Pseudo Threshold Pressure Gradient Research Articles

Experimental study on the pseudo threshold pressure gradient of supported fractures in shale reservoirs

AbstractPseudo threshold pressure gradient (PTPG) exists in the propped fractured reservoir, but its nonlinear flow law remains unclear. The effects of the mineral composition of shale and microstructure of fracturing fluid on PTPG were analyzed by X-ray diffraction and liquid nitrogen quick-freezing method. The results demonstrate that a proppant with a large particle size is more likely to form an effective flow channel and reduce liquid flow resistance, thus decreasing PTPG and increasing conductivity. The polymer fracturing fluid with rectangular microstructures significantly increased the PTPG supporting the fractured core. Experimental results show that the PTPG of the resin-coated sand-supported core in the fracturing fluid with a concentration of 1.2% is 245 times higher than that in the fracturing fluid with a concentration of 0.1% when the confining pressure is 5 MPa. Wetting hysteresis and the Jamin effect are responsible for the rise of PTPG in two-phase flow. The equivalent fracture width shows a good power function relationship with the PTPG. Thus, this study further explains the nonlinear flow behavior of reservoirs with fully propped fractures.

Experimental Study on Compaction Deformation and Gas Permeability Properties for Crushed Limestone.

The mining goaf is enriched in coalbed methane (CBM) resources, and it is imperative to realize its efficient extraction. The gas permeability properties of the crushed coal and rock in the caved zone of mining goaf are the basis for the study of its internal CBM migration and enrichment law. In this study, the compaction deformation and gas permeability properties of crushed limestone with different particle sizes were revealed. The results show that (1) the deformation resistance capacity of the crushed limestone increased with increasing stress. The decreasing trend of porosity of samples with different particle sizes in the early and later compression periods is significantly different. Particle RR of the lower layer is smaller than that of the other layers. (2) The permeability of the sample decreases with decreasing porosity and nitrogen pressure, and it is between 10-12 and 10-10 m2. Nitrogen migration within the crushed limestone requires the pseudo-threshold pressure gradient, which ranges from 64.86 to 311.42 Pa/m. (3) The average permeability growth amplitude of the sample shows a logarithmic decreasing trend with the decrease of porosity. The average permeability growth amplitude of the 5-10 mm sample at the same porosity was 15.9-22.3 times that of the 0.315-0.63 mm sample. (4) The permeability of crushed limestone on both sides of the lower layer in the caved zone is much larger than that of other locations. The results are of great practical significance for accurately predicting the CBM enrichment area of mining goaf and then selecting the final position of the extraction drilling hole.

Investigation of low water recovery based on gas-water two-phase low-velocity Non-Darcy flow model for hydraulically fractured horizontal wells in shale

Various mechanisms are employed to interpret the low water recovery during the shale-gas production period, such as extra-trapped water in the fracture network, water imbibition due to osmotic pressure and capillary pressure. These lead to the difficulty of water flow, which could be described by low-velocity non-Darcy's law known as threshold pressure gradient (TPG). In this paper we firstly employ the low-velocity non-Darcy's law to describe the water flow and use Darcy flow accounting for slip flow and free molecular flow mechanisms to model gas flow in the shale formation. The sensitive study using numerical simulation shows that the proposed flow model could model the low fracturing liquid recovery and that large pseudo TPG leads to lower fracturing liquid recovery. Thus, the proposed model would give new insight to model the low water recovery in shale formations.

Pressure transient analysis of multistage fractured horizontal wells based on detailed characterization of stimulated area

In ultralow permeability tight oil reservoirs, the fracturing scale of multistage fractured horizontal wells (MFHWs) is relatively large, and the artificial fracture system is generally more complex. Analytical and semi-analytical methods are difficult to characterize the stimulated area in detail, which includes main fractures, branch fractures, and microfractures. Numerical methods have unique advantages in studying such problems. The mathematical model of oil–water two-phase seepage is established by the finite element method, the permeability and pseudo threshold pressure gradient that vary with spatial position are proposed to characterize the stimulated area except the main fracture. A single well numerical model was established to study the influence of the width and permeability of the stimulated area on the pressure response. The analysis shows that the transient pressure response of MFHW is controlled by main fracture conductivity. Main fractures have high conductivity can better communicate the stimulated area, and MFHW can be better developed.

A Novel Workflow for Early Time Transient Pressure Data Interpretation in Tight Oil Reservoirs with Physical Constraints

In this work, a novel workflow has been proposed, validated and applied to interpret the early time transient pressure data in tight oil reservoirs with physical constraints. More specifically, the theoretical model was developed to obtain the transient pressure response for a vertical well in tight oil reservoirs with consideration of pseudo threshold pressure gradient (TPG). Then, a physical constraint between the skin factor and formation permeability has been proposed based on the physical meaning of percolation theory. This physical constraint can be applied to determine the lower limit of the skin factor which can reduce the uncertainty during the interpretation process. It is found that the influence range of the skin factor and permeability may partially overlap during the interpretation process without consideration of physical constraints. Additionally, it is found that the equivalent wellbore radius is more reasonable by considering the skin factor constraints. Furthermore, the short-time asymptotic method was applied to separate the small pressure signal at the early time period and a novel type curve was proposed to better analyze the early time pressure response. Subsequently, sensitivity analyses were conducted to investigate the influence of different parameters on the new type curves. It is found that the new type curves are more dispersed and sensitive to the parameters at the early time period which can be beneficial for the early time transient pressure analysis in a tight formation. The proposed method has been validated and then extended to a field application, demonstrating that the transient pressure for a vertical well in a tight formation can be analyzed in a reasonable and accurate manner with only early time transient pressure data.

The coupling effects of pore structure and rock mineralogy on the pre-Darcy behaviors in tight sandstone and shale

The pore structure and mineral composition play a crucial role in controlling the water flow behaviors of low-permeability media, which is characterized by threshold pressure gradient (TPG) and nonlinear flow curve. To figure out the coupling effects of these two factors on pre-Darcy flow regimes, water flow experiments were conducted on four tight sandstones, three shales and one fractured shale. The results indicate that both the TPG and pseudo threshold pressure gradient (PTPG) decrease with an increase in total porosity and macropores porosity. The variation of the nonlinear exponent (n) with total porosity and macropore porosity can be described by an exponential function with three parameters. The clay minerals and brittle minerals exert completely opposite influence on the variation of pre-Darcy flow parameters (PTPG, TPG and n). Both TPG/PTPG and n increase with increasing clay content while reduce with increase in the brittle minerals content. Theoretical analyses based on the disjoining pressure demonstrate that immovable water and electro-viscous effect are mainly responsible for water flow deviating from Darcy's law in tight sandstone and shale. Calculation results show that the proportion of immovable water of intact samples ranges from 23.46% to 89.73%, the movable water content ranges from 10.27%–76.54%. The pre-Darcy flow parameters exponentially increase with increase in immovable water content while exponentially decrease with increasing proportion of movable water. For the shale sample used in this work, the immovable water and electro-viscous effect contributing to the pre-Darcy flow account for 81.11%–90.35% and 9.58%–18.51%, respectively. The different flow regimes are controlled by the pore diameter and the thickness of water with shear fluidity. If the diameter of interconnected pores is larger than 10 μm, the Darcy flow regime dominates. When the diameter of minor pore throat of the flow channels are less than 33.82 nm for sandstones and 37.68 nm for shales, the movement of water in this flow channel would generate the TPG.

A novel model for oil recovery estimate in heterogeneous low-permeability and tight reservoirs with pseudo threshold pressure gradient

Pseudo threshold pressure gradient (PTPG) is one of the main factors affecting the oil recovery of heterogeneous low-permeability and tight reservoirs. When the pressure gradient between the supply boundary and the bottom hole is less than PTPG, the crude oil in the formation cannot flow. In order to accurately measure the relationship between PTPG and permeability, a novel experimental device has been designed and a series of core flooding experiments using brine and oil have been carried out. The new experimental device eliminates the influence of rubber sleeve in core holder and core end-effect on the results, and greatly improves the accuracy of pressure measurement. The experimental results show the PTPG has a power function relationship with permeability, and has no obvious relationship with the viscosity of the fluid. Based on the equation for PTPG and permeability of crude oil and brine fitted by the experimental data, a new heterogeneous reservoir mathematical model considering PTPG were established. The influence of the coefficient of permeability variation, average permeability, and the production rate on oil recovery factor have been studied by this model. The results clearly show that the coefficient of permeability variation has the greatest influence on oil recovery factor, which represents inhomogeneity in low-permeability and tight reservoirs. Also, when the coefficient of permeability variation is less than a certain value (about 0.2 when average permeability is 1mD, in our model), there is only a slight decline in oil recovery factor, and when coefficient of permeability variation is larger than this value, the oil recovery factor decreases rapidly. The finding is consistent with oil field production and helpful to determine whether to take EOR(enhanced oil recovery) measures for a low-permeability heterogeneous reservoirs.

Experimental study on fluid flow in micro-fractures contained within matrix

Two types of artificially fractured cores were prepared in the lab to investigate the effects of micro-fractures on fluid flow in matrix. Using naturally fractured cores and cores without fractures as control group, we analyzed fluid flow behavior in micro-fractures and their effects on fluid flow in matrix itself from the perspectives of threshold pressure gradient and oil displacement efficiency. The experimental results show that, for cores with similar physical properties, the presence of micro-fractures can significantly reduce the real threshold pressure gradient but has negligible effect on pseudo threshold pressure gradient. The matrix system should be classified as parallel or series system based on its relative location to macro-fractures. Pressure gradient in parallel matrix system is usually small and its real threshold pressure gradient is the key factor deciding whether the oil inside can be recovered. On the other hand, pressure gradient in series matrix system is generally large and its pseudo threshold pressure gradient is the key factor deciding whether effective injection-production communication can be established between two wells. Oil displacement efficiency in micro-fractures increases with the increase of micro-fracture aperture and their relationship can be approximated by a quadratic function within a certain range. However, the relationship between oil displacement efficiency in matrix and micro-fracture aperture is not monotone. Pore volumes of micro-fractures, oil displacement efficiency in micro-fractures, and water channeling within micro-fractures are the three main reasons accounting for this phenomenon.

Effect of dynamic pseudo threshold pressure gradient on well production performance in low-permeability and tight oil reservoirs

Pseudo threshold pressure gradient (PTPG) is a significant parameter that characterizes fluid flow in low permeability and tight reservoirs, which would illustrate pressure derivative curves anomaly caused by low-velocity non-Darcy flow. During the development of low-permeability and tight reservoirs, PTPG is a dynamic parameter influenced by effective stress. A series of core flooding experiments have been conducted in this paper to conclude the relationship between effective stress and PTPG with the unique experimental method. In the experiment, the precision of pressure measurement is greatly improved by a novel device and the influence of the core-end effect and the defects of the core holder on the experimental results is eliminated. The results show that PTPG increase along with the increase of effective stress. Based on the conclusion, a dynamic PTPG model is established, and the corresponding parameters are derived by fitting the experimental data. The well performance of a vertical well estimated by this model shows the production rate and recovery factor of non-Darcy flow considering dynamic PTPG are smaller than that of Darcy flow but larger than that of conventional non-Darcy flow. The recovery factor of non-Darcy flow considering dynamic PTPG is 21.2% higher than that of conventional non-Darcy flow when the production time is 800 days. The production rate and recovery factor curves of different overburden pressure show that the higher the overburden pressure is, the worse the productivity of the well is. The recovery factor at an overburden pressure of 50 MPa is 11.1% lower than that at an overburden pressure of 30 MPa.

A FRACTAL MODEL FOR LOW-VELOCITY NON-DARCY FLOW IN TIGHT OIL RESERVOIRS CONSIDERING BOUNDARY-LAYER EFFECT

Flow in nanoscale pore-throats of tight oil reservoirs is strongly affected by boundary-layers, and exhibits low-velocity non-Darcy flow phenomena. The relationship between flow velocity and pressure gradient is highly nonlinear and difficult to be modeled mathematically. This paper proposed a low-velocity non-Darcy flow model which can account for boundary-layer effect in tight oil reservoirs. First, a modified Hagen–Poiseuille equation coupled with boundary-layer effect in a single capillary tube was derived. Then, assuming pores in tight formations following fractal distribution, an analytical expression of nonlinear correlation between flow velocity and pressure gradient in fractal porous media was developed. Finally, the proposed model was validated with experiment data, and parameters influencing low-velocity non-Darcy flow were quantitatively evaluated. The research results show that the decreasing boundary-layer thickness with the increase pressure gradient is the main reason of low-velocity non-Darcy flow in tight oil reservoirs. Our model can effectively describe the nonlinear relationship between flow velocity and pressure gradient. The relationship between threshold pressure gradient (TPG) and pseudo threshold pressure gradient (PTPG) can also be predicted using our model. Fluid viscosity has great impact on nonlinear flow behavior, and with fluid viscosity increasing TPG and PTPG increase significantly. TPG is the function of fluid type, fluid viscosity and maximum pore diameter, and decreases exponentially with the increasing maximum pore size.

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

An improved model based on Biot poroelastic theory is presented incorporating the initial seepage flow in the matrix. The proposed model quantifies wave propagation in the oil field development process as VSP, transient well tests, and seismic production technology. Porosity variation, fluid–solid compressibility, and pseudo-threshold pressure gradient in low permeability reservoir are simultaneously considered, resulting in a modified form of continuity and motion equations. Integrating the equations and decomposition for the fluid–solid displacements helps to derive the analytical wave vectors of the fast P, slow P, and S waves in porous media. The sensitivity of affecting factors, such as petrophysical parameter, fluid property, and vibration frequency, on the wave velocity and attenuation is subsequently evaluated. Furthermore, the Biot model can be considered a special situation when the initial flow rate in this model tends to zero. The increase in initial percolating rate, expressed by the ratio of initial flow rate and solid scalar potential, causes an obvious decrease in the fast P wave velocity and an increase in its quality factor. Propagation of the slow P wave and the S wave is scarcely influenced. Low vibration frequency and low permeability also contribute to a large difference between the wave propagation parameters of the improved and Biot models. Cognition of the proportion in the inertia and viscosity effects is helpful in analyzing the complicated multiple mechanisms in wave propagation in the actual developed layer.

Effect of low velocity non-Darcy flow on pressure response in shale and tight oil reservoirs

Low velocity non-Darcy flow in shale and tight oil reservoirs is described by nonlinear or nonhomogeneous models. These models, especially for well shut-in period, are usually solved by numerical method, since the traditional pressure superposition principle is no longer applicable. The current paper presents a modified pressure superposition principle, accounting for the pseudo Threshold Pressure Gradient (TPG), and its mathematical proof. The proposed principle indicates that the total change of bottom hole pressure (BHP) in shut-in period is equal to the superposition of BHP change in a real well with pseudo TPG and that in a virtual well without pseudo TPG. The new principle is applied to the derivation of an analytical solution to the nonhomogeneous problem during the well shut-in period. Type curves calculated from the analytical solution show that the pseudo TPG leads to curve up-warping in switch-on period but down-warping in shut-in period, which agree with previous numerical results, and can be explained by the moving-boundary theory. Throughout the switch-on period, a closed moving-boundary is generated when the pressure gradient is less than the pseudo TPG. The boundary is closer to the well with higher pseudo TPG. However, during the shut-in period, a supply moving-boundary, which was generated during previous production or injection period, is earlier to be reached for virtual well with higher pseudo TPG. The flow is steady state afterwards. Matching of field data by the analytical solution results in the pseudo TPG in the investigation zone. The interpretation of the field case shows that pseudo TPG equals 0.104 MPa/m, generating a pressure drop as high as 6.35 MPa across the investigation zone during the well testing period.

The Effect of Microstructure on Models for the Flow of a Bingham Fluid in Porous Media: One-Dimensional Flows

The Buckingham–Reiner models for the one-dimensional flow of a Bingham fluid along a uniform pipe or channel are well-known, but are modified here to cover much more general one-dimensional configurations. These include selections of channels with different widths, and five different probability density functions describing distributions of channel widths. It is found that the manner in which breakthrough occurs at the threshold pressure gradient depends very strongly on the type of distribution of pores and that a pseudo-threshold pressure gradient, which might be inferred from measurements of flow at relatively high pressure gradients, may be more than twice the magnitude of the true threshold gradient.

Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient

Threshold pressure gradient (TPG) is an important mechanism for fluid flow through low-permeability reservoirs, which would explain the phenomena that pressure derivative curves exhibit a straight line of slope that is larger than zero after radial flow regime. A mathematical single-phase flow model incorporating pseudo TPG is proposed to describe the flow behavior in low permeability reservoirs. Fully implicit numerical simulation based on PEBI grid is developed to study the transient pressure response. Two field data are used to calibrate and validate the proposed model and the code. Based on one of field data, parametric studies are conducted to investigate the effect of minimum TPG, pseudo TPG and nonlinear exponent on the pressure transient response for a vertical well. We find that pseudo TPG can explain the unique and consistent characteristic of the pressure transient response in low permeability reservoirs. The finding is useful for petroleum engineers to interpret the field data to obtain some basic parameters for low permeability reservoirs.

An experimental study on low-velocity nonlinear flow in vuggy carbonate reservoirs

Vuggy carbonate reservoirs in the Middle East, which have characteristics such as high porosity, low permeability, and few fractures, are significantly different from fractured-vuggy carbonate reservoirs. In this study, single-phase flow experiments and core mercury injection experiments were conducted to analyze the pore size distribution and low-velocity nonlinear flow characteristics of vuggy carbonate rocks in Halfaya oilfield. The results show that the relationship between pseudo-threshold pressure gradient and permeability in matrix carbonate rocks is linear. However, vuggy type does not exhibit the same linear relationship. Compared with matrix type, vuggy carbonate rock has a nonlinear flow zone when the pressure gradient is comparatively low and the nonlinear flow characteristics are quite different from those of low-permeability sandstone reservoirs. Because of the multi-polarization of flow channel radius in vuggy carbonate rocks, fluid stepwise starts flowing as the pressure gradient increases. Vuggy carbonate rock has a pseudo-threshold pressure gradient during the low-velocity flow, but the actual threshold pressure gradient does not exist. The concept of whole channel flow pressure gradient is presented in this paper. The results contribute to improve the understanding of low-velocity flow characteristics of vuggy carbonate reservoirs.

Analytical solution of a double moving boundary problem for nonlinear flows in one-dimensional semi-infinite long porous media with low permeability

Based on Huang’s accurate tri-sectional nonlinear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external moving boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transformation, the nonlinear partial differential equation (PDE) system is transformed into a linear PDE system. Then an analytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact analytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensitive effects of the dimensionless variable on the dimensionless pressure distribution and dimensionless pressure gradient distribution becomemore serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensitive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary. Open image in new window

The Boundary Negative Slippage of Fluid Flowing in Hydrophilic Micro-Channels

In order to analyze the characteristics of the liquid flow in hydrophilic micro-channels, the negative slippage in the hydrophilic micro-channels were studied by molecular dynamics simulation and experimental research in this paper. The simulation results indicate that there exists negative slippage in the small shear rate. The absolute value of slip length decreases with the augment of shear rate and keeps constant when the shear rate increases to a certain extent. In the condition of same wettability, the slip length is only relative to shear rate of fluids near the wall rather than channel widths. At last, a experiment of deionized water flow in the micro-channel of 10 diameter was carried out. The experimental results have a good agreement with the simulation, and there exists Pseudo Threshold Pressure Gradient(PTPG) under low flow velocity. The negative slippage as the reason of existence of PTPG is analyzed in low permeability porous media

Low velocity non-linear flow in ultra-low permeability reservoir

Experimental equipment is designed to investigate single-phase oil/water flow in ultra-low permeability cores, using capillary flow meter to achieve accurate measurement of fluid volume. The results confirm that the single-phase oil/water flow in ultra-low permeability cores is not consistent with Darcy's Law. Typical flow curve is a combination of straight line and concave curve. The lower permeability the core has, the stronger non-linearity the concave curve shows. Pseudo (minimum) threshold pressure gradient exists widely in utra-low permeability cores for different fluid. Physical simulation and theoretical studies have shown that the relationship between threshold pressure gradient and permeability is a power function with the power of −1. Nonlinear factor is defined to describe nonlinear flow characteristics. Higher viscosity leads to larger nonlinear factor and wider distribution of pressure. The minimum threshold pressure gradient can be calculated by pseudo threshold pressure gradient and nonlinear factor.

Development characteristics of low oil saturation reservoirs

Abstract The filtration characteristics of low oil saturation reservoirs are obviously different from that of conventional reservoirs. The development performance and the influence factors for low oil saturation reservoirs were studied using laboratory large model physical modeling and reservoir numerical simulation, to match and establish the empirical formula of water cut variation. In the numerical stimulation process, the effect of threshold pressure on filtration for low permeability reservoirs was considered, which made the results more realistic. There wasn't a period of oil recovery without water for low oil saturation reservoirs; the water cut increased rapidly at the beginning, and dropped slightly before the period of oil production with stable water cut. The higher the initial water saturation, the shorter the production time with stable water cut. Recovery changed greatly with the injection/production pressure gradient when the injection/production pressure gradient was close to the pseudo threshold pressure gradient. Recovery changed little, even no change, with the injection/production pressure gradient when the injection/production pressure gradient was far larger than the pseudo threshold pressure gradient. There was a positive correlation between recovery degree and water injection rate when the injection/production pressure gradient was less than the pseudo threshold pressure gradient.

Pseudo threshold pressure gradient to flow for low permeability reservoirs

Abstract Rate-controlled Hg injection experiments, NMR core tests and core flooding experiments are carried out to study the low permeability cores from the Daqing and Changqing oilfields. The forming and affecting factors are studied to demonstrate why the pseudo threshold pressure gradient to flow should be overcome. Because of the boundary layer caused by interaction between solid and fluid and the micro throats of low permeability reservoirs, the pseudo threshold pressure should be overcome for fluid to flow in low permeability reservoirs. Few throats are involved in the flow and the seepage cross section area is also less at lower pressures. The throats number and the seepage cross section area increase with the increasing of flooding pressure. The pore structure and movable fluid saturation of low permeability reservoirs have remarkable influence on the pseudo threshold pressure to flow, the bigger the mainstream throats and the movable fluid saturation, the less the pseudo threshold pressure to flow. The pseudo threshold pressure gradient to flow is a characteristic parameter of nonlinear flow degree and seepage ability and it is a synthetic symbol of pore structure and movable fluid saturation.