Driving Pressure Ratio Research Articles

Quantitative study of droplet generation by pressure-driven microfluidic flows in a flow-focusing microdroplet generator

To precisely control the size of droplets is of great importance for the applications of the droplet microfluidics. In a flow-focusing microdroplet generator, the pressure-driven microfluidic device is designed to control the flow rates of the fluids. For a specific geometry of the flow-focusing microchannel, a mathematical model of droplet formation is established, and the nonlinear relation between the droplet length and the driven-pressure ratio can be described by our model. For pressure-driven microfluidic flows, the nonlinear relation between the droplet length and the driving-pressure ratio is measured experimentally in the flow-focusing microchannel. Particularly, by using the closed-loop control method of droplet generation, good agreements are shown between the measured size of droplets and the predicted size of the droplets. As a result, the control precision of the droplet size can be increased drastically by the closed-loop control method of droplet generation. Consequently, monodisperse droplets of extremely small size can be produced in the flow-focusing microdroplet generator.

Driving Pressure Is Associated With Outcome in Pediatric Acute Respiratory Failure.

Driving pressure (ratio of tidal volume over respiratory system compliance) is associated with mortality in acute respiratory distress syndrome. We sought to evaluate if such association could be identified in critically ill children. We studied the association between driving pressure on day 1 of mechanical ventilation and ventilator-free days at day 28 through secondary analyses of prospectively collected physiology data. Medical-surgical university hospital PICU. Children younger than 18 years (stratified by Pediatric Mechanical Ventilation Consensus Conference clinical phenotype definitions) without evidence of spontaneous respiration. Inspiratory hold maneuvers. Data of 222 patients with median age 11 months (2-51 mo) were analyzed. Sixty-five patients (29.3%) met Pediatric Mechanical Ventilation Consensus Conference criteria for restrictive and 78 patients (35.1%) for mixed lung disease, and 10.4% of all patients had acute respiratory distress syndrome. Driving pressure calculated by the ratio of tidal volume over respiratory system compliance for the whole cohort was 16 cm H2O (12-21 cm H2O) and correlated with the static airway pressure gradient (plateau pressure minus positive end-expiratory pressure) (Spearman correlation coefficient = 0.797; p < 0.001). Bland-Altman analysis showed that the dynamic pressure gradient (peak inspiratory pressure minus positive end-expiratory pressure) overestimated driving pressure (levels of agreement -2.295 to 7.268). Rematching the cohort through a double stratification procedure (obtaining subgroups of patients with matched mean levels for one variable but different mean levels for another ranking variable) showed a reduction in ventilator-free days at day 28 with increasing driving pressure in patients ventilated for a direct pulmonary indication. Competing risk regression analysis showed that increasing driving pressure remained independently associated with increased time to extubation (p < 0.001) after adjusting for Pediatric Risk of Mortality III 24-hour score, presence of direct pulmonary indication jury, and oxygenation index. Higher driving pressure was independently associated with increased time to extubation in mechanically ventilated children. Dynamic assessments of driving pressure should be cautiously interpreted.

Precise monodisperse droplet generation by pressure-driven microfluidic flows

In a T-junction microdroplet generator, as monodisperse droplets are formed for the droplet digital polymerase chain reaction (PCR), a mathematical model which can describe the nonlinear relation of droplet generation under pressure-driven microfluidic flows is established. For various viscosity of the fluids, the relation between the droplet length and the driving-pressure ratio is measured at a low capillary number (Ca < 0.01) of droplet generation. It can be observed that the droplet length varies nonlinearly with the driving-pressure ratio for a specific geometry of the T-junction. In particular, the relation between the droplet length and the driving-pressure ratio is tested experimentally for different geometries of the T-junctions. At low capillary numbers, the nonlinear relation between the droplet length and the driving-pressure ratio is basically determined by the geometrical parameters of the T-junction. Most importantly, a closed-loop control droplet microfluidic system is demonstrated, and the size of the droplets can be controlled more accurately by pressure-driven flows. The control precision of the droplet size is quantitatively studied for a wide range of typical conditions of droplet generation. In particular, the relative standard deviation of the droplet size for various flow conditions is less than 2%, which is of great importance for improving the detection accuracy of nucleic acid based on the droplet digital PCR.

Optimisation of the fuelling of hydrogen vehicles using cascade systems and ejectors

The present study investigates the replacement of expansion valves, used in the cascade system of hydrogen fuelling stations, by a series of ejectors. The major advantage of using ejectors is to recover part of the kinetic energy lost during the expansion of a high-pressure primary flow, in order to entrain a lower pressure secondary flow; thus resulting in a more efficient fuelling.Firstly, a quasi-steady 1-D simulation model of the ejector was calibrated using computational fluid dynamics in terms of the main geometry and pressure conditions.Secondly, the quasi-steady 1-D model of the ejector was used in a dynamic model of the hydrogen fuelling station, in order to investigate the influence of its geometry on the transient fuelling performances. Different fuelling scenarios were explored with varying number of buffer tanks in the cascade system of the fuelling station, and different initial pressures in the vehicle's tank. The results show that the replacement of the expansion valve by an ejector may reduce the energy consumption for hydrogen compression by up to 6.5% using two buffer tanks in the cascade system. On the other hand, increasing the number of buffer tanks reduces the energy savings as the driving pressure ratio decreases.

Control of pre-existing fabric in fracture formation, reactivation and vein emplacement under variable fluid pressure conditions: an example from Archean greenstone belt, India

Abstract. Most of the upper crustal fluid flows are strongly influenced by the pre-existing fractures/foliations in the rocks under a certain state of tectonic stress and fluid pressure condition. In the present study, we analyzed a wide range of crosscutting fractures that are filled with quartz veins of variable orientations and thicknesses, from the gold-bearing massive metabasalts (supracrustals) of the Chitradurga Schist Belt adjacent to the Chitradurga Shear Zone (CSZ), Western Dharwar Craton, southern India. The study involves the following steps: (1) analyzing the internal magnetic fabric, using anisotropy of magnetic susceptibility (AMS) studies, and determining strength of the host metabasalts, (2) quantifying the fluid pressure condition through lower hemisphere equal area projection of pole to veins by determining the driving pressure ratio (R′), stress ratio (ϕ), and susceptibility to fracturing, and (3) deciphering the paleostress condition using fault-slip analysis. We interpret the NNW–SSE to NW–SE (mean 337/69∘ NE) oriented magnetic fabric in the rocks of the region as having developed during regional D1/D2 deformation on account of NE–SW shortening. However, D3 deformation manifested by NW–SE to E–W shortening led to the sinistral movement along CSZ. As a consequence of this sinistral shearing, fractures with prominent orientations formed riedel shear components, with CSZ as the shear boundary. Subsequently, all the pre-existing fabrics along with the riedel shear components were reactivated and vein emplacement took place through episodic fluid pressure fluctuation from high to low Pf at shallow depth (∼ 2.4 km). However, NNW–SSE orientations were prone to reactivate under both high- and low-Pf conditions, thereby attaining maximum vein thickness along these orientations. The deduced paleostress from fault-slip analysis along with the kinematics of the fractures and veins are in good agreement with previously estimated regional tectonics. Thus, integrating multiple domains of studies helps in the logical interpretation of fluid flow conditions and vein emplacement mechanisms in the study area that has not been ventured before.

Paleostress and statistical analysis using quartz veins from mineralized and non-mineralized zones: Application for exploration targeting

Quartz vein orientations, thickness and spacing data are analyzed from 10 transects each of mineralized and non-mineralized zones of Gadag region, which is a gold-bearing terrain within the Dharwar Craton (Southern India). Paleostress analysis reveals that the veins emplaced when fluid pressure (Pf) varied from Pf>σ2 (intermediate principle stress) to Pf < σ2. Variation in ΔR′ is estimated in the mineralized and non-mineralized zone during Pf fluctuation (Pf > σ2 to Pf < σ2). Variation in driving pressure ratio (ΔR′) for transects in mineralized zone is greater than in non-mineralized zone. Fractal dimension (Dc), Weibull modulus (α), vein intensity (Vi) and coefficient of vein spacing (Cv(S)) are calculated from vein data of each transect. Dc and α values are lower in mineralized zone vis-à-vis non-mineralized zone, thus implying that the former is weaker and has higher growth rate than the latter. Moreover, Vi and mean thickness of veins are higher in the mineralized zone than the non-mineralized zone. These differences in paleostress and vein statistical distributions are exploited to propose a three-axis “mineralization potential plot” designated P-D-F plot. This plot integrates ΔR′, α, Dc and Cv(S) data from each transect and it is established that points representing transects (data) from mineralized zone lie closer to the origin (0,0,0) than those in non-mineralized domain. The distance between origin and the point representing the transect in the P-D-F plot gives the “mineralization potential parameter” (Md). Lower Md implies higher mineralization potential. It is concluded that comparative studies of paleostress and vein distribution in mineralized and non-mineralized zones of an area can be very useful and the P-D-F plot developed through this study can be applied for exploration targeting.

The Complete Performance Map of Gas Wave Ejector and Analysis on the Variation Laws and Limitation of Performance

Abstract The gas wave ejector (GWE) is an efficient gas wave equipment using pressure waves to realize energy exchange. In this paper, a theoretical analysis of the limitation of application range and the factors affecting the performance of GWE was carried out by numerical simulation. And a complete experimental system including an adjustable GWE was employed to obtain the specific performance values in various working conditions. Such theoretical analysis showed that the device became inapplicable with a relatively high driving pressure ratio, resulting from the generation of supersonic flow at the outlet end of the passages. A relatively high supercharging ratio also limited the equipment application because of the weakening of the reflected expansion waves and the enhancement of the reversed compression wave. Furthermore, the mixing, vortex, viscosity, and other flow losses could also affect the equipment performance. Then, a complete performance map indicating the specific performance values in the application range was obtained by plenty of experiments. The performance map proved that GWE had excellent efficiency and broad applicability especially as the driving pressure ratio was lower than 2.6. The results are significant for practical application and performance improvement of GWE.

The relation between differential stress, driving pressure ratio, tensile strength and reservoir failure in a magmatic system – Towards eruption forecasting

In this study a relation is established between differential stress (σd), driving magma pressure ratio (R′) and tensile strength (T) of a rock mass in a volcanic system. It is shown that in σd vs. R′ space, the T curve follows equation of rectangular hyperbola and for dyking or volcanic eruption to occur, this T curve must be exceeded. It is proposed that this theoretical relation can be exploited to understand magma reservoir failure and for volcanic eruption forecasting. Applicability of this concept is demonstrated on Santorini volcanic system (Greece) for which considerable background information is available from previous studies. Published dyke orientation and aspect ratio data from Santorini yield σd and R′ values of 8.04 MPa and 0.22 respectively. Considering a weak quality host rock mass in Santorini, tensile strength curve for T = 1.5 MPa is plotted in σd vs R′ space. Considering magma reservoir volume and rock physical property estimates to be valid, and assuming σd and absolute stress to be constant, it is argued that change in reservoir dynamics would be controlled by variations in volume of magma released from the deeper magma reservoir to shallow reservoir (Vr) in Santorini. Values of R′ and Vr for the events of non-dyking in Santorini are also calculated. Minimum R′ and Vr required to induce dyking and eruption are estimated and it is concluded that the proposed theory can be generally applied for eruption forecasting.

Paleostress and fluid-pressure regimes inferred from the orientations of Hishikari low sulfidation epithermal gold veins in southern Japan

The orientation distribution of dilational fractures is affected by the state of stress around the fractures and by the pressure of the fluid that opened the fractures. Thus, the distribution can be inverted to determine not only the stress but also the pressure condition at the time of vein formation. However, epithermal ore veins that we observe today are the results of a great number of intermittent upwelling of overpressured fluids with different pressures. Here, we define driving pressure index (DPI) as the representative non-dimensionalized fluid pressure for the fluids. We collected the orientations of ∼1000 ore veins in the Hishikari gold mine, which were deposited at around 1 Ma, in southern Kyushu, Japan. It was found that the majority of the veins were deposited under an extensional stress with a NW-SE-trending σ3-axis and a northeasterly-inclined σ1-axis with relatively high stress ratio. The representative driving pressure ratio was ∼0.2. Data sets obtained at different depths in the mine indicated a positive correlation of representative driving pressure ratios with the depths. The correlation suggests repeated formation and break of pressure seals during the mineralization. Our compilation of the Pliocene–Quaternary stress regimes in southern Kyushu, including the result of the present study, suggests that epithermal gold mineralization was associated with distributed extensional deformations in southern Kyushu, and strain localization into an intra-arc rift seems to have terminated the mineralization.

Stress state and fluid pressure analyses using ultramafic dykes and calcite veins, SW Iran

In this paper, orientations of ultramafic dykes and calcite veins of the Tange-Hana area (SW Iran) are used to determine the relative stress and fluid pressure (Pf) conditions by constructing a 3D Mohr circle. The pole distributions of ultramafic dykes have a wide range of orientation and mainly show the girdle pattern. The 3D Mohr circle construction for ultramafic dykes suggests a Pf > σ2 condition and shows high value of fluid pressure (Pf = 939.51) near to the maximum principal stress (σ1). Driving pressure ratio (R′) and stress ratio (O) were calculated as 0.78 and 0.7, for ultramafic dykes, respectively. Calcite vein polar distribution is so limited and mainly shows a cluster pattern. Limited distribution of calcite vein orientation indicates a Pf < σ2 condition. The 3D Mohr circle construction reveals small amount of fluid pressure (Pf = 288.55) near to the minimum principal stress (σ3). The amounts of driving pressure ratio (R′) and stress ration (O) were calculated to be equal to 0.07 and 0.27, for calcite veins, respectively. Our results show the occurrence of ultramafic dykes and that calcite veins are related to different stress phases. Also, according to our results, it revealed that ultramafic and calcite dykes and veins were generated in prolate and oblate stress ellipsoid conditions, respectively.

Delusive Influence of Nondimensional Numbers in Canonical Hypersonic Nonequilibrium Flows

AbstractA finite volume–based unstructured inviscid flow solver has been developed for the study of nonequilibrium effects in high enthalpy flows. Four different inviscid flux computation schemes are tested for literature reported test cases like unsteady wave motion in a shock tube and high enthalpy flow over cylinder/sphere. During the present assessment, encouraging agreement has been noticed in capturing all the essential flow features in the reacting media. Here, the Rusanov scheme is noticed to be computationally cheaper among all the schemes with noticeable diffusion around strong gradients. Shock tube test case revealed the existence of various shock Mach numbers for a given driving pressure ratio in the presence of reactions. Similarly, freestream Mach number is found to have limitations in representing the shock standoff distance in case of high enthalpy flow over cylinder and sphere. In line with this, real gas effects are prominently observed for the case of the cylinder in comparison with the...

Dyke intrusion into a pre-existing joint network: The Aiguablava lamprophyre dyke swarm (Catalan Coastal Ranges)

A structural analysis has been performed in the Upper Permian lamprophyric dyke swarm of Aiguablava (Costa Brava, NE Iberia). Emplacement of sub-vertical dykes is related to the presence of a widespread joint network, mostly developed during the cooling and decompression of the late Variscan leucogranitic host rocks. The joint pattern consists on multiple sub-vertical joint sets among which two orthogonal sets at ≈N23° and ≈N113° are predominant. A sub-horizontal set is also prominent. The sub-vertical dykes have a mean N100°–N125° trend, which corresponds to the trend of one of the main joint sets. However, dyke segmentation is noticeable at the Dm- to cm-scale, and this is inferred to be related to dyke propagation and emplacement along the variably oriented pre-existing joints. A mean robust sub-horizontal NNE–SSW net dilation direction was measured from matching dyke jogs, markers in the host rock and analysis of maximum dyke thicknesses, and this is in line with the minimum principal stress axis (3) derived from a three-dimensional paleostress analysis from dyke orientations. The inferred maximum principal stress axis (1) is sub-vertical, indicating that dykes intruded under conditions of tectonic extension. Furthermore, a Mohr construction allowed calculation of the stress ratio φ=0.29 (close to a prolate stress ellipsoid) and a driving pressure ratio R′=0.27, which corresponds to a magmatic pressure almost equal to the intermediate principal stress axis, σ2. It is inferred that many of the pre-existing joint sets were exploited by the magma, the WNW–ESE joint set (normal to σ3) being the most favorable for dyke emplacement. The present study highlights the structural control of a pre-existing fracture network on emplacement of the Aiguablava lamprophyres in the upper crust during late Permian NNE–SSW brittle extension.

3-D Mohr circle construction using vein orientation data from Gadag (southern India) – Implications to recognize fluid pressure fluctuation

In this paper orientations of quartz veins from the Archaean age lode-gold bearing region of Gadag (southern India) are used to determine the relative stress and fluid pressure (Pf) conditions by constructing 3-D Mohr circle. Anisotropy of magnetic susceptibility (AMS) analysis of the host massive metabasalt reveals that the magnetic foliation is NW–SE striking, which is related to early NE–SW compression (D1/D2 deformation) that affected the region. The quartz veins have a wide range of orientations, with NW–SE striking veins (steep northeasterly dips) being the most prominent. Vein emplacement is inferred to have taken place under NW–SE compression that is known to have caused late deformation (D3) in the region. It is argued that the NW–SE fabric defined the pre-existing anisotropy and channelized fluid flow during D3. The permeability was initially low, which resulted in high Pf (>σ2). 3-D Mohr circle analysis indicates that the driving pressure ratio (R′) was 0.94, a condition that favoured fracturing and reactivation of fabric elements (foliations and fractures) having a wide range of orientations. This led to an increase in permeability and fluid flowed (burped) into the fractures. Resulting vein emplacement and sealing of fractures led to a reduction of Pf (<σ2). It is argued that at this low Pf, NW–SE oriented structures continued to remain susceptible to reactivation and vein emplacement, while fractures of all other orientations were inactive and remained sealed. As a consequence, the study area has a cluster of NW–SE oriented veins. R′ is calculated to be 0.07 from 3-D Mohr circle analysis at low Pf, when fractures with NW–SE orientation only were susceptible to dilation. However, it is envisaged that any emplacement of veins in these fractures would have sealed them, thus reducing the permeability and initiating the next cycle of rise in Pf (>σ2). Thus, it is concluded that the quartz veins in the Gadag region are a consequence of an interplay between conditions that fluctuated from Pf > σ2 to Pf < σ2.

Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method

Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn o , driving pressure ratio P i /P o , and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn o and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn oc = 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.

Experimental studies on heat and mass transfer in tubular generator for R134a-DMF absorption refrigeration system

Experimental investigations have been carried out to study heat and mass transfer during desorption of Tetrafluoro ethane (R134a) from R134a and Dimethyl formamide (DMF) solution in a tubular generator. Absorption refrigeration system has been built with brazed plate heat exchangers as condenser, absorber, evaporator and solution heat exchanger and with stainless steel concentric tubes as the generator. Effects of operational parameters viz., solution two phase Reynolds number, driving temperature ratio, driving pressure ratio, solution initial concentration on generator performance are analyzed. Desorption ratio, Sherwood number and Nusselt number increase as the solution Reynolds number, solution initial concentration, driving temperature ratio increase whereas these parameters decrease as the driving pressure ratio increases. Finally a correlation for Nusselt number and Sherwood number are proposed based on the experimental studies.

Heat and mass transfer studies on compact generator of R134a/DMF vapour absorption refrigeration system

Experimental investigation on the performance of compact generator of R134a/DMF vapour absorption refrigeration system is presented. The system uses brazed plate heat exchangers as generator, condenser, absorber, evaporator and solution heat exchanger and has a rated cooling capacity of 1 kW. The influence of driving temperature ratio, driving pressure ratio, R134a mass fraction and solution two phase Reynolds number is studied. This kind of system can be operated with low grade thermal energy such as solar energy, waste heat, etc. The generator temperature is chosen accordingly between 353 K and 368 K. Desorption ratio and Sherwood number increase as the solution Reynolds number, solution initial mass fraction, and driving temperature ratio increase whereas they decrease as the driving pressure ratio increases. The performance of the compact generator at different operating conditions is presented. Based on the present data, empirical correlations for Nusselt number and Sherwood number are proposed.

Hydrofracturing-related sill and dyke emplacement at shallow crustal levels: the Eastern Elba Dyke Complex, Italy

Abstract An example of sheet-like intrusion emplacement at very shallow crustal levels on Elba Island, Italy, is described. The Eastern Elba Dyke Complex (EEDC) consists of decimetre- to metre-thick sheeted aplites emplaced within intensely folded low-grade metamorphic rocks. Field data indicate that sill and dyke emplacement was controlled by mechanical discontinuities, represented by fractures in the host rocks, and was strongly favoured by magma overpressure. The occurrence of angular fragments of host rocks in the dyke border zones and the branching of sills testify to hydraulic fracturing. Analysis of the spatial distribution and geometry of EEDC sills and dykes provides clues on fluid pressure conditions and the stress state at the time of magma emplacement, as well as on the depth of emplacement. The calculated stress ratio and driving pressure ratio were used to estimate a magma overpressure of 6–54 MPa at the time of emplacement of the EEDC at a depth of about 2 km.

UNIQUE BEHAVIORS OF A BACKWARD-FACINGSTEP FLOW AT MICROSCALE

ABSTRACT The direct simulation Monte Carlo (DSMC) method is used to simulate micro backward-facing step flows in both slip and transition flow regimes. The effects of rarefaction on flow characteristics are analyzed and discussed. It is found that flow separation, recirculation, and reattachment will disappear as Knudsen number Kn exceeds 0.1. The stability of the vortex behind the step relies on the magnitudes of mean and thermal velocities in the region, which are closely related to the Kn number, local temperature, and driving pressure ratio. A highly intensified pressure and velocity region behind the step is identified in the transition flow regime. The mechanism leading to the significant increase of velocity and pressure is discussed. The effect of rarefaction on the surface shear stress and friction coefficient is also studied.

3-D Mohr circle analysis of vein opening, Indarama lode-gold deposit, Zimbabwe: implications for exploration

The Indarama lode gold deposit is hosted by vertically-dipping basalt in the Late Archaean Midlands Greenstone Belt of Zimbabwe. Major deformation events at 2.68 and 2.58 Ga established a complex array of fractures. A limited range of orientations of this fracture network opened towards the end of the younger deformation event, creating a lode pattern where 92% of mineralised veins dip at less than 50°, mainly to the E and W, and most strike directions are represented. A clustered distribution of poles to the quartz–carbonate veins indicates a constrictional stress field at the time of vein opening where σ 1 and σ 2 were near horizontal, (directed NNW–SSE and ENE–WSW, respectively), and σ 3 was near vertical. 3-D Mohr circle analysis demonstrates that σ 2 was approximately 67% of σ 1 (the stress ratio) and that the driving pressure ratio ( R′) was approximately 0.4, reflecting the role of fluid pressure, mean stress, and the maximum shear stress in controlling conditions of fracture opening.

Mechanistic Design of Conventional Plunger-Lift Installation

ABSTRACT A mechanistic model for conventional plunger lift installation design is presented. This model applies to oil wells with high gas-liquid ratios and is based on the fundamental equations of momentum balance and mass conservation. The model considers that the rate of liquid fall-back produced when the plunger rises is a linear function of the average rise velocity. The obtained set of ordinary non-linear differential equations needs to be solved numerically. A Fortran computer program for both personal and mainframe based computers was implemented. This permits the calculation of fall-back losses and allows the estimation of optimum cycle time. The model, verified with field quality data, has been shown to represent observed production trends in the wells studied, in particular the shape of the fall-back versus driving pressure ratio on the plunger is reproduced correctly. Differences between liquid/gas production and model estimations fall in the 15 to 20 percent range. This result is encouraging, considering the difficulty involved in obtaining accurate field measurements. The computer program developed can be effectively used for the design and troubleshooting of conventional plunger lift installations.