validonly in Region III, i.e., when the wormhole develops in the mass-transport-limited regime. This result gives an order of magnitude onthe acid volume required for wormhole extension. If wormhole prop-agation rates are compared at the optimum flow rate, results in Fig. 2show that a four-fold increase of wormhole length requires a seven-fold higher volume of acid and a higher injection rate.

February 2001 SPE Production & Facilities 23

Fig. 1—Effect of the injection rate on wormhole propagation.

Fig. 2—Effect of core length: HCl 7%, 20°C.

A similar approach is used to study optimum injection rates forcores of 5 to 40 cm in length. Fig. 3 depicts optimum flow ratereported from log-log coordinates from experiments in Lavouxlimestone with HCl 7%. Slopes of the lines are 1.75�0.15. Thisexponent is in very good agreement with the fractal exponentfound experimentally of 1.66�0.1 for plaster.14

Scaling to the Reservoir. Previous results show clearly that opti-mum flow rate is associated with a wormhole maximum propaga-tion distance. It follows that extrapolation of data to the reservoirscale where “core length” is infinite cannot be obtained directlyfrom laboratory experiments. In particular, scaling of the optimumflow rate by a factor aiming at maintaining the same interstitialinjection rate in the laboratory and in the field has no meaning; thiswould result in a wormhole length comparable to the core lengthused in the experiments. A recent review shows that, despite mucheffort, models currently introduce too many simplifications to pre-dict injection flow rates and volumes for a well treatment.15 Theseoversimplifications fail to take into account relevant physicalmechanisms of wormhole formation and propagation and, there-fore, models are not reliable enough for extrapolating laboratorydata to the reservoir.

However, experiments confirm qualitatively that high flowrates are required to increase wormhole penetration.16 Therefore,maximum flow rate provides maximum penetration. Note that thiscannot be achieved without an increase of the volume of acidinjected and considerable fluid loss along the wormhole walls.

Effect of Acid Concentration, Temperature, and Permeability.Fig. 4 shows the effect of acid concentration for core samples 20cm in length. Points at low-injection rates are superposed. A highextension of Region II is observed as the concentration increases.In Region III the pore volume of acid injected to breakthroughdecreases with an increase in concentration. The slopes, i.e., inRegion III, of the one-third slope in log-log coordinates areobserved. Optimum injection rate increases with the concentration.Efficiency of different acid fluids is compared in Table 2 based onthe acid quantity injected at the optimum flow rate. Results con-

firm previous trends.2 If injection time is crucial to the cost of treat-ment, a high HCl concentration is better. However, in terms ofusing acid, low concentrations are better.

Fig. 5 shows the effect of temperature. There is a strong effectof temperature on the optimum injection rate. An increase in tem-perature shifts the optimum flow rate to higher values. Acid vol-ume required to breakthrough increases, decreasing efficiency forwormhole formation. Higher permeabilities require higher injec-tion rates and higher volumes at the optimum (Fig. 6).

Recommendations for Laboratory Experiments Methodologyand Behavior of Acid in Emulsion Formulation. This studyemphasizes the need of rigorous experimental conditions to com-pare wormhole propagation rates. Core length is an importantparameter. It has been shown that at high acid injection rate, worm-hole propagation rate does not depend on core length; measure-ments may be made with core samples of different lengths.However, when the injection flow rate is low, great care must betaken with results if the core length is varied. Consequently, coresamples of the same length must be used for an acid injection ratebelow the optimum injection rate.

The preceding study with straight acids provides a possibleguide for understanding the properties of other fluids. We havenow a general frame of reference on the behavior of the limestone/HCl system. Coefficients relating to the dependence of the acidvolume and of wormhole penetration distance on flow rate, effectsof temperature and concentration on wormhole propagation rates,

24 February 2001 SPE Production & Facilities

Fig. 3—Maximum penetration distance at optimum rate. Fig. 4—Effect of HCl concentration: Lavoux limestone, 20°C.

Fig. 5—Effect of temperature: HCl 7%, Lavoux limestone.

and wormhole penetration distances are available now. Theseresults would improve evaluation of new products. We present firstresults on the properties of an acid/diesel emulsion. Interpretationof results is done within the preceding framework. Acids in emul-sion are retarded acids, i.e., they limit the limestone dissolution rate.The role of using a diesel emulsion is to act as a barrier between theacid and the rock by decreasing the acid diffusion coefficient,17,18

then limiting the reaction rate between acid and calcite. This givesthe acid the ability to penetrate deeper in the formation. Recentstudies7 show a renewal of interest in these products.

Experimental conditions for a commercial product acid/dieselemulsion are: acid 15% weight, 50°C, Lavoux limestone, and core20 cm in length. Fig. 7 shows a very different behavior ofacid/diesel emulsion compared to straight acid. First, wormholepropagation rate slightly decreases continuously when the acidinjection rate is increased. No optimum injection rate is found. Incontrast to straight acid, acid emulsion is very efficient at low flowrate where wormhole breakthrough is observed in conditionswhere regular acid gives compact dissolution. That means thatacid/diesel emulsion is able to penetrate deeper into the core thanregular acid. In addition, much lower acid volumes are injected forwormhole breakthrough. It is also shown that acidizing is muchless sensitive to injection rate, because the acid volume required tobreakthrough varies only slightly with the injection rate.19 Thismakes acid emulsion a promising product for matrix acidizing, par-ticularly for heavily damaged formations where the injection flowrate is expected to be very low.

Acid FracturingGelled acids are the most common products for acid fracturing.Their advantage is to form a polymer layer and to restrict leak-off, as in conventional hydraulic-fracturing process. We presenthere a new experimental design and a methodology based onmeasurements in a tangential cell for evaluating performancesof acid in conditions representative of the acid-fracturingprocess. This evaluation includes measurement of the acid-propagation rate, leak-off rate, and an investigation of worm-hole pattern with x-ray tomography. Other studies have mademeasurements of wormhole propagation rates from acid break-through times.12 However, breakthrough time is not sufficient tocharacterize leak-off rate. Because filtration occurs at wormholewalls, it is important to evaluate whether or not gel hinders acidfiltration. For this purpose, our device is able to record thecumulative volume of fluid and to give the mean leak-off recov-ered over the experiment.

Another difficulty arising with measurements in tangentialflow is the choice of experimental conditions, and particularly,the choice of pressure gradient. The paper has shown that worm-hole formation and propagation involve complex mechanismsand occur only in a limited range of injection rates. Based on the

results of the preceding experiments, we present a methodologyfor defining experimental conditions suitable for evaluating acidsin acid-fracturing applications.

Experimental Device. The experimental setup depicted in Fig. 8is designed to reproduce the geometry of flow at the fracture face.Acid fluid is circulating in a slot tangential to the core sample.Core diameter is 5 cm and the length may be varied up to 40 cm.Penetration of fluid into the core occurs through a constant pres-sure drop applied between the inlet and the outlet of the core. Thecenterpiece of the apparatus is the acid leak-off cell, designed tosimulate acid leak-off under dynamic conditions. The cell is simi-lar to a tangential TEMCO™ core holder, still used for measuringleak-off for conventional fracturing fluids,11,20 but was modified toaccept long acid residence times. With the TEMCO™ core holder,dissolution of the core face leads to a gap between the core holderand inlet face of the rock sample. When the gap enlarges, the con-fining pressure ruptures the rubber sleeve and the experimentaborts. To solve this problem, the Inst. Français du Pétrole (IFP)designed a modified tangential cell especially for acidizing exper-iments. Flow in the slot is 50 mL/min. On the effluent side, a back-pressure regulator is set to maintain the CO2 produced by chemicalreaction in the aqueous phase. Two stainless fluid cells receivewater or acid. The acid leak-off apparatus can be operated at tem-peratures from ambient to 120°C (250°F) and at pressures fromatmospheric to 250 bar (3,500 psi). Measurements are made undera confinement of 40 bar.

Fig. 9 shows a sample of data recorded in a computer file includ-ing inlet pressure, flow rate in the slot, differential pressure betweenthe entrance and the exit of the core, and measurement of the cumu-lative filtration volume (leak-off) as function of time. The experi-

February 2001 SPE Production & Facilities 25

Fig. 6—Effect of permeability: HCl 7%, 50°C. Fig. 7—Comparison of acid-in-diesel emulsion and straightacid: 50°C, Lavoux limestone.

Fig. 8—Schematic of tangential setup.

ment is terminated when the pressure variation becomes negligible,blocking an automatic valve at the exit of the tangential cell.

Gelled acids are evaluated at acid concentrations of 7 and 15-wt %. As a comparison, we also evaluated straight acids in thesame conditions.

Data Analysis. The following values are calculated from theexperimental results (see the Nomenclature):

• Mean leak-off velocity: ratio of the fluid volume leakingthrough the core per unit area to the duration of the experiment.

• Wormhole-propagation rate: ratio of core length to the dura-tion of the experiment.

• Apparent viscosity of acid in porous media, in conditions ofthe experiment: ratio of the initial flow rate calculated fromDarcy’s law to the measured leak-off rate. This coefficient is usedto compare filtration properties of gelled fluids. A value of 1 indi-cates a complete loss of viscous properties of acid during filtration.A value near the relative viscosity of the acid solution would indi-cate an entire control of acid flow.

Methodology for the Choice of the Experimental Conditions.Because gelled acids are supposed to restrict acid flux in the coreand wormhole development, gelled acids must be evaluated inconditions where wormholes form with regular acids. Thus, our

methodology consists of defining the most appropriate range ofpressure conditions by constructing a pressure diagram based ondata collected with regular acids. Two constraints restrict therange of pressure values suitable for experiments. First, the initialleak-off rate must be set to a minimum value corresponding to theoptimum flow rate inferred from the preceding study for reachingthe mass-transfer-limited kinetics regime corresponding towormhole formation and wormhole breakthrough. If the initialflow rate is too low, wormhole breakthrough will not occur.Second, a minimum backpressure is required at the core outlet tomaintain CO2 in the aqueous phase. Minimum backpressuredepends on temperature and acid concentration. This limits theavailable pressure range for flow in the core. As an example, at50°C and 15% HCl, a minimum outlet pressure of 160 bar isrequired to maintain the CO2 in the aqueous phase. Because themaximum working pressure of the device is 210 bar, the maxi-mum pressure available for flow is 50 bar. On the other hand,optimum flow rate for HCl 15% at 50°C is 0.8 cm/min, corre-sponding to a differential pressure of 8 bar (Darcy’s law).Therefore, the pressure window for experiments includes pres-sures ranging from 8 to 50 bar, corresponding to initial leak-offrates ranging from 0.8 to 6 cm/min, respectively.

Diagrams presented in Fig. 10 are constructed to define theoperating window depending on rock permeability, temperature,acid concentration, and core length. Points inside the window arethe most appropriate conditions for performing the experiments.

Shape of the Leakoff Curves for Gelled Acids. Leak-off behaviorof gelled acid fluids is different from the filtration behavior of ordi-nary viscous fluids as those used in hydraulic fracturing.19 Forhydraulic-fracturing fluids, the shape of leak-off curves are charac-terized by a rapid increase of volume at the beginning of the exper-iment, referred to as the spurt volume; a second step correspondingto cake buildup; and a constant flow rate filtration of fluid throughthe core. As shown in Fig. 9, leak-off curves with gelled acids can-not be interpreted in terms of spurt and cake buildups. They show alinear increase in leak-off volume vs. time since the early times.Neither a spurt nor a cake buildup can be distinguished.

Results With Low-Permeability Limestone. Experimental con-ditions are: 15% HCl, 50°C, Lavoux limestone, and pressurerange from 8 to 50 bar. Fig. 11 shows the cumulated volume as afunction of time for different pressure gradients. At low-pressuregradient, no breakthrough of acid occurs within the 16 minutes ofthe experiment. However, when the pressure gradient is increasedonly slightly, the wormhole breaks through at very small times.As the pressure gradient increases, efficiency of the gelling agentto protect the core surface decreases. As an example, with a pres-

26 February 2001 SPE Production & Facilities

Fig. 11—Filtration of gelled HCl in low-permeability limestone:15%, 50°C.

Fig. 9—Data recorded during an “acid fracturing” experimentwith an acid gel.

Fig. 10—Pressure diagrams for tangential experiments.

sure gradient of 3 bar/cm, breakthrough occurs within 2 minutes.However, comparison with results shown in Fig. 7 indicates astrong decrease of wormhole propagation rate due to addition ofthe gelling agent. Wormhole propagation rates are divided by afactor of 10 in comparison with straight acids. Even if the gellingagent is not able to block the wormholing process, it slows downthe acid-limestone reaction.15

The added polymer has a low efficiency in terms of leak-offrates (Table 3). With a viscosity of near 85 cp, a drastic reductionof the filtration rate was expected. In fact, the Ca coefficient indi-cates that filtration is reduced by a factor of only 4 to 7 comparedto water filtration. This is poor performance, relative to the highconcentration of polymer used.

Results With High-Permeability Limestone. Experimental con-ditions are: HCl 7 or 15%, 50°C, Estaillades limestone, core length20 cm, and pressure range from 0.4 to 50 bar. According to themethodology used for evaluating gelled acids in the tangentialdevice, low-pressure gradients are applied to the core sample,mainly because permeability is at a high value. Fig. 12 shows thecumulative volume recorded as a function of time. In contrast tothe behavior of gelled acid in Lavoux limestone, all experimentsshow wormhole breakthrough, even at low-pressure gradients.Breakthrough times are short, as for the Lavoux limestone.

The added polymer has a low efficiency for reducing leak-offrate. As shown in Table 3, the Ca coefficient is comprised between5 and 10, meaning that the filtration rate with gelled acid is reducedby a factor of only 5 to 10 compared to water. This is also very lowcompared to the 85 cp of injected product.

Summary on the Behavior of Gelled Acid in Acid FracturingApplications. Figs. 13 through 15 summarize data on a 3D dia-gram where filtration rates and wormhole propagation rates arereported as a function of the pressure gradient applied to the coresample. The diagram is very illustrative of the behavior of gelledacid. It is shown that low filtration rates for gelled acid are associ-

February 2001 SPE Production & Facilities 27

Fig. 12—Filtration of gelled HCl in high-permeability limestone:15%, 50°C.

Fig. 13—3D diagram of gelled acid behavior: 15% HCl, 50°C.Fig. 14—Wormhole-dissolution figures from x-ray computedtomography-3D reconstruction: HCl 15%, 50°C, Lavoux limestone.

ated with low wormhole propagation rates. The behavior of gelledacid in Lavoux or Estaillades limestone is very similar, even ifpressure gradients are much lower for the high-permeabilityEstaillades limestone. However, when considering straight acids,wormhole propagation rates are much higher even if filtration ratesare of the same order of magnitude.

ConclusionsA methodology using injections at constant flow rate or constantpressure drop is developed for evaluating acid fluid properties, i.e.,acid/wormhole propagation velocity, acid leak-off, and dissolutionpattern in conditions representative of acidizing operations.

For matrix acidizing:1. Data are presented on behavior of straight acids providing a

frame of reference for wormhole formation and propagation.2. Optimum injection rate increases with acid concentration, tem-

perature, and limestone permeability.3. Optimum flow rate is related to a maximum penetration distance.4. To increase the wormhole penetration distance, high injection

rates are required. Low acid concentrations are more effectivethan higher ones.

5. Acid-in-diesel emulsion is more effective than straight acid.

For acid fracturing:1. A methodology in representative flow conditions is developed

for evaluating gelled acids.2. Gelled acids are effective in reducing wormhole propagation

rates and leak-off rates.3. Viscosifying acid reduces water filtration by a factor ranging

from 3 to 10.4. Reduction in fluid loss is smaller than might be anticipated

based on the viscosity of the gelled acid.

AcknowledgmentsWe gratefully acknowledge the support of members of ARTEP, anassociation of the French petroleum companies. We thank C. Schlitter,D. Suida, and G. Thibaut, who performed the experimental work.

NomenclatureA � core sectionL � core length, L, mt � breakthrough time, t, seck � permeability, L2

P � pressure difference imposed during a tangential experi-ment, m/Lt2, psi

Ca � leak-off coefficient, L/tV � leak-off volume, L3

vi � interstitial velocity of injected solution in the tangentialdevice with respect to viscosity, permeability, and pressure gradient, L/t

vw � interstitial velocity that would have the water in a tangential injection experiment performed in the samecondition as with gel, L/t

vwh � wormhole or acid propagation velocity; it is the ratio ofthe length of the core to the breakthrough time, L/t

vf � leak-off or filtration velocity, L/t

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28 February 2001 SPE Production & Facilities

Fig. 15—Lavoux limestone, tangential injection: HCl 15%, 50°C.

February 2001 SPE Production & Facilities 29

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SI Metric Conversion Factorscp � 1.0* E ��03 � Pa·s°F � (°F�32)/1.8 � °C

*Conversion factor is exact.

Brigitte Bazin is Senior Research Engineer in charge of well-stimulation studies in the Reservoir Engineering Dept. at the IFPin Rueil-Malmaison, France. e-mail: brigitte.bazin@ifp.fr. Herresearch interests are in well productivity and injectivity. Sheholds a degree in chemical engineering from the Inst. Natl. desSciences Appliquées.

SPEPF