Society of Petroleum Engineers

SPE 28452

The Influence of Stress Anisotropy on Horizontal Well PerformancePredicted Via Special Core Analysis Under True Triaxial ConditionsB,R. Crawford and B.G,D. Smart, Heriot-Watt U.SPE Members

Copyright 1994, Society of Petroleum Engineers, Inc.

mds paper was prepared for presentation at the SPE 69th Annual Technical Conference and Exhlbltlon held In fkIW Orleens, LA, U.S.A., 25-2S September 1994.

This paper was selected for presentation by an SPE Pm9rmn Committee fOllOwlngreview Of infOrmatlon contained in en ebstract submitted by the author(s). Contents of the paper,as prssented, have not been reviewed by the SocletY of Petroleum Englnears and are subject tO Wrectlon by the authOr(s). The material, as presented, does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or member% Pspers presented at SPE meetings are subJectto publlcat[on review by Editorial Committees of the societyof Petroleum Engineers. Permlsslon to COPYis restrictedto en abstract of not morsthan W words. lllus~atlons may not be Wed. The abstract should contain cmsplcuous acknowledgmentof where and by vdiom ths paper 18 presented. Write Librarian. SPE, P.O. q OX833836, Richardson, TX 7508S-3S38, U.S.A. Telex, 16S24S SPEUT.

AbstractFor optimisation of recovery, a thorough understanding ofreservoir heterogeneity and anisotropy on as detaited a scaleas possible is a prerequisite. Despite recent developments inprobe permeametry enabling quantification of sedimentaryheterogeneity down to the lamina-scale, no parallel advance hasbeen evident in the field of core analysis with regard toimproving the realism of the applied stress field. Theconventional triaxial method can only achieve vertical stressanisotropy and is limited to axisymmetric uniform radialpressure. Thus it is incapable of adequately simulating the irzsitu rock stress field, CTv?$qq# ah. Accordingly, a new truetriaxial cell and servo-control system has been developed whichis capable of applying independent and unequal radial stressesto the curved surface of a cylindrical core plug. Pulse decaypermeability experiments have been conducted on threereservoir sandstone analogues showing different degrees ofgeological heterogeneity. Perrneabilities were measured underboth true triaxial and conventional triaxial conditions, for thepurposes of comparison. In terms of mean stresses,(rYv+oH+cTh)/3,stress-sensitive permeability profiles were verymuch influenced by Iithology. Complex interaction betweenstress anisotropy and rock fabric resulted in a non-systematicvariation in permeability with mean stress for the laminated,heterolithic rock type. For the scenario of a horizontal wellboredrilled parallel to the minimum principal stress, ah, themeasured permeabilities were used to calculate ~-factors

References and illustrations at end of paper.

(P=) for simple productivity evacuation. This sensitivityanalysis indicated that well performance curves were alsosusceptible to the degree of stress anisotropy. The effect wasevident in discrepancies of up to several hundred feet incalculated horizontal wellbore lengths required to achievedesired levels of productivity.

IntroductionWith less than one-quarter of additions to the worlds oilreserves coming from new discoveries, over three-quarters isnecessarily sourced through better management of existingreservoirs. Thus profitability is dependent on increasingrecovery from already producing fields. 1 Perhaps the singlemost important prerequisite for optimisation of recovery is athorough understanding of reservoir heterogeneity (differentproperties at different locations) and anisotropy (differentproperties in different directions) on as detailed a scale aspossible.

Geological heterogeneity (sedimentary structures and tectonicdiscontinuities) governs the relative connectivity/compartmentalisation of the reservoir, sweep efficiencies andresidual oil saturations, all critical factors in the determinationof recovery. Such complex variability involves manifoldgeometries at a diffuse range of length scales from Iamina (mm~o cm) to bedding (cm to m) to formation (m to 100s m)2.Whilst 3-D seismic can distinguish sedimentological structureand fault geometries on an interwell scale, it still lacks theresolution to pick out fine detail. However, via the

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2 THE INFLUENCE OF STRESS ANISOTROPY ON HORIZONTAL WELL PERFORMANCE SPE28452PREDICTED VIA SPECIAL CORE ANALYSIS UNDER TRUE TRIAXIAL CONDIITONS

geopseudo approach3~4 heterogeneity on the laminaset scalecan be directly incorporated into numerical simulationinvolving metre-scale gridblock. Flow properties at the mm-scale are generated from absolute permeability variationsmeasured by probe permeametry. Probe (or mini)permeameters, and especially the newly developed profilepermeameter5, are becoming increasingly more important dueto their high-density measurement capability, which enablesmapping of fine-scale permeability cotitrasts between Iaminae.

With the portable nature of the probe permeameter lending,itself particularly to heterogeneity quantification on the outcropscale, it is not surprising that potential stress effects on fluidflow at reservoir conditions are often neglected, outcropsrepresenting largely passive, de-stressed reservoir analogues.Indeed, in order to compare core plug with probe permeameterdata (the former being conducted under confining pressure andthe latter under zero stress conditions) core measurements aredetermined under mutiple confining stresses, and thenextrapolated to zero stress conditions.

The nature of the in situ rock stress field can be regarded asbeing both heterogeneous with respect to pointdeterminations7, and anisotropic with respect to mutuallyperpendicular far-field principal stress magnitudes. Whilstequipment developtient and advances in numerical techniquesas mentioned above, have ensured that quantification ofgeological heterogeneity has significantly progressed, a similarprogression in the field of core analysis, with particular regardto quantification of stress effects, is not immediately apparent.Routine examination is still based on the application ofhydrostatic stress. Indeed, special core analysis utilises onlyconventional rock mechanical apparatus to quantifypermeability under various uniform radial confining pressures,with stress anisotropy only in the vertical plane.

An attempt to redress this imbalance, as presented below,outlines permeability results from a new true triaxiat cell,capable of subjecting core plugs to a general 3-D stress fieldtruly analogous to that of the in situ reservoir environment. Inthe present study, vertical and horizontal plug permeabilitiesmeasured under true triaxial applied stresses, are comparedwith those evaluated under conventional axisymmetric triaxialconditions. The consequence of determining permeability underreal reservoir stress as opposed to approximations, is furtherquantified in terms of significant differences in calculatedhorizontal wellbore lengths required to achieve a certainproductivity. Therefore, with horizontal well performancedepending critically on the ratio of kv to kh, it is suggested thatas early as the vertical pilot-hole stage, reservoircharacterisation with respect to fine-scale geologicalheterogeneity, is also augmented by special core analysis undertrue triaxial stress conditions.

Theory

Theoretically, stress is a property at a point, and as it is asecond rank tensor quantity, requires six independentcomponents (three normal stresses and three shear stresses) tofully characterise it. However, it is conventional to describe thein situ rock stress field using the magnitudes and directions ofthe three principal stresses, 01>cY2>039. With a principal stress

being defined as a stress acting perpendicular to a plane onwhich there are no shear stress components, for essentially flat-Iying sediments with the earths surface acting as a free-boundary, the simplifying assumption that one principal stressis vertical, crv, so that the other two are necessarily horizontal,cHXJh (principal stresses being mutually perpendicular) isgenemlly safe, Early in the history of rock stress determination,Hast *0 recognised that stress differences between all threeprincipal stresses at a point are characteristic of the in situstress state, Cv # 6H # Oh. Over any significant horizontalsurface within the ground, the average vertical stress mustequilibrate the downward force of the weight of overlying rockand so approximate to the product of the average unit weight ofthe rock and the desired depth. Although this relationship hasbeen supported by numerous stress measurements 1, it can beviolated by the effects of geological structure (e.g. folding) andby abnormal pore pressure effects. Whilst the vertical stressmagnitude is constrained by the above relationship, thehorizontal stress magnitude can lie anywhere in a range ofvalues between two extremes corresponding to conditions ofnormal faulting, in which GV=GI and failure is by horizontalextension, to conditions for reverse faulting, in which (JV=CT3and failure is by horizontal compression 12. In deep, normallypressurised reservoirs, the compressive stress due to the weightof the overburden load is usually the primary stress, Cv=ol 13.

Holt 14 provides both a summary of previous stress-dependentpermeability measurements conducted under hydrostaticconditions, and presents permeability reduction data induced bynon-hydrostatic stress fields. Low permeability sandstonesshowed a decrease of 50% for lmD and 80 to 99% for O.OlmDsandstones on increasing the hydrostatic stress from 3.45MPa(500psi) to 34.5Mpa (5000psi)15. In a complementary study onhigh permeability sandstones, over the same hydrostatic stressincrement only a 5% decrease in permeability was observed for500 to 1000mD sandstones 16. Holt investigated the effects ofnonhydrostatic triaxial stress configurations on highporosity/high permeability sandstone core plugs. Whilstnonhydrostatic applied stresses produced permeabilityreductions in excess of those resulting from hydrostaticcompression, in particular, as failure was approached in eithertriaxial loading or unloading, permeability decreased to

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SPE 28452 B. R. CRAWFORD AND B. G. D. SMART 3

stress. For hydrostatic pressure application a simple hydraulicbomb is adequate, however for the application ofnonhydrostatic triaxial stress states, the ability to apply anaxial stress to the specimen independent of the radial confiningpressure is fundamental. In such conventional triaxiaI testingof core plugs, a uniform radial stress is applied hydraulically tothe curved surface of the rock cylinder, whilst simultaneouslythe prepared flat and parallel specimen ends are loaded axiallythrough spherical seats and platens. In terms of equipment used,radial pressurisation or confinement is usually achieved througha pressure vessel 17!18 in which hydraulic fluid at pressure, p,acts on a synthetic rubber membrane sheathing the sample.Axial load is generated parallel to the specimen long axis via astiff, servo-hydraulic compression machine. In this manner,axial loading over the specimen cross-sectional area results inan axial stress, ~a, wholly independent of p.

Two admissible stress field conditions are within thelimitations of conventional triaxial testing, resulting fromindependent control of ~a and p:

(i) triaxial compressiort, where~a=~1>~2=~3=pand,

(ii) triaxial extension, in which(Jl=~2=p>03=~a

For configurations (i) and (ii) it is evident that two of the threeprincipal stresses are equal at any one time. Such axisymmetrictriuxial stress distributions, resulting directly from applicationof a uniform-radial hydraulic pressure, p, represent specialcases of a general 3-D or true triuxial stress state in which 01> cr2 > ts3. To avoid confusion, the term triaxial in invertedcommas will be used here to indicate the axisymmetricconfiguration. Thus it is evident that even non-hydrostatictriaxial testing only approximates to a realistic irrsitu rockstress field in which av # o H # cJh, as conventionallaboratory equipment is incapable of reproducing horizontalanisotropy.

Xhe True Triax ial CellIn experimental rock mechanics, to assess the effects of a truetriaxial (+polyaxial~multiaxial) stress field on rockproperties, the cubic configuration has been most commonlyused, whereby three independently variable principal stressesare applied to the opposing faces of a rock cube. Recentpolyaxial testing using variations on the cubic geometry 19! 20$21 has focussed on evacuating the effect of 02 on rock strength,mapping failure surfaces in 3-D and formulating generalisedconstitutive laws for various geomaterials. However, thepolyaxial cubic method is definitely non-ideal, with particularregard to petroleum-related rock mechanical requirements, for anumber of reasons:

(i) the large sample size r~uired fortesting is uneconomical withva[uable whole core,

(ii) the cubic geometry poses problems forsample preparation, especially withregard to weak reservoir sandstones,

(iii) the difficulties inherent in the testingmethod, including platen interferenceon specimen deformation, andmaintenance of uniformity in the

applied stresses.

Ideally, what is required for strength, deformation and fluidflow measurement under truly realistic in situ reservoir stressconditions, is the ability to subject small-diameter cylindricalcore plugs to true triaxial stress fields, by means of a simpleexperimental facility as operationally uncomplicated as thefamiliar axisymmetric triaxial method. To meet this need, anew tme triaxial pressure cell has been designed, fabricated,proved and patented by the Rock Mechanics Group within theDepartment of Petroleum Engineering, Heriot-Watt University,to enable special core analysis under anisotropic confiningpressures.

Only brief design details for the true triaxial cell will be givenhere, as these have been fully reported elsewhere22, Whilstaxial specimen loading is achieved through platens in anequivalent manner to the conventional test, via a stiff, servo-hydraulic compression machine, the innovation lies in theindependent application of radial pressure to the core plugcurved surface. This is developed in a stepwise manner,enabling an approximately elliptical radial stress distribution tobe produced in a right circular cylindrical specimen 30mm indiameter, with a length to diameter ratio of 2.25:1. Radialpressure variation is achieved by using specially formedtrapped tubes, that is pvc tubes which are aligned with thespecimen long axis and are trapped between the curved surfaceof the specimen and the cell wall. The trapped tubes, whichpossess initially circular cross-sections, are formed to retain aflat face, so that under hydraulic pressure these faces expandagainst the core. Due to their trapped nature, the tubes canoperate well above their rated unconfined burst capacity, andare resilient enough to withstand pressure differences in excessof 6.9Mpa (1000psi) between adjacent tubes. Coupling ofopposing banks of trapped tubes into independent hydrauliccircuits enables different pressures to be applied to thespecimen circumference, and hence radial stress anisotropy tobe imposed on the core plug. The true triaxial cell currentlyoperates with three such hydraulic circuits arranged as shown inFigure 1, enabling a maximum azimuthal radial stressdifference of 13.8MPa (2000psi) to be maintained. Aninexpensive means of multiple pneumatic-hydraulic servo-control has been developed in-house for the trapped tube array,capable of maintaining pressures on specimen dilatancy orcontractancy to within *0.5MPa (70psi) of initial input values.Obviously, the greater the number of hydraulic circuits, thegreater the potential magnitude of radial stress anisotropy, andthe closer the approximation to true elliptical confinement.Whilst the current cell utilises 24 trapped tubes configured intothree hydraulic circuits to give the simplest arrangement forproving the capability, additional servo-units would enable amaximum stress difference of 4 1.4MPa (6000psi) to begenerated on the specimen circumference using sevenindependent hydraulic circuits. The system benefits from rapidresponse computer control and data logging.

Permeability measurement utilises a peripheral pulse decaypermeameter, originally developed for use with theconventional triaxial cell to study the effects ofnonhydrostatic stress on fluid ftow23. The pulse decay method,as opposed to a steady-state procedure, was favoured in order tominimise the migration of fines liberated during potentialanelastic deformation processes, and to allow measurements onlow permeability cores (clmD). The transient technique used is

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4 THE INFLUENCE OF STRESS ANISOTROPY ON HORIZONTAL WELL PERFORMANCE SPE28452PREDICTED VIA SPECIAL CORE ANALYSIS UNDER TRUE TRIAXL4L CONDITIONS

based on an integration of Darcys law over the decay durationof an induced pressure pulse. With reference to the systemdepicted in Figure 2, a pulse decay permeability measurementunder a constant stress state is conducted as follows: with thecore plug in direct contact with both the upstream anddownstream reservoirs, prior to the application of a pressurepulse and with both valves VI and V2open, the pump is used topressurise the entire system to some initial pressure; valve V2 isthen shut to generate an upstream pressure pulse around0.2MPa (30psi) over the system pressure ; with the pumpswitched off and VI shut to prevent leakage through the pumpseals, pressure pulse decay across the sample is monitored via adifferential pressure transducer. An X-Y-t recorder is used toprovide a hardcopy pressure-time decay curve, the integrationof which provides a measure of plug permeability. Currentdesign allows pore pressures up to 34.5MPa (5000psi) witheither refined oil, brine or artificial seawater permeants.

The fundamental difference between the conventional and thetrue triaxial cells, lies in the radial stress distribution applied byeach to a cylindrical core specimen. In the former it isconstrained to be uniform, whilst in the latter an anisotropicdistribution is possible, the true triaxial cell providing a closerapproximation to the in situ condition, To gauge the impact ofhorizontal as well as vertical stress anisotropy, an example isconsidered involving the measurement of kv and kh for asimple horizontal well productivity analysis. Using a verticaland a horizontal core from three reservoir sandstone analogues,permeability measurements in the true triaxial cell arequantified, under both axisymmetric and anisotropic confiningpressures. The influence of applied stress is then assessed, notonly in terms of differences in magnitude, but by plugging themeasured values into standard performance equations. Foresuch a comparative study, the simplest and clearest analogy isthat of a horizontal well drilled parallel to the direction of ~.Relative orientations between wellbore axis and far-fieldprincipal stresses are considered in terms of core plugs used toassess drainage ratios, and the stresses that should be applied inthe laboratory to reproduce the reservoir environment mostprecisely.

Experimental MethodologyIn order to stimulate a horizontal well within a matrixpermeability horizon by means of multiple orthogonalhydraulic fractures, it is necessary to drill the wellbore parallelto oh. Also, in drilling a horizontal well to intersect and drainthe maximum number of natural open fractures/joints, or toprovide optimum linkage of individual fault-bounded trapswithin a normally faulted horizon (assuming concurrencebetween the palaeostress and the contemporary stress field)then the wellbore should also invariably align with ah, as thestrike of the fracture planes theoretically parallels ~H.Horizontal wells are more sensitive to azimuthal variation instress than vertical wells. From the above it is apparent that, inboth matrix permeability and naturally fractured reservoirs, it isadvantageous to discern the directions of horizontal stressanisotropy. It is evident that, frequently, a horizontal well isconfigured with respect to the in situ stress field, so that thewellbore axis Parallels the direction of Oh. For this specificorientation, consider the stress distribution on both vertical andhorizontal core plugs associated with evaluating the drainageratio, kv/kh. For a horizontal wellbore drilled parallel to ah, it

is apparent from Figure 3 that vertical and horizontal core plugsare configured inthe following manner with respect to far-fieldstresses:

(i) for vertical drainage, av on theprepared flat specimen ends and bothcrH and ~ acting orthogonally on thecircumference,

(ii) for horizontal drainage, ~ on theprepared flat specimen ends and bothav and m acting orthogonally on thecircumference.

The axisymmetric triaxial compression test is incapable ofreproducing the true in situ scenario, CTvxrI-l>~. Instead, onlyapproximations to the reservoir stress environment can bemade, due to the constraint of uniform radial confinement. Forthe vertical core plug, the conventional pressure vessel forcesthe assumption of horizontal isotropy, c7H=0h=p, whilstequivalency between the overburden stress and the minimumhorizontal stress, (Jv=(Jh=p, is the result with respect to thehorizontal plug. For the far-field stress configurations shown inFigure 3, the effect of measuring vertical and horizontal plugperrneabilities under true triaxial stress states, as opposed toaxisymmetric approximations, was evaluated for three differentsandstone types. In order to compare kv and kh valuesmeasured under both conventional and true triaxial stresses, thestress configurations as illustrated diagrammatically in 13gure 4were applied to three different vertical and horizontal core plugpairs. For each measurement, the downstream reservoir wasopen to atmospheric conditions. A maximum confiningpressure differential of 13.8MPa (2000psi) is sustainable over aspecimen curved surface. As a consequence of this workinglimitation, the applied stress magnitudes given in Figure 4 wereselected, namely:

q = 4 1.4MPa (6000psi)cq+ = 34.5MPa (5000psi)~ = 27.6MPa (4000psi)

These values are typical of inreservoirs of moderate depth 24.

situ stress magnitudes in

With regard to vertical core plugs, three different stressscenarios or Cases were investigated: uniform radialconfinement equal to the minimum horizontal stress (Case 1);true triaxial stress (Case 2); and uniform radial confinementequal to the maximum horizontal stress (Case 3). The influenceof five different stress cases on horizontal core plugpermeability were studied: two axisymmetric approximationsinvolving application of a uniform radial confining pressureequal to the minimum horizontal stress (Case 1) and to theoverburden stress (Case 5); two true triaxial approximationsinvolving application of isotropic horizontal stresses ofmagnitudes equal to the minimum horizontal stress (Case 2)and to the maximum horizontal stress (Case 4); and a truetriaxial stress state (Case 3).Thus, for comparative purposes, inorder to assess the full significance of the capabilities of thenew cell as opposed to existing techniques, the true triaxial cellwas also used to apply uniform radial confinement. Case 2 andCase 3 alone of the vertical and horizontal core plugmeasurements respectively, correctly reproduce the in situ

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SPE 28452 B. R. CRAWFORD AND B. G. D. SMART 5

stress field. Only far-field true triaxial stresses are considered inthe above discussion, in order to investigate stress-sensitivityunder the simplest possible conditions. Of course, such anapproach necessarily ignores the effect of induced stressesassociated with the wellbore, and is thus applicable onlyoutwith a zone extending approximately three times thewellbore diameter, beyond which the principal stresstrajectories can be considered to experience only negligibledeflection,

The above defined stress configurations of Figure 4 wereapplied to vertical and horizontal core plug pairs sourced fromthree lithologically diverse reservoir sandstone analogs.Geological details of each rock type are given in Table 1. TheClashach sandstone, a yellow subarkosic arenite with quartzovergrowths, appears homogeneous on the specimen scale, withno traces of any sedimentary structure, The Locharbriggssandstone, a red sandstone with haematite cement, showsIamina-scale heterogeneity defined by planar layers richer indiagenetic haematite, Dalquhandy sandstone is a stronglyheterolithic calcareous sandstone with quartz/dolomite-richIaminae alternating with carbonaceous/clay-rich laminae.

ResultsFrom Figure 4 it is evident that the applied mean stress,(crvKrI-I+qJ/3, increases in 2.3MPa (333psi) increments, fromCase 1 to Case 3 and from Case 1 to Case 5 for the vertical andhorizontal core plugs respectively. Figures 5-7 show plots ofabsolute permeability against mean stress for the Clashach,Locharbriggs and Dalquhandy sandstone specimensrespectively; tested under varying degrees of stress anisotropy.Variations in permeability as depicted are the result ofextremely modest changes in applied stress magnitudes. Meanstress increases by only 4.6MPa (667psi) or by 9.2MPa( 1334psi) for the vertical and horizontal specimensrespectively, and principal stress differences are never in excessof 13.8Mpa (2000psi). As a result, specimen deformation islargely recoverable, the observed fluctuations in permeabilitybeing due, presumably, to elastic pore closure with perhapssome minor anelastic grain-boundary sliding. In direct contrast,permeability permutations in the present study should becompared with profile-s from previous experimentation, inwhich measurements were taken over the complete stress-straincurve within the true triaxial ce1122.

From Figures 5-7, it is evident that, for all three rock typestested, vertical permeability is less than horizontal permeability,and the permeability profiles are different for each lithology.Clashach sandstone shows a 60% decrease in kh withincreasing mean stress, and a markedly convex downwardsshape, whereas Locharbriggs shows a straight line decrease inkh of 15%. The influence of sedimentary heterogeneity can begauged by comparing homogeneous Clashach results with thosefrom the cross-laminated Locharbriggs specimens. With fluidflowing parallel to the sedimentary fabric, kh of the horizontalLocharbriggs specimen is greater than that of the Clashachspecimen. However, when drainage is directed across-layering,as for fluid flow in vertical plugs, kv is greater in the Clashachthan in the Locharbriggs sample. Whilst vertical permeabilitymagnitude for the above two lithologies shows little changewith increasing mean stress, it is interesting to note that thelowest values for both curves were measured under true ratherthan axisymmetric triaxial conditions. The Dalquhandyspecimens are the most structurally heterogeneous, possessing

pronounced heterolithic lamination. Vertical and horizontalpermeabilities are, as a result, of much lower magnitude thaneither the Clashach or Locharbriggs samples. The horizontalpermeability profile is non-systematic with increasing meanstress, with a pronounced trough representing a measuredminima under true triaxial conditions. Conversely, verticalpermeability shows a definite maxima under comparablestresses, Thus, application of realistic in situ stresses to thelaminated Dalquhandy samples is seen to produce a dramaticincrease in the kvlkh ratio over those measured under otherstress configurations.

Error in permeability measurement is primarily due to thegraphical method of integrating the pulse decay curve. This isachieved by measuring the area under a pressure-time plot witha digital planimeter. Error in the mean stress at which a specificpermeability is measured, is a combination of the error in themeasured confining pressure applied by the true triaxial cell,and the error in axial stress applied by the stiff compression rig.With the hydraulic circuit servo-mechanisms controlling cellpressures to roughly &O.5MPa (70psi), error bars primarilyreflect a transient decline in applied axial load over eachpermeability test, associated with operating the compression rigunder closed-loop displacement control.

The results detailed above represent, perhaps for the first time,core plug permeabilties measured under realistic true triaxialreservoir stress conditions. Three reservoir sandstone analoguesshowing different degrees of sedimentary heterogeneity havebeen tested to date. Using the true triaxial cell to measureadditional permeabilities on the same core plugs under (i)conventional axisymmetric triaxial stresses and (ii) theapproximation of uniform in situ horizontal stress (6H=CJh)indicates that stress anisotropy has a substantial effect on fluidflow. Also, the data suggests that permeability- susceptibility toapplied stress is strongly dependent upon lithologyt and inparticular on sedimentary heterogeneity.

Confirmation of the relative significance of stress anisotropy onpermeability, can be gained from an assessment of the order ofmagnitude influence of such an effect on production. Usingrecognised productivity equations which directly incorporateboth kv and kh, the relative productivity of a horizontal (ascompared to a vertical) well can be calculated as a function ofhorizontal wellbore length. As wellbore length increases, ahorizontal well becomes more advantageous. Also, as the kv/khratio increases, the horizontal/vertical productivity ratioincreases. Thus the consequence of both vertical and horizontalpermeability-sensitivity to applied anisotropic stresses can begauged in terms of a projected horizontal wellbore lengthcalculated to achieve a certain productivity. The reservoirengineering concepts underlying such productivity evaluationare summarised below, followed by an appraisement ofpermeability results from the three reservoir sandstoneanalogues.

DiscussionWell Performance EvamThe potential benefit of drilling a horizontal well is bestevaluated through simple production analysis25~ 26, in whichthe performance of a horizontal well is compared to that of avertical well. The following comparison is applicable only tofully completed wells operating under steady-state conditions inthe absence of any skin effects.

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6 THE INFLUENCE OF STRESS ANISOTROPY ON HORIZONTAL WELL PERFORMANCE SPE28452PREDICTED VIA SPECIAL CORE ANALYSIS UNDER TRUE TRIAXIAL CONDITIONS

The steady state solution for radial flow into a vertical wellboreis easily derived from Darcys law, giving the familiarequation27:

0.007078khhAp% = p.131n(r~rw) ..... (1)

Whilst severa[ derivations are outlined in the literature tomedict the steadv state flow rate into a horizontal we112829~erhaps the mos~ rigorous is that proposed by Joshi30. In thisapproach the three-dimensional horizontal well problem isdivided into two, two-dimensional problems, the vertical andhorizontal flow components. The mathematical solutions toeach are subsequently summed in order to calculate thehorizontal well flow rate:

m 2)+(h / L)In[h / (2rw)]

where:

Routine reservoir engineering analysis normally considers thevertical permeability, kv, to be ~ l/10th the horizontalpermeability, kh, as the assumption of a very low kv, and hencea negligible vertical flow component, ensures that flow to thevertical wellbore is essentially radial, as required by Equation(l). However, the steady state solution of Equation (2) is onlyvalid for conditions of permeability isotropy, kv=kh. Forcomparative studies, it is therefore necessary to modifyEquation (2) to account for reservoir anisotropy, kv ?$ kh. Whhthe steady-state horizontal well solution of Equation (2)representing the sum of the vertical and horizontal flowsolutions, Joshi modified the vertical part of the steady-stateequation to include the effect of permeability anisotropy, bymultiplying the net pay thickness, h, by ~ = ~- andreplacing the permeability in the vertical plane by a geometricaverage permeability,

~kv.hThis modification is

recommerided by Joshi for a conservative production forecast.

The well productivity index, Pl, is defined as q/Ap, in oil fieldunits of STB/day-psi, therefore from Equation (1) and themodified Equation (2), the steady-state productivity ratio isgiven by26:

!!?!)!L= In(reh/rW)

P1)V m-()+(~h / L)In[~h / (2rw )]

B-Factorstress ~~nslt~ W. . .vUsing Equation (4) as defined above, the effect of evaluatingthe ~-factor under different degrees of stress anisotropy can beassessed in terms of variation in wellbore length to achieve arequired PI-ratio. For horizontal well lengths rubitrarily rangingfrom 200 to 2000ft, Equation (4) being defined in terms of oilfield units, corresponding PI-ratios have been calculated forvarious measured ~-values, using the following constants:

(i) h = 100ft (arbitrary value)(ii) rw = 0.354ft (for 8.5 recommended

bit and hole size)(iii) re = 1489ft (for North Sea average

drainage area of 160acres)

The various ~-factors (as calculated from kv and kh valuesmeasured under different stress states applied using the truetriaxial cell) are tabulated in Table 2. Seven ~-factors aredefined for each reservoir sandstone analogue, based ondifferent combinations of the three vertical and five horizontalmeasured permeabilities. Whh reference to Table 2, ~-factor Ireflects the assumption that the in situ horizontal stress field isuniform and equal to the minimum value, Ov>crH=csh, whilst ~-factor III reflects the same assumption of horizontal stressisotropy but of uniform magnitude equal to the maximumvalue, ov>r3h=rJH. only ~-factor II corresponds topermeabilities measured under realistic reservoir stresses,Cv>q-p%, as ~-factors IV to VII reflect various combinationsof permeability measurements made under conventionalaxisymmetric triaxial conditions. The range in ~-factormagnitude for the different lithologies, therefore wholly reflectsrelatively small magnitude changes in the stress field appliedduring permeability evaluation. From Table 2, ~-factors forClashach, Locharbriggs and Dalquhandy sandstones, asmeasured under true triaxial stress conditions, are 1.63, 4.53and 1.05 respectively. Percentage ~-factor variations withreference to those evaluated under true triaxial conditions are:Clashach sandstone -21 to +34%; Locharbriggs sandstone -20to +3%; Dalquhandy sandstone +5 to +34%.

From Equation (4) it is evident that the PI-ratio increases as Lincreases, h decreases and ~ decreases (or kv/kh increases). Fora given payzone, the key is vertical permeability, for if kv ishigh compared to kh, then potentially more hydrocarbons canreach the well, and the advantages of a horizontal wellborebecome overwhelming. In Figures 8-10 (Clashach,Locharbriggs and Dalquhandy sandstones respectively)calculated PI-ratios for 200ft horizontal wellbore lengthincrements and for the measured ~-factor ranges depicted inTable 2, are plotted against L. Interpolated curves for themaximum and minimum $vahres of each lithology are shownas full lines, whilst intermediate values are represented as finedots. Values calculated using ~-factors determined underrealistic reservoir true triaxial conditions are shown as crosses.

Assuming a PI-ratio of two as an arbitrary minimumrequirement26, it is apparent that the effect of evaluating coreplug permeabilities under a variety of different anisotropicapplied stresses, is to produce a span of horizontal wellborelengths required to achieve production viability. Formeasurements made under true triaxial conditions on Clashachspecimens, the required well length is some 530ft, with upper

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SPE 28452 B. R. CRAWFORD AND B. G. D. SMART 7

and lower limits due to testing under conventional triaxialstresses lying some 110ft either side. In the case ofLocharbriggs sandstone, with the true triaxial valueapproximately defining the upper wellbore length limit of some1170ft, simplifying the applied stress to axisymmetricconditions in order to evaluate kv and kh, lowers the requiredL-value by some 230 ft. Finally, for the Dalquhandy coreanalyses, the j3-factor measured under true triaxial appliedstress delineates a lower-bound horizontal wellbore length of370ft, with this time the assumption of uniform in situhorizontal stress resulting in an estimated increase of 100ft onthis value.

The above analysis indicates that the relative susceptibility ofcore plug permeability to the degree of applied stressanisotropy, can result in variations in the estimated horizontalwel[bore [ength required to meet desired productivity of up toseveral hundred feet. This effect would be multiplied forreservoir rocks with larger kv/kh ratios, and for greater PI-ratiominimum requirements.

ConclusionsPermeability studies have been conducted within a unique newtrue triaxial cell, on three reservoir sandstone analoguesshowing different degrees of sedimentary heterogeneity. Forthe first time, plug permeabilities are presented which weremeasured under azimuthally varying horizcntal stresses, asopposed to conventional triaxial uniform radial pressures.The ability to vary three independent stresses from an initiallyhydrostatic value, each by a maximum of 13,8MPa (2000psi)has a first order effect on measured absolute permeabilityvalues. Stress-sensitivity of core data is thus shown to besusceptible, not only to the magnitude of the applied stressfield, but also to the degree of anisotropy. For confidentextrapolation of core plug data to the reservoir environment,permeabilities must therefore be determined under as realistican in situ stress state as possible, The relative susceptibility ofplug permeability to changes in applied anisotropic stress isaffected by initial rock fabric. With increasing mean stress, anddependent on the degree of sedimentary heterogeneity,permeability variation can be non-systematic. Thus for arealistic comparison of stress-dependency with otheruncertainties in the reservoir description and evaluationprocedures, direct measurement under true triaxial stress, asopposed to extrapolation from different conventional triaxialmeasurements is ideally required.

Using a simple example to assess the effects of a generaltriaxial in situ stress field, that of a horizontal wellbore drilledparallel to the minimum principal stress, Oh, productivityrelative to that of a vertical well was calculated using ~-factors(-) measured under true triaxial as well as conventionaltriaxial stresses. For a productivity ratio of two, discrepanciesin the required horizontal wellbore length of up to severalhundred feet were calculated. Thus the influence of stressanisotropy is also evident in the prediction of well lengthsrequired to achieve desired performance levels. With the aid ofnumerical modelling to evaluate stress distributions, deviatedwellbores oblique to the principal stress axes could also beevaluated in the same manner. Likewise, the influence ofinduced welbore stresses and yield zone development could bestudied in the laboratory, under 3-D polyaxial stresses, in orderto quantify stress-induced skin factors.

Future work will concentrate on evaluating relativepermeabilities under true triaxial conditions, combined withperipheral microseismics. Active P- and orthogonal S-wavevelocity measurements plus passive acoustic emisionmonitoring will hopefully enable stress-induced permeabilitytransients to be related to various microstructural deformationprocesses. A recently fabricated Mark II true triaxial cell,capable of measuring orthogonal radial permeabilites on asingIe core plug, will also be commissioned. As well aspermeability measurement, the effects of stress anisotropy onacoustic propagation and electrical current flow will beinvestigated, in order to provide log calibration data obtainedunder realistic in situ stress conditions.

NomenclatureB:h:

k~kv:LP:

%:re:

refirw

P:Ap:

w(S1:02:rY3:CTa:

%:wql:

formation volume factor (RB/STB)reservoir thickness (ft)horizontal permeabilityvertical permeabilityhorizontal well length (ft)confining pressurevertical well oil flow rate (STB/D)drainage radius (ft)drainage radius of horizontal well (ft)wellbore radius (ft)wpressure drop from drainage radius towellbore (psi)viscosity (cp)maximum principal stressintermediate principal stressminimum principal stressaxial stressminimum horizontal stressmaximum horizontal stressoverburden stress

AcknowledgementsThe authors gratefully acknowledge the Petroleum Science andTechnology Institute for their continued funding of thisresearch, constituting part of a project investigating, TheInfluence of Pore Fluid Chemistry and Stress State OnReservoir Permeability. The expertise of D. McLaughlin isalso acknowledged for fabricating the prototype cell,implementing design improvements and ,assisting with theexperiments detailed here.

S1 Metric Conversion Factorslbf/in.2 (psi) X 6.894757 E + 03 = Pa

References1. Briggs, P., Corrigan, A., Fetkovich, M., Gouillard,

M,, Lo, T., Paulsson, B., Saleri, N., Warrender, J. & Weber, K.1992. Trends in reservoir management. Oiljield Review pp.8-24.

2. Ringrose, P., Sorbic, K., Corbett, P. & Jensen, J.1993. Immiscible flow behaviour in laminated and cross-bedded sandstones. JPSE 9(2) pp. 103-124.

3. Corbett, P., Ringrose, P., Jensen, J. & Sorbic, K.1992. Laminated clastic reservoirs - the interplay of capillarypressure and sedimentary architecture. SPE24699, Ann. Tech.Conf. Washington pp.365-376.

929

.*

8 THE INFLUENCE OF STRESS ANISOTROPY ON HORIZONTAL WELL PERFORMANCE SPE28452PREDICTED VIA SPECIAL CORE ANALYSIS UNDER TRUE TRIAXIAL CONDITIONS

4. Corbett, P., & Jensen, J. 1993. An application ofprobe permeametry to predictions of two-phase flowperformance (Lower Brent Group, North Sea). Marine & Pet.Geol. 10(4) pp.335-346.

5. Jones, S. 1992. The profile permeameter - a new,fast, accurate minipermeameter. SPE24757t Ann. Tech. Conf.Washington.

6. Jones, S. 1988. Two-point determinations ofpermeability and PV vs. net confining stress. SPE FormationEvaluation pp.235-241.

7. Harper, T. & Szymanski, J. 1991. The nature anddetermination of stress in the accessible lithosphere. In,Tectonic Stress In the Lithosphere. Proceedings of a RoyalSociety discussion meeting held on 10 and 11 April 1991.Whitmarsh, P., Bott, M., Fairhead, J. & Kusznir, N. (eds,) pp.5-24 The Royal Society. London.

8. Economies, C., Ebbs, D. & Meehan, D. 1990,Factoring anisotropy into well design. Oilfield Review 2(4)pp.24-33.

9. Hudson, J. & Cooling, C. 1988. In situ rock stressesand their measurement in the U.K. - Part I. The current state ofknowledge. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.25(6) pp.363-370.

10. Hast, N. 1967. The state of stresses in the upper partof the earths crust. Eng. Geol. 2(1) pp.5- 17.

11. Brown, E. & Hock, E. Trends in relationshipsbetween measured in situ stresses and depth. Int. J. Rock Mech.Min. Sci. & Geomech. Abstr. 15pp.211 -215.

12. Goodman, R. 1989. Introduction to Rock Mechanics.(2nd. Edn.) John Wiley& Sons. N.Y. 562pages.

13. Skopec, R. 1991. In-situ stress evaluation in coreanalysis. SCA9103, 5th. Ann. Tech. Conf. Dallas.

14. Holt, R. 1990. Permeability reduction induced by anonhydrostatic stress field. SPE Formation Evaluation pp.444-448.

15. Kilmer, N., Morrow, N. & Pitman, J. 1987. Pressuresensitivity of low permeability sandstones. JPSE 1 pp.65-81.

16. Yale, D. 1984. Network Modelling of Flow, Storageand Deformation In Porous Rocks. Ph.D dissertation, StanfordU., Stanford.

17. Hock, E. & Franklin, J. 1968. A simple triaxial cellfor field and laboratory testing of rock. Trans. Inst. Min. Metall.77(A) pp.22-26.

18. Franklin, J. & Hock, E. 1970. Developments intriaxial testing equipment. Rock Mechanics 2 pp.223-228.

19. Hojem, J. & Cook, N. 1968. The design andconstruction of a triaxial and polyaxial cell for testing rockspecimens. South African Mech. Engr. 18 pp.57-61.

20. Gau, Q., Cheng, H. & Zhuo, D. 1983. The strength,deformation and rupture characteristics of red sandstone underpolyaxial compression. Proc. 5th. Int. Cong. Rock Mech.Melbourne, Australia, VOI.A, pp. 157-160.

21. Esaki, T. & Kimura, T. 1989. Mechanical behaviourof rocks under generalised high stress conditions. In, Rock atGreat Depth. Maury, V. & Fourmaintraux, D. (eds.) Balkema,Rotterdam. Vol. 1 pp. 123-130.

22. Smart, B. & Crawford, B. 1993. An innovative newcell for testing rock core under true triaxial stress states.SCA9320, 7th. Ann. Tech. Conf. Houston.

23. Main, I., Smart, B., Shimmield, G., Elphick, S.,Crawford, B., & Ngwenya, B. 1992. The effect of combinedchanges in pore fluid chemistry and stress state on reservoir

analogues. 3rd. Int. Confi On North Sea Oil and GasReservoirs. 25. pp.357-370. Trondheim, Norway.

24. Pearson, C., Bond, A., Eck, M. & Schmidt, J. 1992.Results of stress-orientated and aligned perforating in fractureddeviated wells. JPZ 44(1) pp. 10-18.

25, Joshi, S. 1991. Horizontal Well Technology.PennyWell Books, Tulsa. 535pages.

26. Milne, A. 1991, Horizontal Well Completion andStimulation Technology. Dowell Schlumberger, U.S.A.

27. Archer, J. & Wail, C. 1986. Petroleum EngineeringPrinciples and Practice. Graham & Trotman, London,362pages.

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SPE 28452 B.R. CRAWFORD AND B.G.D. SMART

Table 1

Geological and mineralogicaldetails of the three reservoir sandstoneanaloguesused in this study.

9

Reservoir Source Porosity *S@stone Lwdity Age

Permeability**Litbology Mineralogy (%) (mD)

Anedogne

pale-fawn, sub-romrdrd quartzcommercial medium-coame (89%),

%ggrained, fresh-attered

CLASHACH Permo-Triassic well-sorted K-/eJ;;yar 13.9 142Scotland subarkosic

arcnite secondaryquartzovergrowths

sub-rounded-commercial red, roundedquartz

qoany, medium-coarse (83%);OCHARBRIGGS Dumfries, Permian grrdned, feldspar(16%) 22.2 268

Scotland sandstone haematitecoatinggrainsas cement

(l%)

sub-angularopencast quartz(71%)colliery, heterolitbic, K-feldspar(3%)

DALQUIL4NDY Coa[bum, Carboniferous tine-grained, Kaolinite(2%) 13.2 4Scotland sandstone pore-filling

Siderite(5%)Dolomite(Ig%)

* from Helium Boyles lawporosimeter.** klinkenbergfromNitrogenp ermeameter.

Table 2

Effect of the ambient stress field on core plug permeability, as reflected in kv/kh-ratios and b-values (see text for details).

kv/kh StreSS stress state approx.n: CLASHACH LOCHARBRIGGS: DALQUHANDY:onflgurations k, kh kvikh I P

A~(%)* kv/kh I P 1A~(%) * kv/kh I P A~(%) *

I m .38 1.63 0 .07 3.82 -16 .50 1.41CASE2+34

6H-h CTr+=q

II M .38 1.63 0 .05 4.53 0 .90 1.05 0CASE3 OV>Cr.r>UhOV>G@Sh

III = .48~h=~

1.45 -11 .05 4.41 -3 .54 1,36Crb=GH

+30

Iv - .24 2.04 +25 .07 3,88 -14 ,58~r.r=~h

1.31cf=~h

+25

vW .53CASES

1.38 -15 .05 4,35 -4 .82 1.10 +5Gh=GH Uh=rr

VI a .21 2.18 +34 .05 4.67 +3~h=CrH

.74 1.16 +10CASE1 Ov=Oh

VII = .60 1.29 -21 .08 3.62 -20 .65 1.24 +1sCASES oH=Gh ~h=~v

* Percentage difference in j3-values compared with that measured under a realistic true triaxial stress state.

931

.THE INFLUENCEOF STRESS ANISOTROPYON HORIZONTALWELL PERFORMANCEPREDICTEDVIA SPECIAL CORE ANALYSISUNDERTRUE TRIAXIALCONDITIONS

932

SPE 28452

*SPE 28452 B.R. CRAWFORD AND B.G.D. SMART

Stress Configurations On Vertical Core Plug for kV Determinations:

6000 6000 6000

4ooo&4000 4000$5000 5ooo&5000

CASE 1 CASE 2 CASE 3Axisymmetricapproximation True triaxialstressstate Axisysmnetric approximation

OH= Oh= 4000pSi 3v>0H>Oh oh= OH= 5000psiOH compromised rerdistic of in situ field ah compromised

Stress Configurations On Horizontal Core Plug for kh Determinations:

4000

G+!&

Axisymmetric approximationCASE 1 ~v = oh =bo(x)psi

. 5000 CSvcompromised4000

6000

&

True triaxial approximation ofIateral stress equivalency

4000CASE 2 OH= q = 4000psi

~H compromised4000

6000

&

True triaxial stressstate CASE 3 Dv>GH>Crh. 5000 realistic of in situ field

4000 6000

&

True triaxial approximation oflateral stress equivalency

5000 CASE 4 ah= OH= 5000@oh compromised

5000 6000

G&&

Axisymmetric approximation

CASE 5 oh= rsv= 6000psi5000

~h compromised6000

. ..- -..-. . . . -.. . .

11

I

Figure 4 Various tar-tield stress combinations applled to core plugs m truetriaxial cell (see text for details).

933

12 THE INFLUENCEOF STRESS ANISOTROPYON HORIZONTALWELL PERFORMANCEPREDICTED VIA SPECIAL CORE ANALYSISUNDERTRUE TRIAXIALCONDITIONS

*

\

SPE 28452

:~2s 30 35 40 4Mean Stress (MPa)

445

Figure 5 Permeability versus mean stress profiles for Clashach core plug pair

20

~ v

o

25 30 35 40

Mean Stress (MPa)Figure 6 Permeability versus mean stress profiles for Locharbriggs core plug pair

:~30 35 40 45

Mean Stress (MPa)Figure 7 Permeability versus mean stress profiles for Dalquhandy core plug pair

934

v.,

SPE 28452 B.R. CRAWFORDAND B.G.D. SMART

6,

,0-

3

I IIII04 1 I I

0 400 8C4 1200 1600 2000

HorizontalWell Length (ft)Figure 8 Effects of anisotropic stress on PI ratios for Clashach reservoir sandstone analogue

Figure 9

is

Effects of

3-

2- -

1 -

IIIIII11

00 400 800 1204 1600 2(

HorizontalWell Length (ft)

)0

anisotropic stress on PI ratios for Locharbtiggs reservoir

6.0-

S.o -

4.0-

3.0 -

2.0 -- ------- --------- ---------- ---------- . . . . . . . . .

1.0 -IIIIII

0.00 400 800 1200 1600 2000

13

sandstone analogue

HorizontalWell Length (ft)

Figure 10 Effects of anisotropic stress on PI ratios for Dalquhandy reservoir sandstone analogue

935