Effect Of Threshold Pressure Gradient Research Articles

Investigating optimal development approaches via bottom hole pressure control in stress-sensitive tight oil reservoirs

After volumetric fracturing, the conventional recovery methods for tight oil reservoirs rely on natural energy depletion. However, the production rate rapidly declines due to their intricate characteristics, such as threshold pressure gradient (TPG), stress sensitivity, and multi-scale porous media. This study plotted permeability loss charts based on stress sensitivity experiments. A pressure distribution equation incorporating TPG and flow in different regions was developed, and production prediction methods for tight oil reservoirs were established. The results revealed the effects of TPG and multi-region flow on pressure distribution, demonstrating the need to control bottom hole pressure (BHP) in tight oil reservoirs. Accordingly, methods to improve tight oil reservoir development were proposed by controlling BHP. Reducing BHP, increasing the imbibition displacement, and improving oil-phase mobility proved conducive to enhanced oil recovery. The development model featuring BHP control for 1000 days with initially rapid and subsequently slower BHP declines demonstrated the highest recovery rate, surpassing depletion development by 7.404%. This research helps us to optimize tight oil reservoir development plans while offering significant practical guidance for developing similar oil reservoirs, which is of the reference value for the industry.

Productivity Formula of Horizontal Well in Low-Permeability Gas Reservoir considering Multiple Factors

For horizontal well in low-permeability gas reservoir, the effects of threshold pressure gradient, stress sensitivity, and gas slippage have significant impacts on the well productivity. At present, there are few productivity formulas for horizontal gas well considering all these factors. In this paper, based on the flow analysis of horizontal well in low-permeability gas reservoir, the whole flow field was divided into two parts, namely, far wellbore region and near wellbore region, among which the far wellbore region is composed of plane linear flow region and plane radial flow region and the near wellbore region is composed of vertical plane radial flow region and spherical plane central flow region. Then, a new productivity formula is established based on the steady-state seepage theory and the equivalent seepage resistance method, with the consideration of threshold pressure gradient, stress sensitivity, and gas slippage effect. The accuracy of the formula in this paper is verified through comparing with other classical models, and the influence of various factors on the well productivity is analyzed. The analysis results show that stress sensitivity has the most significant effect on horizontal gas well production, followed by threshold pressure gradient, and the gas slippage has the least effect. With the consideration of all influencing factors, the higher the formation pressure and reservoir thickness, the higher the productivity, and the increase of productivity increases with the increase of flow pressure difference. The increasing trend of gas productivity index per meter with the increase of reservoir permeability is first fast and then slow. When the reservoir permeability is greater than 1.2 mD, the increment of gas productivity index per meter (MGPI) decreases. When the length of horizontal well is greater than 1400 m, the increment of gas productivity index per meter decreases with the increase of gas reservoir thickness. Therefore, it is recommended to control the horizontal well length within 1400 m in low-permeability gas reservoir. In addition, the absolute open flow charts corresponding to reservoir thickness and horizontal well length under different reservoir permeability conditions were also given, which can provide theoretical guidance for the selection of horizontal well length during the development of low-permeability gas reservoirs.

Pressure transient analysis for multi-stage fractured horizontal wells considering threshold pressure gradient and stress sensitivity in tight sandstone gas reservoirs

Tight sand gas reservoirs are characterized with low porosity and low permeability. The threshold pressure gradient (TPG) and stress sensitivity effect are particularly apparent during gas production in tight sand gas reservoirs, causing the pressure transient analysis (PTA) curves of multi-stage fracturing horizontal wells (MFHWs) in tight sand gas reservoirs to be abnormally upward and making it challenging to match current PTA models. Therefore, in this work, a new PTA model for MFHW considering TPG and stress sensitivity was established. Based on the point source function, a semi-analytical solution of the model could be obtained using the properties of series function, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. Moreover, the effects of TPG, stress sensitivity, well parameters, and fracture parameters on the PTA curves were analyzed. Overall, we believe that the results of this study can guide the pressure transient analysis of MFHWs in tight sand gas reservoirs and provide help for engineers with regard to evaluating the parameters of reservoirs and fractures more accurately.

Numerical simulation of fractured horizontal well considering threshold pressure gradient, non‐Darcy flow, and stress sensitivity

AbstractConventional numerical simulators cannot accurately predict the production of fractured horizontal wells in tight sandstone gas reservoirs due to the threshold pressure gradient (TPG) and stress sensitivity. Additionally, non‐Darcy flow in hydraulic fractures further complicates the prediction. Therefore, a numerical simulation model was developed to accurately predict the production of fractured horizontal wells that considers the TPG, non‐Darcy flow, and stress sensitivity using the embedded discrete fracture model. The model was solved using the automatic differentiation framework of MATLAB Reservoir Simulation Toolbox. The numerical simulation demonstrated that the Darcy flow model provided an optimistic prediction of the productivity of fractured gas wells in tight reservoirs. The TPG, non‐Darcy flow, and stress‐sensitive phenomena reduced the productivity of gas wells to varying degrees and severely affected the production of gas wells. The TPG effect, non‐Darcy effect, and stress sensitivity phenomenon reduced the gas well production by 1.66%, 12.9%, and 42.42%, respectively, compared with that of the Darcy flow. In contrast to the conventional Darcy flow model, the model established in this study can accurately predict the production of gas wells in production history matching.

Recognition and Classification for Inter-well Nonlinear Permeability Configuration in Low Permeability Reservoirs Utilizing Machine Learning Methods

Machine learning methods have become the leading research algorithm enjoying popularity for reservoir engineering evaluation. In this paper, one machine learning method is selected and optimized for the recognition and classification of inter-well nonlinear permeability configurations between injection and production wells in the low permeability reservoir. The above configurations are divided into four classes, i.e., homogeneous, linear increment, convexity increasing (logarithmic function), and convex downward increasing (exponential function). According to four kinds of nonlinear permeability distributions in low permeability reservoirs and the increased effect of threshold pressure gradient, the productivity formula is established. Then the decision tree, neural networks (NN) and support vector machines (SVM) are utilized for training dynamic data under the influence of the training model, i.e., the configuration in low-permeability reservoirs. The data set is formed with dynamic production data under different configuration permeability, well spacing, thickness, pressure, and production. The recognition and classification of the permeability configuration are performed using different machine learning models. The results show that compared with NN and decision tree, SVM presents better performance in the accuracy of verification, true positive rate (TPR), false-negative rate (FNR) and receiver operating characteristic (ROC). Moreover, SVM verification results are placed on the brink of the training methods. This paper provides new insights and methods for the recognition and classification of inter-well nonlinear permeability configuration in low permeability reservoirs. Additionally, the research method can also apply to solve similar theoretical problems in other unconventional reservoirs.

Investigation of the impact of threshold pressure gradient on gas production from hydrate deposits

Many hydrate-bearing sediments are featured with unconsolidated argillaceous siltstones, which exist the non-Newtonian flow and threshold pressure gradient due to the high content of clay. In this study, the threshold pressure gradient of hydrate reservoir in the South China Sea is experimentally clarified. The quantitative relationship between it and the reservoir parameters is established. The function of threshold pressure gradient has been added into TOUGH + HYDRATE simulator. Here, site SH2, a candidate for field testing comprising a clayey silt gas hydrate reservoir in the Shenhu area of the South China Sea, was chosen to investigate the effect of threshold pressure gradient on gas production behavior through numerical simulations. The simulation results show that threshold pressure gradient has a significant impact on gas extraction. When the experimental value was applied, the gas production was enhanced unexpectedly, where cumulative gas output doubled in 5 years. The active hydrate dissociating area (gas, water and hydrate coexist) has notably extended, accompanying with the expanding cool zone. Water blockage near well was relieved. However, with the increasing of threshold pressure gradient, propagation of pressure would be restrained seriously. The pressure and hydrate of far-field formations stay “frozen”. The bottom water invasion was weakened.

Study on the Effect of Threshold Pressure Gradient on Remaining Oil Distribution in Heavy Oil Reservoirs

Due to the spatial network structure, heavy oil has a high threshold pressure gradient when it flows through porous media, and the threshold pressure gradient plays a crucial role in the distribution of remaining oil. In previous study, the common methods to measure the threshold pressure gradient include the microflow-established differential pressure (MFEDP) method, capillary equilibrium method, and the percolation curve fitting method. In this study, a sample from the SZ36-1 oilfield was analyzed for the basic physical properties based on the comparison of the previous measurement to study the influence of mobility on the threshold pressure gradient and then an independently developed numerical simulator was established to study the effect of the threshold pressure gradient on the remaining oil distribution considering the permeability range, crude oil viscosity, well network deployment, well spacing, and fluid recovery rate. The results show that the SZ36-1 oilfield fluid belongs to Bingham fluids with yield stress and the mobility having an exponent relation to the threshold pressure gradient based on the measurement of the MFEDP method. Considering the threshold pressure gradient of heavy oil, the uneven distribution of remaining oil is intensified and the remaining oil is enriched. This study provides a reference for efficient development of heavy oil reservoirs.

Numerical simulation of fractured vertical well in low-permeable oil reservoir with proppant distribution in hydraulic fracture

In this paper, numerical simulations of fractured vertical well in low-permeable oil reservoir are carried out and two issues: threshold pressure gradient (TPG) in reservoir matrix and proppant distribution in hydraulic fractures are focused on. A physical definition of effective fracture length (EFL) is presented to evaluate the fracture effectiveness due to uneven proppant distribution. In terms of numerical processing for TPG, based on the subsurface Darcy's flow module in COMSOL Multiphysics, an effective numerical simulation method is adopted by substituting the gravitational acceleration vector in Darcy's law (Liu et al., 2019b). The simulation results show that, proppant distribution has great influence on fracture effectiveness. Unappealing proppant distribution can reduce effective fracture length by 49.6%, which is negative for low-permeable oil reservoir development. TPG in reservoir matrix mainly affects the moving boundary and pressure-disturbed area in reservoir. When TPG in matrix reduces from 0.02 MPa/m to 0 MPa/m, the distance of moving boundary at 300 days could increase for almost double and pressure-disturbed area enlarged drastically for around 74%. Furthermore, a heterogenous low-permeable oil with secondary fracture networks is designed to study the joint effect of TPG and proppant distribution. If we neglect these two factors, cumulative oil rate will be greatly overestimated by 38.6% at 1000 days. At the same time, the existence of natural fractures could also affect the streamline distribution in low-permeable oil reservoir and contribute to fluid flow in reservoir.

A 3D Gas and Water Simulator Considering Nonlinear Flow Behaviors for Abnormal High-Pressure Tight Gas Reservoirs

Fluid flow in tight gas reservoirs with abnormal high pressure presents nonlinear behaviors. A mathematical description of these behaviors is essential for establishing the flow model. In this study, a mathematical model is presented that describes the effect of threshold pressure gradient and rock deformation on gas flow parameters in a tight gas reservoir. A fully implicit 3D gas and water phase numerical model was derived using the finite difference method. Based on software engineering principles, a 3D gas and water simulator was developed, which can be used in research on nonlinear flow mechanisms and flow simulation in abnormal high-pressure gas reservoir. The simulator proved to be reliable through a comparison with a commercial simulator, and it was used successfully for prediction of gas production in the M reservoir.

Semi-analytical modeling of advanced water injection in low permeability reservoirs under non-Darcy-flow condition

Water flooding is widely used to enhance oil recovery in the oilfield. Advanced water injection technology has proven to be an effective method of development for these low permeability reservoirs. Nevertheless, the fluid flow in a low permeability reservoir is governed by non-Darcy flow and the threshold pressure gradient effect. Several efforts have been made experimentally and numerically to design and optimize the field operation parameters. However, it is still challenging to simulate and predict the impact of various injection parameters on well performance in a computationally efficient manner. A simple and efficient semi-analytical model is developed for advanced water injection which considers non-Darcy flow and threshold pressure effects. The stimulated reservoir volume can be evaluated by calculating the pressure gradient distribution. The impact of water injection rate, total injection volume, and injection time on stimulated reservoir volume is investigated. Finally, a field-scale numerical simulation and experiment are conducted to validate the proposed model. This model provides reservoir engineers a simple and accurate tool for predicting, evaluating, and optimizing the advanced water injection operation practices.

Numerical simulation of multi-stage fractured horizontal well in low-permeable oil reservoir with threshold pressure gradient with moving boundary

A stimulation technology of multi-stage fractured horizontal well is commonly used for enhancing the productivity in the development of low-permeable oil reservoirs. However, it is well known that the fluid flow in low-permeable oil reservoirs doesn't obey conventional Darcy's law, and the threshold pressure gradient exists; as a result, in fact, the model of multi-stage fractured horizontal well in low-permeable oil reservoirs belongs to a nonlinear moving boundary problem. And realization of the numerical simulation for the model is very complicated and difficult. It is significant to figure out the threshold pressure gradient effect on the numerical simulation results for the solution of actual engineering problems. In view of the concerns, based on the subsurface Darcy's flow module in COMSOL Multiphysics, an effective numerical simulation method is presented here: The non-Darcy kinematic equation at the full pressure gradient range is expressed at the interface of the gravitational acceleration vector in Darcy's law. Furthermore, the simulation method is strictly verified through the comparison with two analytical solutions for a one-dimensional case and a two-dimensional case (radial flow) respectively. Consequently, according to a constructed model, which can cover non-Darcy flow in the unstimulated reservoir area with threshold pressure gradient, Darcy's flow in the stimulated reservoir area and Darcy's flow in the main hydraulic fractures, the two-dimensional numerical simulation of the multi-stage fractured horizontal well in the low-permeable oil reservoir is realized just through the subsurface Darcy's flow module.Finally, through analyses and discussions on the numerical results for several designed simulation scenarios, some significant conclusions are obtained such as due to the threshold pressure gradient effect, there exists large undeveloped areas in low-permeable oil reservoirs, which don't change with the production time for the constant well production pressure condition; SRV fracturing can largely improve the utilization degree of the low-permeable reservoir area between the adjacent main hydraulic fractures at the early production period; it is very necessary to incorporate the threshold pressure gradient effect in the simulation for the optimal well spacing design in the development of low-permeable oil reservoirs.

Study on the productivity of the multi-stage fractured horizontal wells in tight oil reservoirs

In this paper, a comprehensive dual-porosity and dual-permeability oil/water flow model that uses experimentally determined reservoir properties to simulate well performance of a multi-stage fractured horizontal well in tight oil reservoirs was established. The numerical simulation results was validated by the commercial simulator Eclipse and field production data. Besides, the effect of threshold pressure gradient, stress-sensitive matrix permeability, stress-sensitive fracture conductivity, and capillary pressure was conducted, revealing that those factors affect the well productivity in different degrees. The results indicate that the threshold pressure gradient can significantly reduce the well productivity. The impact of stress-sensitive coefficient should be significant to oil production in high stress-sensitive tight oil reservoirs. Also, the effects of fracture conductivity and capillary pressure on oil production was studied. This study provides a basis for long-term tight oil production analysis of hydraulically fractured tight oil wells. [Received: October 8, 2016; Accepted: January 28, 2017]

A multi-linear transient pressure model for multistage fractured horizontal well in tight oil reservoirs with considering threshold pressure gradient and stress sensitivity

In general, tight oil reservoirs has a numerous tiny and complicated throats, and ultra-low permeability, which leads to a low-velocity non-Darcy flow when the fluid flows in tight reservoirs. The permeability of tight oil reservoirs is no longer a constant, but a variable, which is dependent on reservoir pressure. In other word, the tight oil reservoir is stress sensitive media. The low-velocity non-Darcy flow and stress sensitivity will greatly affect the bottom hole pressure response. So, the low-velocity non-Darcy flow and stress sensitivity should be taken into consideration when researching the transient pressure behaviors of multistage fractured horizontal wells. Currently, there are many researches on transient pressure behaviors of the multistage fractured horizontal well, but none of these researches has taken the low-velocity non-Darcy flow and stress sensitivity into consideration simultaneously. In this paper, threshold pressure gradient and permeability modulus are used to characterize the low-velocity non-Darcy flow and stress sensitivity, respectively. And, a multi-linear transient pressure model of multistage fractured horizontal well with considering low-velocity non-Darcy flow and stress sensitivity is established. The Pedrosa's transformation, perturbation theory, Laplace transformation and stehfest numerical inverse are used to solve this transient pressure model. The novel model is verified by comparing the result of proposed model with that of Ekaterina Stalagorova's model. According to the dimensionless pressure derivative curve, the flow process can be identified as six regimes: ①the main fracture linear flow stage, ②the first transition flow stage, ③dual-linear flow stage, ④the second transition flow stage, ⑤the formation linear flow stage, ⑥the boundary flow stage. Finally, the effects of threshold pressure gradient, permeability modulus and fracture density of stimulated reservoir on dimensionless pressure derivative are analyzed. This research provides theoretical support for correctly understanding the flow law of multistage fractured horizontal well.

Numerical simulation of pressure gradient of coalbed gas outburst and migration considering moving boundary

The gas flow model is developed considering effects of gas convection, diffusion and slippage based on pore characteristics of medium and gas seepage theory in order to study the slippage effect and the effect of threshold pressure gradient on gas migration through the coal seam and determine the reasonable diameter of exposed surface. The numerical model was solved using the multiple physical coupling analysis software COMSOL Multiphysics, and good agreement was obtained by comparing the solution of numerical model with measured results. The speed of pressure change is larger when slippage effect is considered than the migration velocity of gas when slippage effect is not considered, and smaller of pressure decreases for the same cross-section. It is also concluded that the gas pressure changes faster in the coal seam, and the gas starting pressure gradient gets lower when the diameter of the exposed surface is larger. The model can be used to analyze the law of gas migration in coal seam and to determine the position of the cracking surface in coal seam effectively.

An analytical model of SAGD process considering the effect of threshold pressure gradient

An analytical model is proposed for the development of super-viscous oil deposits by the method of steam-assisted gravity drainage, taking into account the nonlinear filtration law with the limiting gradient. The influence of non-Newtonian properties of oil on the productivity of a horizontal well and the cumulative steam-oil ratio are studied. Verification of the proposed model based on the results of physical modeling of the SAGD process was carried out.

The threshold pressure gradient effect in the tight sandstone gas reservoirs with high water saturation

From research and field development, the threshold pressure gradient (TPG) in tight formations is required before the fluid starts to flow. This paper addresses the different factors that affect the TPG in tight sandstone gas reservoirs with high water saturation. First and foremost, the petrophysical properties were obtained through the following tests: X ray diffraction, scanning electron microscope and nuclear magnetic resonance using cores from Sulige gas field in China. Secondly, the TPG experimental investigations were performed using air bubble method, and a TPG correlation was obtained considering the influences of permeability, connate water and movable water. Finally, a gas production model was established with the TPG, slip and diffusion effects taken into account, and its applications were discussed using actual reservoir parameters. The results showed that the cores have plenty of clay minerals and high connate water saturation. Besides, the throat radii from NMR mainly are distributed between 0.0004 and 0.1 µm, with a few between 0.1 and 0.4 µm. The clay depositions decrease the pore and throat diameters, which result in Jamin effect. The experimental results showed that the TPG exists at the connate water saturation, and increase exponentially with either an increase in dimensionless water saturation or decrease in permeability. The IPR curves showed the TPG effect on gas production is very serious i.e. production loss degree decreases especially at high bottom hole pressure, and the production loss degree decreases as the bottom hole pressure decreases. The greater the water saturation or the smaller the permeability, the greater the production loss degree. In addition, the TPG affects the intercept of the abscissa of the flow curve, and the slope of the curve decreases as water saturation increases.

Numerical research on CO2 storage efficiency in saline aquifer with low-velocity non-Darcy flow

Low permeability saline aquifers, which are widely distributed around this world, have great potential for injected CO2 storage. Fluid flow in low permeability layers shows characteristics of low-velocity non-Darcy flow. A mathematical model considering the effect of threshold pressure gradient (TPG) for CO2 flow and storage in low permeability saline aquifer has been developed, and the corresponding numerical model has been formulated and solved. From the numerical results, we can conclude that the injection rate, cumulative CO2 injected, and the storage efficiency for the case with TPG are always less than those of the case without TPG because of the sharp pressure decline and increased energy consumption. Under this paper's calculation condition, the storage efficiency when considering TPG is about 10% less than the case without considering TPG. If the TPG effect was to be ignored in the design of CO2 storage in low permeability saline aquifers, the CO2 storage efficiency will be overestimated. The research enlarges the theoretical basis of carbon capture and storage (CCS) and provides a more accurate method to evaluate CO2 storage efficiency.

Dynamic threshold pressure gradient in tight gas reservoir

Experimental approach was performed in this paper to study the threshold pressure gradient (TPG) in tight gas reservoir. The nonlinear flow behavior of tight gas reservoir was investigated at first, three zones of flow curve are divided to describe the nonlinear behavior of gas flow in tight formation: solid–gas viscous force zone, slippage zone and low-speed turbulent zone. On this basis, experiments using modified procedure were made in order to clarify the influence of pore pressure on TPG, results show that TPG of tight gas reservoir is highly effected by pore pressure and conventional experimental methods will lead to a significant error. And then, TPG during the development of tight gas reservoir was tested. The results we obtained demonstrated that there exists ‘Dynamic TPG Effect’ during the development process of tight gas reservoir: TPG is increasing along with the decrease of reservoir pressure (pore pressure). New concepts of ‘TPG Rising Cone’ and ‘TPG Sensitivity Coefficient’ are defined to characterize the dynamic TPG of tight gas reservoir. Finally, experiments were carried out to investigate the influence of permeability and water saturation on dynamic TPG. Results indicate that ‘TPG Rising Cone’ is more significant in reservoir with low-permeability or high water saturation.

Applied Mechanics in Moving Boundary Problems of One-Dimensional Non-Darcy Flow in Semi-Infinite Long Porous Media

Dimensionless mathematical models of the fluid flow in the semi-infinite long porous media with constant production pressure on the inner boundary conditions are built, which include the effect of threshold pressure gradient (TPG). The analytical solutions of these dimensionless mathematical models are derived through new definitions of dimensionless variables. Comparison curves of the dimensionless moving boundary under different values of dimensionless TPG are plotted from the proposed analytical solutions. For the case of constant production pressure, a maximum moving boundary exists, beyond which the fluid flow will not occur. The value of maximum boundary distance decreases with increasing TPG. However, the velocity of pressure propagation decreases with time. The larger the TPG is, the steeper the curve of pressure depression cone is and the shorter the distance of the pressure propagation is.

The Moving Boundary Movement of Vertical Fractured Well in Tight Oil Reservoir

Because of the obvious non-Darcy characteristic of fluid flowing in tight reservoirs, there is a virtual moving boundary at the flow edge, and these percolation models of fractured wells with Darcy formula are no longer applicable. Based on the threshold pressure gradient effect, the unsteady seepage flow model of vertical fractured well was established in the drain area by means of Source and Green's Functions. With the flow characteristics at the boundary of tight reservoir, the motion equation of axes of moving boundary was obtained. By Example analysis, its proved that the moving boundary is approximate circular in the far-field, and it will move slower with the increase of the threshold pressure gradient.