Impacts of proppant distribution on development of tight oil reservoirs with threshold pressure gradient

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.

Effect of quadratic pressure gradient term on a one-dimensional moving boundary problem based on modified Darcy's law

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 equa- tions with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be sta- bly 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 conclu- sion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equa- tions; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pres- sure gradient increasing for the one-dimensional problem.

Cirrhosis and portal hypertension: The importance of risk stratification, the role of hepatic venous pressure gradient measurement

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.

Comparison of hepatic venous pressure gradient and endoscopic grading of esophageal varices

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 mmHg as measured using the end hole catheter method and 16.5 mmHg as measured using the balloon catheter method. Mean HVPG (both EH-HVPG 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 mmHg 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; EH-HVGP, 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.

Hepatic venous pressure gradient measurement before TIPS for acute variceal bleeding

Hepatic venous pressure gradient(HVPG)is an independent predictor of variceal rebleeding in patients with cirrhosis.After pharmacological and/or endoscopic therapy,the use of a transjugular intrahepatic portosystemic shunt(TIPS)may be necessary in HVPG non-responders,but not in responders.Thus,HVPG measurement may be incorporated into the treatment algorithm for acute variceal bleeding,which further identifies the candidates that should undergo early insertion of TIPS or maintain the traditional pharmacological and/or endoscopic therapy.The potential benefits are to reduce the cost and prevent TIPS-related complications.

Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics

For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.

Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

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.

Correlation of pressure gradient in three hepatic veins with portal pressure gradient

BACKGROUND The liver is one of the most important organs in the human body,with functions such as detoxification,digestion,and blood coagulation.In terms of vascular anatomy,the liver is divided into the left and the right liver by the main portal vein,and there are three hepatic efferent veins(right,middle,and left)and two portal branches.Patients with impaired liver function have increased intrahepatic vascular resistance and splanchnic vasodilation,which may lead to an increase in the portal pressure gradient(PPG)and cause portal hypertension(PHT).In order to measure the increased pressure gradient of portal vein,the hepatic venous pressure gradient(HVPG)can be measured to reflect it in clinical practice.The accuracy of PPG measurements is directly related to patient prognosis.AIM To analyze the correlation between HVPG of three hepatic veins and PPG in patients with PHT.METHODS From January 2017 to December 2019,102 patients with PHT who met the inclusion criteria were evaluated during the transjugular intrahepatic portosystemic shunt procedure and analyzed.RESULTS The mean HVPG of the middle hepatic vein was 17.47±10.25 mmHg,and the mean HVPG of the right and left hepatic veins was 16.34±7.60 and 16.52±8.15 mmHg,respectively.The average PPG was 26.03±9.24 mmHg.The correlation coefficient and coefficient of determination of the right hepatic vein,middle hepatic vein,and left hepatic vein were 0.15 and 0.02(P=0.164);0.25 and 0.05(P=0.013);and 0.14 and 0.02(P=0.013),respectively.The mean wedged hepatic vein/venous pressure(WHVP)of the middle and left hepatic veins was similar at 29.71±12.48 and 29.1±10.91 mmHg,respectively,and the mean WHVP of the right hepatic vein was slightly lower at 28.01±8.95 mmHg.The mean portal vein pressure was 34.11±8.56 mmHg.The correlation coefficient and coefficient of determination of the right hepatic vein,middle hepatic vein,and left hepatic vein were 0.26 and 0.07(P=0.009);0.38 and 0.15(P<0.001);and 0.26 and 0.07(P=0.008),respectively.The average free hepatic venous pressure(FHVP)of the right hepatic vein was lowest at 11.67±5.34 mmHg,and the average FHVP of the middle and left hepatic veins was slightly higher at 12.19±4.88 and 11.67±5.34 mmHg,respectively.The average inferior vena cava pressure was 8.27±4.04 mmHg.The correlation coefficient and coefficient of determination of the right hepatic vein,middle hepatic vein,and left hepatic vein were 0.30 and 0.09(P=0.002);0.18 and 0.03(P=0.078);and 0.16 and 0.03(P=0.111),respectively.CONCLUSION Measurement of the middle hepatic vein HVPG could better represent PPG.Considering the high success rate of clinical measurement of the right hepatic vein,it can be the second choice.

Discontinuous element pressure gradient stabilizations for compressible Navier-Stokes equations based on local projections

A pressure gradient discontinuous finite element formulation for the compressible Navier-Stokes equations is derived based on local projections. The resulting finite element formulation is stable and uniquely solvable without requiring a B-B stability condition. An error estimate is Obtained.

Computed tomography perfusion in liver and spleen for hepatitis B virus-related portal hypertension:A correlation study with hepatic venous pressure gradient

BACKGROUND Hepatic venous pressure gradient(HVPG)is the gold standard for diagnosis of portal hypertension(PH).However,its use can be limited because it is an invasive procedure.Therefore,it is necessary to explore a non-invasive method to assess PH.AIM To investigate the correlation of computed tomography(CT)perfusion of the liver with HVPG and Child-Pugh score in hepatitis B virus(HBV)-related PH.METHODS Twenty-eight patients(4 female,24 male)with gastroesophageal variceal bleeding induced by HBV-related PH were recruited in our study.All patients received CT perfusion of the liver before transjugular intrahepatic portosystemic stent-shunt(TIPS)therapy.Quantitative parameters of CT perfusion of the liver,including liver blood flow(LBF),liver blood volume(LBV),hepatic artery fraction,splenic blood flow and splenic blood volume were measured.HVPG was recorded during TIPS therapy.Correlation of liver perfusion with Child-Pugh score and HVPG were analyzed,and the receiver operating characteristic curve was analyzed.Based on HVPG(>12 mmHg vs≤12 mmHg),patients were divided into moderate and severe groups,and all parameters were compared.RESULTS Based on HVPG,18 patients were classified into the moderate group and 10 patients were classified into the severe group.The Child-Pugh score,HVPG,LBF and LBV were significantly higher in the moderate group compared to the severe group(all P<0.05).LBF and LBV were negatively associated with HVPG(r=-0.473,P<0.05 and r=-0.503,P<0.01,respectively),whereas splenic blood flow was positively associated with hepatic artery fraction(r=0.434,P<0.05).LBV was negatively correlated with Child-Pugh score.Child-Pugh score was not related to HVPG.Using a cutoff value of 17.85 mL/min/100 g for LBV,the sensitivity and specificity of HVPG≥12 mmHg for diagnosis were 80%and 89%,respectively.CONCLUSION LBV and LBF were negatively correlated with HVPG and Child-Pugh scores.CT perfusion imaging is a potential non-invasive quantitative predictor for PH in HBV-related liver cirrhosis.

Riemann problem of a Chapman-Jouguet combustion model for pressure-gradient system

In this paper,the Riemann problem of a Chapman-Jouguet combustion model for the pressure-gradient equations is considered.By analyzing in phase space,existence and uniqueness of the solution to the Riemann problem are obtained constructively under the global entropy conditions.

THE EFFECT OF MAGNETIC FIELDS ON LOW FREQUENCY OSCILLATING NATURAL CONVECTION WITH PRESSURE GRADIENT

The oscillating natural convection in the presence of transverse magnetic field with time depending pressure gradient is studied. The analysis of the problem is carried out by assuming that the fluid is flowing in a parallel plate configuration. The emphasis is on low frequency oscillating convective flows induced by g-jitter associated with micro gravity because of their importance to the space processing materials. A general solution for an oscillating flow in the presence of transverse magnetic field is carried out. Some special cases of the oscillating flow and its response to an applied magnetic field are performed. It was observed that the behavior of oscillating free convective flows depends on frequency, amplitude of the driving buoyancy forces, temperature gradient,magnetic field and the electric conditions of the channel walls. In the absence of magnetic field, buoyancy force plays a predominant role in driving the oscillatory flow pattern, and velocity magnitude is also affected by temperature gradients. To suppress the oscillating flow external magnetic field can be used. It is also found that the reduction of the velocity is inversely proportional to the square of the applied magnetic field with conducting wall but directly proportional to the inverse of the magnetic field with insulating wall. Detailed calculations and computational results are also carried out to depict the real situation.

TRANSIENT PRESSURE OF PERCOLATION THROUGH ONE DIMENSION POROUS MEDIA WITH THRESHOLD PRESSURE GRADIENT

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 are 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 with threshold pressure gradient.

Collagen proportionate area correlates to hepatic venous pressure gradient in non-abstinent cirrhotic patients with alcoholic liver disease

AIM To explore the relationship between collagen proportionate area(CPA) and portal hypertension-related clinical manifestations in alcoholic liver disease(ALD).METHODS Retrospective study with chart review of patients with ALD adressed to our center between January 2012 and December 2013 for a transjugular liver biopsy(TJLB) and hepatic hemodynamic study. Patients were included if they met the following criteria:(1) Medical indication for a liver biopsy in the setting of ALD;(2) recent(< 15 d) clinical, radiological, endoscopic and biological data available; and(3) estimated follow-up of at least 6 mo. Liver tissue from cirrhotic subjects obtained from transjugular liver biopsies was stained with Picro Sirius red and computer-assisted digital image analysis to determine fibrosis density using CPA was performed. RESULTS We included 61 patients with alcoholic ALD, subdivided in 41 active alcohol drinkers and 20 durably abstinent patients. Nine healthy liver donors served as controls. Mean CPA in patients with ALD was 7.1%, with no difference between active drinkers and abstinent patients(P = 0.17). Using a fibrosis density cutoff of 5%, we observed a positive correlation between high fibrosis density and the hepatic venous pressure gradient(HVPG) only in active drinkers(P = 0.02). At 12-mo of follow-up, in the group of active alcohol drinkers, patients reaching a composite outcome showed a higher HVPG value as compared to those who did not(18.5 mm Hg vs 14.5 mm Hg P < 0.04) whereas CPA values were similar(6.9% vs 11%, P = 0.23).CONCLUSION In active alcoholic ALD, CPA correlates to portal pressure but only HVPG predicts clinical events, pointing to the role of alcohol as a modulator of portal hypertension.

Sildenafil does not influence hepatic venous pressure gradient in patients with cirrhosis

AIM： To investigate if sildenafil increases splanchnic blood flow and changes the hepatic venous pressure gradient （HVPG） in patients with cirrhosis. Phosphodiesterase type-5 inhibitors are valuable in the treatment of erectile dysfunction and pulmonary hypertension in patients with end-stage liver disease. However, the effect of phosphodiesterase type-5 inhibitors on splanchnic blood flow and portal hypertension remains essentially unknown. METHODS： Ten patients with biopsy proven cirrhosis （five females/five males, mean age 54：1：8 years） and an HVPG above 12 mmHg were studied after informed consent. Measurement of splanchnic blood flow and the HVPG during liver vein catheterization were done before and 80 min after oral administration of 50 mg sildenafil. Blood flow was estimated by use of indocyanine green clearance technique and Fick＇s principle, with correction for non-steady state. RESULTS： The plasma concentration of sildenafil was 222 ± 136 ng/mL 80 min after administration. Mean arterial blood pressure decreased from 77 ±7 mmHg to 66 ± 12 mmHg, P = 0.003, while the splanchnicblood flow and oxygen consumption remained unchanged at 1.14 ± 0.71 L/min and 2.3 ± 0.6 mmol/ min, respectively. Also the HVPG remained unchanged （18 ± 2 mmHg vs 16 ± 2 mmHg） with individual changes ranging from -8 mmHg to ±2 mmHg. In seven patients, HVPG decreased and in three it increased. CONCLUSION： In spite of arterial blood pressure decreases 80 min after administration of the phosphodiesterase type-5 inhibitor sildenafil, the present study could not demonstrate any clinical relevant influence on splanichnic blood flow, oxygen consumption or the HVPG.

Experimental study on moisture migration of remodeled clay under different overburden pressure and temperature gradients

Unidirectional freezing experiments under overburden pressure were carried out, in order to study the driving force of mois- ture migration of remodeled clay during freezing, through improving the indoor moisture migration test device. Overburden pressure and cooling temperature with the same circumstance were changed to determine the influence on water migration of a single factor. Results show that water content increases above the location of the final ice lenses and decreases below the loca- tion. When the overburden pressure increases, water intake gradually decreases and the time starting to absorb water is delayed. The location of the final ice lens is not sensitive to overburden pressure but influenced by the temperature boundary. The im- pact of overburden pressure and maximum temperature is not obvious. Freezing rate is not sensitive to overburden pressure but influenced by temperature, and it increases when the cold temperature decreases. Frost heave and water intake flow in- creases with increasing time and rises up to a peak value, and then decreases. During the freezing process, water intake flow increases when freezing rate decreases. Water intake flow decreases when the overburden pressure increases when the cold temperature decreases. Finally, we expanded the segregation theory, and proposed a model to describe the relationship between water intake flow and freezing rate.

Characteristics of unsteady flow in porous media while considering threshold pressure gradient with Green＇s function

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.

Characteristics of pressure gradient force errors in a terrain-following coordinate

A terrain-following coordinate （a-coordinate） in which the computational form of pressure gradient force （PGF） is two-term （the so-called classic method） has significant PGF errors near steep terrain. Using the covariant equations of the a-coordinate to create a one-term PGF （the covariant method） can reduce the PGF errors. This study investigates the factors inducing the PGF errors of these two methods, through geometric analysis and idealized experiments. The geometric analysis first demonstrates that the terrain slope and the vertical pressure gradient can induce the PGF errors of the classic method, and then generalize the effect of the terrain slope to the effect of the slope of each vertical layer （φ）. More importantly, a new factor, the direction of PGF （a）, is proposed by the geometric analysis, and the effects of φ and a are quantified by tan φ.tan a. When tan φ.tan a is greater than 1/9 or smaller than -10/9, the two terms of PGF of the classic method are of the same order but opposite in sign, and then the PGF errors of the classic method are large. Finally, the effects of three factors on inducing the PGF errors of the classic method are validated by a series of idealized experiments using various terrain types and pressure fields. The experimental results also demonstrate that the PGF errors of the covariant method are affected little by the three factors.

Prediction of Pressure Gradient and Holdup in Small Eoetvoes Number Liquid-Liquid Segregated Flow

The segregated flow pattern, which occurs in a 26.1 mm diameter, horizontal, stainless steel test section, is investigated. Pressure gradient and in situ phase distribution data were obtained for different combinations of phase superficial velocities ranging from 0.05 m.s^-1 to 0,96 m.s^-1. For the current small Eoetvoes number liquid-liquid system （EOD=4.77）, the dominant effect of interfacial tension and wall-wetting properties of the liquids over the gravity is considered. The approach introduces the closure relationship for the case of turbulent flow m a rough pipe, and attempts to modify the two-fluid model to account for the curved interface. In present flow rates range, wave amplitudes were found small, while interfacial mixing was observed. An adjustable definition for hydraulic diame- ters of two fluids and interfacial friction factor is adopted. The predicted pressure gradient and in situ phase distribution data have been compared with present experimental data and those reported in the literature.

Local topography-induced pressure gradient effects on the wake and power output of a model wind turbine

Wind-tunnel experiments were performed to study the effect of favorable and adverse constant pressure gradients(PG)from local changes in the topography right downwind of a model wind turbine.Particle image velocimetry was used to characterize the near and intermediate wake regions.We explored five scenarios,two favorable,two adverse PG,and a case with negligible PG.Results show that the PGs induce a wake deflection and modulate the wake.They imposed a relatively small impact on the turbulence kinetic energy and kinematic shear stress but a comparatively dominant effect on the bulk flow on the flow recovery.Based on this,a simple formulation is used to describe the impact of PG on the wake.We modeled the base flow through a linearized perturbation method;the wake is obtained by solving a simplified,integrated streamwise momentum equation.This approach reasonably estimated the flow profile and PG-induced power output variations.