Optimizing Reformer Tube Life by Employing a Realistic Condition-Based Methodology

Optimizing Reformer Tube Life by Employing a Realistic Condition-Based Methodology

Authors:

B. E. SHANNON, IESCO, Inc. 3445 Kashiwa Street, Torrance, CA 90505, USA
C. E. JASKE, CC Technologies, 5777 Frantz Road, Dublin, OH 43017, USA

This paper was first published at the Nitrogen conference, Vienna, Austria in March 2006

Centrifugally-cast materials, namely HK40, HP Modified, and micro-alloy materials, are used world wide for tube materials in steam reformer furnaces.  These materials undergo various stresses resulting in damage which can manifest itself in several ways. The quantification of damage is of vital importance if furnace life is to be predicted accurately.  A comprehensive inspection technology has been developed to assess the exact degree of damage.  The ‘H’ SCAN® technology  utilizes several NDE techniques, including ultrasonic and eddy current examinations.  Combined with custom software (WinTUBE), the technology allows plant operators to correctly assess furnace tube condition and plan for tube replacements.  The methodology allows modeling of tube life scenarios by altering various plant operating parameters.  The approach has been adopted by several owners around the world.  Field experiences and finding are discussed in the paper.

INTRODUCTION

Primary reformer furnaces are widely used in the chemical and petroleum industries.  These reformers are an essential component of traditional ammonia and methanol plants.  They also are used to produce hydrogen in refineries.  Reformer furnaces need to operate reliably and without unplanned shut-downs to keep plants online and running effectively.  Unplanned shut-downs usually lead to significant economic losses.  Such unplanned shut-downs are often caused by catalyst tube failures.  It is important to avoid such failures by replacing tubes in a timely manner during planned maintenance shut-downs.  In order to replace catalyst tubes before they fail but not when they still have significant useful life, an accurate, reliable method of assessing tube life is required.

Reformer tubes are made of centrifugally cast heat-resistant alloys.  In the 1960s and 1970s, most tubes were made of alloy HK-40 (25Cr-20Ni-Fe).  In the 1980s and early 1990s, many reformers started using Nb-modified HP alloy (25Cr-35Ni-Nb-Fe) because it has been creep strength than the HK-40 alloy.  From the mid-1990s to the present, micro-alloyed HP (25Cr-35Ni-Nb-Ti-Fe) tubes are becoming widely used because their creep strength is even better than that of Nb-modified HP alloy tubes.  Thus, reformer tube materials have been improved over the last 40 years to increase their creep strength.  The improved creep strength allows tubes to operate at higher temperatures or higher stresses (thinner tubes) or gives improved tube life at comparable operating conditions.

Reformer tubes typically operate at metal temperatures in the range of 820 to 950ºC (1510 to 1740ºF) with internal pressures in the range of 2,000 to 3,500 kPa (300 to 500.psig).  The long-term operating life of reformer tubes under such operating conditions is typically governed by the creep strength of the tube material.  Figure 1 shows a typical creep-rupture failure of a reformer tube.  The final failure consists of a longitudinal split in the tube because the largest primary stress in a tube under internal pressure is the circumferential or hoop stress.  The creep cracking develops perpendicular to this stress.  Accurate assessment of reformer tube life requires the application of a model that realistically predicts the development of such creep damage and cracking under tube operating conditions.  The design and life assessment of reformer tubes were recently reviewed in detail1.  They are briefly summarized in the following two sections of this paper to provide background information for the reader.

FIG. 1: CREEP RUPTURE FAILURE OF A REFORMER TUBE

REFORMER TUBE DESIGN

Builders of reformer furnaces typically design catalyst tubes using an in-house approach similar to that of API STD 5302.  API STD 530 includes materials design data for various wrought steels, stainless steels, and Fe-Cr-Ni alloys as well as for the cast HK-40 alloy.  However, it does not include data for other cast alloys, so design engineers have to use their own materials properties database for tubes made of Nb-modified HP and micro-alloyed HP.  The lack of standard design data for these materials may lead to differences in the final tube design.

The creep-rupture data for the HK-40 alloy in API STD 530 are characterized using the Larson-Miller parameter (LMP).  The Larson-Miller parameter is defined by the following expression:

LMP = T (log tr + C)

where T is the absolute temperature (ºK), tr is the time to rupture (h), C is the Larson-Miller constant.

The value of C for a material is determined by fitting of the stress-rupture data for that material. API STD 530 does not contain creep deformation data that are required by a detailed creep stress analysis, which is usually performed using the finite element method.

Without creep deformation data, there is no way of predicting the expected creep strain in a tube during high-temperature operation.

For tube design, the stress (σ) is calculated using the mean-diameter formula, as follows:

where P is the internal pressure in the tube, Do is the tube outside diameter (OD), D´i is the tube inside diameter (ID), t is the tube wall thickness.

The stress given by equation 2 is only the pressure-induced mean hoop stress.  The variation of stress through the tube wall, the thermal stress, the axial stress, and the effects of cyclic operation are not taken into account by this simplified method of calculation.

Typically, the tube inside diameter and internal pressure are selected to satisfy process require-ments, and then equation 2 is used to establish the minimum tube wall thickness, taking into account allowances for potential corrosion.  In most cases, the design stress used in equation 2 is based on 100,000 hours (11.4 years) minimum creep-rupture life.

Depending on the relation of the operating pressure and temperature to the design values and the amount and severity of cyclic furnace operation, the design life determined by this simplified method may be either a conservative or a non-conservative estimate of actual tube life in service.

COMPUTERIZED MODEL FOR LIFE PREDICTION OF REFORMER TUBES

Because of the limitations of predicting tube life using simplified design-type calculations, a special-purpose computerized model3,4 was developed for predicting the life of reformer tubes.  To help understand the basis for the model, the mechanisms and evolution of creep damage in reformer tubes are reviewed.  Then, the details of the earlier TUBE and pcTUBE™ versions of the model are reviewed.  Finally, the improved WinTUBE™ version of the model that utilizes information directly from tube inspection is described.

Mechanisms and evolution of creep damage in reformer tubes

Table 1 shows the approximate relationship between reformer tube creep damage and tube life5 developed from industry experience.  High-temperature creep damage in reformer tubes made of cast heat-resistant alloys typically initiates as isolated creep voids between the inner surface and the mid-wall.  As creep damage progresses, numerous creep voids form and become aligned in the radial direction perpendicular to the hoop stress.  Next, the voids link up and form a number of small cracks or creep fissures in the inner half of the tube wall.  Then, the creep voids and fissures begin to spread into the outer half of the tube wall.  Finally, some of the large fissures link up and grow through the tube wall resulting in failure.  Figure 2 shows advanced creep damage in sections cut from reformer tubes5.  Even at this advanced stage the major portion of the damage is limited to the inner half of the tube wall.

FIG. 2: TYPICAL CREEP DAMAGE DISTRIBUTION IN A REFORMER TUBE

This creep damage process is important to keep in mind in developing a model to predict the creep life of reformer tubes.  Creep stress analysis for a thick-walled tube under constant pressure predicts that the highest stress is initially at the inner surface of the tube and that the stationary or long-term location of highest stress is at the outer surface of the tube.  However, the creep damage and cracking typically initiates within the tube wall and not at either the inner or outer surface.  This occurs because there is thermal gradient through the catalyst tube wall, with the outer surface being hotter than the inner surface.  The thermal gradient induces stresses in the tube wall that relax and redistribute during operation between start-up and shut-downs or operating trips.  The complex stress history must be modeled in order to properly predict the initiation and growth of creep damage and hence tube life.

Creep also can cause permanent changes in tube dimensions – increased diameter and decreased wall thickness.  These changes may or may not be accompanied by creep damage in the form of voids and fissures.  This type of excessive straining can occur because of short-term overheating or pressure increases.  Extremely excessive overheating to well above 90% of the homologous temperature of the tube metal can result in creep damage and cracking by a grain-boundary sliding mechanism.  This type of damage is not normal and occurs only severe in operating upsets.  Creep deformation that leads to changes in tube dimensions also affects tube life and must be incorporated into the tube life prediction model.

Development of computerized life prediction model

Because of the limitations of the design life prediction method, research6 was undertaken to develop a realistic model for creep analysis of reformer tubes.  The final product of this work was the special-purpose finite element computer program TUBE7.  The TUBE computer program uses a simplified finite element model, as illustrated in Fig. 3, and computes stresses and strains caused by pressure, thermal, and axial loading using elastic-creep finite element analysis (FEA).  The input data are streamlined to facilitate use of the computer program.  A material creep model is incorporated in the TUBE program.  Thermal analysis is included in TUBE so that either heat flux or metal temperature at the inner surface can be specified and used to compute the thermal gradient through the tube wall.  Automated time-step selection and modeling of cyclic loading are also features of TUBE.  TUBE is capable of predicting creep damage and life for HK-40 alloy reformer tubes under simulated operating conditions.

FIG. 3: ILLUSTRATION OF FINITE ELEMENT MODEL FOR REFORMER TUBE LIFE ASSESSMENT

Application of the TUBE computer program required an experienced analyst and a mainframe com-puter system, so it was not widely used by industry.  With the advent of high-speed personal computers in the late 1980s, the computer program was adapted for use on personal computers.  The resulting computer program8 (named pcTUBE™) is commercially available.  Just like its predeces-sor, the program predicts local material damage related to internal pressure, operating temperature, thermal stress gradient, and cyclic operation.  It includes material properties, creep deformation models, and creep damage relations for the HP-50 alloy and Nb-modified HP alloy, as well as those for the HK-409.

The pcTUBE™ program also computes stresses and caused by pressure, thermal, and axial loading using the elastic-creep FEA model illustrated in Figure 3.  A segment of the tube wall typically is divided into 12 discrete elements.  Using a segment of the tube wall is reasonable because the effects circumferential thermal gradients on hoop stress are not significant.  The accumulation of creep damage in each element is computed during simulated long-term operation.  Important cyclic operations, such as start-ups/shut-downs and operating trips, are modeled using a table of input parameters.

Stress relaxation and redistribution during steady operation are modeled.  Upon initial loading, a through-wall thermal stress is produced by the thermal gradient through the wall.  Creep causes the thermal stress to relax and redistribute with time.  The repeated process of application of thermal stress followed by stress relaxation and redistribution are modeled during start-ups/shut-downs and operating trips.

When cyclic operation of a reformer is modeled, pcTUBE™ correctly predicts that the maximum amount of creep damage will develop between the inner surface and mid-wall (see Figure 2).  It also correctly predicts that tube life is significantly reduced by relatively small changes in operating temperature or by typical cyclic operation (compared with the ideal case of steady operation throughout tube life).  A 20 to 30ºC increase in maximum operating temperature reduces tube life by 50% or more.  Two to four start/stop cycles per year may decrease tube life by 50% or more compared with the ideal case of continuous steady operation with no shut-downs.  Thus, the program is a valuable tool for predicting the service life of reformer tubes.

Inspection and condition assessment

To fully evaluate reformer tubes for damage, a series of inspections are performed.  While several alternative inspection techniques are available, careful consideration must be given to the inspection effectiveness or performance of the approach.

When developing an inspection plan, four key issues need to be evaluated.

Sensitivity

The ability of the technique to detect and quantify damage greater than a required minimum value with required sizing accuracy.

Coverage

The ability of a technique to adequately scan the areas of the tubes where damage will manifest itself with consideration to defect morphology and location.

Reliability

Requires the measurement of both the probability of detection (POD) and the number of false calls (NFI).

Speed

The ability to efficiently scan the tubes within the shut-down window.

Extensive lab and field validations have been performed to assess inspection approaches.  Field experiences for operating companies have also pointed out the need for multiple techniques to correctly identify tube condition11.  The referenced chart offers an objective overview of the effect-iveness of non-destructive examinations at quantifying damage in reformer tubes (See Table 3).

DISCUSSION

Diametrical growth (creep strain)

The principal rationale behind this technique is that, as creep damage occurs, the tube bulges.  Each material type has its own nominal value of diameter change where creep is considered to have occurred.  The following rules of thumb have been reported by various operators over the years.  As an example:

HK40: 2-3%, HP45:  5-7%

Yet, recent findings show that in some cases, significant growth may be apparent, but the tube may show the absence of internal damage.10,12  Using diametrical growth (OD  and ID) may provide a very general indication of tube condition; however, using diametrical growth as a stand-alone method for measuring creep damage, or lack of damage as the case may be, may lead to a significant false call on the actual condition of the tube.

Wall thickness measurement

As creep strain occurs, an apparent decrease in wall thickness is evident.

Replication

Replication is useful for in-situ assessment of reformer tube outside surfaces, to detect overheating that causes microstructural changes.  Replication is a “spot” type assessment and is normally used as a supplemental technique.  Only the advanced stages of creep damage can be assessed utilizing in-situ replication.

Radiography

Random radiographic examination is normally used as a supplementary technique to confirm the presence of severe cases of creep damage.  It is reasonable to expect to locate such damage when it has extended 50% in the thru-wall direction, when the tubes are filled with catalyst and isotopes are used instead of an X-ray tube.  Although using an X-ray tube provides an improved quality image, it is not normally employed, because of practical conditions on site.

Eddy current

Eddy current techniques have been used for a number of years on HK40 and HP45 tubes.  The technique relies on changes in electric circuit conditions; the circuit being the instrumentation, cables, sensing coil, and the item under test.

As the mechanical properties of the test materials change, a change in overall circuit impedance occurs, which is displayed on an oscilloscope.  By monitoring these changes, it can be inferred that creep damage is present, based on observation of the signal parameters in comparison to similar changes that occurred on known creep-damaged materials.  The depth of penetration of eddy currents is primarily influenced by frequency, conductivity, and relative permeability.

Eddy current coil design is important to obtain adequate sensitivity and signal to noise ratio.

Some tubes, such as HP40 and similar materials that have a high percentage of nickel, require the use of specialized coils to reduce the effects of material permeability variations.  This improves the signal to noise ratio so a reliable test result is obtained, allowing adequate discrimination of creep damage from general material property characteristics.

The eddy current operator evaluates these changes in signal response.  Other factors that the opera-tor considers are:

  • Varying lift-off, influencing the signal response, scale and welds being typical examples
  • Overheating that causes chromium migration, scale formation, and a significant eddy current response in terms of phase and amplitude changes
  • Variations in material permeability

Eddy current examination is not reliable in the detection of early damage (i.e. less than 30% through-wall).

Ultrasonic

The primary ultrasonic technique utilized for the detection and estimation of creep damage is through transmission ultrasonic attenuation.  Recent validations have again found that ultrasonic is more reliable at the detection and quantification of creep damage, particularly in its early stages.13

COMBINING NDE TECHNIQUES – ‘H’ SCAN® TECHNOLOGY

Review of the NDE techniques outlined above illustrates some of the advantages and disadvantages associated with each individual technique.  Extensive trials have been conducted to determine the viability and optimization of the various techniques.

It is currently concluded that no one technique can in all cases provide stand-alone information that will allow complete quantitative assessment of tube condition.  It is therefore prudent to combine NDE techniques ‘H’ SCAN® to improve the overall reliability of reformer tube condition evaluation.

Acquisition of NDE data is accomplished by the use of a powered carrier mechanism that traverses the length of a tube.  The following NDE sensors are loaded onto a carrier mechanism for simultaneous data collection:

  • Ultrasonic (attenuation, scattering and wall thickness)
  • Eddy current
  • Profilometry (ID/OD Dimensions)

Figure 4 shows an IESCO ‘H’ SCAN® assembly of carrier and sensors.  It takes about one hour to set up such a system on-site and two to four minutes per tube for data collection and to assign a provisional condition status.

FIG. 4: SCANNING PROCESS UTILIZING ‘H’ SCAN® TECHNOLOGY

The NDE specialists evaluate each tube and assign a damage grade per tube determined on the worst section of tube.  These grades are assigned based on comparison of each tube to the NDE responses obtained from samples subjected to metallography confirmation.

Final evaluation tube grading and dimensions are then transferred automatically to a life assessment software.

INSPECTION AND CONDITION ASSESSMENT CONCLUSIONS

Tube condition cannot be determined by one stand-alone technique, as the degree of damage within a particular tube may not lend itself to that specific NDE technique.  The reliability of NDE evalua-tion of reformer furnace tube condition can be improved by combining a variety of advanced NDE techniques (‘H’ SCAN® Technology) that individually monitor differing physical parameters.  The advantages and disadvantages of each technique, when compared against each other, reduces the occurrence of false calls, improves tube condition assessment and can increase overall furnace reliability.  The ‘H’ SCAN® approach has been proven reliable in managing steam reformer tube assessments.14

Using inspection data to improve life prediction

Operators of reformers wish to predict the remaining life of in-service tubes.  Before the remaining lives of tubes can be calculated, their current condition must be determined.  One can either measure the current condition by some destructive or non-destructive test method or calculate it using an analytical model, such as the pcTUBE™ computer program.  The major drawback of the latter approach is that the uncertainty of knowing the past operating conditions leads to a large uncertainty in analytically predicting the current condition of the tube material.  Therefore, it is preferable to measure the current tube material condition and just use the analytical model to predict the future tube life based on anticipated operating conditions.  The anticipated operating conditions may be similar to past ones or significantly different.

Based on the model used in the TUBE and pcTUBE™ programs, CC Technologies and IESCO developed the WinTUBE™ software.  It provides reliable predictions of remaining tube life by combining the calculation model with the results of the H-Scan® multiple technique tube inspection10.  Creep damage and remaining life are computed for each tube in the reformer using inspection results and anticipated operating conditions.  The initial damage state of each element in the model is set using material grades obtained from the inspection data.  This approach closely approximates the manner in which damage develops during actual service.  The diameter and wall thickness of the tube model also are set using the inspection data.  Anticipated operating conditions used in the model include the number, duration and type cycles, outer surface tube temperature and heat flux along the tube, and internal pressure in the tube.  Properties for the micro-alloyed HP material have been added to the model.  Thus, using WinTUBE™ inspection results are combined with expected operating conditions and materials behavior to accurately predict remaining reformer tube life.

As is illustrated in Fig. 5, which shows a plan view of a reformer furnace, the remaining life distribution is determined.  Remaining life is predicted for each tube based on realistic inspection and operating data.  These predictions are directly coupled with the inspection data to provide an integrated analysis of the reformer tubes.  The remaining creep rupture life of each tube is estimated on a realistic basis, taking into account both NDE measurements on the tube and anticipated operating conditions.  The calculations are incorporated into WinTUBE™ to make the results available shortly after the inspection and in a timely fashion for decision-making by the furnace operator.  In addition to making predictions for the anticipated operating conditions, the potential effects of alternative operating scenarios can be rapidly evaluated.

FIG. 5: DISTRIBUTION OF CALCULATED MINIMUM REMAINING TUBE LIFE IN A REFORMING FURNACE

Changes in the initial state of elements in the model can be used to account for material defects. Depending on the location of elements selected for modification, the simulated defect can be surface-connected or volumetric.  The effects of corrosion can be taken into account by modeling material loss from either the inner and/or outer surface as a function of time.  The effects of wall thickness, diameter, metal temperature, cyclic operation, amount of local heat flux, and material selection on tube life also can be evaluated by means of parametric studies.

EXAMPLE TUBE LIFE PREDICTIONS

To illustrate application of the WinTUBE™ software, sample tube life calculations were performed1.  First, the API STD 530 approach was applied to a reformer tube with the following parameters:

  • HK40 alloy
  • Outside diameter (OD) = 127 mm (5.00 in.)
  • Inside diameter (ID) = 101.6 mm (4.00 in.)
  • Wall thickness (t) = 12.7 mm (0.50 in.)
  • Internal pressure (P) = 3.45 MPa (500 psi)
  • Maximum operating metal temperature (Tmax) = 860ºC (1580ºF)
  • Peak heat flux (Hf) = 113,600 watts/m2 (250 Btu/hr-in.2) Applying Equation (2) yields

σ = 3.45/2 (127/12.7 – 1) = 15.5 MPa (2,250 psi)      (3)

For this stress level, the minimum Larson-Miller parameter in API STD 530 is 22,660.  Solving Equation (1) for tr gives

tr = 10(LMP/(tTmax + 273) – C) = 10(22,660/1133 – 15) = 100,000 h     (4)

This is the minimum calculated tube life using this simple approach

The computerized model was then used to compute comparable minimum tube lives for three operating scenarios:

  • Case 1 is four start-up/shut-down cycles and two hot trips per year.
  • Case 2 is two start-up/shut-down cycles per year.
  • Case 3 is one start-up/shut-down cycle per year.

Case 1 represents fairly severe cyclic operation, whereas Cases 2 and 3 represent moderate cyclic operation.  The computed minimum life for Case 1 is 91,120 hours or slightly less than that cal-culated using the simplified approach.  The computed minimum life for Case 2 is 182,800 hours or about twice that for Case 1 and much greater than that calculated using the simplified approach. The computed minimum life for Case 3 is 205,700 hours, or about 13% greater than that for Case 2. These results indicate the significant effect that cyclic operations can have on reformer tube life.FIG. 6: CALCULATED MINIMUM TUBE LIFE AS A FUNCTION OF WALL THICKNESS FOR HK40 ALLOY AND THREE OPERATING SCENARIOS

Case 1: four start-up/shut-down cycles and two hot trips per year

Case 2: two start-up/shut-down cycles per year

Case 3: one start-up/shut-down cycle per year

FIG. 7: CALCULATED MINIMUM TUBE LIFE AS A FUNCTION OF WALL THICKNESS FOR  Nb-MODIFIED HP ALLOY AND HK40 ALLOY AND THREE OPERATING SCENARIOS

Case 1: four startup/shutdown cycles and two hot trips per year

Case 2: two startup/shutdown cycles per year

Case 3: one startup/shutdown cycle per year

 

FIG. 8: CALCULATED MINIMUM TUBE LIFE AS A FUNCTION OF WALL THICKNESS FOR MICRO-ALLOYED HP AND Nb-MODIFIED HP ALLOY AND THREE OPERATING SCENARIOS

 Case 1: four start-up/shutdown cycles and two hot trips per year

Case 2: two start-up/shutdown cycles per year

Case 3: one start-up/shutdown cycle per year

To investigate the effect of tube wall thickness on minimum tube life, these calculations were repeated for wall thicknesses less than and greater than 12.7 mm (0.5 in.), keeping the tube inside diameter constant.  The results are shown in Fig. 6.  Comparable results for tubes made of the Nb-modified HP material and the micro-alloyed HP material are shown in Figs 7 and 8.  For thin-walled tubes the effect of more severe cyclic operation is small, but it becomes larger as the tube wall thickness increases.  The HP alloys give significantly longer tube lives than the HK-40 alloy. Tubes of the micro-alloyed HP material have longer lives than those of the Nb-modified HP material, but this benefit is minimal under the more severe cyclic operating conditions.  This parametric study shows how the computerized models can be used to evaluate different tube designs, materials, and operating conditions.

Figure 9 shows the results of calculations for three Grade 5 Nb-modified HP alloy tubes that were found in the inspection.  In this case, the operator wanted to know the maximum tube metal operating temperature for a minimum expected tube life of 2/3 year.  This was the amount of time needed to schedule replacement of the three tubes.  As shown in Fig 9, the maximum temperature is 850 C.  Operation with Grade 5 tubes is not recommended because they are susceptible to failure if operating conditions are not controlled rigorously.

Figure 10 shows the effect of maximum tube metal operating temperature for new (Grade 1) Nb-modified HP alloy tubes under three different operating scenarios: (1) ten start-up/shut-down cycles per year, (2) two start-up/shut-down cycles per year, and (3) zero start-up/shut-down cycles per year (the ideal case of continuous operation for the life of the tubes).  At the reported design temperature of 888 C, even the ideal case of no cycling has a predicted minimum tube life of slightly less than 10 years, indicating that the tube design is marginal.  The predicted minimum tube life is significantly decreased by cyclic operation, more so as the temperature decreases.  This example shows how WinTUBE™ can be applied to assess the influence of various potential operating scenarios and even help establish tube design parameters.

FIG. 9: EFFECT OF TUBE METAL OPERATING TEMPERATURE ON PREDICTED MINIMUM REMAINING LIVES OF THREE GRADE 5 Nb-MODIFIED HP ALLOY TUBES

FIG. 10: EFFECT OF OPERATING TEMPERATURE AND AMOUNT OF CYCLIC OPERATION (START-UP/SHUT-DOWN) ON THE PREDICTED LIFE OF NEW (GRADE 1) Nb-MODIFIED HP ALLOY TUBES

CONCLUSIONS

Tube lives predicted using simple design methods do not reflect actual operating lives.  Specialized stress analysis and life prediction models, such as the WinTUBE™ computer program described in this paper, provide realistic tube life predictions.  The specialized model used in the WinTUBE™ software is not well suited to computing the condition of tubes in service unless past operating conditions are known very well, which is typically not the case.  Coupling specialized analytical models with the H-Scan® multiple technique inspection results provides a realistic prediction of remaining tube life.  Parametric evaluations performed using such models provide a realistic means of evaluating the effects of design, material, and operating variables on reformer tube life.

References:

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