Acid Treatment in Limestone

Stability of an Open Hole Completed in aLimestone Reservoir With and Without

Acid TreatmentsNobuo Morita, Tomoki Doi, and Takanori Kinoshita, Waseda U.

SummaryBecause a borehole in a limestone formation is more stable thanexpected, an openhole completion without a slotted/perforatedliner has become popular recently. However, the following threeitems are not clear: (1) Why a borehole in a limestone formation isso stable, (2) why a borehole in a limestone formation can becompleted without a liner regardless to the formation strength, and(3) the question of stability after acid treatments. To answer thesequestions, two types of laboratory experiments are conducted. Oneof them is a series of borehole stability experiments using 1.5- and2.36- to 2.39-in.-diameter borehole in a 10.5×10.5×17.5-in. lime-stone blocks with polyaxial confining pressures simulating a hori-zontal well with three different principal in-situ stresses. Twotypes of limestones are used with and without borehole acid treat-ments and two borehole sizes are used to check the size effect.Another type of experiment is the acid squeezing experiment, inwhich 15% HCl acid solution is squeezed from one end of acylindrical core and the change of porosity, permeability, andhardness are measured throughout the cores.

The results showed the following new discoveries:1. The limestones have two distinct failure envelopes. The fail-

ure plastic strain is relatively small for normal shear failure, whileit becomes as much as 10 times larger when a shear failure isinduced after pore collapse.

2. One of the limestones used in these experiments has only1,751 psi UCS, yet the borehole was unexpectedly stable. Thereason was that the borehole failure is induced by a shear failureafter pore collapse. It is well known that pore collapse is inducedwithin a formation during compaction; however, a shear failureafter pore collapse has never been observed when one boundary isopen like an open hole.

3. The confining stress inducing borehole failure was not sig-nificantly different between hydrostatic and directional loadings.According to the Kirsch’s solution, the directional load shouldsignificantly increase the stress concentration. It is well known thatthe nonlinearity of rock reduces the stress concentration inducedby directional loading; however, the present experiments showedthat the magnitude of the reduction of stress concentration waslarger than expected.

4. Wormholes stabilize boreholes even though acidizing weak-ens formation. Therefore, enhancing wormholes is recommendedwhen a borehole in a limestone formation is acidized.

Normally, because limestones are relatively strong, open holesare likely stable; however, the strength must be checked if theyneed to be completed without a linear protection. To help a readerapplying the laboratory results to field problems, a guideline tocomplete an open hole without a liner protection in limestonereservoirs is provided, with calculation results using a nonlinearfinite-element model.

IntroductionWhen an openhole completion was selected in a limestone reser-voir, the well used to be completed with a perforated/slotted liner.1

A perforated/slotted liner was economical, and so using it as a wellprotection did not significantly increase the well completion cost.However, a perforated liner became an obstacle later when the wellwas recompleted. Field trials showed that even if a formation wasnot significantly strong, an open hole remained open without col-lapsing without the support of a perforated liner.2 On the otherhand, common sense suggests that, if a formation is too weak withrespect to the magnitude of in-situ stress, a borehole cannot remainopen. In addition, it is a common method to use an acid to stimu-late a limestone reservoir. Any acid should weaken a limestoneformation. However, field observation seemed to show that anopen hole remains stable even after acid stimulation. We need toknow why an open hole remains stable although we know acidsshould weaken formation after acid treatments.

No large-scale laboratory experiments have appeared in theliterature on borehole collapse problems for limestone reservoirs,although many papers have appeared on wormholes.3 To answerwhy a borehole in a limestone formation is stable, and why aciddoes not change the borehole stability, two types of experimentsare conducted in this work.

1. First, there are fundamental experiments to know the lime-stone property: Complete triaxial stress strain curves are measuredfor two types of limestone for several confining pressures. In ad-dition, acidflood experiments are conducted to measure the poros-ity change, permeability change, strength change, and magnitudeof limestone dissolution at acid limestone interface.

2. One-half- to one-third-scale models are used for boreholestability experiments to measure the well collapse condition withand without acid treatments. Uniform and directional confiningpressures are used to simulate vertical and horizontal wells. Thechange in borehole diameters is measured at several points of theborehole while the confining pressure is increased until the bore-hole starts collapsing.

The present work is the first publication appearing in the lit-erature to show a series of large-scale borehole stability experi-ments for limestones with and without acid treatments.

Experimental Setup and ProcedureBorehole Stability Test Using a Large Polyaxial Cell. A largepolyaxial pressure cell shown in Fig. 1 equips a flexible squarejacket to hold a rock sample. Unlike other large polyaxial cells,because a hydrostatic stress is applied through the jacket by thesurrounding oil, a high confining pressure up to 25 kpsi may beapplied to the rock sample. After applying the hydrostatic stress, apolyaxial load may be added to the rock sample through the load-ing plates installed at the four faces of the jacket with loadingpistons behind the jacket. A cubic sample (10.5×10.5×17.5-in.)with a borehole (diameter 1.5 in. and 2.25 to 2.29 in.) is insertedinto the flexible jacket shown in Fig. 1. The three confining pres-sures (two horizontal and one vertical), borehole pressure, and thepore pressure may be independently changed.

The borehole deformation is measured in two perpendiculardirections (normally, in the largest and smallest horizontal in-situstress directions) at two locations with a set of cantilever defor-mation gages. A cubic sample is saturated with 3% NaCl waterbefore testing. Normally, the confining pressure is applied and thepressure is cycled several times to check whether the boreholecantilever is properly seated at the borehole wall. After pressurecycle, the confining pressure is increased to a desired pressure.

Copyright © 2005 Society of Petroleum Engineers

This paper (SPE 77776) was first presented at the 2002 SPE Annual Technical Conferenceand Exhibition, San Antonio, Texas, 29 September–2 October. Original manuscript receivedfor review 13 January 2003. Revised manuscript received 2 July 2004. Manuscript peerapproved 9 February 2005.

105June 2005 SPE Journal

Then, one horizontal stress is increased until a borehole failureis observed.

Triaxial Tests. It is important to know the elastic and plastic prop-erties of the rock. The standard triaxial tests are conducted for twotypes of limestones used in this work. The sample is a cylindricalcore 1.5 in. in diameter and 3 in. in length and saturated with 3%salt water. The confining pressure is 0, 0.5, 1, 2, 4, and 7 kpsi, andthe tests were conducted by increasing the axial stress until afailure was observed for each confining pressure.

Acidflood Test. Solid samples (1.5 in. in diameter and 3 in. inlength) or sliced cylindrical samples (a cylindrical core 1.5 in. indiameter and 3 in. in length sliced into eight thin pieces and puttogether with paper filter between the thin plate-shaped cores) areused for acidflood tests as shown in Fig. 2. For the solid core, thehardness of the rock is measured by an acme rebound hardnesstester, which measures the bouncing-back ability (ratio of reboundand impact heights) of a rock surface. The hardness distribution ismeasured from the acid-etched surface. The rock sample is fixed incement slurry to avoid the end effect of the hardness tester. Forsliced cores, the porosity change distribution is measured beforeand after acidflooding by the sample weight with and without watersaturation. Permeability change is also measured for sliced rocks.

Experimental ResultsMechanical Properties of the Limestones. Two types of lime-stones are used. Limestone A has 4,716 psi unconfined rockstrength (UCS), 0.159 porosity, and 8.6 md permeability. Lime-stone B has 1,751 psi UCS, 0.267 porosity, and 56.7 md perme-ability. Although these rocks are relatively homogeneous, the per-meability variation is significant, as with most other limestones.

Figs. 3 through 6 show the stress strain curves and yield andfailure curves for 1,751-psi rock. These limestones have two dis-tinct failure envelopes. The failure plastic strain is relatively smallfor normal shear failure while it becomes as much as 10 timeslarger when a shear failure is induced after pore collapse. Fig. 6shows that the critical plastic strain with a confining pressure lessthan 500 psi was as small as 0.002, while it jumps up to 0.03 forhigher confining pressures. Fig. 4 plots the shear yield points andpore collapse yield points. The pore collapse yield point is ellip-tical, while the shear yield points flatten at a higher confiningpressure. The following mechanical properties peculiar to lime-sones may partially give abnormal borehole stability:

1. The critical plastic strain becomes significantly large if thestress state exceeds a pore collapse point.

2. Pore collapse is induced with a relatively low mean stress.

Rock Property Change During Acidflooding. Two pore volumeof 15% HCl solution are injected into the samples. The descriptionof the samples is shown in Tables 1 and 2. Solid cylindrical coresand sliced cylindrical cores are used for testing. The solid cores areused for the hardness tests because the hardness tests require areasonably large sample. The sliced cores are used to measure theporosity and permeability change through the cores. The injectionpressure is 5 atm, which may be common during field acid treat-ments. The injected acid volume is approximately 27 and 47 cc forLimestone A and B, respectively, and their pore volumes are ap-proximately 13.68 and 23.65 cc, respectively. The weight andlength losses were 9.5 and 5.24 g, or 0.15 and 0.083 in. for thesolid and sliced 3-in. Limestone A samples. The weight and lengthlosses were 24.04 and 11.25 g or 0.43 and 0.2 in. for the solid andsliced 3-in. Limestone B samples.

Fig. 7 shows Limestone A sample after being sliced to checkthe penetration of acid. The face contacting the acid solution be-

Fig. 1—Large triaxial cell for borehole stability experiments.

Fig. 2—A high-pressure Hasler type coreholder for testingstrength reduction and pore enlargement caused by acid flow.

Fig. 3—Triaxial tests for the 1,75-psi limestone. Fig. 4—Yield envelope for the 1,751-psi limestone.

106 June 2005 SPE Journal

comes wavy, and buggy cavities are sporadically formed. Theporosity is increased as far as 0.2 in. from the acid-core interface;however, no change is observed from visual check beyond 0.2 in.Figs. 8 and 9 show the change in weight, permeability, and hard-ness for Limestone A and B, respectively. After acidflooding,approximately 0.083 and 0.20 in. core lengths are lost because ofthe chemical reaction for Limestone A and B, respectively, so thatthe weight-loss curves start from these points. The weight losscontinues up to 0.3 in. from the initial core-face position. Thehardness reduction is high at the reaction face; however, it recoversrapidly and no change is observed beyond 0.3 in. from the reactionface. The permeability becomes lower after injection because ofthe fine particles generated by the chemical reaction flowing withthe filtrate through the core.

The results of the acidflood experiments enlighten the boreholestability problems after acid treatments as follows:

1. Acid treatments mainly enlarge borehole size and the surfacebecomes wavy. Because of the size effect and the wavy surface,the borehole may lose some strength.

Fig. 6—Critical plastic strain for the 1,751-psi limestone.

Fig. 5—Volumetric change for the 1,751-psi limestone.


2. Acid reaction reduces bulk strength of acid-penetrated zonesbecause of the porosity loss; however, the remaining grains are stillintact and bond tightly, so that the local strength should remainfairly constant. The affected zone is only 0.2 to 0.3 in. from theacid-contact surface.

3. Buggy cavities or wormholes may be developed, resulting ina lower bulk Young’s modulus, although microscopic Young’smodulus remains the same. It means that the borehole inner surfacebecomes more deformable without a shear failure.

Borehole Stability. Most borehole experiments are conductedwith a 2.34- to 2.39-in. borehole. Tables 3 and 4 show the bore-hole experiments for the A and B samples, respectively. Becausethe rock strengths are approximately three times (i.e., 4,716 vs.1,751 psi UCS), the borehole strengths are also approximatelythree times for each rock.

Fig. 10 shows Test A2, wherein, after the confining pressure isincreased to 5 kpsi, one horizontal stress is increased to 7.2 kpsi.The deformation perpendicular to the maximum horizontal stressreduces and creates an elliptical borehole shape initially; however,after a 0.6-kpsi horizontal stress increase from the hydrostaticstress, the borehole diameter in all directions starts shrinking. AsFig. 11 shows, the borehole has small zigzag shear cracks at thetop and bottom surface when one horizontal stress has reached 7.2kpsi. After releasing the confining pressure and the borehole fail-ure is examined, the confining stress is increased to 5 kpsi and,thereafter, one horizontal stress is increased to 11 kpsi as shown inFig. 12. Fig. 13 shows that large breakouts are induced in perpen-dicular to the maximum horizontal stress direction.

Fig. 12 compares the borehole stability for the hydrostatic load-ing and nonhydrostatic loading with 5 kpsi confining pressure.According to the Kirsch’s solution, the stress concentration shouldbe significant for nondirectional loading. However, amazingly, thedeformation curves are similar between hydrostatic and nonhydro-static loadings. In addition, the borehole strengths are also notsignificantly different. It is true that nonlinearity of rock deforma-tion should reduce the stress concentration; however, Fig. 12shows that the magnitude of the reduction is more than expected.

After acidizing boreholes, borehole stability tests are conductedfor a hydrostatic loading path and for a directional loading path.Five acidizing tests are conducted as shown in Table 4 for SampleA. During acid circulation, the boreholes were enlarged, and thesurface became slightly wavy. To ensure deep acid penetration,dry rock samples are used during acidizing. 1000- or 2000-cc HClsolutions are completely reacted with the limestones while they arestirred in the borehole. After acidizing, the rock samples are saturatedwith 3% NaCl water before borehole stability tests are conducted.

Figs. 14 and 15 show the borehole test for a sample with2000-cc HCl solution reaction. The borehole strength seems toslightly be lowered compared to nonacid-treated cases, but thereduced strength is not significant. As shown in Fig. 15, the bore-hole is enlarged because of acid reaction with a wavy surface.When the stress is reduced after testing, the borehole surface is stillintact; however, small application of shear stress yields rock frag-ments from the borehole surface as shown in Fig. 16. The frag-ments have a reasonable strength. Figs. 14 and 17 show the resultswith 2000-cc HCl flooding with directional loading path. Theborehole strength is slightly reduced compared to the nonacidborehole; however, the strength reduction was trivial. The bore-hole breakout occurred in parallel with the smallest horizontalstress direction. Fig. 14 also shows that the deformation curves andborehole strengths are similar between hydrostatic and nonhydro-static loadings.

Table 4 shows the conditions of the borehole stability tests forSample B. Although all the samples look similar, some strengthdifference is observed because of rock heterogeneity. B1 and B2samples seem to be slightly stronger than other rocks, although B1and B3 experiments are conducted with the same condition with aslightly different borehole size.

Fig. 18 shows the borehole stability tests without acidizing.The borehole surface slightly protrudes inward while the surfacesporadically breaks because of shear failure. Fig. 18 shows that fordirectional stress, the borehole diameter slightly enlarges duringinitial application of a horizontal stress in one direction, althoughafter further directional stress application, the borehole size shrinksin all directions regardless of the directional loading. Fig. 18 alsoshows that the deformation curves and borehole strengths are simi-lar between hydrostatic and nonhydrostatic loadings.

Fig. 19 shows the borehole deformation with a 2000-cc HClsolution reaction with hydrostatic and directional loadings. Theborehole deformations reach as much as 20% of the boreholediameter without borehole collapse. However, after releasing the

Fig. 7—Acid-rock interface of Lime A after 2 pore volume 16%HCl injection.

Fig. 8—Rock property change after acidization (normalized withthe properties before acidization, Lime A).

Fig. 9—Rock property change after acidization (normalized withthe properties before acidization, Lime B).


confining stress, large fragmented rock chips fell in the boreholewhile the borehole deformation measurement assembly was removed.

Tables 3 and 4 summarize the results. These results show:1. Acidflooding seems to reduce slightly the borehole stability;

however, the strength reduction is small. The small reduction seemsto be caused by borehole enlargement and wavy borehole surface.

2. Once one horizontal stress is increased from a hydrostaticstress state, the borehole diameter perpendicular to the additionalhorizontal stress slightly starts increasing initially; however, afterincreasing some amount, the diameter in all directions starts re-ducing before borehole failure occurrs. These phenomena havenever been observed for borehole stability experiments with othertypes of rocks. The borehole strengths for hydrostatic and nonhy-drostatic loadings are not significantly different.

AnalysisTo interpret the experimental results, a numerical analysis is con-ducted using a nonlinear finite-element model. Fig. 20 shows the

finite-element model used in this analysis. Because the experi-ments are conducted with symmetrical boundary conditions, 1⁄4 ofthe domain is simulated. The constitutive relation used for themodel consists of poroelastic-plastic stress strain with pore col-lapse and shear nonlinear plastic strains simulating the empiricaltriaxial curves shown by Figs. 3 through 5.

A model simulation is conducted for the Sample A condition.Because the rock deformation properties for acidized section couldnot be measured (it was not possible to make uniform acidizedsamples for triaxial tests, because acid only reacts at near-rocksurface), it is assumed here that the acidized section (approxi-mately 0.22 in. from the borehole surface) behaves like Sample B.Note that Sample A has 0.159 porosity and Sample B has 0.267

Fig. 10—Borehole deformation (Lime A2, Dw=2.36 in., Pc=5 kpsi).Fig. 11—Borehole deformation stopped at �H1=5 kpsi, �H2=7.2kpsi, Lime A2, small shear cracks at bottom and bottom side wall.


porosity and the UCS strengths are 4,716 and 1,751 psi, respec-tively. As Fig. 21 shows, the stress path first reaches a shearenvelope at the borehole without a surface load, expands the shearenvelope, and finally reaches the pore collapse plastic strain. Thestress state locates on both the shear-failure and pore collapseplastic envelopes, expanding both until reaching a shear-failurestress state. Comparing Fig. 21 with nonacidized cases, the failurepoints are almost identical, although the acidized formation at theinner surface is significantly weaker. The reason is that because theacidized formation has a smaller Young’s modulus because of ahigh porosity, the tangential stress at the borehole surface does notsignificantly increase. The load is mostly supported by the sur-rounding formation with a higher Young’s modulus. The maxi-mum confining stresses to induce borehole failure are not signifi-cantly different between hydrostatic and directional loading pathsbecause significant nonlinearity reduces the stress concentrationfor directional loading.

Field Application

Using a nonlinear finite-element borehole stability model, the res-ervoir depletions inducing borehole collapse are calculated usingthe constitutive relations constructed for Rock A and B. Constitu-tive relations matching with the triaxial data (for example, Figs. 3and 5 for Rock B) are constructed. The critical plastic strain is usedfor the failure theory (for example, Fig. 6 for Rock B). The fol-lowing loading path is assumed as field conditions simulating theinitial condition before drilling until a well collapse during a res-ervoir pressure depletion:

1. The in-situ stress is given as a residual stress at the initialcondition. The stress in equilibrium to the in-situ stress is appliedto the borehole surface, simulating the condition before drilling.

2. The borehole stress is reduced to the pore pressure to simu-late the condition after drilling.

3. The reservoir pressure is reduced until the borehole plasticstrain reaches the failure plastic strain. When the pore pressure isreduced, the horizontal and vertical effective stresses are increasedwith a specified Poisson’s ratio � during reservoir depletionwith a specified horizontal/vertical effective stress ratio given by

��He =

�

1−��V

e +E�1−2�m�

�1−��Em�p with a small grain compressibility,

E(1−2�m)/[(1−�)Em]≈0.4. The drawdown is ignored.Tables 5 and 6 show the calculated reservoir depletions induc-

ing borehole collapse for 4,716- and 1,746-psi UCS limestones.Overall analysis of the results is as follows:

1. The final failure effective in-situ stress is high for a higherinitial in-situ effective stress. The reason is that the loading pathsare different between releasing from the initial in-situ stress andadding effective stress by depleting reservoir pressure. A boreholeis generally very stable when a borehole stress is released from theinitial in-situ stress to the borehole pressure after being drilled.

2. Vertical wells are normally stable because the load appliedduring reservoir depletion is in the borehole axis direction.

3. When the stress path shifts from the shear yield curve, toelastic region, to pore collapse yield curve, and finally to the shearyield curve, the borehole collapse condition becomes very com-plex as observed at �H

e /�Ve �0.25 and ��0.3 for a vertical well in

Table 6.

Fig. 12—Borehole deformation (Lime A11, Dw=2.36 in., hydrostatic; Lime A12, Dw=2.36 in., Pc=5 kpsi, nonhydrostatic).

Fig. 13—Borehole deformation stopped at maximum failurestress, Lime A12, large shear cracks at bottom and bottomside wall.


Table 5 shows the reservoir depletions to induce a boreholecollapse, assuming the formation has 4,716 psi UCS. Note that theeffective maximum overburden stress (�V

e +vertical stress inducedby depletion) to induce a horizontal borehole collapse ranges from8.6 to 15.97 kpsi, with a 12.3-kpsi average. The maximum con-fining stress inducing the borehole collapse for Rock A for thelaboratory tests from Table 3 ranges from 9.4 to 11.9 kpsi, with anaverage of 10.65 kpsi. This difference is mainly caused by thelarger stress concentration around a borehole (diameter 2.36 in.)within 10.5 in. finite square blocks while in the field, the stressaround a borehole is less because the in-situ stress is applied frominfinite distance. The stress supported by the block is approxi-mately 10.5-in. (10.5 in. to 2.36 in.) higher with a given �H for thelaboratory experiments. A horizontal borehole is very stable if theformation strength is as high as 4,716 psi. Table 5 also shows thereservoir depletions to induce a borehole collapse for a verticalwell, assuming the formation has 4,716 psi UCS. A vertical well isvery stable because the horizontal load (or in-situ stress) collapsingthe borehole in the radial direction is not significantly increasedeven after reservoir pressure depletion. However, if the well depthis too large and the in-situ stress is too large, even a vertical well

Fig. 14—Borehole deformation (Lime A7, Dw=2.39 in., hydrostatic, 2000 cc HCl; Lime A8, Dw=2.39 in., nonhydrostatic, Pc=5 kpsi,2000 cc HCl).

Fig. 15—Borehole deformation stopped at maximum failurestress, Lime A7, large shear cracks at entire wall, 2000 cc HCl.

Fig. 16—Fragments from borehole wall fallen after releasing theconfining stress for acidized borehole A7.

Fig. 17—Borehole deformation at maximum failure stress, LimeA8 for 2000 cc HCl acid treatment, �H1=5 kpsi, �H2=10 psi.


can be collapsed because of the significantly increased effectiveoverburden pressure.

Tables 6 shows horizontal and vertical well stabilities for 1,751psi UCS formation. Because the UCS of Rock B is one-third ofRock A, the effective in-situ stresses inducing a borehole collapsebecomes also one-third of a formation of 4,716 psi UCS rock. Ahorizontal well is significantly stable even for a reservoir with alow �H

e /�Ve ratio. Generally speaking, a horizontal borehole sur-

rounded by Rock A and B can sustain in-situ stress and reservoirdepletion with the maximum effective stresses approximately 2.6times those of the UCS values. The application of Tables 5 and 6to field problems is illustrated as follows.

Field Example 1. Suppose a reservoir depth is 10,000 ft. Theinitial pore pressure is 5,000 psi. The UCS of the rock is 2,000 psi.The Poisson’s ratio is approximately 0.2. The vertical and hori-zontal in-situ stress gradients are 1 and 0.75 psi/ft. The final res-ervoir pressure is 1,000 psi. A horizontal well is drilled.

Evaluation:1. �H

e /�Ve �0.5, and the final maximum effective stress is

�Ve �8 kpsi.

2. The ratio �Ve /UCS�4.

3. According to Table 5 or 6, the average value of �Ve /UCS at

collapse is approximately 2.6 for 0.2 Poisson’s ratio. Therefore,borehole collapse is likely without a protective liner for the givenfield conditions.

Field Example 2. This is the same condition with Example 1except UCS�4 kpsi.

1. The ratio for this example is �Ve /UCS�2.

2. Now, because the average ratio of �Ve /UCS for Rock A

or B is 2.6, it is possible to complete the well without aliner protection.

3. Although the rock property is different between limestones,30% (2.6/2�1.3) extra rock strength may be sufficient for a bore-hole even with other limestone rocks.

Fig. 18—Borehole deformation (Lime B3, Dw=2.39 in., hydrostatic; Lime B2, Dw=2.34 in., Pc=3 kpsi, nonhydrostatic).

Fig. 19—Borehole deformation (Lime B7, Dw=2.39 in., hydrostatic, 2000 cc HCl; Lime B8, Dw=2.39 in., Pc=3 kpsi, nonhydrostatic,2000 cc HCl).


4. Because actually the rock property may be different to somedegree, a triaxial test may be performed using six to seven 1.5-in.plug cores (the plug diameter exceeding 1.5 in. is recommended toget accurate stress strain curve and strength). Using a nonlinearborehole stability model, the evaluation of borehole stability maybe confirmed.

Conclusion1. The present experiments found that abnormal ductility of lime-

stones and increased pore volume due to acid treatment enhanceborehole stability with the magnitude beyond expectation. Notethat no publications have appeared on large-scale experimentsof openhole stability in limestones with and without acid treatment.

2. Plastic strain failure envelopes for limestones consist of twodistinct surfaces before and after pore collapse. The criticalplastic strain becomes up to 10 times as large after pore collapse.

3. Pore collapse around a borehole is unlikely under normal cir-cumstances because one side is open for an open hole. However,unlike with other stones, borehole failure in a limestone forma-tion is induced by a shear failure after pore collapse. Pore col-lapse alters a limestone to a very ductile rock.

4. Because of the significant plastic yielding, the maximum cross-sectional effective in-situ stress �e

max to induce a horizontal

well failure is not significantly different for a wide range ofhorizontal to vertical effective in-situ stress ratio. The differenceis significantly smaller than expected because we are used to theKirsch’s linear elasticity solution, which emphasizes the highstress concentration induced by directional loading. This is thereason that a horizontal well in a limestone reservoir is abnor-mally stable.

5. Acid stimulation mostly enlarges a borehole and creates a wavyborehole surface and wormholes. Because of the size effect andwavy surface, the borehole stability is slightly lowered. How-ever, the acid-treated zone has some wormholes or the pores areenlarged. Because the Young’s modulus is also reduced becauseof wormholes, the reduction of rock strength does not signifi-cantly reduce borehole stability. Therefore, it is important forfield applications to enhance creating wormholes without uni-formly weakening limestone formation during acid treatment.

6. Normally, because a limestone has a relatively high UCS, it islikely that a protective slotted/drilled hole liner can be deletedfor openhole completion. However, it is not always the case forrelatively high in-situ stress with medium-strength rocks; there-fore, the UCS and rock deformation must be measured to evalu-ate an openhole stability.

NomenclatureDw � borehole diameterPc � confining pressure� � Poisson’s ratio used for calculating effective

horizontal stress change during a reservoirdepletion

�H1,�H2,�V � Two principal horizontal stresses, vertical stress�H

e , �Ve � effective stress

References

1. Krawietz, T.E. and Rael, E.L.: “Horizontal Well Acidizing of a Car-bonate Formation: A Case History of Lisburne Treatments, PrudhoeBay, Alaska,” SPEPF (November 1996) 238.

2. Mackay, A. et al.: “Horizontal Well With Two Lateral Holes in Lay-ered Limestone Reservoir: Performance and Test Interpretation,” paperSPE 25594 presented at the 1993 SPE Middle East Oil TechnicalConference and Exhibition, Bahrain, 3–6 April.

3. Buijse, M.A.: “Understanding Wormholing Mechanism Can ImproveAcid Treatments in Carbonate Formations,” paper SPE 38166 pre-sented at the 1997 SPE European Formation Damage Conference, TheHague, 2–3 June.

Fig. 21—Borehole deformation with acidized material where the formation penetrated with acid behaves like Rock B (0.22 in. fromwall) while the rest of the material is Rock A, directional loading with Pc=5 kpsi.

Fig. 20—Finite element model and mesh.


Nobuo Morita is a professor of resources and environmentalengineering at Waseda U., Tokyo. His current areas of interestare borehole stability, sand-production problems, and devel-oping numerical models for fluid-flow and rock-mechanicsproblems. He holds a BS degree from the U. of Tokyo and MSand PhD degrees from the U. of Texas at Austin, all in petroleum

engineering. Tomoki Doi is a sales engineer at NEC Corpora-tion, Fukuoka, Japan. He holds BS and MS degrees in resourcesand environmental engineering from Waseda U. Takanori Ki-noshita is a rock mechanics engineer at H&B System Corpora-tion, Tokyo. He holds a BS degree in resources and environ-mental engineering from Waseda U.


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Acid Treatment in Limestone