Multi-stage and multi-layer percolation model of tight gas reservoir based on pressure gradient and stress sensitivity

In petroleum engineering, a low permeability reservoir is an oil reservoir whose permeability of porous media lower than 50 micro-Darcy. Due to the existence of the threshold pressure gradient (TPG), it is hard to describe the seepage characteristics of the low permeability reservoir, and there is no ideal model of this kind. Considering the force between liquid and solid surface, the authors derived a new liquid flow model based on the negative slip boundary model of a micro-channel. Firstly, after defining the non-flowing liquid layer close to the solid surface as the boundary stick layer, and using the inverse proportion of the boundary stick layer to the pressure gradient, the authors derived the formula of the distribution of the flow rate and the flow formula of a round channel; Then, the authors got the low permeability seepage model with consideration of capillaries model; Finally, the authors derived the TPG of low permeability reservoir after testing the flow of the samples. The results show that there does not exist TPG on the low permeability reservoirs on the whole. However, it can be seen in small parts with low pressure gradient. After different power fitting of the experimental data, we find that the first power exponential function fitting is relatively accurate.

<strong>Background </strong>Nowadays, critical carotid stenosis lacks appropriate treatment standards, and carotid artery stenting (CAS) needs more direct guidance. This study aims to investigate the possibility of applying pressure wire in CAS, and the guidance of pressure gradients in choosing indications of CAS. <strong>Methods</strong> From May 2012 to October 2012, 32 consecutive cases with carotid stenosis undergoing CAS were enrolled. Preoperative and postoperative carotid ultrasound and CT perfusion imaging were performed, and intraoperative measurements of endovascular pressure gradients before and after stent implantation were recorded to evaluate intracranial circulation compensation. <strong>Results</strong> Preoperative carotid ultrasound showed the rate of stenosis in 32 cases was ≥ 70% or nearly total occlusion. Doppler measurement of peak systolic velocity (PSV) of the stenosed vessel ranged 184-718 cm/s. Digital subtraction angiography (DSA) examination showed the stenosis rates were 50%-70% in 7 cases, 70%-90% in 16 and &gt; 90% in 9. The coincidence rate of carotid ultrasound and DSA was 84.38% (27/32), and the acquisition rate of intraoperative carotid pressure gradients was 100% . Pressure gradients before stent implantation were 10-92 mm Hg, with an average of (41.45 ± 25.50) mm Hg, and pressure gradients after stent implantation were 0-15 mm Hg, with an average of (3.44 ± 3.47) mm Hg. DSA revealed 4 cases with good intracranial circulation compensation and 28 cases with poor intracranial circulation compensation. <strong>Conclusion</strong> Pressure wire can be safely and effectively used in CAS to acquire pressure gradients between the two ends of stenosis segment. For carotid artery stenosis patients lacking of intracranial circulation compensation, pressure gradients become higher as stenosis rate increases within a certain range. Therefore, CAS for stenosis with lower pressure gradients should be reconsidered. <br />

With further progress of oilfields' development all over the world, more and more low permeability reservoirs are being put in production. However, fluid flow in low permeability porous media deviates from the classic Darcy's law and instead conforms to the one of non-Darcy seepage. Most mature commercial numerical simulation softwares may cause error in simulating development performance of low permeability reservoirs. So a non-Darcy seepage numerical simulation software has been developed. In this paper, non-Darcy seepage mathematical model was proposed. In addition, on the basis of practical field and laboratory experiment data, an ideal model of five-spot well pattern was also established. Under the same reservoir condition, the non-Darcy simulation, conventional Darcy simulation and the simulation of threshold pressure gradient were conducted. The comprehensive comparison and analysis of the simulation results of Darcy flow, threshold pressure gradient flow and non-Darcy flow were provided. Research shows that compared to the results of Darcy flow, when considering non-Darcy flow, the oil production is low, and production decline is rapid; the fluid flow in reservoir consumes more driving energy which reduces the water flooding efficiency. Darcy flow model overstates the reservoir flow capability, and threshold pressure gradient flow model overstates the reservoir flow resistance. In the low permeability reservoirs, non-Darcy seepage dominates in a large scale of formation and the non-Darcy simulation result shows excellent agreement with the production data. Therefore taking the non-Darcy seepage into account is more suitable to reflect the percolation mechanism and development performance of low permeability reservoirs. This numerical simulation method has been applied successfully in Shengli oilfields.

Previous work on the subject of laminar compressible boundary layers has considered the flat plate without a pressure gradient (Karmen, Emmons and Brainerd), the flat plate with a pressure gradient (Illingworth), and the cone without pressure gradient (Hantzsche and Wendt). It is the purpose of this investigation to determine the effect of pressure gradient on the boundary layer thickness and skin friction for a figure of revolution in compressible flow. The basic momentum, continuity, and energy equations of viscous, compressible flow are reduced to an approximate form in the neighborhood of the surface of a figure of revolution by the usual boundary layer assumptions and the particular assumptions that no heat is transferred between the figure of revolution and the fluid and that the Prandtl number is equal to unity. An integral relation is then developed for the approximate equations and is subsequently reduced to a differential equation in which the boundary layer thickness is the dependent variable. In addition to considering the case of compressible flow with a pressure gradient, three other cases are examined in order to aid in the interpretation of the results. These are: compressible flow with no pressure gradient, and incompressible flow with and without pressure gradient. The equations are then applied to a figure of revolution over which pressure distributions have been experimentally determined at two Mach numbers and two Reynolds numbers. The resulting boundary layer thickness distributions are then used to determine the skin friction drag for the various cases. The effects of boundary layer velocity profile relation on skin friction drag coefficient are considered in some detail. The results of the investigation indicate that the usual practice of applying flat plate laminar skin friction drag coefficients (either compressible or incompressible) to figures of revolution in supersonic flow may be unconservative by a considerable margin. It is also shown that resulting drag values are considerably dependent on the boundary conditions used to obtain the boundary layer velocity profile.

Thirteen patients with HBsAg-positive cirrhosis were studied to investigate the relationship between esophageal variceal pressure and portal pressure, and the role of variceal pressure measurements in the management of portal hypertension. The intravariceal pressure, esophageal variceal pressure gradient, wedged hepatic venous pressure and hepatic venous pressure gradient were 21.4±2.8 mmHg, 16.2±2.2 mmHg, 23.1±5.5 mmHg and 14.7±3.9 mmHg, respectively. Linear regression analysis showed poor correlation between wedged hepatic venous pressure and intravariceal pressure or between hepatic venous pressure gradient and esophageal variceal pressure gradient. In nine patients receiving intravenous infusion of vasopressin (1 IU), both esophageal variceal pressure gradient (15.7±2.0 vs. 11.2±2.6 mmHg, p＜0.01) and hepatic venous pressure gradient (14.7±3.5 vs. 11.0±2.9 mmHg, p＜0.0l) were reduced. The reduction of esophageal variceal pressure gradient after vasopressin infusion (4.4±1.4 mmHg, 29.0±11.4%) tended to correlate with that of hepatic venous pressure gradient (3.4±0.9 mmHg, 24.2±3.8%) (r=0.64, p=0.06). These results indicate that esophageal variceal pressure measurements cannot be used as estimations of portal pressure in HBsAg-positive cirrhotics. However, the measurement of esophageal variceal pressure may be valuable in assessing potential drug effects in the management of portal hypertension.

Two major techniques are commonly used to model secondary and tertiary hydrocarbon migration: Darcy flow and invasion percolation. These approaches differ from each other in many ways, most notably in the physical modeling, the methods of resolution, and the type of results obtained. The Darcy approach involves not only buoyancy, capillary pressures, and pressure gradient, but also transient physics, thanks to the viscous terms. Although it can be numerically difficult and therefore time consuming, it is appropriate for slow hydrocarbon movement and it is able to provide a good description of cap-rock leakage. The invasion percolation approach, at least in the context of the implementation used in our examples, does not consider either viscosity or permeability; only buoyancy and capillary pressures drive the hydrocarbon migration. This method is relatively quick and especially useful to simulate secondary migration. Nevertheless, the viscous terms cannot be universally neglected as they can impact the timing of trap filling.

The well productivity prediction is a very important field development in the work and mission. At present, gas production can predict by a variety of ways, but steady percolation theory is still an important theoretical basis to predict the gas well productivity. This paper bases on the theory of steady flow, which conducts the thorough research on the quadratic trinomial, three trinomial's compatibility. Examples show that the quadratic trinomial not only determines the absolute open flow gas, but also gets the important parameters of gas well's critical production, which uses to determine the reasonable working system. It is feasible to use three trinomial to determine the high pressure and high production gas well's absolute open flow. On this basis, respectively, consider the text of the pressure gradient and slip effects and taking into account the effect of pressure gradient and slip the well productivity formula, deformable medium gas well productivity formula and other new theories were briefly discussed.

Unconventional gas resources from low-permeability formation, i.e., tight and shale gas, are currently received great attention because of their potential to supply the entire world with sufficient energy for decades to come. In the past few years, as a result of industry-wide R&D effort, progresses are being made towards commercial development of gas and oil from such unconventional resources. However, studies, understandings, and effective technologies needed for development of unconventional reservoirs are far behind the industry needs, and gas recovery from those unconventional resources remains low (estimated at 10-30% of GIP). Gas flow in low-permeability unconventional reservoirs is highly nonlinear, coupled by many co-existing, processes, e.g., non-Darcy flow and rock-fluid interaction within tiny pores or micro-fractures. Quantitative characterization of unconventional reservoirs has been a significant scientific challenge currently. Because of complicated flow behavior, strong interaction between fluid and rock, the traditional Darcy law may not be applicable for describing flow phenomena in general. In this paper, we will discuss a general mathematical model and use both numerical and analytical approaches to analyze gas flow in unconventional reservoirs. In particular, we will present analytical solutions of incorporating Klinkenberg effect, non-Darcy flow with threshold pressure gradient, and flow behavior in pressure sensitive media. We will discuss the numerical implementation of the mathematical model and show applications of the mathematical model and solutions.

Energy transport by conduction and diffusion is considered in chemically-reacting, gaseous mixtures which have a pressure gradient parallel to the temperature gradient. As a consequence of pressure diffusion and other mechanisms, the pressure gradient can influence energy transport, and this effect is given particular emphasis. The use of an idealized flow model and a perturbation technique makes it possible, with a relatively simple analysis, to deduce many of the features of energy transport in multicomponent, gaseous media. The dissociation reaction of a diatomic gas, with the ratio (reaction rate/diffusion rate) either large or small, is studied. When the flow is chemically frozen, the extension of the analysis to include any number of components would be straightforward, in principle. However, when the gas is in local chemical equilibrium, the binary case is unique in that the diffusion velocities are then proportional to the local temperature gradient, but independent of the local pressure gradient. Consequently, there exists an effective thermal conductivity. The order of the governing set of equations is therefore the same as for a simple, single-component gas, and the effect of the wall surfaces on reaction rates is confined to reaction boundary layers. Two other examples illustrate that the order of the equations is higher when the equilibrium flow comprises more than two components, although there are still reaction boundary layers. The additional boundary conditions associated with the higher order are determined, through integral conditions, by the proportions of the chemical elements present. The results show that in many high-temperature gasdynamics problems of current interest the presence of a pressure gradient may have an important influence on energy transport.

For the characteristics of horizontal fractures in shallow low-permeability oil layers after hydraulic fracturing in multilayer reservoirs, horizontal fractures are taken equivalent to an elliptical cylinder with the reservoir thickness using the equivalent permeability model; then, upon the elliptic seepage theory, the seepage field which has led by a vertical well with horizontal fractures is divided into two parts: (1)radial flow from the external formation to the equivalent area of horizontal fracture and (2) elliptic flow in the equivalent area of horizontal fracture. The loss of pressure caused by threshold pressure gradient, material balance in the reservoir, and multi-well pressure superposition principle are synthesized to calculate the performance. Finally, separate-layer multi-stage horizontal fractured well performance is deduced by summing the performance of high-permeability oil layers and fractured thin low-permeability oil layers. Low-permeability thin oil layers in Xing Shu-Gang oilfield are taken as practical cases, and the well space limits and economic reservoir thickness limits are calculated by the performance model; the relationship among recovery and productivity intensity, and the ratio of thin low-permeability oil layers thickness to the total thickness are also discussed.

Finding ways to accelerate the effective development of tight sandstone gas reservoirs holds great strategic importance in regard to the improvement of consumption pattern of world energy. The pores and throats of the tight sandstone gas reservoir are small with abundant interstitial materials. Moreover, the mechanism of gas flow is highly complex. This paper is based on the research of a typical tight sandstone gas reservoir in Changqing Oilfield. A strong stress sensitivity in tight sandstone gas reservoir is indicated by the results, and it would be strengthened with the water production; at the same time, a rise to start-up pressure gradient would be given by the water producing process. With the increase in driving pressure gradient, the relative permeability of water also increases gradually, while that of gas decreases instead. Following these results, a model of gas-water two-phase flow has been built, keeping stress sensitivity, start-up pressure gradient, and the change of relative permeability in consideration. It is illustrated by the results of calculations that there is a reduction in the duration of plateau production period and the gas recovery factor during this period if the stress sensitivity and start-up pressure gradient are considered. In contrast to the start-up pressure gradient, stress sensitivity holds a greater influence on gas well productivity.

Background There are a large number of methods, approaches, models describing the effect of the grid density of wells, their location relative to each other on the coefficient of oil recovery. With the advent of hydrodynamic models, it becomes possible to verify the previously obtained dependence of the oil recovery factor (ORF) on the well grid density. This is especially important for conditions of low-permeability reservoirs, where one can not form a single filtration field. Aims and Objectives The study on the basis of hydrodynamic modeling of the effect of the well grid density on the oil recovery factor in a low permeable reservoir for Newtonian and non-Newtonian oil flow types. Results As a result of research there received: 1. The dependence of the oil recovery factor for the Newtonian oil flow does not correspond to the traditional concepts, when it is believed that an increase in the net well density leads to a decrease in the ORF. Here we observe the inverse relationship - increasing the density of the well grid increases the ORF. 2. The manifestation of structural and mechanical properties of oil significantly changes the nature of the dependence. For large values of dynamic shearing pressure gradient the main role in the development of oil reserves is played by regions with large gradients of reservoir pressure, the volume of which increases with increasing number of wells, especially injection wells. Therefore, the development of oil reserves of low-permeability reservoirs must be carried out on the basis of intensive development systems. 3. An important issue for the development of low-permeability reservoirs is the time to develop reserves. Therefore, it is necessary to analyze the complex parameter ORF / T (an analogue of the average rate of production of reserves). For this parameter, there is a traditional dependence - a decrease with increasing net well density. At the same time, the manifestation of structural and mechanical properties of oil enhances this dependence (increases the rate of decline).

An analytical and experimental study has been made of the turbulent mixing layer in a pressure gradient. Theory predicts the possible existence of equilibrium flows, and this was confirmed experimentally for turbulent shear layers between streams of helium and nitrogen. The only case for which similarity is possible is for ρ_2U_2%2 = ρ_1U1^2, since then P_2(x) = P_1(x). These equilibrium flows are of the form U_1 ~ x^α and δ ~ x where α = u/U-1 dU_1/dx is a non-dimensional pressure gradient parameter. The experimental investigation was conducted in the facility designed by Brown to produce turbulent flows at pressures up to 10 atmospheres. The adjustable walls of the test section of the apparatus were modified in order to set the pressure gradient. Shadowgraphs of the mixing zone for α = 0 and α = - 0.. 18, at different Reynolds numbers, revealed a large scale structure noticeably different for each α. The similarity properties of the shear layer were established from mean profiles of total head and density. In addition, the rms density fluctuations were found to be self-preserving. From the mean profiles, the spreading rate, turbulent mass diffusion, Reynolds stress and Schmidt number distributions were calculated from the equations of motion. The experimental results show that the spreading rate for the adverse pressure gradient is 60% greater than for the α = 0 case. The maximum shearing stress is 70% larger and the maximum value of the turbulent mass diffusion is 20% larger than their α = 0 counterparts. The maximum rms density fluctuations are approximately O.2 in both flows. Surprisingly low values of turbulent Schmidt numbers were found; e.g. , at the dividing streamline Sc_t ~ 0.16 for α = 0 and Sc_t = 0.33 for α = -0.18.

Stress sensitivity of tight reservoirs and its effect on oil saturation: A case study of Lower Cretaceous tight clastic reservoirs in the Hailar Basin, Northeast China

In this paper unsteady flow of viscoelastic fluids through a rectilinear pipe of uniform cross section has been discussed. The section of the pipe is a paralleogram. A few particular cases of results with pressure gradient as any function of time i.e. flow under an impulsive pressure gradient, flow under constant pressure gradient and flow under harmonically oscillating pressure gradient have been discussed in detail.