Patent Description:
Oil and gas piping networks may be susceptible to corrosion over time. For example, acidic and mineral-laden crude oil is highly corrosive to metals. In extreme cases, a pipe segment may corrode to the point of leaking. Because such leakages may interfere with efficient operation of piping networks, corrosion in pipelines is typically monitored.

Corrosion sensors and/or monitors are used in the detection and monitoring of loss of material, such as the internal surface of a pipeline wall, due to corrosion and/or erosion from interaction between the material and the environment in contact with the material. Some types of corrosion monitors use electrical resistance methods to detect loss of material thickness in the pipe wall due to corrosion. Other types of monitoring methods may involve X-ray or ultrasound evaluation of the thickness of pipe walls. Typically, the monitoring takes place at multiple, discrete locations along a pipe network because the large scale of such networks inhibits global monitoring of corrosion.

However, there is no standard for the selection of the individual monitoring sites along the piping networks. For handheld-type monitors, corrosion is monitored at locations selected by the operator of the device. Generally, these locations are determined by operator intuition. Certain types of electrical resistance corrosion monitors are permanently mounted to individual locations on the pipe. As with the handheld devices, there are no guidelines to determine optimal placement of such monitors. US patent application no. <CIT> describes a system for monitoring at least one parameter of interest relating to a flow conduit having a through passage and a fluid flow therein. US patent no. <CIT> describes procedures in which pipeline data and satellite data are used to provide surveillance for a pipeline.

In certain embodiments, provided herein are methods and systems for prediction of localized fluid dynamics parameters in piping networks under turbulent flow conditions. Predicting fluid dynamics parameters using correlation of the fluid behavior in the pipe with shear stress hot spots may assist refinery or other pipeline operators in identifying local maximum shear stress spots. For example, embodiments of the disclosed embodiments may be applied to refineries that include piping networks for crude oil and its fractionates.

In one embodiment, the disclosed embodiments provide a method that includes receiving information about a piping network for fluids, wherein the information comprises geometrical parameters, operating condition parameters, and fluid properties for the piping network; correlating the fluid dynamics of the piping network with shear stress using non-dimensional transfer-functions; and determining a location of one or more local shear stress maxima based on the correlation.

In another embodiment, the disclosed embodiments provide a method that includes receiving information about a piping network for fluids, wherein the information comprises geometrical parameters, operating condition parameters, and fluid properties for at least two piping components in the piping network; and determining a location of a local shear stress maximum for each of the at least two piping components based on the information.

The claimed embodiment provides a method that includes receiving a location of a local shear stress maximum for each at least two piping components, wherein the location is determined by modeling localized fluid dynamics of the at least two piping components using one or more non-dimensional transfer functions; and placing a corrosion monitor at the location of the local shear stress maxima of the at least two piping components.

In another embodiment, the disclosed embodiments provide a computer readable medium that includes code for: receiving information about a piping network for fluids, wherein the information comprises geometrical parameters, operating condition parameters, and fluid properties for at least two piping components in the piping network; and determining a location of a local shear stress maximum for each of the at least two piping components based on the information.

In another embodiment, the disclosed embodiments provide a corrosion monitoring system that includes a processor, wherein the processor is configured to receive information about a piping network for fluids, wherein the information comprises geometrical parameters, operating condition parameters, and fluid properties for at least two piping components in the piping network, and wherein the processor is configured to determine a location of a local shear stress maximum for each of the at least two piping components based on the information.

The file of this patent contains at least one drawing executed in color. Copies of this patent with color drawing(s) will be provided by the Patent and Trademark Office upon request and payment of the necessary fee.

In certain embodiments, provided herein are methods and systems for predicting the location of the highest shear stress points in a piping network. Knowing the location of local shear stress maxima may enable operators of piping networks to monitor locations of high shear stress in order to prevent leaks or other damage at those locations. Generally, pipes undergoing corrosion experience a loss of material in the pipe wall, leading to weakening of the pipes. This may be in part the result of repeated exposure to acidic crude oil or other fluids. Corroded pipes may be more likely to leak at areas of the pipe that also experience high shear stress. In addition, shear stress may accelerate the corrosion process. For example, in areas experiencing high shear stress, naturally occurring protective films containing sulfide that reduce the corrosion in the pipe may not have a chance to form. Similarly, in some cases protective additives may be added to the fluid in the pipe. In areas experiencing high shear stress, these additives, which may include sulfides or phosphates, may not have a chance to form protective films or coating on the pipe. Accordingly, areas of high shear stress may represent potential hot spots for pipe failure. In certain embodiments, the disclosed embodiments also provide information about the magnitude of local shear stress maxima and other fluid dynamics parameters in refinery piping systems. These local maxima of shear may then be arranged in order of magnitude, and decisions on which individual locations to monitor may be made depending upon the availability of the monitoring tools. The disclosed embodiments may identify a location, or range of locations that corrosion monitoring tools may be placed or located. The locations may be specified in certain embodiments to within a location of less than about <NUM>% or less than about <NUM>% of the total span or surface area of an individual piping component.

Corrosion monitors are placed at area of high shear stress in order to more accurately predict and/or prevent pipe failure. The disclosed embodiments may enable operators of piping networks to more effectively estimate pipe corrosion by enabling corrosion monitors to be placed on or near areas of pipe experiencing high shear stress. Accordingly, is envisioned that certain embodiments may be used in conjunction with systems for monitoring pipe corrosion. In the embodiment illustrated in <FIG>, an exemplary system <NUM> may include a controller <NUM> that communicates with pipe corrosion monitors <NUM> mounted on an exemplary piping network <NUM>. The pipe corrosion monitors <NUM> may include any suitable corrosion monitors, including ultrasound, X-ray, or resistance-based monitors. In one embodiment, an appropriate corrosion monitor is the Predator® Resistance Corrosion Monitor (General Electric, Trevose, PA). In such an embodiment, the corrosion monitor <NUM> may be permanently mounted to one or more locations on the piping network.

A computer <NUM> may be coupled to the system controller <NUM>. Data collected by the sensors <NUM> may be transmitted to the computer <NUM>, which includes a suitable memory device and processor. Any suitable type of memory device, and indeed a computer, may be adapted specific embodiments, particularly processors and memory devices adapted to process and store large amounts the data produced by the system <NUM>. Moreover, computer <NUM> is configured to receive commands, such as commands stored upon or executed by computer-readable media (e.g. a magnetic or optical disk). The computer <NUM> is also configured to receive commands and piping network parameters from an operator via an operator workstation <NUM>, typically equipped with a keyboard, mouse, or other input devices. An operator may control the system via these devices. In certain embodiments, an operator may input data related to the pipes and pipe networks into the computer <NUM>. Where desired, other computers or workstations may perform some or all of the functions of certain embodiments. In the diagrammatical illustration of <FIG>, a display <NUM> is coupled to the operator workstation <NUM> for viewing data related to shear stress locations in the piping network. Additionally, the data may also be printed or otherwise output in a hardcopy form via a printer (not shown). The computer <NUM> and operator workstation <NUM> may be coupled to other output devices which may include standard or special-purpose computer monitors, computers and associated processing circuitry. One or more operator workstations <NUM> may be further linked in the system for outputting system parameters, requesting examinations, viewing images, and so forth. In general, displays, printers, workstations and similar devices supplied within the system may be local to the data acquisition components or remote from these components, such as elsewhere within an institution or in an entirely different location, being linked to the monitoring system by any suitable network, such as the Internet, virtual private networks, local area networks, and so forth. In one embodiment, the system <NUM> may be partially or completely contained in a handheld device (not shown). Such a device may include a portable corrosion monitor <NUM>.

<FIG> is a flowchart <NUM> according to one embodiment. The steps of the flowchart <NUM> may be performed in conjunction with a computer <NUM> containing a processor programmed with instructions to perform the steps, such as a system <NUM> as provided herein. In step <NUM>, a given piping network, such as a high temperature single or multiphase regime, may be modeled in order to reduce a complex system into a series of modular parts. Any suitable series of modular parts may be identified. In a specific embodiment, modular parts may be separated according to distributions in pipe geometry. For example, modular parts may be delineated by a change in geometry that occurs along the flow path of the fluid. A straight pipe may be a single modular component, regardless of length, and may join another modular component that is characterized by a bend, turn, connection, or arc. The modular components are separated for the purposes of modeling fluid dynamics and may or may not be components that are physically separable from one another. It should be understood that a series of modular components may form a seamless piping system or subsystem.

In the single-phase regime embodiment or the multi-phase regime embodiment, factors that may be considered when modeling the system include velocity of fluid, viscosity of fluid, density of fluid, dimensions of the configuration, and surface roughness of the pipe. Variation in velocity, temperature, viscosity, density and dimensions of components may be taken into account for a wide range of operating conditions and fluids, such as crude oils. In some embodiments, the internal surface of the piping components may be assumed to be smooth. In such embodiments, the shear stress prediction may result in lower values associated with the magnitude of the stress as a result of the smooth, rather than rough, surface. However, the location prediction may be generally unchanged. In any piping, roughness is a function of age of piping and its material. At locations where shear is higher, the pipe surface may become rougher with time, thus resulting in even more increased shear stress at those points.

Once separated into its modular components, the individual components may be further characterized in step <NUM>. Generally, such further characterization may include specific geometric properties of the individual components and may further include relative relationships between different modular components. In one embodiment, once the characteristics of a particular piping network have been determined, these characteristics may be used as a reference for similar networks. Once the parameters associated with the fluid and each modular component have been determined, the parameters may be further analyzed in step <NUM> to determine one or more locations of shear stress maxima in each component. The analysis may involve correlating the fluid dynamic parameters with shear stress locations and magnitude. The correlation may involve fluid dynamic modeling to determine one or more non-dimensional transfer functions that describe the system. In addition, the correlation may involve using empirically derived data to describe the fluid dynamic properties and/or validate the equations determined by the model. Upon determining one or more shear stress maxima, the location of the maxima on the modular component may be communicated to an operator in step <NUM>. The operator may then monitor the pipe for corrosion at the shear stress maxima locations.

<FIG> is a flowchart <NUM> of a specific embodiment of the disclosed embodiments. In step <NUM>, the piping network may be simplified into certain standard parts <NUM>, such as straight pipes 44a, bends 44b (such as U-bends), reducers 44c, and/or joints 44d. In step <NUM>, an operator may determine a value or a range of value for multiple parameters associated with the pipe and the fluid in the piping network. For example, an operator may determine pipe geometry parameters <NUM>, such as the length, diameter, and shape of each component. For components including bends, the operator may determine the degree of the bend, and the arc length. For reducers, the operator may determine the degree or angle of tapering in the pipe. In addition, the operator may determine the composition of the pipe, including the surface roughness on the inside wall of the pipe. An operator may also determine the fluid property parameters <NUM>, include fluid composition, the number of phases (liquid, solid, or gas), corrosivity, acidity, density and viscosity. Additionally, certain parameters of the operational conditions <NUM> may be determined, such as fluid temperature and flow velocity. The flow may be turbulent, which in certain embodiments may be defined as a Reynolds number ~<NUM>e7.

In certain embodiments, in step <NUM>, the disclosed embodiments may use fluid dynamic modeling to determine one or more non-dimensional transfer functions that may be solved for each of the different components that take into account all possible ranges of operating conditions, geometrical parameters and fluid properties and their interaction effects. A modular approach is first adopted and the network is simplified into commonly used piping components. A range of operating conditions, geometrical parameters and fluid properties are then identified for the region of interest. In certain embodiments, the shear stress at the pipe wall may be represented by τo = τo (µ,ρ,V,D,e), where µ is the dynamic or absolute viscosity, ρ is the density of the fluid, V is the mean velocity of the flow, e (or ε) is the surface roughness of the pipe, and may also be related to the geometry. As noted, the surface of the pipe may be assumed to be smooth in certain embodiments. The complexity may be reduced to two variables by use of non-dimensional variables. The non-dimensional shear stress can be expressed as: <MAT> <MAT> Reynolds number (non- dimensional), and <MAT>.

The shear stress is also related to geometric parameters. For example, for <NUM>° circular bend and U bend, the radius of curvature of the bend (R) and the radius of pipe (r) may be taken into account. For a tee-joint, the radius of pipe (r), and for a reducer, the inlet radius to reducer, the outlet radius to reducer, and the reducer length. Using the inputs for individual components, the desired outputs are local maximum shear <NUM> (τmax(local)) and location <NUM> of shear maxima (θ<NUM> & θ<NUM> and x). Input and output parameters may be converted into non-dimensional form using any suitable technique, such as the Buckingham Pi theorem. Non-dimensional inputs and outputs obtained for circular bend & U-bends are Re and Radius ratio (inputs) and τmax(local), θ<NUM>, θ<NUM>, x (outputs); for tee-joints are Re (inputs) and τmax(local), θ<NUM>, θ<NUM>, x (outputs); and for reducers are Re, slope, and Diameter ratio (inputs), and τmax(local) (outputs). In certain embodiments, τmax(local) may be expressed as: <MAT> <MAT> where <MAT>, and the <MAT>.

In certain embodiments, a range of these non-dimensional inputs may be identified for the range of operating conditions, fluid properties and geometrical parameters. One particular embodiment for a range of Re is provided in Table <NUM>.

The disclosed embodiments may use modified k-ε models with mesh resolved up to the wall. Realizable k-ε model has analytically-derived differential formulas for effective viscosity that accounts for low Reynolds number effects. Velocity inlet boundary condition may be used where a uniform velocity profile is specified. For turbulence parameters, turbulent intensity and hydraulic diameter are specified as inputs; which are calculated depending upon the Reynolds number and pipe diameter. For hydraulic diameter, the equation may be expressed as Hydraulic diameter = Diameter of the pipe, and for the turbulent intensity, the equation may be expressed as Turbulent intensity = <NUM> (Re)-<NUM>/<NUM>. Outflow boundary condition may be used, i.e. normal gradient of velocity may be assumed to be zero. In certain embodiments, the pressure outlet condition gives identical results. In certain embodiments, no slip boundary condition is specified at the walls.

FLUENT® <NUM> (Fluent Inc. , Lebanon, NH) was used to solve the governing equations with appropriate discretization schemes and boundary conditions. A three-dimensional incompressible turbulent steady state case may be solved in double precision. Higher order schemes may be used for discretizing momentum and turbulence equation; the first cell size requirement is of order <NUM>-<NUM>, which may be appropriate for increased accuracy relative to wall effects. It has been observed that pressure discretization scheme has insignificant effects on wall shear stress.

The present techniques relate to correlating fluid dynamic parameters with shear stress hot spots. As noted, the correlation may take the form of fluid dynamic modeling to generate one or more non-dimensional transfer equations that may be solved for specific parameters unique to a particular piping system. In one embodiment, a general non-dimensional transfer equation may be developed that describes the piping system as a whole, including various types of piping components with different geometry. In another embodiment, a series of non-dimensional transfer equations may describe a series of different piping components. In another embodiment, the correlation may be developed at least in part by using empirically derived data. For example, such data may include wall thickness measurements of piping systems that are taken over time, combined with the geometric and operating parameters of such systems. In one embodiment, mathematically derived correlations may be validated using empirical data such that any equations that describe the piping system may be improved over time as empirical data becomes available.

The following examples provide specific embodiments of the present techniques.

The disclosed embodiments were used to examine the flow properties of an exemplary <NUM>° circular bend. The naming conventions used for the modeling of the <NUM>° circular bend are shown in <FIG>. The <NUM>° circular bend was modeled at three different radius ratios; <NUM>, <NUM> and <NUM>, under three operating conditions, and at Reynolds numbers <NUM>× <NUM><NUM>, <NUM>× <NUM><NUM> and <NUM>× <NUM><NUM>. <FIG> is a velocity profile of the <NUM>° circular bend. From the velocity profile shown in <FIG> at the symmetry plane, with velocity magnitudes in axis <NUM> it was observed that, as the fluid moves along the bend, maximum velocity, shifts from inner side of the bend <NUM> to the outer side <NUM>. This outer higher velocity zone keeps moving with the flow even up to diameters of <NUM> or greater. However, no change in the shear stress location and magnitude was seen even when the exit length of the pipe is decreased/ increased. <FIG> shows the static pressure, magnitude shown in axis <NUM>, at the bend wall, whereby pressure at the inner wall <NUM> is lower than the outer wall <NUM>, which is a result of the balance of the centrifugal force. There was a boundary layer separation observed some distance away from the bend outlet as shown in <FIG>. This is because in the region <NUM> velocities are very low in the vicinity of the wall and adverse pressure gradient develops. <FIG> shows velocity vectors at cross sections A, B, C, and D, shown in <FIG>. It was observed that the flow is towards the outer side of the bend nearer to the symmetry plane. This is because centrifugal forces are higher in this zone (low radius of curvature) as well as the tendency of the fluid to cover least distance as the fluid came towards the inner radius. This created Dean's Vortices in which the area of recirculation shifts towards the inner portion of the bend as the fluid moves in the bend. This is a result of centrifugal forces decreasing due to lesser fluid in the inner zone as the fluid moves in the bend.

<FIG> is a graph of velocity profile comparison at the symmetry plane line of the <NUM>° circular bend at a point <NUM><NUM><NUM> away from the bend inlet. The lowest possible radius graphed on the x-axis is <NUM> (inner zone), with <NUM> as the highest radius outer zone of the bend. On this plane, velocities were higher at the inner wall because the bulk fluid would follow the least radius path, i.e. the inner radius and then shift outwards due to centrifugal action because of the curvature of the bend. This effect was observed in the graph in <FIG>, which shows the comparison at a plane <NUM> one diameter away from the bend outlet. The experimental data was compared with computational results and reflected that model captured the flow physics. The slight difference between the experimental and computational values may be attributed to either experimental error or certain parameters like uneven surface, which were eliminated in the calculations.

<FIG> is a schematic of the location of the shear stress hot spots <NUM>, <NUM>, and <NUM> observed for the modeled <NUM>° circular bend. It was observed that maximum value of shear stress varied with radius ratio and Reynolds number. Three local shear maxima were seen in the cases studied for three radius ratios and three Reynolds numbers. One maximum <NUM> was noticed just after the bend inlet, which is due to change in axial velocity - primary flow gradients. The second two maxima <NUM> and <NUM> were the result of change in secondary current and are mirror images of each other. These are located between the outlet of the bend and centre of the bend. It has been observed that the ratio between the maxima arising out of secondary flows and primary flow varies from <NUM> to <NUM>.

<FIG> is a graph that shows the variation in magnitude of local maximum non-dimensional shear stress because of primary flow (local maximal) with Reynolds number and radius ratio. As Reynolds number is increased (while keeping the radius ratio constant), the shear decreases. This is because an increase in Reynolds number means either decreasing viscous forces that leads to decrease in shear or increase in convection part. This leads to increase in shear but a much higher increase in convection part, which again causes the non-dimensional shear to decrease. It was observed that as the radius ratio is increased, this may lead to increase in convection term and hence decrease in non-dimensional shear. Similar results were seen in the trends for local maxima <NUM> & <NUM>, shown in <FIG>, which were the results of secondary flow gradients.

A transfer function fitted for these local maxima takes the functional form: <MAT> where a, b and c for the modeled bend are shown in Table <NUM>.

It was observed that variation in location for these maxima is within <NUM>% of the total span of the circular bend, as shown in Table <NUM>.

Accordingly, a modular component with the geometric characteristics of a <NUM>° circular bend, or a similar shape, may be modeled with a non-dimensional transfer equation. Certain geometric parameters, as well as operating and fluid parameters, may be used as inputs to the equation to locate or predict local shear stress maxima for this component.

The disclosed embodiments were also used to examine the flow properties of an exemplary U bend. The naming conventions used for the modeling of the <NUM>° circular bend are shown in <FIG>. A pipe U bend was investigated for two different radius ratios, <NUM> and <NUM>, under three operating flow conditions, at Reynolds number <NUM>× <NUM><NUM>, <NUM>× <NUM><NUM> and <NUM>× <NUM><NUM>. <FIG> shows the flow physics for U-bend. It may be seen from the velocity profile that, as the fluid moves along the bend, maximum velocity shifts from inner side of the bend <NUM> to the outer side <NUM> (velocity magnitudes shown in axis <NUM>). This outer higher velocity zone keeps moving with the flow even up to diameters of <NUM>. No change in the shear stress location and magnitude was observed even when the exit length of the pipe is decreased/ increased. <FIG> also shows the static pressure at the bend wall. Pressure at the inner wall <NUM> is lower than the outer wall <NUM> (pressures magnitudes shown in axis <NUM>), which is an effort by the flow field to balance the centrifugal force. Boundary layer separation in region <NUM> is observed some distance away from the bend outlet and is captured by the model as depicted in <FIG>. This is because, in this region, the velocity is relatively low in the vicinity of the wall, and pressure is increasing i.e. an adverse pressure gradient has formed. <FIG> shows velocity vectors at cross sections labeled A, B, and C (see <FIG>, increasing in flow direction). It was observed that the flow is towards the outer side of the bend near to the symmetry plane. This is the result of higher centrifugal forces in this zone (low radius of curvature) as well as the tendency of the fluid to cover least distance, because fluid will try to come towards the inner radius. This creates Dean's Vortices. The area of recirculation shifts towards the inner portion of the bend as the fluid moves in the bend. This is because centrifugal forces decrease as a result of less fluid in the inner zone as the fluid moves in the bend.

<FIG> is a graph of the mean axial velocity at the outlet of the bend on the symmetry plane, where <NUM> is the lowest radius (inner zone) and <NUM> is the highest radius in the outer zone of the bend. Velocities in the outer zone may be higher as a result of the centrifugal forces shifting fluid to the outer radius. The results were compared to experimental observations. It was observed that the difference between the predicted values and experimental results is within <NUM>%. In the lower radius zone (<NUM>), the model under-estimates the value, while in the central zones it overestimates it.

<FIG> is a schematic view of the locations of the shear stress maxima <NUM>, <NUM>, <NUM>, and <NUM> for the U bend pipe component. It was observed that maximum value of shear stress varied with radius ratio and the Reynolds number. Four local shear maxima were seen in all the cases studied for two radius ratios and three Reynolds number. One maximum <NUM> is noted just after the bend inlet, which is a result of the change in primary flow gradients. One maxima <NUM> also occurs just after the bend and is again the result of change in primary flow. While the remaining two maxima <NUM> and <NUM> stem from a change in the secondary current and are symmetric, they are located between the outlet of the bend and centre of the bend. It has been observed that the ratio between the maxima arising out of secondary flows and primary flow varies from <NUM> to <NUM>. Hence a non-dimensional transfer function is developed to predict the variation in local shear maxima magnitude and location for these three maxima.

<FIG> is a graph that shows the variation in magnitude of local maximum non-dimensional shear stress because of primary flow (local maximal) with Reynolds number and radius ratio. As the Reynolds number is increased while keeping the radius ratio constant, the non-dimensional shear decreases. This is a result of the effect that an increase in Reynolds number means either decreasing viscous forces or increasing the convection part. It was observed that as the radius ratio is increased either by increasing the radius of curvature, which may lead to decrease in centrifugal force and then to lower shear and hence lower non-dimensional shear, decreasing the radius of pipe, or increasing the velocity for maintaining same Reynolds number, which may lead to increase in convection term and hence decrease in non-dimensional shear. Similar trends were seen even for the other local maxima, <FIG> shows the variation for maxima <NUM> & <NUM>.

If a transfer function is fitted for these local maxima the functional form would be: <MAT> where a, b and c for all the maxima are shown in Table <NUM>.

It was observed that location of maximum <NUM> in peripheral direction did not change with different parameter inputs and was observed to be <NUM>°. While the change in flow direction follows a monotonic behavior, the variation is again well within <NUM>% of total span. It was also observed that location of maximum <NUM> in peripheral direction did not change and was observed to be <NUM>°. While the change in flow direction follows a monotonic behavior, the variation is again well within a small percentage of the span. It was observed that locations of maxima <NUM> & <NUM> in the peripheral direction did not change and was observed to be <NUM>° ± <NUM>°. It was seen that, if the intersection of the span covered by maximum to <NUM> maximum was studied, the span formed a streak. The streak varied, from <NUM>° to <NUM>° for all the cases. For selecting a monitoring point, any point within the streak may be monitored. These locations are tabulated in Table <NUM>.

Accordingly, a modular component with the geometric characteristics of a U bend, or a similar shape, may be modeled with a non-dimensional transfer equation. Certain geometric parameters, as well as operating and fluid parameters, may be used to locate or predict local shear stress maxima for this component.

The disclosed embodiments were also used to examine the flow properties of an exemplary tee junction. The naming conventions used for the modeling of the tee junction are shown in <FIG>. A tee junction was studied for three operating conditions, at Reynolds number <NUM>× <NUM><NUM>, <NUM>× <NUM><NUM> and <NUM>× <NUM><NUM>. <FIG> shows the velocity profile and vector plot on the symmetry plane capturing the boundary layer separation and pressure distribution at the junction. From the velocity profile, it was observed that the flow takes a turn in a similar manner as the U-bend and circular bend, but with a sharper degree. The flow tends to project outward due to relatively high centrifugal forces. As seen in <FIG>, static pressure at the inner wall <NUM> is lower than the outer wall <NUM> to balance this centrifugal force. <FIG> shows boundary layer separation in region <NUM>, which is located just after the corner of the tee junction. In the corner region, an adverse pressure gradient leads to the boundary layer separation. <FIG> is a graph that shows velocity vectors on cross sections labeled <NUM> to <NUM>. It was observed that at sections A and B, flow is towards the centre, which indicates smooth boundary layer development, while in section C, just upstream of the corner, there is a tendency of the fluid to adjust itself for an imminent separation. Secondary flow currents along with circulatory motions are found in section D, downstream of the separation bubble at the corner.

<FIG> is a schematic view of two local shear stress maxima <NUM> and <NUM> for the modeled tee junction. The maximum value of shear stress was observed to be strongly dependent on Reynolds number. Four local shear stress maxima are seen in all the cases studied for three different Reynolds number. Two local maxima <NUM> and <NUM>, shown in <FIG>, are observed just at the corner, which arises due to combined effects of sudden change in velocity direction and secondary currents. The other two maxima (not shown) are the result of a change in the secondary current and are symmetric, located just after the corner on the top surface. It was observed that the ratio between the maxima arising out of secondary flows and primary flow varied from <NUM> to <NUM>. The secondary maxima were lower in magnitude compared to the primary maxima, however its confidence value was higher. In embodiments in which the corner might not be as sharp, the secondary maxima may increase significantly in magnitude.

<FIG> is a graph shows the variation in magnitude of local maximum non-dimensional shear stress for local maxima <NUM> and <NUM>. It was observed that, as Reynolds number is increased, non-dimensional shear stress decreases. This is due to the fact that an increase in Reynolds number indicates either decreasing viscous forces or an increase in convection part ,which leads to increase in shear but a much higher increase in convection.

A transfer function is developed for these local maxima given by: <MAT> where i indicates the maxima number, and values of these constant corresponding to these maxima is shown in Table <NUM> below.

It was observed that the location of these maxima did not change with operating conditions and covered a span that is shown in Table <NUM> below.

One of the other most commonly found flow configurations, a blocked tee, in refineries is shown in <FIG>. A blocked tee is commonly found at locations where control valves are placed to control the flow distribution. In addition to Reynolds number, blocked tube length may be another parameter influencing the location & magnitude of shear stresses on the walls of the tee junction. The minimum "blocked" length observed in refineries may be modeled as having a length of at least 2d. In a blocked tee, the location of shear stress may be at the downstream corner of tee junction as is shown in <FIG>. In this embodiment, only one local shear maxima <NUM> was observed. It was also observed that shear stress in the blocked tee was <NUM>/<NUM> less than the shear stress in a tee junction under normal operating conditions (i.e., open flow). The blocked tee has insignificant (<<NUM>%) changes in shear stress magnitude with changes in length of the blocked portion, while for location no change is observed for different blockage lengths.

<FIG> shows the variation of non-dimensional shear stress with Reynolds number, the relationship given by: <MAT> where values of constants a and c are tabulated in Table <NUM>.

Accordingly, a modular component with the geometric characteristics of a tee junction, or a similar shape, may be modeled with a non-dimensional transfer equation. In addition, tee junctions that are blocked at an inlet or outlet may also be modeled. Certain geometric parameters, as well as operating and fluid parameters, may be used to locate or predict local shear stress maxima for this component.

The disclosed embodiments were also used to examine the flow properties of an exemplary reducer. The naming conventions used for the modeling of the tee junction are shown in <FIG>. The reducer was studied under Reynolds numbers <NUM>× <NUM><NUM>, <NUM>× <NUM><NUM> and <NUM>× <NUM><NUM>, and for two slopes, <NUM> and <NUM>, where the slope is given by <MAT>. <FIG> shows the velocity profile at the symmetry plane. From the velocity profile it may be observed that, as the fluid enters in the reducer, average fluid velocity increases due to decrease in cross sectional area, which gives rise to increase in local velocities too.

Maximum shear stress was observed to be at the outlet of the reducer. This may be the result of velocities being higher in the lowest diameter pipe section while the outlet of the reducer flow may be in a developing zone of flow. Maximum shear stress was a strong function of Reynolds number (on the basis of outlet diameter of reducer) and slope of reducer. Maximum shear stress <NUM> is observed at the outlet of the bend, shown in the schematic of <FIG>.

<FIG> is a graph that shows the variation with Reynolds number in magnitude of local maximum non-dimensional shear stress for local maxima <NUM> and <NUM>. It was observed that, as Reynolds number increased, non-dimensional shear stress decreased. It was also observed that higher slope related to higher shear stress.

A transfer function is developed for these local maxima given by: <MAT> Values of these constants are in Table <NUM>.

It was observed that location of these maxima in all the cases studied was at the exit of the reducer.

Accordingly, a modular component with the geometric characteristics of a reducer, or a similar shape, may be modeled with a non-dimensional transfer equation. Certain geometric parameters, as well as operating and fluid parameters, may be used to locate or predict local shear stress maxima for this component.

In addition to modeling shear stress in individual components, the disclosed embodiments may also take into account the interaction between the components. For example, the interaction between different <NUM>° circular bends was studied under a range of operating conditions. Three common configurations for circular-to-circular bend combinations are shown in <FIG>. In such configurations, flows through these components have very high inertia forces and gravity effects may be insignificant. Accordingly, the relative orientation matters more than absolute orientation.

In addition, the shear stress difference may be studied in a downstream or upstream manner. In looking at downstream effects, the difference between shear stresses in the bends was analyzed for an exemplary highest Reynolds number and low radius of curvature with zero interaction length. For example, the combination with cross orientation in <FIG> showed a <NUM>% difference in shear stress magnitude between components. Turning to upstream effects, if a percentage change in shear stress in a bend is observed, it is found that the a difference of <NUM>% or less may be considered insignificant. It was generally observed that, though upstream effects were not significant, downstream effects were considerably high. Table <NUM> shows the percentage difference for the combinations.

As having two bends and entry length and exit length increases the computational domain and the computational efforts, an approach may be adopted in which the exit profile from the single bend studies after 1D length from the bend are taken in as inlet profile for the next bend. To address the relative orientation, these profiles were rotated at appropriate angles. In this approach, a validation was done to check range of validity. These combinations were studied at an interaction length of 2d, and are compared with a case with 1D entry length where the inlet profile from the single bend studies is plugged in after 1D length from the bend exit. These cases are shown in <FIG>.

Table <NUM> shows the variation of percentage change in shear stress at the second of the three bends in the combinations due to truncation. It was found that the change in magnitude and location was insignificant (<<NUM>%). Accordingly, the approach of truncating introduces insignificant error and may be used as an effective modeling technique. As the interaction length between the components may influence the velocity profile of the flow into the next component, it may be advantageous to study its effect. <FIG> shows the effect of interaction length on non-dimensional shear stress magnitude in a single bend. It was observed that, as interaction length is increased, there was a percentage change decays, but after about 30d exit length the change is saturated to a value of about <NUM>% with a maximum difference observed of <NUM>%.

Claim 1:
A method (<NUM>), comprising:
receiving information about a piping network (<NUM>) for fluids, wherein the information comprises geometrical parameters, operating condition parameters, and fluid properties for at least two piping components in the piping network (<NUM>);
correlating the fluid dynamics of the piping network (<NUM>) with shear stress using non-dimensional transfer-functions;
determining (<NUM>) a location of one or more local shear stress maxima for each of the at least two piping components based on the correlation; and
identifying one or more locations for placement of corrosion monitoring tools based on the locations of one more local shear stress maxima.