Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Bas...Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.展开更多
The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving ...The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.展开更多
The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow fo...The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.展开更多
The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,...The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.展开更多
This paper studies the transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient, the differential equations are derived and solved with nu...This paper studies the transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient, the differential equations are derived and solved with numerical computation. Basing on numerical solution, it is analyzed that: 1. the relation between the steady pressure at well bore (or at endpoint) and threshold pressure gradient, shut-in time, and the corresponding formulae ore derived; 2. the regulation of transient pressure peak. The result is very useful and will help experiments and applications in the development of low permeability reservoirs withthreshold pressure gradient.展开更多
Compared with conventional well, herringbone-like laterals wells can increase the area of oil release, and can reduce the number of wellhead slots of platforms,?and?also can greatly improve the development efficiency....Compared with conventional well, herringbone-like laterals wells can increase the area of oil release, and can reduce the number of wellhead slots of platforms,?and?also can greatly improve the development efficiency. Based on threshold pressure gradient in heavy oil reservoir,?and?the applied principle of mirror reflection and superposition, the pressure distribution equation of herringbone-like laterals wells is obtained in heavy oil reservoir. Productivity model of herringbone-like laterals wells is proposed by reservoir-wellbore steady seepage. The example shows that the productivity model is great accuracy?to?predict the productivity of herringbone-like laterals wells. The model is used to analyze the branching length, branching angle, branching symmetry, branching position and spacing and their effects on productivity of herringbone-like laterals wells. The principle of optimizing the well shape of herringbone-like laterals wells is proposed.展开更多
Some authors believe that a minimum pressure gradient(called threshold pressure gradient(TPG))is required before a liquid starts to flow in a porous medium.In a tight or shale oil formation,this TPG phenomenon becomes...Some authors believe that a minimum pressure gradient(called threshold pressure gradient(TPG))is required before a liquid starts to flow in a porous medium.In a tight or shale oil formation,this TPG phenomenon becomes more important,as it is more difficult for a fluid to flow.In this paper,experimental data on TPG published in the literature are carefully reviewed.What we found is that a very low flow velocity corresponding to a very low pressure gradient cannot be measured in the experiments.Experiments can only be done above some measurable flow velocities.If these flow velocities and their corresponding pressure gradients are plotted in an XY plot and extrapolated to zero velocity,a non-zero pressure gradient corresponds to this zero velocity.This non-zero pressure gradient is called threshold pressure gradient in the literature.However,in the regime of very low velocity and very low pressure gradient,the data gradually approach to the origin of the plot,demonstrating a non-linear relationship between the pressure gradient and the velocity.But the data do not approach to a point of zero velocity and a threshold pressure gradient.Therefore,the concept of threshold pressure gradient is a result of data misinterpretation of available experimental data.The correct interpretation is that there are two flow regimes:nonlinear flow regime(non-Darcy flow regime)when the pressure gradients are low,and linear flow regime(Darcy flow regime)when the pressure gradient is intermediate or high.The nonlinear flow regime starts from the origin point.As the pressure gradient is increased,the curve becomes a straight line demonstrating the linear flow regime.We have verified our views by first analyzing the causes of non-Darcy flow,and then systematically analyzed typical experimental data and correlations in the literature.We conclude that TPG does not exist.We also use several counter examples to support our conclusion.展开更多
This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high visco...This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high viscous oils(202 and 630 mPa⋅s)in a steel pipe of length 11.25 m and length-to-diameter ratio of 708.In addition,the experimental data from the literature comprising wide range of flow and fluid properties is analyzed.For the analysis,the liquid-liquid pipe flow data is categorized into two as:stratified and dispersed.The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase,interfacial curvature(contact/wetting angle-in lieu of material of the pipe)and fluid phase fraction.In the two-fluid model of stratified flow,the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers.Similarly,for dispersed flow,an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases.Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation,an effective friction factor for oil-water flow is proposed.Employing the proposed correlations,the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations.The average error and standard deviation values of−7.06%,20.72%and 0.31%,18.79%are found for stratified flow and dispersed flow respectively.展开更多
A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous po...A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.展开更多
BACKGROUND It is controversial whether transjugular intrahepatic portosystemic shunt(TIPS)placement can improve long-term survival.AIM To assess whether TIPS placement improves survival in patients with hepaticvenous-...BACKGROUND It is controversial whether transjugular intrahepatic portosystemic shunt(TIPS)placement can improve long-term survival.AIM To assess whether TIPS placement improves survival in patients with hepaticvenous-pressure-gradient(HVPG)≥16 mmHg,based on HVPG-related risk stratification.METHODS Consecutive variceal bleeding patients treated with endoscopic therapy+nonselectiveβ-blockers(NSBBs)or covered TIPS placement were retrospectively enrolled between January 2013 and December 2019.HVPG measurements were performed before therapy.The primary outcome was transplant-free survival;secondary endpoints were rebleeding and overt hepatic ence-phalopathy(OHE).RESULTS A total of 184 patients were analyzed(mean age,55.27 years±13.86,107 males;102 in the EVL+NSBB group,82 in the covered TIPS group).Based on the HVPG guided risk stratification,70 patients had HVPG<16 mmHg,and 114 patients had HVPG≥16 mmHg.The median follow-up time of the cohort was 49.5 mo.There was no significant difference in transplant-free survival between the two treatment groups overall(hazard ratio[HR],0.61;95%confidence interval[CI]:0.35-1.05;P=0.07).In the high-HVPG tier,transplant-free survival was higher in the TIPS group(HR,0.44;95%CI:0.23-0.85;P=0.004).In the low-HVPG tier,transplantfree survival after the two treatments was similar(HR,0.86;95%CI:0.33-0.23;P=0.74).Covered TIPS placement decreased the rate of rebleeding independent of the HVPG tier(P<0.001).The difference in OHE between the two groups was not statistically significant(P=0.09;P=0.48).CONCLUSION TIPS placement can effectively improve transplant-free survival when the HVPG is greater than 16 mmHg.展开更多
BACKGROUND Portal hypertension(PHT)in patients with alcoholic cirrhosis causes a range of clinical symptoms,including gastroesophageal varices and ascites.The hepatic venous pressure gradient(HVPG),which is easier to ...BACKGROUND Portal hypertension(PHT)in patients with alcoholic cirrhosis causes a range of clinical symptoms,including gastroesophageal varices and ascites.The hepatic venous pressure gradient(HVPG),which is easier to measure,has replaced the portal venous pressure gradient(PPG)as the gold standard for diagnosing PHT in clinical practice.Therefore,attention should be paid to the correlation between HVPG and PPG.METHODS Between January 2017 and June 2020,134 patients with alcoholic cirrhosis and PHT who met the inclusion criteria underwent various pressure measurements during transjugular intrahepatic portosystemic shunt procedures.Correlations were assessed using Pearson’s correlation coefficient to estimate the correlation coefficient(r)and determination coefficient(R^(2)).Bland-Altman plots were constructed to further analyze the agreement between the measurements.Disagreements were analyzed using paired t tests,and P values<0.05 were considered statistically significant.RESULTS In this study,the correlation coefficient(r)and determination coefficient(R2)between HVPG and PPG were 0.201 and 0.040,respectively(P=0.020).In the 108 patients with no collateral branch,the average wedged hepatic venous pressure was lower than the average portal venous pressure(30.65±8.17 vs.33.25±6.60 mmHg,P=0.002).Hepatic collaterals were identified in 26 cases with balloon occlusion hepatic venography(19.4%),while the average PPG was significantly higher than the average HVPG(25.94±7.42 mmHg vs 9.86±7.44 mmHg;P<0.001).The differences between HVPG and PPG<5 mmHg in the collateral vs no collateral branch groups were three cases(11.54%)and 44 cases(40.74%),respectively.CONCLUSION In most patients,HVPG cannot accurately represent PPG.The formation of hepatic collaterals is a vital reason for the strong underestimation of HVPG.展开更多
A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related n...A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.展开更多
After analyzing many studies of fluid flow theory of multi-porous media in low and extra-low permeability reservoirs and the numerical simulation of non-Darcy flow, we found that a negative flow rate occurs in the exi...After analyzing many studies of fluid flow theory of multi-porous media in low and extra-low permeability reservoirs and the numerical simulation of non-Darcy flow, we found that a negative flow rate occurs in the existing non-Darcy flow equation, which is unreasonable. We believe that the existing equation can only be considered as a discriminant to judging Darcy flow or non-Darcy flow, and cannot be taken as a fluid flow governing equation of multi-porous media. Our analysis of the experimental results shows that the threshold pressure gradient(TPG) of low and extra-low permeability reservoirs is excessively high, and does not conform to fluid flow through multi-porous media in the actual reservoir situation. Therefore, we present a reasonable TPG ranging from 0.006 to 0.04 MPa/m at the well depth of 1500 m and oil drainage distance of 500 m. The results of our study also indicate that the non-Darcy flow phenomenon will disappear when the TPG reaches a certain value. In addition, the TPG or non-Darcy flow in low and extra-low permeability reservoirs does not need to be considered in the productivity prediction and reservoir numerical simulation. At present, the black oil model or dual-porous media is suitable for simulating low and extra-low permeability reservoirs.展开更多
BACKGROUND Hepatic venous pressure gradient(HVPG)is the gold standard for diagnosis of portal hypertension(PH),invasiveness and potential risks in the process of measurement limited its widespread use.AIM To investiga...BACKGROUND Hepatic venous pressure gradient(HVPG)is the gold standard for diagnosis of portal hypertension(PH),invasiveness and potential risks in the process of measurement limited its widespread use.AIM To investigate the correlation of computed tomography(CT)perfusion parameters with HVPG in PH,and quantitatively assess the blood supply changes in liver and spleen parenchyma before and after transjugular intrahepatic portosystemic shunt(TIPS).METHODS Twenty-four PH related gastrointestinal bleeding patients were recruited in this study,and all patients were performed perfusion CT before and after TIPS surgery within 2 wk.Quantitative parameters of CT perfusion,including liver blood volume(LBV),liver blood flow(LBF),hepatic arterial fraction(HAF),spleen blood volume(SBV)and spleen blood flow(SBF),were measured and compared before and after TIPS,and the quantitative parameters between clinically significant PH(CSPH)and non-CSPH(NCSPH)group were also compared.Then the correlation of CT perfusion parameters with HVPG were analyzed,with statistical significance as P<0.05.RESULTS For all 24 PH patients after TIPS,CT perfusion parameters demonstrated decreased LBV, increased HAF, SBV and SBF, with no statistical difference in LBF. Compared withNCSPH, CSPH showed higher HAF, with no difference in other CT perfusion parameters. HAFbefore TIPS showed positive correlation with HVPG (r = 0.530, P = 0.008), while no correlation wasfound in other CT perfusion parameters with HVPG and Child-Pugh scores.CONCLUSIONHAF, an index of CT perfusion, was positive correlation with HVPG, and higher in CSPH thanNCSPH before TIPS. While increased HAF, SBF and SBV, and decreased LBV, were found afterTIPS, which accommodates a potential non-invasive imaging tool for evaluation of PH.展开更多
Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper ...Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper establishes a dual-porosity rate transient decline model for the horizontal well with consideration of the threshold pressure gradient, which represents the non-Darcy flow in a fracture system. The solution is obtained by employing the Laplace transform and the orthogonal transform. The bi-logarithmic type curves of the dimensionless production rate and derivative are plotted by the Stehfest numerical inversion method. Seven different flow regimes are identified and the effects of the influence factors such as the threshold pressure gradient, the elastic storativity ratio, and the cross flow coefficient are discussed. The presented research could interpret the production behavior more accurately and effectively for tight gas reservoirs.展开更多
An autonomous altitude adjustment system for a stratospheric satellite(StratoSat)platform is proposed.This platform consists of a helium balloon,a ballonet,and a two-way blower.The helium balloon generates lift to bal...An autonomous altitude adjustment system for a stratospheric satellite(StratoSat)platform is proposed.This platform consists of a helium balloon,a ballonet,and a two-way blower.The helium balloon generates lift to balance the platform gravity.The two-way blower inflates and deflates the ballonet to regulate the buoyancy.Altitude adjustment is achieved by tracking the differential pressure difference(DPD),and a threshold switching strategy is used to achieve blower flow control.The vertical acceleration regulation ability is decided not only by the blower flow rate,but also by the designed margin of pressure difference(MPD).Pressure difference is a slow-varying variable compared with altitude,and it is adopted as the control variable.The response speed of the actuator to disturbance can be delayed,and the overshoot caused by the large inertia of the platform is inhibited.This method can maintain a high tracking accuracy and reduce the complexity of model calculation,thus improving the robustness of controller design.展开更多
By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical...By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green's function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal's approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal's approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What's more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.展开更多
A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecti...A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations.Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model,a corresponding numerical solution method is presented.First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy's flow problem, the exact analytical solution for the case of Darcy's flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform.A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporatethe quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.展开更多
AIM: To determine the correlation between the hepatic venous pressure gradient and the endoscopic grade of esophageal varices.METHODS: From September 2009 to March 2013, a total of 176 measurements of hepatic venous p...AIM: To determine the correlation between the hepatic venous pressure gradient and the endoscopic grade of esophageal varices.METHODS: From September 2009 to March 2013, a total of 176 measurements of hepatic venous pressure gradient(HVPG) were done in 146 patients. Each transjugular HVPG was measured twice, first using an end whole catheter(EH-HVPG), and then using a balloon catheter(B-HVPG). The HVPG was compared with the endoscopic grade of esophageal varices(according to the general rules for recording endoscopic findings of esophagogastric varices), which was recorded within a month of the measurement of HVPG.RESULTS: The study included 110 men and 36 women, with a mean age of 56.1 years(range, 43-76 years). The technical success rate of the pressure measurements was 100% and there were no complication related to the procedures. Mean HVPG was 15.3 mm Hg as measured using the end hole catheter method and 16.5 mm Hg as measured using the balloon catheter method. Mean HVPG(both EHHVPG and B-HVPG) was not significantly different among patients with different characteristics, including sex and comorbid factors, except for cases with hepatocellular carcinoma(B-HVPG, P = 0.01; EH-HVPG, P = 0.02). Portal hypertension(> 12 mm Hg HVPG) occurred in 66% of patients according to EH-HVPG and 83% of patients according to B-HVGP, and significantly correlated with Child's status(B-HVPG, P < 0.000; EHHVGP, P < 0.000) and esophageal varies observed upon endoscopy(EH-HVGP, P = 0.003; B-HVGP, P = 0.006). One hundred and thirty-five endoscopies were performed, of which 15 showed normal findings, 27 showed grade 1 endoscopic esophageal varices, 49 showed grade 2 varices, and 44 showed grade 3 varices. When comparing endoscopic esophageal variceal grades and HVPG using univariate analysis, the P value was 0.004 for EH-HVPG and 0.002 for B-HVPG. CONCLUSION: Both EH-HVPG and B-HVPG showed a positive correlation with the endoscopic grade of esophageal varices, with B-HVPG showing a stronger correlation than EH-HVPG.展开更多
Portal hypertension is the main prognostic factor in cirrhosis. The recent emergence of potent antiviral drugs and new algorithm of treatment for the management of complications due to portal hypertension have sensibl...Portal hypertension is the main prognostic factor in cirrhosis. The recent emergence of potent antiviral drugs and new algorithm of treatment for the management of complications due to portal hypertension have sensibly changed our perception of cirrhosis that can be now considered as a multistage liver disease whose mortality risk can be reduced by a tailored approachfor any stage of risk. Experts recommend to move toward a pathophysiological classification of cirrhosis that considers both structural and functional changes. The hepatic venous pressure gradient HVPG, is the reference gold standard to estimate the severity of portal hypertension in cirrhosis. It correlates with both structural and functional changes that occur in cirrhosis and carries valuable prognostic information to stratify the mortality risk. This article provides a general overview of the pathophysiology and natural course of cirrhosis and portal hypertension. We propose a simplified classification of cirrhosis based on low, intermediate and high mortality stage. The prognostic information provided by HVPG is presented according to each stage. A comparison with prognostic models based on clinical and endoscopic variables is discussed in order to evidence the additional contribute given by HVPG on top of other clinical and instrumental variables widely used in clinical practice.展开更多
基金The authors gratefully acknowledge the financial supports from the National Science Foundation of China under Grant 52274027 as well as the High-end Foreign Experts Recruitment Plan of the Ministry of Science and Technology China under Grant G2022105027L.
文摘Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.
基金Project supported by the National Natural Science Foundation of China(Grant No.51404232)the China Postdoctoral Science Foundation(Grant No.2014M561074)the National Science and Technology Major Project,China(Grant No.2011ZX05038003)
文摘The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.
基金Project(51304220) supported by the National Natural Science Foundation of ChinaProject(3144033) supported by the Beijing Natural Science Foundation,ChinaProject(20130007120014) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.
基金National Basic Research Program of China(2007CB209506)
文摘The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.
文摘This paper studies the transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient, the differential equations are derived and solved with numerical computation. Basing on numerical solution, it is analyzed that: 1. the relation between the steady pressure at well bore (or at endpoint) and threshold pressure gradient, shut-in time, and the corresponding formulae ore derived; 2. the regulation of transient pressure peak. The result is very useful and will help experiments and applications in the development of low permeability reservoirs withthreshold pressure gradient.
文摘Compared with conventional well, herringbone-like laterals wells can increase the area of oil release, and can reduce the number of wellhead slots of platforms,?and?also can greatly improve the development efficiency. Based on threshold pressure gradient in heavy oil reservoir,?and?the applied principle of mirror reflection and superposition, the pressure distribution equation of herringbone-like laterals wells is obtained in heavy oil reservoir. Productivity model of herringbone-like laterals wells is proposed by reservoir-wellbore steady seepage. The example shows that the productivity model is great accuracy?to?predict the productivity of herringbone-like laterals wells. The model is used to analyze the branching length, branching angle, branching symmetry, branching position and spacing and their effects on productivity of herringbone-like laterals wells. The principle of optimizing the well shape of herringbone-like laterals wells is proposed.
基金The work presented in this paper is supported by the U.S.Department of Energy under Award Number DE-FE0024311.
文摘Some authors believe that a minimum pressure gradient(called threshold pressure gradient(TPG))is required before a liquid starts to flow in a porous medium.In a tight or shale oil formation,this TPG phenomenon becomes more important,as it is more difficult for a fluid to flow.In this paper,experimental data on TPG published in the literature are carefully reviewed.What we found is that a very low flow velocity corresponding to a very low pressure gradient cannot be measured in the experiments.Experiments can only be done above some measurable flow velocities.If these flow velocities and their corresponding pressure gradients are plotted in an XY plot and extrapolated to zero velocity,a non-zero pressure gradient corresponds to this zero velocity.This non-zero pressure gradient is called threshold pressure gradient in the literature.However,in the regime of very low velocity and very low pressure gradient,the data gradually approach to the origin of the plot,demonstrating a non-linear relationship between the pressure gradient and the velocity.But the data do not approach to a point of zero velocity and a threshold pressure gradient.Therefore,the concept of threshold pressure gradient is a result of data misinterpretation of available experimental data.The correct interpretation is that there are two flow regimes:nonlinear flow regime(non-Darcy flow regime)when the pressure gradients are low,and linear flow regime(Darcy flow regime)when the pressure gradient is intermediate or high.The nonlinear flow regime starts from the origin point.As the pressure gradient is increased,the curve becomes a straight line demonstrating the linear flow regime.We have verified our views by first analyzing the causes of non-Darcy flow,and then systematically analyzed typical experimental data and correlations in the literature.We conclude that TPG does not exist.We also use several counter examples to support our conclusion.
文摘This paper aims to propose correlations to predict pressure gradient,friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow.To develop the correlations,experiments are conducted using high viscous oils(202 and 630 mPa⋅s)in a steel pipe of length 11.25 m and length-to-diameter ratio of 708.In addition,the experimental data from the literature comprising wide range of flow and fluid properties is analyzed.For the analysis,the liquid-liquid pipe flow data is categorized into two as:stratified and dispersed.The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase,interfacial curvature(contact/wetting angle-in lieu of material of the pipe)and fluid phase fraction.In the two-fluid model of stratified flow,the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers.Similarly,for dispersed flow,an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases.Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation,an effective friction factor for oil-water flow is proposed.Employing the proposed correlations,the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations.The average error and standard deviation values of−7.06%,20.72%and 0.31%,18.79%are found for stratified flow and dispersed flow respectively.
基金the National Science Fund for Distinguished Young Scholars of China (Grant No. 51125019)the National Key Basic Research and Development Program of China (973 Program, Grant No. 2011CB201005)the Research Foundation of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University (Grant No. PLN-ZL201201)
文摘A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.
基金Supported by the National Natural Science Foundation of China,No.81900552Nanjing Health Science,Technology Development Special Fund Project-Key project,No.ZKX19015+1 种基金Outstanding Youth Fund project,No.JQX20005Funding for Clinical Trials from the Affiliated Drum Tower Hospital,Medical School of Nanjing University,No.2022-LCYJ-MS-13.
文摘BACKGROUND It is controversial whether transjugular intrahepatic portosystemic shunt(TIPS)placement can improve long-term survival.AIM To assess whether TIPS placement improves survival in patients with hepaticvenous-pressure-gradient(HVPG)≥16 mmHg,based on HVPG-related risk stratification.METHODS Consecutive variceal bleeding patients treated with endoscopic therapy+nonselectiveβ-blockers(NSBBs)or covered TIPS placement were retrospectively enrolled between January 2013 and December 2019.HVPG measurements were performed before therapy.The primary outcome was transplant-free survival;secondary endpoints were rebleeding and overt hepatic ence-phalopathy(OHE).RESULTS A total of 184 patients were analyzed(mean age,55.27 years±13.86,107 males;102 in the EVL+NSBB group,82 in the covered TIPS group).Based on the HVPG guided risk stratification,70 patients had HVPG<16 mmHg,and 114 patients had HVPG≥16 mmHg.The median follow-up time of the cohort was 49.5 mo.There was no significant difference in transplant-free survival between the two treatment groups overall(hazard ratio[HR],0.61;95%confidence interval[CI]:0.35-1.05;P=0.07).In the high-HVPG tier,transplant-free survival was higher in the TIPS group(HR,0.44;95%CI:0.23-0.85;P=0.004).In the low-HVPG tier,transplantfree survival after the two treatments was similar(HR,0.86;95%CI:0.33-0.23;P=0.74).Covered TIPS placement decreased the rate of rebleeding independent of the HVPG tier(P<0.001).The difference in OHE between the two groups was not statistically significant(P=0.09;P=0.48).CONCLUSION TIPS placement can effectively improve transplant-free survival when the HVPG is greater than 16 mmHg.
文摘BACKGROUND Portal hypertension(PHT)in patients with alcoholic cirrhosis causes a range of clinical symptoms,including gastroesophageal varices and ascites.The hepatic venous pressure gradient(HVPG),which is easier to measure,has replaced the portal venous pressure gradient(PPG)as the gold standard for diagnosing PHT in clinical practice.Therefore,attention should be paid to the correlation between HVPG and PPG.METHODS Between January 2017 and June 2020,134 patients with alcoholic cirrhosis and PHT who met the inclusion criteria underwent various pressure measurements during transjugular intrahepatic portosystemic shunt procedures.Correlations were assessed using Pearson’s correlation coefficient to estimate the correlation coefficient(r)and determination coefficient(R^(2)).Bland-Altman plots were constructed to further analyze the agreement between the measurements.Disagreements were analyzed using paired t tests,and P values<0.05 were considered statistically significant.RESULTS In this study,the correlation coefficient(r)and determination coefficient(R2)between HVPG and PPG were 0.201 and 0.040,respectively(P=0.020).In the 108 patients with no collateral branch,the average wedged hepatic venous pressure was lower than the average portal venous pressure(30.65±8.17 vs.33.25±6.60 mmHg,P=0.002).Hepatic collaterals were identified in 26 cases with balloon occlusion hepatic venography(19.4%),while the average PPG was significantly higher than the average HVPG(25.94±7.42 mmHg vs 9.86±7.44 mmHg;P<0.001).The differences between HVPG and PPG<5 mmHg in the collateral vs no collateral branch groups were three cases(11.54%)and 44 cases(40.74%),respectively.CONCLUSION In most patients,HVPG cannot accurately represent PPG.The formation of hepatic collaterals is a vital reason for the strong underestimation of HVPG.
文摘A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.
基金sponsored by National Key Project of Science and Technology of the Ministry of Science and Technology(MOST)(Grant No.2011ZX05043-002)
文摘After analyzing many studies of fluid flow theory of multi-porous media in low and extra-low permeability reservoirs and the numerical simulation of non-Darcy flow, we found that a negative flow rate occurs in the existing non-Darcy flow equation, which is unreasonable. We believe that the existing equation can only be considered as a discriminant to judging Darcy flow or non-Darcy flow, and cannot be taken as a fluid flow governing equation of multi-porous media. Our analysis of the experimental results shows that the threshold pressure gradient(TPG) of low and extra-low permeability reservoirs is excessively high, and does not conform to fluid flow through multi-porous media in the actual reservoir situation. Therefore, we present a reasonable TPG ranging from 0.006 to 0.04 MPa/m at the well depth of 1500 m and oil drainage distance of 500 m. The results of our study also indicate that the non-Darcy flow phenomenon will disappear when the TPG reaches a certain value. In addition, the TPG or non-Darcy flow in low and extra-low permeability reservoirs does not need to be considered in the productivity prediction and reservoir numerical simulation. At present, the black oil model or dual-porous media is suitable for simulating low and extra-low permeability reservoirs.
基金Supported by the National Natural Science Foundation of China General Program,No. 81871461
文摘BACKGROUND Hepatic venous pressure gradient(HVPG)is the gold standard for diagnosis of portal hypertension(PH),invasiveness and potential risks in the process of measurement limited its widespread use.AIM To investigate the correlation of computed tomography(CT)perfusion parameters with HVPG in PH,and quantitatively assess the blood supply changes in liver and spleen parenchyma before and after transjugular intrahepatic portosystemic shunt(TIPS).METHODS Twenty-four PH related gastrointestinal bleeding patients were recruited in this study,and all patients were performed perfusion CT before and after TIPS surgery within 2 wk.Quantitative parameters of CT perfusion,including liver blood volume(LBV),liver blood flow(LBF),hepatic arterial fraction(HAF),spleen blood volume(SBV)and spleen blood flow(SBF),were measured and compared before and after TIPS,and the quantitative parameters between clinically significant PH(CSPH)and non-CSPH(NCSPH)group were also compared.Then the correlation of CT perfusion parameters with HVPG were analyzed,with statistical significance as P<0.05.RESULTS For all 24 PH patients after TIPS,CT perfusion parameters demonstrated decreased LBV, increased HAF, SBV and SBF, with no statistical difference in LBF. Compared withNCSPH, CSPH showed higher HAF, with no difference in other CT perfusion parameters. HAFbefore TIPS showed positive correlation with HVPG (r = 0.530, P = 0.008), while no correlation wasfound in other CT perfusion parameters with HVPG and Child-Pugh scores.CONCLUSIONHAF, an index of CT perfusion, was positive correlation with HVPG, and higher in CSPH thanNCSPH before TIPS. While increased HAF, SBF and SBV, and decreased LBV, were found afterTIPS, which accommodates a potential non-invasive imaging tool for evaluation of PH.
基金Project supported by the National Key Basic Research Development Program of China(973 Program,Grant No.2014CB239205)
文摘Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper establishes a dual-porosity rate transient decline model for the horizontal well with consideration of the threshold pressure gradient, which represents the non-Darcy flow in a fracture system. The solution is obtained by employing the Laplace transform and the orthogonal transform. The bi-logarithmic type curves of the dimensionless production rate and derivative are plotted by the Stehfest numerical inversion method. Seven different flow regimes are identified and the effects of the influence factors such as the threshold pressure gradient, the elastic storativity ratio, and the cross flow coefficient are discussed. The presented research could interpret the production behavior more accurately and effectively for tight gas reservoirs.
基金the National Natural Science Foundation of China(No.52175103)。
文摘An autonomous altitude adjustment system for a stratospheric satellite(StratoSat)platform is proposed.This platform consists of a helium balloon,a ballonet,and a two-way blower.The helium balloon generates lift to balance the platform gravity.The two-way blower inflates and deflates the ballonet to regulate the buoyancy.Altitude adjustment is achieved by tracking the differential pressure difference(DPD),and a threshold switching strategy is used to achieve blower flow control.The vertical acceleration regulation ability is decided not only by the blower flow rate,but also by the designed margin of pressure difference(MPD).Pressure difference is a slow-varying variable compared with altitude,and it is adopted as the control variable.The response speed of the actuator to disturbance can be delayed,and the overshoot caused by the large inertia of the platform is inhibited.This method can maintain a high tracking accuracy and reduce the complexity of model calculation,thus improving the robustness of controller design.
基金Project supported by the Fundamental Research Funds for the Central Universities(Grant No.2652014066)
文摘By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green's function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal's approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal's approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What's more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.
基金funding by the project (Grant 51404232) sponsored by the National Natural Science Foundation of Chinathe National Science and Technology Major Project (Grant 2011ZX05038003)+1 种基金the China Postdoctoral Science Foundation project (Grant 2014M561074)the China Scholarship Council for its generous financial support of the research
文摘A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations.Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model,a corresponding numerical solution method is presented.First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equations with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be stably numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy's flow problem, the exact analytical solution for the case of Darcy's flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform.A comparison of these model solutions leads to the conclusion that such moving boundary problems must incorporatethe quadratic pressure gradient term in their governing equations; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pressure gradient increasing for the one-dimensional problem.
基金Supported by the Research Program of the National Research Foundation of Koreafunded by the Ministry of Education and Science and Technology No.2010-0011678and the Soonchunhyang University Research Fund
文摘AIM: To determine the correlation between the hepatic venous pressure gradient and the endoscopic grade of esophageal varices.METHODS: From September 2009 to March 2013, a total of 176 measurements of hepatic venous pressure gradient(HVPG) were done in 146 patients. Each transjugular HVPG was measured twice, first using an end whole catheter(EH-HVPG), and then using a balloon catheter(B-HVPG). The HVPG was compared with the endoscopic grade of esophageal varices(according to the general rules for recording endoscopic findings of esophagogastric varices), which was recorded within a month of the measurement of HVPG.RESULTS: The study included 110 men and 36 women, with a mean age of 56.1 years(range, 43-76 years). The technical success rate of the pressure measurements was 100% and there were no complication related to the procedures. Mean HVPG was 15.3 mm Hg as measured using the end hole catheter method and 16.5 mm Hg as measured using the balloon catheter method. Mean HVPG(both EHHVPG and B-HVPG) was not significantly different among patients with different characteristics, including sex and comorbid factors, except for cases with hepatocellular carcinoma(B-HVPG, P = 0.01; EH-HVPG, P = 0.02). Portal hypertension(> 12 mm Hg HVPG) occurred in 66% of patients according to EH-HVPG and 83% of patients according to B-HVGP, and significantly correlated with Child's status(B-HVPG, P < 0.000; EHHVGP, P < 0.000) and esophageal varies observed upon endoscopy(EH-HVGP, P = 0.003; B-HVGP, P = 0.006). One hundred and thirty-five endoscopies were performed, of which 15 showed normal findings, 27 showed grade 1 endoscopic esophageal varices, 49 showed grade 2 varices, and 44 showed grade 3 varices. When comparing endoscopic esophageal variceal grades and HVPG using univariate analysis, the P value was 0.004 for EH-HVPG and 0.002 for B-HVPG. CONCLUSION: Both EH-HVPG and B-HVPG showed a positive correlation with the endoscopic grade of esophageal varices, with B-HVPG showing a stronger correlation than EH-HVPG.
文摘Portal hypertension is the main prognostic factor in cirrhosis. The recent emergence of potent antiviral drugs and new algorithm of treatment for the management of complications due to portal hypertension have sensibly changed our perception of cirrhosis that can be now considered as a multistage liver disease whose mortality risk can be reduced by a tailored approachfor any stage of risk. Experts recommend to move toward a pathophysiological classification of cirrhosis that considers both structural and functional changes. The hepatic venous pressure gradient HVPG, is the reference gold standard to estimate the severity of portal hypertension in cirrhosis. It correlates with both structural and functional changes that occur in cirrhosis and carries valuable prognostic information to stratify the mortality risk. This article provides a general overview of the pathophysiology and natural course of cirrhosis and portal hypertension. We propose a simplified classification of cirrhosis based on low, intermediate and high mortality stage. The prognostic information provided by HVPG is presented according to each stage. A comparison with prognostic models based on clinical and endoscopic variables is discussed in order to evidence the additional contribute given by HVPG on top of other clinical and instrumental variables widely used in clinical practice.
