Abstract: The invention relates to false echo storage in the area of level measurement. The decision as to whether or not to initialize and/or update the false echo memory is made using at least one value for the sensor-inherent noise, container noise and/or EMC noise for this purpose. This may make it possible to avoid identifying a false echo as the level echo.

Abstract: A method and system for calibrating a digital speedometer display to match an analog speedometer indicated value. The method generally includes calibrating each analog speedometer unit such that the exact deviation or “offset” from the center point of the analog speedometer is known. This measured deviation is then used to adjust the value input to the digital display thereby making the digital display value match the indicated value of the analog speedometer.

Abstract: Method of calibration intended to be used in a process of determining the content of a plurality of compounds contained in a drilling fluid, the method comprising obtaining a calibration mud; performing a gas extraction from said calibration mud with at least two extraction stages in order to obtain at least two extracted gases; measuring parameters representative of the quantities of said calibration compounds in said extracted gases; and calculating correction factors using said measured parameters, the correction factors being intended to be used in said process.

Abstract: The present invention provides automated systems and methods for monitoring column performance in process chromatography, and applications thereof. In an embodiment, column performance is monitored by generating a plurality of process values such as, for example, conductivity values or pH values with a detector during a chromatography step transition between a first mobile phase liquid and a second mobile phase liquid. The process values are transformed to form transformed process values in which noise present in the process values is suppressed. Column performance parameters are calculated based on the transformed process values and displayed during movement of the second mobile phase liquid through the chromatography column.

Abstract: The present invention includes systems, methods and apparatus for detecting whether an acceptable mixture of fluid and water has been delivered by a vending machine. Embodiments of the invention utilize one or more second flow meters located downstream of a mix manifold. The additional flow meter allows the controller of the delivery system or vending machine to monitor and compare the volume of water to the volume of the final mix in order to determine whether an appropriate volume of syrup has or has not been mixed in the dispensed beverage.

Abstract: A method for calibrating a sensor for measuring turbidity and/or solids content of a medium, wherein the sensor comprises at least one transmitting unit and at least two receiving units. The method comprises the steps of registering at least two measurement signals, which depend on the intensity of light scattered in the medium, wherein the light is sent from the transmitting unit and received by the receiving unit, abstracting the measurement signals to a feature vector, automatic selecting of a calibration model based on the feature vector, wherein the feature vector is transmitted to an earlier trained classifier and the classifier associates the calibration model with the feature vector, and calibrating the sensor with the automatically selected calibration model.

Abstract: A method and system for performing a criticality analysis of a water distribution network is provided. The method and system provides for segmentation of the system which allows a user to determine the set of elements that comprise segments, which in turn are the smallest portion of a water distribution system that can be isolated by valving. Isolating valves are included as elements in the set of elements that are used by an associated hydraulic solver engine to segment the water distribution network. Once the network has been segmented, a criticality analysis is performed whereby a hydraulic simulation is run for an outage of one or more segments, and the shortfall in demand supplied to other segments is calculated. The system provides for a linking of the ability to automatically identify segments with a hydraulic analysis model to enable a user not only to identify segments, but to rank their importance based on a variety of user defined metrics.

Abstract: Apparatus and associated systems and methods relate to automated learning of a baseline differential pressure (dP) characteristic to monitor the performance of a field-installed gas flow meter by comparing on-line dP measurements to the learned baseline dP characteristic. In an exemplary embodiment, a first baseline dP characteristic may be learned in a first mode over a first predetermined period of time according to a first set of learning criteria, and a second baseline dP characteristic may be learned in a second mode over a second predetermined period of time according to a second set of learning criteria. The first period of time may be substantially shorter than the second period of time. The first set of criteria may be substantially more relaxed than the second set of criteria. During the second mode, meter performance degradation may be diagnosed by comparing measured dP against the first baseline dP characteristic.

Abstract: Disclosed is a method of correcting a response of an instrument. The method includes determining an inverse convolution function, the inverse convolution function being in the time domain. A response of an instrument to an exhaust sample is recorded as a function of time. The recorded response is then convolved with the inverse convolution function, the result being a convolution corrected instrument response.

Abstract: Flow meter validation techniques are herein disclosed. An illustrative system includes a flow meter and display logic coupled to the flow meter. The flow meter is configured to provide information indicative of a parameter of fluid flow through the meter. The display logic is configured to provide a display of the information. The display includes an indication of a possible range of values of the parameter. An indication of a baseline portion of the range is also provided. The baseline portion of the range designates preferred values of the parameter. The display further includes an indicator designating the value of the parameter.

Abstract: An air pollution sampling system and a method thereof applied to a wide-area air sampling are revealed. Air is forced into an air sampling unit by movement of a vehicle, for performing an active air sampling without a power source. An air sampling unit includes a plurality of baffle plates so as to adjust air sampling rate and avoid interference caused by turbulence generated during the movement of the vehicle. A positioning device provides geographic coordinates, vehicle speed and time. An information processing device integrates sampling flow and positioning information from the positioning device, collects information generated by the sampling system, and computes statistics of the accumulated samples and relative sampling positions. By the collected sampling positions, time and flow rate, the sampling amount is obtained through data processing and calculation. In combination with the display of positioning data, the geographic area represented by the air samples could be understood more clearly.

Abstract: A correction method in which characteristic curves and/or correction values are produced, by way of which the drive current for one or more electrically activated hydraulic values operated in an analog fashion is measured during a pressure regulation in such a way that, during the operation of an anti-lock regulation, one or a respective characteristic curve is first prescribed and then the prescribed characteristic curve is corrected, particularly in a learning process, wherein, after a pressure build-up phase, the current pressure model value (Pmod) is compared to and/or analyzed using a model locking pressure level (Pmax).

Abstract: Multi-phase flow is estimated in a flow meter by measuring fluid pressure within the flow meter and using the measured pressure to calculate a density of the flow. A total flow rate through the flow meter is estimated based on the calculated density and a PVT analysis of the fluid. A corrected total mass flow rate is calculated using a liquid/gas slip correction technique. Fluid flow rates are further corrected with a discharge coefficient that varies with changes in the Reynolds number of the fluid. The gas and oil fractions can be determined from the corrected total mass flow rate and gas fraction.

Abstract: An object is to detect an abnormality when the inside of a gas cutoff apparatus is submerged. A flow rate computing unit 15 computes an instantaneous flow rate from a detected value of a flow rate detecting unit 8 for measuring a flow rate, and an amplification degree determining unit 18 determines signal amplification adjusted by the flow rate detecting unit 8, and timing is started when the amplification degree is a predetermined value or more, and a measurement condition setting unit 16 sets a measurement condition of the flow rate detecting unit 8 from the flow rate obtained by the flow rate computing unit 15, and a measurement ratio computing unit 20 obtains a measurement condition ratio during predetermined time from a time measuring unit 19 and the measurement condition setting unit 16, and it is determined that the flow rate detecting unit 8 is abnormal when the measurement ratio is a predetermined ratio or more, and a cutoff unit 22 breaks supply of gas.

Abstract: A control system is disclosed for regulating the flow of a liquid from a liquid provider through a liquid distribution system. The distribution system has a major liquid distribution channel connected to a plurality of minor liquid distribution channels providing the liquid to a multiplicity of users. A plurality of controllable user valves are interposed in the multiplicity of user channels. A liquid monitor senses a liquid flow characteristic within the liquid distribution channel. A user control changes selective controllable user valves for restoring a desired liquid flow characteristic within the liquid distribution channel.

Abstract: A system is provided to control fluid flow in a wastewater treatment system. The wastewater treatment system may include a wastewater treatment plant and a main that connects a plurality of pump stations to the wastewater treatment plant. Each of the plurality of pump stations may include a wet well and a pump carried by the wet well to pump the wastewater. The system may include a central server and a sensor in communication with the central server to sense a level of wastewater within the wet well. The pump may be moved to an on position when the level of the wastewater in the wet well is at or above a first level. The level of wastewater within the wet well may be systematically manipulated responsive to the central server to control the fluid flow in the wastewater treatment system.

Abstract: The present invention relates to a method for determining the identity of a microfluidic device and a home position by means of a set of home position marks on the microfluidic device, which is of the type used in a microfluidic system. Said method comprises following phases: a microfluidic device scanning phase, wherein a microfluidic device is scanned for mark identifiers; a microfluidic device identifying phase, wherein at least one a characteristic feature of the set of home marks is/are determined and used for identifying the identity of the microfluidic device; a home position determining phase, wherein the home position is determined by the use of at least a subset of the home position marks identified during said previous phases. The present invention relates to a set of home marks, a microfluidic device carrying such a set of home marks, a microfluidic system, a computer program product and a computer program on a computer usable medium.

Abstract: A method for operating a Coriolis mass flow measuring device having at least one measuring pipe through which a medium flows, at least one vibration generator, at least a first vibration sensor, at least a second vibration sensor and at least a control and analyzing unit. The detection of measurement variables or diagnosis parameters is achieved with increased accuracy and security in that the control and analyzing unit calculates, at least indirectly and in a ratiometric manner, at least a derived secondary variable based on a primary measurement, wherein interested primary measurement signals are transmitted alternately to the control and analyzing unit via different measurement channels and wherein, based on the various values obtained from the different measurement channels regarding the primary measurement signals, compensation values of the transmitted primary measurement signals are calculated and used as a basis for the calculation of the derived secondary variable.

Abstract: A well passing through a geological formation is fitted with a tube, open at its bottom end, that is filled with a fluid. Another fluid is in the annular space between the tube and the wall of the well, the two fluids exhibiting an interface situated in the annular space. A hydraulic balance of the fluids of the well is disturbed and the trend of certain quantities is measured. These measurements are moreover simulated by computer by using different sets of values for the physical parameters, and efforts are made to estimate the geological formation. A comparison of the measurements with the simulation results makes it possible to identify an optimum set of values for the parameters.

Abstract: A method for determining a concentration of an analyte is disclosed. The method includes applying a potential excitation to a fluid sample containing an analyte and determining if a current decay curve associated with the fluid sample has entered an analyte depletion stage. The method also includes measuring a plurality of current values associated with the fluid sample during the analyte depletion stage and calculating an analyte concentration based on at least one of the plurality of current values.

Abstract: The invention relates to the method and apparatus for forming the calibration chart used to measure the amount of fuel inside the fuel tanks (1) which comprises at least one laser distance measurement device (2) positioned inside said fuel tank (1) and measuring the distance between itself and the inner wall of said fuel tank (1) at separate points, at least one main shaft (14) providing said distance measurement device (2) with rotational movement circularly in the direction of B through up to 360 degrees and in the upward-downward direction of A through up to 270 degrees and at least one inclinometer (4) positioned on the surface (9) and measuring the angle X between said fuel tank (1) and the ground on which it is located.

Abstract: A system to monitor a status from a secondary location of a plurality of equipment on a drilling site, while simultaneously enabling preventive maintenance is described herein. A user can view at least one cycle, at least one control state, and at least one pressure. The user can also view equipment information, equipment repair history, and other information necessary to ensure that a piece of equipment has minimal down time.

Abstract: The invention relates to the area of thermophysical studies of media and is intended for the determination of thermal properties of solid media by placing a measuring device on the surface of the medium. A heater, which is made in the form of a flexible membrane capable of taking the shape of the solid body surface under the action of the hold-down pressure and which additionally serves as a temperature sensor, is pressed to the solid body surface by using a hold-down element in such a way as to ensure that the heater shape fits the shape and irregularities of the solid body surface. The heater temperature is registered throughout the heater surface during and after the heating. The thermal conductivity and thermal diffusivity of the solid body are determined by processing the heater temperature measurement data both in the time range from the start of the solid body heating to the start of the thermal convention of the ambient medium and after the termination of the solid body heating process.

Abstract: A method to monitor a status from a secondary location of a plurality of equipment on a drilling site, while simultaneously enabling preventive maintenance for the plurality of equipment is described herein. A user can view at least one cycle, at least one control state, and at least one pressure. The user can also view equipment information, equipment repair history, and other information necessary to ensure that a piece of equipment has minimal down time.

Abstract: A computer assisted method to monitor a status from a secondary location of a plurality of equipment on a drilling site, while simultaneously enabling preventive maintenance is described herein. A user can view at least one cycle, at least one control state, and at least one pressure. The user can also view equipment information, equipment repair history, and other information necessary to ensure that a piece of equipment has minimal down time.

Abstract: In an electronic device and a method of correcting time-domain reflectometers, two channels of a time-domain reflectometer are connected to a corrector using cables, and the two channels are enabled to transmit pulses. Parameters Step Deskew and Channel Deskew of the two channels are zeroed. Resistance values of the two channels are measured simultaneously, and the value of the parameter Step Deskew of one of the two channels is adjusted according to the Resistance values of the two channels. Times of achieving the same resistance value of the two channels are measured after the cables and the connector have been disconnected, and the value of the parameter Channel Deskew of one of the two channels is adjusted according to the times of achieving the same resistance value. The adjusted values of the parameters Step Deskew and Channel Deskew are displayed through a display unit.

Abstract: A system and method allow a sensor device that is used in a process stream to be efficiently calibrated and monitored as to its operating condition. The sensor device is a measuring probe with a sensor portion, a memory device and an electrical input/output port, arranged so the memory device is in communication with both the sensor portion and the input/output port. The sensor device may be connected through an electrical connector to either a first external source, such as a personal computer having an input/output port, remote from the process stream, or a second external source, such as a transmitter, proximate to the process stream. Operating software is accessible to at least the first external source for monitoring and calibrating. Database software is accessible to each of the external sources, for storing data on every measuring probe used in the system.

Abstract: Switching a transmitting and receiving direction of two transducers (2,3) in the forward and the reverse direction, a time differential memory part (17b) storing a propagation time differential every K times a unit measurement process being executed, the propagation time differential being a differential between a propagation time of the ultrasonic wave signal in a forward direction and in a reverse direction, a flow rate calculating part (15) calculating a flow rate of a passing fluid based on a lump sum of propagation times in both the forward and the reverse directions obtained at least every K times of a unit measurement process being executed, an estimating part (18) estimating a change in a momentary flow rate of the fluid based on the time differential obtained every K times of the unit measurement process being executed and storing thereof in a time differential memory part (17b), thus obtaining an accurate flow rate and detecting the change in the momentary flow rate.

Abstract: A method to calibrate a flow meter includes passing a predetermined volume of fluid through a flow meter for calibration and determining a time duration of calibration from a start time to a stop time. One or more characteristics of the flow rate of the fluid is measured with the flow meter during the time duration and a plurality of time stamped measurements based on the one or more measured flow rate characteristics are generated. The flow meter is then calibrated based on the start time, the stop time, and the plurality of time stamped measurements.

Abstract: There is described herein a method for calibrating gas flowmeters comprising only one calibration procedure performed at the device level. The step of calibrating the differential pressure sensor itself may be omitted, and the design of the sensor may therefore be simplified by eliminating the sensor conditioner and instead using a microcontroller on the device for signal processing. This is done by a two-point calibration procedure with the use of three correction coefficients to compensate for the variability of flow tubes and pressure sensors.

Abstract: A processing system for delivering a process gas to a reaction chamber using a recipe having a recipe flow rate is provided. The processing system includes a gas flow delivery system configured for delivering the process gas, wherein said gas flow delivery system controlled by a mass flow controller (MFC) to an orifice. The predicted flow rate is previously computed by pressurizing a gas. The predicted flow rate further being previously computed measuring a set of upstream pressure values of the gas via at least one sensor. The processing system also includes a programmed computing device configured for applying a calibration factor of a set of calibration factors to determine the predicted flow rate, the calibration factor being a ratio of an average of the set of upstream pressure values to an average of a set of golden upstream pressure values.

Abstract: Signal processing is disclosed for a Coriolis mass flow meter with one or more measuring tubes and meter electronics, which includes determining relevant modal properties of the flow meter during a measurement process, and adaptively correcting a current measurement result with the relevant modal properties of the flow meter obtained during the measurement process.

Abstract: A method for operating a fuel quantity gauging system is described. The method includes utilizing redundant sensor sets at separate locations within a fuel tank to measure properties of the fuel mixture within the fuel tank, inputting the measured properties into a fuel regression equation, a separate fuel regression equation for each sensor set location, solving the multiple fuel regression equations to determine a slope and intercept and define a fuel regression curve for the fuel mixture, and utilizing the defined fuel regression curve to calculate at least a quantity of fuel in the fuel tank.

Abstract: There is described herein a flow sensing device having offset compensation and an offset compensation method, the flow sensing device having two separate and independent thermal flow sensors, each containing a heater and at least one temperature-sensitive element. The components of the two thermal flow sensors are connected such that flow-dependent contributions of each sensor into a common output signal have opposite signs after passing through a subtracting node. Heating pulses are applied to the heaters of the two thermal flow sensors out of phase, and an output signal is measured for each heat pulse applied. A net output signal is then determined by calculating a difference between a last output reading and at least one previous output reading.

Abstract: The present invention relates to a system, method, and computer program product for determining the flow rate of a fluid. The system, method, and computer program product generate a thermal sensor based mass flow rate for the fluid, where the thermal sensor based mass flow rate is determined at least in part from the thermal sensor signal (36). The system, method, and computer program product generate a pressure sensor based mass flow rate for the fluid, wherein the pressure sensor based mass flow rate is determined at least in part from the pressure sensor signal (51a). The system, method, and computer program product generate at least one calibration factor (?) using the thermal sensor based mass flow rate and the pressure sensor based mass flow rate. The system, method, and computer program product may generate a calibrated pressure sensor based mass flow rate by using the at least one calibration factor (?) to modify the pressure sensor based mass flow rate.

Abstract: A system in which a fluid flows characterized by a change with time in space. A preselected place in the system is monitored to collect data at two or more time points correlated to a system event. The data is indicative of a system parameter that varies with time as a function of at least two variables related to system wash-in and wash-out behavior. To select time points a calibration map is calculated using color hue indicative of wash-out and color intensity indicative of wash-in. A color coded output map is developed. The calibration map, the color coded output map and image are novel implementations.

Abstract: Increasing the effective aperture of an ultrasound imaging probe by including more than one probe head and using the elements of all of the probes to render an image can greatly improve the lateral resolution of the generated image. In order to render an image, the relative positions of all of the elements must be known precisely. A calibration fixture is described in which the probe assembly to be calibrated is placed above a test block and transmits ultrasonic pulses through the test block to an ultrasonic sensor. As the ultrasonic pulses are transmitted though some or all of the elements in the probe to be tested, the differential transit times of arrival of the waveform are measured precisely. From these measurements the relative positions of the probe elements can be computed and the probe can be aligned.

Abstract: A hydrocarbon exploration method is disclosed for generating anisotropic resistivity models of a subsurface reservoir from seismic and well data using a rock physics model. In one embodiment, the method comprises: selecting wells within a region of interest (101); obtaining a plurality of rock properties (102) and adjusting selected rock parameters (103) in the calibration of the rock physics model at the well locations; inverting porosity and shale content from seismic data (107); propagating the calibrated rock physics model to the region of interest (109) and calculating effective resistivity for the entire region of interest (109). The inventive method also provides for analyzing the uncertainty associated with the prediction of the resistivity volume.

Abstract: Drive techniques for a digital flowmeter are described. The drive techniques account for delays caused during digital signal processing of sensor signals that correspond to a motion of a flowtube, as well as drive signals that impart motion to the flowtube. Such delays may be caused by a variety of factors, including delays associated with analog/digital conversion of the signals and/or filtering of the signals. The techniques include open-loop techniques and closed-loop techniques, which can be used separately or together during the start-up and operation of the digital flowmeter.

Abstract: A fluid flow monitoring system is provided that has a processor utility which is connectable to an acoustic generator associated with acoustic ports and is operable for generating signals S0 to activate the acoustic ports for irradiating a region of interest with acoustic radiation of a certain frequency range centered at a frequency F0 and is connectable to at least one light output port associated with one or more light detectors for receiving light of at least one wavelength ? from the region of interest including light tagged by said acoustic radiation. The processor utility may be configured for analyzing the generated signals S0 and data indicative of the received light including light tagged by the corresponding acoustic radiation and determining correlation between the signals S0 and the data indicative of the received light, the correlation being informative of a measure of fluid flow in a turbid medium.

Abstract: In a cooling section having a plurality of coolant outlets, the coolant outlets are supplied with the coolant via transmission lines and a mutual main line. Individually opening and closing valves are disposed in the transmission lines. An automation device of the cooling section opens and closes the valves at valve-specific opening and closing times during the normal operation of the cooling section in order to apply coolant to the rolling stock according to a quantitative target coolant course. During the determination of the opening times, the automation device considers a respective valve-specific characteristic. In calibration operation of the cooling section, the respective characteristic is initially determined at least for some of the valves by opening and closing the respective valve, and detecting the chronological course of the quantitative coolant flow effected thereby by a measuring arrangement disposed in the main line.

Abstract: A soot discharge amount is calculated by multiplying a “steady discharge amount” by a “transient correction value.” The steady discharge amount is a soot discharge amount in a steady operation state, and is acquired through table search. For each of a plurality of factors which affect the soot discharge amount, a steady value (value obtained through table search) of the factor and a transient value (current value) of the factor are substituted for a characteristic equation which represents a change in the soot discharge amount with the value of the factor, whereby a steady characteristic value and a transient characteristic value are acquired. The “ratio between the steady characteristic value and the transient characteristic value” is then calculated for each factor. The transient correction value is obtained by multiplying together all values of the “ratio between the steady characteristic value and the transient characteristic value” obtained for the factors.

Abstract: A method and apparatus for monitoring multiphase fluid flow passing within a pipe is provided.

Abstract: Said method for predetermining at least one conversion parameter uses at least one transfer between a liquid phase and a gas phase, wherein: a gas phase is injected into a liquid phase so as to form a heterogeneous flow including a series of bubbles, formed from the gas phase, within the liquid phase; said heterogeneous flow is caused to occur within a flow member so as to carry out at least one transfer between the liquid and gas phases; the decrease in the volume of the bubbles is observed along said flow member; and said at least one parameter is derived therefrom.

Abstract: A multi-phase process fluid is passed through a vibratable flowtube. Motion is induced in the vibratable flowtube. A first apparent property of the multi-phase process fluid based on the motion of the vibratable flowtube is determined, and an apparent intermediate value associated with the multi-phase process fluid based on the first apparent property is determined. A corrected intermediate value is determined based on a mapping between the intermediate value and the corrected intermediate value. A phase-specific property of a phase of the multi-phase process fluid is determined based on the corrected intermediate value.

Abstract: Water droplets in exhaust gas that is, or was, analyzed by a remote emissions sensing system are detected. The detection may be made using measurements generally captured by the remote emissions sensing system during typical operation. As such, the detection may be applied “on site” as remote emissions sensing analysis is ongoing, or may be applied post hoc from data previously acquired by a remote emissions sensing system. The detection may be implemented without requiring additional sensors, more sophisticated sensors, and/or other additional or more sophisticated equipment being included in the remote emissions sensing system.

Abstract: A disposable conduit 1 includes piezo-electric elements 2a and 2b and a memory chip 10 in which calibration data specific to the relevant conduit is stored. Before measurement, a non-disposable electrical measuring circuit reads the calibration data out of the memory chip 10 to prepare a calibrating equation or a calibration table. A flow speed of a blood passing through the conduit or a flow rate calculated from the flow speed is corrected in accordance with the calibrating equation or calibration table.

Abstract: There is provided an electromagnetic flow meter that applies magnetic fields with a first frequency and a second frequency, to a fluid to be measured, calculates a first flow rate, calculates a second flow rate, performs low-pass filtering on the first flow rate to calculate a first low-pass filtered flow rate, and performs low-pass filtering on the second flow rate to calculate a second low-pass filtered flow rate, the electromagnetic flow meter including: an abnormality detecting unit that detects an abnormal state in which, the fluid is at non-full level on the basis of at least one of the first flow rate and the second flow rate; and an abnormality removing unit that removes the abnormal state on the basis of the first low-pass filtered flow rate and the second low-pass filtered flow rate, when the abnormality detecting unit does not determine that the fluid is in the abnormal state.

Abstract: Method for operating a vortex flowmeter device for measuring the flow of a fluid that flows through a measuring tube in which a baffle is arranged for producing eddies in the fluid. A signal-processing device processes signals of first and sensors produced by pressure fluctuations. A first signal is obtained by multiplication of the signal of the first sensor with a correction factor, and the second signal is obtained by multiplication of the signal of the second sensor with another correction factor such that a wanted signal is obtained from the deviation between the first signal and second signals, and a sum signal is formed from the sum of the first and second signals. A correlation between the wanted signal and the sum signal is determined and the correlation is minimized by variation of the correction factors, whereby same-phase interfering signals superimposed on anti-phase sensor signals are at least minimized.

Abstract: A finite difference level set projection algorithm on multi-staged quadrilateral grids for simulation of a split liquid film between two rollers. From one stage to the next, the number of meshes in the vertical direction changes by a select factor to provide a good balance between resolution and number of meshes. Having fewer meshes at the nip (the smallest gap between the rollers), the multi-staged quadrilateral grid allows a much bigger time step and requires much less CPU time to reach the steady state.