Dynamic Differential Pressure Research Articles

Visualization-based experimental investigation of microscopic sand production characteristics and mechanisms in weakly consolidated sandstone reservoirs

Sand production is a troublesome problem in the petroleum industry, especially in relation to weakly consolidated formations. In this work, a visual experimental apparatus, which allows sand particles to be observed, has been constructed to simulate sand production in weakly consolidated sandstone core. The experimental apparatus can accommodate sandstone core flakes as a reactor. The experiment aims to investigate the microscopic sand production mechanism of the weakly consolidated sandstone reservoir under the influence of high water cut, high clay content and polymer aging blockage. Core flakes were produced using simulated formation sands with median particle sizes of 160 μm and uniformity coefficients of 2.5, 4.6, 7.3 and 12.6, as well as clay (content 5%, 10%, 20%, 30%, respectively) and aged polymers in the wells. A total of 17 sets of experimental tests were carried out with water injection. The visual experimental results show that sand morphology presents complex wormhole. Morphology is particularly affected by core strength and heterogeneity. Based on dynamic differential pressure of experimental results, most sand production process is divided into two obvious stages, that is, the cavities formation stage of sharp sand production and the stable sand production stage. Analysis of sensitive factors revealed that the sand production rate is strongly influenced by the core strength and related to clay content, formation heterogeneity and production program. The volumetric sand production ratio decreases with the increase of core strength, with the volumetric sand production ratio (VSPR) reaching up to 0.24%. It is found that about 38% clay (1–3.91 μm) was produced in the initial stage of low flow, which is particularly evident in cores with high clay content. Moreover, for weakly consolidated reservoir, the particle competition peeling mechanism of wormhole front is proposed, and the strengthening bonding effect of aging polymer and the pore blockage effect of fine clay are clarified. The findings could contribute to better understanding of the mechanisms underlying sand production in weakly consolidated sandstone reservoirs, which also provide a solid evidence base for accurate sand production prediction and more targeted sand control.

The measurement of deformation rate of flexible container based on constant conductance element in molecular regime

An innovative method using constant conductance element to measure the deformation rate of flexible container was proposed based on the theoretical model of dynamic micro-flow detection. The measurement system of dynamic deformation rate was built by using the semi-flexible container encapsulated with polyimide film, and a constant conductance element was installed between the flexible container and the pressure stabilizing chamber to provide a constant micro-flow rate. The dynamic differential pressure variation between the inlet and the outlet of the constant conductance element was measured and then the deformation rate of flexible container could be obtained through the iterative calculation of the measured differential pressure change over time. The results show that the deformation rate gradually decreases with the increase of differential pressure. In addition, Boyle's law was used to verify the experimental results of dynamic micro-flow detection method, and it is revealed that the measurement error is less than 11%. Finally, a standard leak element was applied to simulate the leak source of flexible container. The conductance of standard leak element and the leak rate of flexible container have been successfully predicted by using the measured deformation rate.

The influence of an annular moonpool on towing resistance of a separated polar ocean nuclear energy platform

Offshore nuclear energy platforms may need to be pulled to ports for refueling every 2–3 years. At the initial stages of platform design, the towing resistance of the platforms must be studied. And the platform's towing resistance will be impacted by the moonpool. In this article, the moonpool of a separated polar ocean nuclear energy platform, originally circular, has become annular due to the presence of a floating body. This paper employs both numerical and model test approaches to investigate the impact of the annular moonpool on the towing resistance of the platform. The results demonstrate that a sequence of vortices will form inside the moonpool, and the moonpool will disrupt the flow field around the platform, increasing the platform's circumferential dynamic pressure and differential pressure resistance. As a result, the moonpool will eventually lead to a 6%–7% increase in overall towing resistance. And the frictional resistance only makes up a minor portion of the overall resistance of the two platforms because the two platforms aren't streamlined structures; instead, the differential pressure resistance makes up the majority of the total resistance. The results of the study provide a reference for calculating towing resistance for large conical platforms.

Characterization of the average pore diameter of nanoporous media by gas permeability measurement technique in transitional flow regime

In this paper, a gas permeability measurement technique in transitional flow regime was proposed, which could characterize the average pore diameter of nanoporous media non-destructively. With high purity argon and carbon dioxide, the conductance of three groups of porous anodic alumina was tested respectively in the transitional flow regime by the dynamic differential pressure attenuation test system, and the average pore diameter of porous anodic alumina was derived. The average pore diameters obtained through the gas permeability measurement technique are consistent with the SEM image analysis results, and the relative error is less than 8%. This method based on the improved transitional flow conductance theory extends the pore-size range of gas permeability measurement technique from micrometer to the nanometer scale, and does not require high pressure or high vacuum. It has the advantages of non-destruction, high-accuracy and large-area-measurement, which brings significant practical application value.

A newly-developed wide range molecular flow meter based on AAO leak element

An innovate constant volume flow meter (ICVFM) using AAO leak element was developed, and then applied to measure the pumping speed of dry vacuum pumps. The AAO leak element was calibrated with dynamic differential pressure decay method. The results imply that the conductance of AAO leak is inversely proportional to the square root of the molecular mass, and remains unchanged with pressure varying from vacuum to atmosphere. Then the pumping speed was measured by a simple test system. In the end, the uncertainties of calibrating AAO leak element and measuring pumping speed were considered to confirm the measurement capability. The newly developed flow meter enables flow measurements at pressures ranging from vacuum through atmospheric pressure, which has potential application in the semiconductor industry.

Volume measurement based on dynamic differential pressure decay using AAO leak element

A new technique to measure the volume of the metal container based on dynamic differential pressure decay by using anodic aluminum oxide (AAO) leak element is presented. The AAO is chosen as the leak element because its conductance remains constant from vacuum to atmosphere. The container to be measured is connected to the vacuum system via the AAO leak element. The dynamic differential pressure decay with time between the inlet and outlet of AAO leak assembly was measured and fitted by an exponential function, followed by volume calculation. The volume of two different containers has been obtained using this method with nitrogen, helium, and argon, respectively. The influence of temperature fluctuation on experimental results under vacuum and atmospheric pressure outlet conditions was discussed. For vacuum outlet conditions, the temperature change caused by pressure decay in one single experiment is small enough to satisfy the isothermal hypothesis, which makes the influence of temperature fluctuation on the experimental results negligible. The preliminary results compared with the static expansion method demonstrate that this novel volume measurement technique is accurate, simple and efficient.

Influence of magnetic field on barium sulfate incrustation from aqueous solutions

The formation of scales in the petroleum industry, such as those composed of calcium and barium sulfates, may reduce productivity since these sediments can partially or totally obstruct the pipes. The mitigation of these inorganic precipitates can be accomplished by using scale inhibitors or by non-intrusive physical technologies. Here, we investigated the influence of magnetic field on the incrustations of barium sulfate by analyzing the concentration of barium and sulfate ions, the solution flow rate, the capillary tube geometry, and the magnetic field intensity in a homemade experimental unit supported on the monitoring of the dynamic differential pressure. The results show that the saline concentration and the flow rate of the solutions and the geometry of the capillary tube have a significant influence on the dynamics of barium sulfate incrustation. The presence of the magnetic field tends to prolong the induction time of the barium sulfate precipitation. A semi-empirical model was used to describe the effect of the studied variables on the barium sulfate incrustation behavior. The X-ray diffraction data of the precipitated particles analyzed using the Rietveld method suggest that the use of the magnetic field favor the formation of more crystalline particles and with smaller crystallite size than those formed in the absence of a magnetic field. Optical and scanning electron microscopy measurements also corroborate with these findings. The results from this study suggest that magnetic fields can be of interest in practical crystallization processes of barium sulfate and successfully applied to decrease the speed of barium sulfate incrustation in pipelines.

Measurement and Prediction of Discharge Coefficients in Highly Compressible Pulsating Flows to Improve EGR Flow Estimation and Modeling of Engine Flows

An assumption of constant discharge coefficient (Cd) is often made when modeling highly compressible pulsating engine flows through valves or other restrictions. Similarly, orifices and flow nozzles used for real-time EGR flow estimation are often calibrated at a few steady-state points with one single constant Cd that minimizes the error over the selected points. This assumption is based on near constant Cd observed at high Reynolds number for steady flow. It has been shown in this work that this assumption is not reasonable for pulsating flow, particularly at large amplitudes and low flow rates. The discharge coefficient of a square-edged orifice placed in the exhaust stream of a diesel engine produced Cd’s varying between 0.60-0.90 for the resulting critical/near-critical flows. A novel pulsating flow measurement apparatus that allowed independent variation of pressure, flow rate and frequency and allowed reproducible measurements independent of transducer characteristics, produced Cd’s in the range of 0.25-0.60 with a similar square-edge orifice. The variation in Cd was characterized by two dimensionless variables that normalized the standard deviation of the pulsating signal with dynamic pressure and average differential pressure drop respectively. The results raise important questions that can potentially initiate fundamental work to fill the gap in the literature that exists for highly compressible pulsating flows.

Non-Klinkenberg slippage phenomenon at high pressure for tight core floods using a novel high pressure gas permeability measurement system

Klinkenberg slippage theory has been widely used to predict the percolation rules at high pore pressure for conventional core floods. However, recent studies have shown deviations to applications of Kinkenberg slippage theory at low back pressure for tight cores. A novel phenomenon of deviation to apparent gas permeability by Klinkenberg slippage theory as pressure differential increase for tight core is reported. To overcome problems of measuring apparent gas permeability for tight core accurately, a system of three novel equipment is invented composed of a high pressure micro flow meter, a high pressure micro flow experimental pressure control system, and a high pressure dynamic micro differential pressure gauge. Nitrogen permeability as a function of pressure gradient in tight core at high pressure differed than that at atmospheric pressure where nitrogen permeability varied inversely with pressure gradient according to Klinkenberg slippage theory. A novel phenomenon observed in this study was that as pore pressure increased passed an inflection pressure point, nitrogen permeability became directly related to pressure gradient contrary to the trend predicted by Klinkenberg slippage theory. As pore pressure became greater, the magnitude of nitrogen permeability enhancement is enhanced.

Visual Criteria for Measuring Two-phase Flow Rate in Venturi with Flow Homogenizer

A simple use of Venturi might be used to measure two-phase flow rate within relatively low GVF(gas volume fraction). Upstream flow entering Venturi can be improved with installed flow homogenizer which is easily fabricated by 3-dimensional printer with multiple holes. Simultaneous measurement between high-speed flow visualization and dynamic differential pressure measurement was made to find visual criteria for two-phase flow rate measurement with different GVF ranged from 0% to 30%. It was observed that the two-phase flow rate can be reliably measured up to 15% of GVF using flow homogenizer. FFT(Fast-Fourier Transform) results proved that the long flow homogenizers (type 2 and 4) showed a lower amplitude of differential pressure (Δp) than the short flow homogenizers (type 1 and 3) respectively. So the optimized flow homogenizer can be useful to measure two-phase flow rate at low GVF.

Characteristic Variables Extracting of the Gas-Liquid Two-Phase Flow through V-Cone Flowmeter Based on Adaptive Optimal-Kernel Theory

In order to study the mechanism of gas-liquid two-phase flow, a method of characteristic variables extracting based on Adaptive Optimal-Kernel (AOK) theory was represented in the paper. First, to collect dynamic differential pressure signal of gas-liquid two-phase flow through a horizontal V-cone flow meter, and then the AOK theory was used to analyze the dynamic differential pressure signal. The movement law of two-phase flow was discussed through the time-frequency spectrum. Finally, four characteristic variables were defined by using the time-frequency spectrum and the ridge of AOK. After the characteristic variables were visual analyzed, the relationship between the different combination of characteristic variables and the flow pattern was obtained. The results show that, characteristic variables defined by this method can get a clear description of the flow information. This method provides a new way for the flow patterns identification.

Time-Frequency Signal Processing for Gas-Liquid Two Phase Flow Through a Horizontal Venturi Based on Adaptive Optimal-Kernel Theory

A time-frequency signal processing method for two-phase flow through a horizontal Venturi based on adaptive optimal-kernel (AOK) was presented in this paper. First, the collected dynamic differential pressure signal of gas-liquid two-phase flow was preprocessed, and then the AOK theory was used to analyze the dynamic differential pressure signal. The mechanism of two-phase flow was discussed through the time-frequency spectrum. On the condition of steady water flow rate, with the increasing of gas flow rate, the flow pattern changes from bubbly flow to slug flow, then to plug flow, meanwhile, the energy distribution of signal fluctuations show significant change that energy transfer from 15–35 Hz band to 0–8 Hz band; moreover, when the flow pattern is slug flow, there are two wave peaks showed in the time-frequency spectrum. Finally, a number of characteristic variables were defined by using the time-frequency spectrum and the ridge of AOK. When the characteristic variables were visually analyzed, the relationship between different combination of characteristic variables and flow patterns would be gotten. The results show that, this method can explain the law of flow in different flow patterns. And characteristic variables, defined by this method, can get a clear description of the flow information. This method provides a new way for the flow pattern identification, and the percentage of correct prediction is up to 91.11%.

Time-frequency spectral analysis of gas-liquid two-phase flow’s fluctuations

In order to study different flow patterns’ dynamic characteristics of gas-liquid two-phase flow, three time-frequency analysis methods are introduced to process the dynamic differential pressure signal of gas-liquid two-phase flow, such as the wavelet transform, Hilbert-Huang transform and adaptive optimal-kernel method. The results show that the main part of energy is transferred from frequency band 15—35 Hz to 0—8 Hz when the flow pattern changes from bubbly flow to slug flow and plug flow, and two spectrum peaks are observed at slug flow. The experimental results show that the time-frequency resolution of Hilbert-Huang transform and adaptive optimal-kernel is higher than that of wavelet transform. The extractions of ridge information based on adaptive optimal-kernel overcome the influence of fuzzy plane windowing effect, and enhance the readability of time-frequency plane information. The time-frequency analysis clearly shows the dynamic characteristics of different flow patterns, and describes the variation rules with time. It is helpful to further study the mechanism of gas-liquid two-phase flow.

Neural networks approach for prediction of gas–liquid two-phase flow pattern based on frequency domain analysis of vortex flowmeter signals

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas–liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, a three-layer, feed-forward neural network was designed, and adopted inputs all representing the characteristics of the power spectral density distributions of dynamic differential pressure fluctuations were obtained from a vortex flowmeter. The validity of the adopted inputs for the flow pattern identification was evaluated by a proposed effectiveness factor. Results show that the designed neural networks predict the flow patterns successfully comparing with the flow pattern by visual observation. These findings provide the possibility of using only a vortex flowmeter for the identification of gas–liquid two-phase flow patterns with the help of neural networks.

On fluctuation of the dynamic differential pressure signal of Venturi meter for wet gas metering

Venturi meters are playing an increasingly important role in wet gas metering in natural gas and oil industries. Convincible measurement of the flowrate of wet gas requires two parameters, namely, the whole mass flowrate and its quality. It is commonly believed that the two parameters can be obtained if the Venturi meter is combined with another device of a different principle. However, this is not always the case. Owing to the complexity of the model for wet gas metering, the problem of multiple solutions may occur. Proceeding from a static model on the differential pressure (DP) signal of the Venturi meter, a dynamic model is presented that can provide an extra functional relation to resolve this problem without the need of adding a third device. This functional relation monotonously maps the relative fluctuation of the DP signal to the quality of the wet gas and simplifies the selection of the true solution. Experiments have been carried out within static pressure range of 0.3–0.8 MPa, gas flowrate range of 50–100 m 3/h and quality range of 0.06–0.412. Emphasis of the experiments has been on the demonstration of the validity of the static and dynamic models. Finally, appropriate discussions and conclusions are given.

Dynamic Differential Pressure Effects on Drilling of Permeable Formations

In the mathematical modeling of bit penetration rate for tri-cone roller bits in permeable formations, virtually all of the current techniques assume that the differential pressure between the bottom-hole wellbore pressure and the formation is a “static” value. This work shows that the appropriate differential pressure is a dynamic quantity, because for overbalanced drilling, fluid filtrate from the wellbore requires a finite time to flow into the formation, producing a changing pressure gradient ahead of the bit. Moreover, this dynamic gradient is directly dependent upon the rate of drill bit penetration, which is in turn dependent upon the dynamic gradient itself. Accordingly, coupled penetration rate and dynamic gradient equations must be solved, which frequently result in the prediction of higher drilling penetration rates than when the static gradient is used. The appropriate dynamic differential pressure equations are developed and applied to an example drilling situation. It is shown that with water-based drilling fluids, for rock with permeability greater than a few microdarcies at virtually all penetration rates, and for penetration rates less than 3 m/h (9.84 ft/h) at permeabilities greater than 1 μd (microdarcy), the dynamic differential pressure is significantly less than the static differential pressure. Accordingly, using the conventional static differential pressure results in the prediction of penetration rates that are much too low. Moreover, using measured penetration rates from the field, the conventional approach yields predicted in-situ rock strength that is much too high.