Annular Material Research Articles

Evaluation of the controlling effect of new annulus materials on casing deformation in shale gas wells

Shale gas horizontal wells have severe problems of casing deformation and failure due to formation displacement during fracturing. Statistics show that casing deformation problems occur frequently in the development of shale gas, especially in Sichuan Basin. Furthermore, the phenomenon of formation extrusion and fault slip is serious, which has caused great obstacles to the development of shale gas in China. In view of the current lack of casing deformation control methods, a finite element model of a wellbore under formation displacement load is established in this paper. The stress and deformation of the casing are simulated, and the mitigating effects of new annular materials such as a modified cement sheath and rubber are evaluated. Results indicate that the formation extrusion and fault slip can cause radial oval deformation and axial S-shaped deformation of the production casing, respectively. The use of a modified cement sheath can provide a little mitigating effect on casing deformation. Meanwhile, using rubber cementing can play a strong protective role for the production casing and avoid casing deformation to a certain extent. This research can provide a new way and important reference for the prevention and control of casing deformation in shale gas wells.

Investigation on the microstructure and mechanical property of friction stir lap welded acrylonitrile butadiene styrene/polycarbonate produced by double-pin tool

Friction stir lap welding (FSLW) of dissimilar acrylonitrile butadiene styrene (ABS) and polycarbonate (PC) was conducted using a double-pin tool. The formation process of the weld and the influences of rotational speed on the microstructure and mechanical property were investigated. It was found that the weld was generated accompanying with the closure of old cavities in the front of the pins and the simultaneous regeneration of new cavities in the rear of the pins. Annular material flow on the vertical and horizontal directions occurred during FSLW. With the increase of the rotational speed, the PC anchors resulted from the upflow of plasticized PC layer and the shoulder affected zone both enlarged. Microstructure analysis of the weld nugget showed that PC was fragmented into lamellar, columnar, and spherical particles and their dimensions decreased when rotational speed increased. Lap-shear tensile tests showed that the weld strength increased with higher rotational speed and the maximum strength of the weld produced under 800 r/min reached 19.38 MPa, which was comparable to the ABS/PC welds produced by a tapered pin under the optimal parameters. Through the further optimization of such FSLW process, it was potential to join dissimilar polymeric components in future industrial manufacturing field.

Behavior of hybrid FRP-concrete-steel double-skin tubular beams with ultra-high strength concrete and PBL shear connectors under bending

Hybrid double-skin tubular beams (DSTBs) with the external fiber-reinforced polymer (FRP) tube-annular concrete-inner steel tube configuration have excellent mechanical performance and corrosion resistance, but are prone to slip problems. In this study, perfobond shear connectors (PBLs) are proposed to reduce the slip between infilled concrete and inner steel tube. Moreover, using ultra-high strength concrete (UHSC) as the annular material could further improve the structural performance and magnify the lightweight merit of hybrid DSTBs, while hybrid DSTBs with PBLs and UHSC have not been investigated yet. To this end, three-point bending experiments were conducted to hybrid DSTBs with PBLs and UHSC to study the flexural behavior. The mid-span load–deflection curves revealed a three-branched behavior: (i) a first linear ascending branch up to the first yielding at the extreme tension fiber of inner steel tube; (ii) a transition branch to the peak load with a significant slope deterioration when infilled concrete in the compression side reached the unconfined failure strain; (iii) a post-peak residual branch characterized by progressive load reductions over a number of load plateaus. The adoption of UHSC could significantly delay the plastic hinge formation in inner steel tube, and meanwhile improve the bond with PBLs. Thus, the slips between infilled concrete and inner steel tube were minimal (less than 0.2 mm) for most of the specimens, except for those with foamy sheet insertions between PBLs (at around 1 mm). In the end, the design loads of the hybrid DSTBs were predicted by a sectional analysis with high level of accuracy (average error at 6%).

A RARE CASE OF A 27-YEAR-OLD FEMALE PRESENTED WITH DUODENAL OBSTRUCTION DUE TO ANNULAR PANCREAS

Background. Annular pancreas is a rare congenital abnormality characterized by a ring of pancreatic tissue surrounding the descending portion of the duodenum. It is thought to originate from the incomplete rotation of the ventral pancreatic bud. Objective. To present a case description of a 27-year-old female with duodenal obstruction due to annular pancreas Material and methods. The clinical manifestations, laboratory and instrumental findings of a female patient. Results. We report the case of a 27-year-old female with 3 months history of upper abdominal pain, nausea, postprandial fullness, and recurrent vomiting. Physical examination revealed nothing except for the thin-built body. Routine biochemical and hematological investigations were within normal limits. The patient's standing direct abdominal graphy revealed air-fluid level and dilated both stomach and the first part of duodenum. Upper gastrointestinal series showed circumferential extrinsic compression on the 2nd portion of the duodenum. Abdominal computerized tomography (CT) and ultrasonography (USG) revealed a ring of pancreatic tissue encircling the second part of the duodenum. We present the clinical presentation, treatment plan which is performed through a duodenojejunostomy bypass procedure, and follow-up of the patient. Conclusions. Annular pancreas is associated with duodenal atresia. It usually appears in infancy but might become clinically evident in adulthood with obstruction of the duodenum. The symptoms include constipation, nausea, and vomiting. and usually arise due to obstruction to gastric emptying. In order to confirm the presence of annular pancreas, abdominal CT scans with high resolution and angiography protocols as well as magnetic resonance imaging are helpful.

Ultrasonic Measurements Evaluate and Qualify Annular Creep Barriers

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 208782, “Annular Creep Barrier Evaluation and Qualification Using Ultrasonic Measurements,” by Eric van Oort, SPE, The University of Texas at Austin, and Akshay Thombare, SPE, and Munir Aldin, SPE, Metarock Laboratories, et al. The paper has not been peer reviewed. Creep barriers can simplify well abandonments, particularly in high-cost offshore environments. Evaluation and qualification of creep barriers in the field, however, have proven challenging and labor-intensive when casing is perforated and annular rock material is pressure-tested to verify its sealing ability. This work seeks to eliminate the need for pressure testing by allowing the barrier to be qualified using only cased-hole log measurements. Creep Barrier Formation and Stimulation Plastically deforming shale and salt or evaporite formations under certain conditions can move into uncemented or poorly cemented annular spaces, filling them and contacting the casing to form an effective pressure-tight barrier. Supporting evidence overwhelmingly points toward creep as the fundamental rock-mechanical mechanism behind this type of barrier formation. Creep barriers have, in fact, become commonplace considerations in the plugging and abandonment of offshore wells in the UK and the Norwegian sectors of the North Sea, leading to simplified and more-cost-effective rigless offshore well-plugging operations. The latter is accomplished by eliminating the need for casing cutting and pulling or casing milling followed by setting openhole abandonment plugs. Materials that present alternatives to ordinary Portland cement (OPC) for well plugging-and-abandonment barrier construction include the use of shale or salt as a barrier (SAAB). Comparison of category scores for SAAB with other materials reveals that SAAB offers a well-rounded performance envelope with no weaknesses in any categories, whereas the other materials, including cement, show weaknesses in one or more categories. A main advantage of SAAB is that it offers the ability to “replace” the caprock, the desired goal in most well abandonments. Moreover, for many materials including OPC, long-term (i.e., hundreds or thousands of years and beyond) sealing performance is unknown for well abandonment. The only category in which SAAB technology appears to lag is in its technology readiness level score. This, then, provides motivation for further research.

Characterization of Annular Cement Permeability of a Logged Well Section Using Pressure–Pulse Decay Measurements

Abstract The cement behind casings is an important barrier element in wells that should provide zonal isolation along the well. The hardened cement does not always isolate permeable formations, either due to placement issues or loads that over time compromise the integrity of the barrier. The modern method used to characterize the annular material is ultrasonic logging which provides essential information concerning the type of material behind casing, but no measurement of the annular permeability. This study provides permeability characterization of a casing-cement sandwich joint retrieved from a 33 years old production well that has been logged at surface using a state-of-the-art ultrasonic tool. The joint contains an interval of low-permeable cement that previously has prevented permeability measurement by gas injection. A pressure–pulse decay test method has now been performed that is based on monitoring the evolution of a pressure pulse through the joint. Long-term pressure measurements show communication through the entire joint and are in qualitative agreement with the log. A pressure diffusion model is used to estimate local permeability along the joint, enabling comparison of log response and permeability. The low-permeable region is relatively short, situated directly on top of a casing collar, and has permeability that is orders of magnitude lower than the cement above and below. In the longer term, results from this and related studies can be used as input for future sustained casing pressure evaluations or for quantifying seepage risk behind casings for abandonment designs.

Identification of Breakout Behind Casing: Methodology to Obtain Openhole-Equivalent Caliper Measurements Through Slotted Liner Using the Density Tool

Growth in the coal seam gas industry in Queensland, Australia, has been rapid over the past 15 years, with greater than USD 70 billion invested in three liquified natural gas export projects supplied by produced coal seam gas. Annual production is of the order of 40 Bscm or 1,500 PJ, with approximately 80% of this coming from the Jurassic Walloon Coal Measures of the Surat Basin and 20% from the Permian Coal Measures of the Bowen Basin. The Walloon Coal Measures are characterized by multiple thin coal seams making up approximately 10% of the total thickness of the unit. A typical well intersects 10 to 20 m of net coal over a 200- to 300-m interval, interbedded with lithic-rich sandstones, siltstones, and carbonaceous mudstones. The presence of such a significant section of lithic interburden within the primary production section has led to a somewhat unusual completion strategy. To maximize connection to the gas-bearing coals, uncemented slotted liners are used; however, this leaves fluid-sensitive interburden exposed to drilling, completion, and produced formation fluids over the life of a well. External swellable packers and blank joints are therefore used to isolate larger intervals of interburden and hence minimize fines production. Despite these efforts, significant fines production still occurs, which leads to the failure of artificial lift systems and the need for expensive workovers or lost wells. Fines production has major economic implications, with anecdotal reports suggesting up to 40% of progressive cavity pump artificial lift systems in Walloon Coal Measures producers may be down at any one time. The first step in solving this problem is to identify the extent and distribution of fines production. The wellbore completion strategy above, however, precludes the use of mechanical calipers to identify fines-production-related wellbore enlargement. A new caliper-behind-liner technique has therefore been developed using a multiple-detector density tool. Data from the shorter-spacing detectors are used to characterize the properties of the liner as well as the density of the annular material. This is particularly important to evaluate as the annulus fill varies between gas, formation water, drilling and completion fluids, and accumulated fines. The longer-spacing detector measurements are then used in conjunction with pre-existing openhole formation density measurements to determine the thickness of the annulus, and hence hole size, compensating for liner and annulus properties.

Mechanics of adhesives under annular confinement: internal pressure, force, and interfacial area.

Closed annular adhesive interfaces are commonly found in nature as well as in many existing and developing technologies. Such contacts provide enhanced control of interfacial history by prescribing whether interfacial separation occurs at the outer or inner edge, and whether internal pressure affects the required force for separation. To facilitate the development of technologies involving annular contacts, we have experimentally measured the relationship between applied displacement, resulting force and internal pressure, and annular interface dimensions for the contact between a rigid annular probe and an adhesive layer with finite thickness. Experiments were validated by finite element analysis models, which were used to develop semi-empirical analytical relationships for the changes in contact compliance as a function of material properties and geometric constraints. Additionally, the change in internal pressure was modeled as a function of annular contact dimensions and adhesive layer material properties. This model predicts the critical volume where internal pressure changes alters critical force for separating an annular contact interface. The results discussed here provide a foundation for new experimental protocols for characterizing soft materials, including pressure-sensitive adhesives, as well as guidelines for designing annular interfacial materials with controlled separation histories.

FEM-based evaluation of friction and initial imperfections effects on sandwich pipes local buckling

Sandwich pipes have been studied as one option to overcome the high pressure problems in deep and ultra-deep waters. They have become a possible alternative solution for submarine infrastructure due to its thermal insulation capacity. This contribute to preventing the pipeline from clogging due to the difference in temperature between reservoir fluids and water at the bottom of the sea. The pipelines in ultra-deepwater are continually exposed to severe operating conditions, such as the effect of high levels of external pressure that can cause local deformation or even collapse of the pipe. Thus, a greater understanding of the mechanical behavior of sandwich pipes is required. This paper presents a FEM-based evaluation of friction and initial imperfection effects on sandwich pipes local buckling. The non-linear evaluation was carried out in FEM of local buckling of two sandwich pipes, with polypropylene and cement as filled annular material. The influence of initial imperfections and the degree of friction, between the annular material and the steel pipes, as well as geometric variations of the pipe were considered. The numerical simulations results indicate a capacity to withstand ultra-deep waters collapsing pressures, around 3000 m, either for polypropylene or cement filled annular material model. In addition, the results indicate that the collapse pressure is inversely proportional to the increase in annular thickness and directly proportional to the decrease in friction which have an impact and contribution on the carrying capacity of the sandwich pipe. Further research will consider a design of experiments analysis of reported effects for different diameter-to-thickness ratios.

Mapping of ultrasonic Lamb-wave field in elastic, layered structures using acoustic and laser probes

In the oil and gas industry, the nondestructive evaluation of cemented steel pipes in subterranean wells commonly involves the use of ultrasonic, guided Lamb waves. These measurements help ensure that the cement annulus between the rock formation and the steel pipes provide hydraulic isolation between different depth zones of the well. Such techniques employ the excitation of leaky flexural and extensional waves inside the highly contrasting steel layer to distinguish solids from liquids in the inaccessible region outside the pipe. Furthermore, the annular cement layer may exhibit defects such as cracks or channels which may compromise zonal isolation. We present laboratory measurements using piezo-electric needle probes and laser interferometry, as well as comparative modeling results along spatial and temporal dimensions to visualize and quantify leaky-Lamb-wave propagation for a variety of homogeneous liquid and solid layers behind a steel sheet in planar and cylindrical geometries. We characterize several annular materials with compressional velocities, which are higher or lower than the Lamb phase speed to demonstrate the effect on mode dispersion and attenuation. Furthermore, we study the effects on transmission and reflection of Lamb waves at discontinuities such as conduits in the inaccessible layer.

Visualization of Leaky Ultrasonic Lamb Wave Experiments in Multilayer Structures

Leaky ultrasonic Lamb waves propagating in liquid-filled steel pipes are widely used by the oilfield service industry in wellbores to measure the acoustic properties of the material located outside the pipe. Typically, the annular region between the steel pipe and the geological formation is cemented to provide mechanical integrity and to ensure hydraulic isolation between different geological layers in the well. We present results from an experimental study along spatial and temporal dimensions to visualize the propagating waveforms of such measurements for liquid or solid annular materialsbehind the steel pipe. Our measurements focus on the lowest-order flexural waves. These radiate energy into neighboring layers if the flexural phase speed is supersonic with respect to the bulk compressional- or shear-wave phase speeds of the adjacent media. In the case of a compressional phase speed higher than the flexural phase speed, the resulting flexural mode attenuation is then strongly reduced. Several annular materials with compressional velocities higher and lower than the flexural phase speed were investigated to demonstrate this effect. Finally, the propagation of compact flexural-wave packets along the steel pipe was recorded, and the results were compared with computed modal dispersion and attenuation curves.

Collapse of sandwich pipes with PVA fiber reinforced cementitious composites core under external pressure

Sandwich pipes (SP) with steel tubes and a lightweight flexible core are under consideration as a potential solution for ultra-deepwater submarine pipelines, combining high structural resistance with thermal insulation. Besides polymeric materials, strain hardening cementitious composites (SHCC) reinforced with polyvinyl alcohol (PVA) fibers, a micromechanically designed material with high tensile ductility, can be an option for the annular material. The purpose of this work was to investigate experimentally and numerically the collapse behavior of SP filled with SHCC under external hydrostatic pressure. The preparation procedure for SHCC and the fabrication process for SP were presented in detail. The full-scale laboratorial tests of SP were performed using a hyperbaric chamber to analyze the collapse pressure subjected to external pressure. The mechanical behavior of SHCC was simulated using a concrete damaged plasticity (CDP) model provided by the commercial finite element package ABAQUS, whose parameters were estimated by tension and compression tests. In addition, a systematic parametric study was performed to analyze the effects of ovality, thickness and outer/inner radius ratio on the collapse pressure of SP with SHCC core.

Transcatheter prosthetic paravalvular leak closure

Summary Paravalvular leak affects up to 27% of all prosthetic heart valves implanted by conventional surgery. Patients with paravalvular regurgitation can be asymptomatic or may present with symptoms of congestive heart failure and/or haemolytic anaemia. Assessment and quantification of these paravalvular leaks are difficult since transthoracic colour flow Doppler images may be obscured by annular calcifications and prosthetic material. Surgical re-intervention is the conventional treatment of choice for severe cases but is associated with significant morbidity and mortality, and is not always successful because of underlying tissue fragility. Over the last decade, transcatheter treatment of paravalvular leaks has emerged as an attractive alternative to surgery for high-risk patients and is now favoured as the initial approach in some experienced centres. Transcatheter repair is technically feasible in 60 to 90% of cases according to different published series. Technical success is associated with clinical improvement in 50 to 90% of the cases.

Ultimate strength behaviour of sandwich pipes filled with steel fiber reinforced concrete

Sandwich pipes (SP) can be an effective solution for the ultra-deepwater submarine pipeline, combining high structural resistance with thermal insulation capability. Besides polymer, steel fiber reinforced concrete (SFRC) can be an another choice for the annular material, based on the characteristics of high fracture toughness and good adhesion with metal. The purpose of this work was to investigate numerically the ultimate strength of SP filled with SFRC under external pressure and longitudinal bending. The mechanical behaviour of SFRC was simulated using a Concrete Damaged Plasticity (CDP) model whose parameters were estimated by uniaxial tension, compression and four-point bending tests. The applicability of the parameters obtained was verified by simulating the compression and four-point bending tests, where the results showed good correlation between measured and predicted numerical values. Pressure–curvature ultimate strength for SP with perfect adhesion and no adhesion interface condition was obtained. Besides, a parametric study was performed to investigate the effect of the thickness of each layer on the pressure–curvature collapse envelope of SP. It was found that the adhesion between layers and the lateral confinement effect on SFRC play a dominant role in the ultimate strength behaviour of SP, which lead to the non-monotonicity of the collapse envelope.

Effect of contact area variation on squeal propensity of disc modes

The squeal propensity associated with the contact area variation is studied using the finite element method and the analytical contact and rotating modeling. The disc brake system is modeled as a rotating finite element disc in contact with annular sector-friction material. The squeal propensity is numerically determined with respect to the contact span angle and the radial contact length which define the contact geometry. The results show that the squeal propensity is strongly influenced by the contact area variation. Particularly, the squeal propensity of the transverse doublet mode changes periodically with the variation of the contact span angle. However, the in-plane dominant modes have the decreased squeal tendency as the span angle increases. The variation in the radial contact length is also shown to make contribution to the change in squeal propensity for both the transverse and in-plane modes.

Dynamic surface characteristics during disc brake squeal: non-linear modelling and simulation

This article studies the non-linear dynamic behaviour of a disc brake system during squealing induced by a disc doublet mode. The disc brake system is modelled as a rotating annular plate in contact with annular sector-friction material. In order to investigate the possibility of detachment over the contact area between the disc surface and friction material during squealing, the lift-off condition is applied to this model. Also, the non-linearity arising from the contact stiffness is considered on the basis of the load–deflection test for the friction material. Numerical results show that the vibration after the onset of squeal reaches the limit cycle. In the steady-squealing response, several interesting phenomena are observed: the stick-slip and lift-off over the specific regime of the contact area. It is shown that the dynamic surface pattern rotates due to the forward travelling wave of the squealing surface. However, the mark of the surface pattern does not seem to move because the speed of the travelling wave fluctuates at a double frequency of squeal vibration.

Supercontinuum optical vortex pulse generation without spatial or topological-charge dispersion

A new achromatic method to generate the optical vortex was proposed and supercontinuum optical vortex generation ranging approximately 500 to approximately 800 nm was experimentally demonstrated without spatial nor topological-charge dispersions. In addition, polarization evolution in our system using Jones vectors and matrices was discussed and the condition of the polarizer to transfer polarizations was elucidated. This method is useful for the application to time-resolved nonlinear spectroscopy utilizing ultrabroadband optical vortex pulses in topological materials such as ring-shaped crystals or annular materials.

Determining Long-Term CO2-Containment Performance: Cement Evaluation

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 115707, "Assessing Long-Term CO2-Containment Performance: Cement Evaluation in Otway CRC-1," by Matteo Loizzo, SPE, and Sandeep Sharma, SPE, Schlumberger Carbon Services, originally prepared for the 2008 SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, 20-22 October. The paper has not been peer reviewed. The full-length paper focuses on an in-depth evaluation of the annular material on the Otway CRC-1 well that is being used to inject CO2 in the CO2CRC pilot geological-storage project. The evaluation will draw on the design and job data, and on a detailed analysis of the high-resolution 3D cement-imaging log, to characterize the cement and ensure the long-term risk of containment breach is minimized. Introduction Cement slurries are exposed to a number of phenomena during mixing and placement that can lead to set-cement properties that are very different from their design value. Density-control problems (both for continuous and batch mixing), contamination, channeling, and fluid loss can and do cause slurry dilution/concentration and chemical incompatibility, which in turn can have a major negative effect on the capacity of cement to guarantee hydraulic isolation. Currently it is debated if 10 m or more of competent cement, well bonded to casing and formation, would degrade during the expected isolation time frame for CO2-geological-sequestration wells (thousands to 10 thousand years). This is because competent cement, although reactive if exposed to CO2, has a very low permeability on the order of 0.5 to 5 µd. This low permeability means that most CO2 will travel by diffusion, a very slow process over the length scale of a meter. Cement with a high water/cement ratio, however, could have a much higher permeability, less resistance to CO2 aggression, and more-frequent defects related to slurry settling. Defects such as liquid channels in cement can provide direct pathways for CO2 leaks that could not be healed by calcite precipitation during the CO2 attack. Some of these phenomena can be predicted, but cannot be controlled easily; others (such as fluid loss) can hardly be predicted at all. In any case, they belong to the class of fault-free risk, sometimes called residual risk: events causing substandard system performance that cannot be engineered away and that may happen even when the job is executed well. Mitigation measures must be adopted in this case to ensure a robust design. This is especially true for wells entering CO2-storage reservoirs, where storage containment is a key performance factor and CO2/cement reactions may cause leaks to grow over time. The full-length paper studies a well recently completed in Australia for CO2 injection, and identifies how fluid loss, contamination, and channeling affected the petrophysical properties (i.e., density, porosity, and permeability) of set cement. Background The Cooperative Research Centre for Greenhouse Gas Technologies is a joint venture engaged in research on carbon capture and storage, a proposed technology that captures CO2 from fossil-fuel power-plant effluents and injects it into geological formations for permanent storage.

Glycation increases human annulus fibrosus stiffness in both experimental measurements and theoretical predictions

One of the primary age-related changes to collagenous tissues is the increased concentration of advanced glycation endproducts (AGEs). Although AGEs have been shown to increase the mechanical stiffness of many tissues, their influence on the mechanical properties of the annulus fibrosus has not been measured experimentally. In previous theoretical work, we hypothesized that the mechanical influence of AGEs on the annulus could be represented in an additive strain energy function with a separate crosslinking term, but the material coefficients associated with this term were not correlated with AGE concentration. In the current study, we measured the tensile stress–strain response of the human annulus in the axial direction both before and after glycation with methylglyoxal. Using nonlinear regression, the strain energy function was simultaneously applied to these new data and to data from a wide range of experimental protocols reported in the literature to determine values for the material coefficients appearing in the constitutive equation. Nonenzymatic collagen crosslinking induced a statistically significant change in annular material properties. Furthermore, the concentration of AGEs correlated positively with the material coefficients found in the terms of the strain energy function that we associate with collagen crosslinking. These data suggest that AGEs contribute to age-related disc stiffening as well as validate the hypothesis that biochemical constituents can be related mathematically to tissue behavior. In the future, this structurally guided constitutive relationship may provide further insight into the structure–function relationships of the annulus fibrosus.

Biaxial Testing of Human Annulus Fibrosus and Its Implications for a Constitutive Formulation

Internal pressure in the healthy human annulus fibrosus leads to multiaxial stress in vivo, yet uniaxial tests have been used exclusively to characterize its in vitro mechanical response and to determine its elastic strain energy function (W). We expected that biaxial tension tests would provide unique and necessary data for characterizing the annular material response, and thereby, for determining W. We performed uniaxial and biaxial tests on specimens of annulus, then developed an objective methodology for defining an appropriate form for W that considers data from multiple experiments simultaneously and allows the data to dictate more directly the form and the number of parameters needed. We found that the stresses attained in the biaxial tests were higher, while the strains were considerably lower, than those observed in the uniaxial tests. A comparison of strain energy functions determined from the different data sets demonstrated that constitutive models derived from uniaxial data could not predict annulus behavior in biaxial tension and vice versa. Since the annulus is in a state of multaxial stress in vivo, we conclude that uniaxial tests alone are insufficient to prescribe a physiologically relevant W for this tissue.