Derivative Curves Research Articles

Pressuredrop Response Characteristics for Multi-Injection Well Interfered Vertical Well in Heterogeneous Fractured Anticline Reservoirs

AbstractFractured anticline reservoirs are mostly developed by a line production well located at the top position and a line injecting well located at the bottom position. The production well is often interference with by multiple injecting wells, but there is little related research about multiple injecting well interferences. To solve this problem, an extended bottom-hole pressuredrop (BHPD) response model for production well interfered with by multiple injection wells was presented to capture the injection interference and gravity effect. The proposed model's correctness is validated by the software numerical simulation, and low regimes were identified by the BHPD and its derivative curve. Research results show that: (i) the BHPD derivative curve has a one-half slope line, V-shape, and one slope line in reservoir linear flow regime, inter-porosity flow regime, and interference flow regime, respectively; (ii) the drop rate of pressure increases with the increase of formation transmissibility and storability. The bigger the fracture storability, the more obvious the V-shape feature in the derivative curve of BHPD. As the inter-porosity flow coefficient increases, the V-shape feature emerges later; (iii) the beginning time of the interference flow becomes later when the interference distance increases. When the injection rate trends to the production rate, the BHPD curve shows a slight drop and its derivative curve has an intermittent rupture; (iv) the influence of the gravity effect is not ignored. Due to the gravity effect, the BHPD interfered by constant injection well like the BHPD's behavior interfered by the closed boundary. This work provides technical support for capturing the source and degree of interference from well group in the heterogeneous fractured anticline reservoir.

Rate Decline of Acid Fracturing Stimulated Well in Bi-Zone Composite Carbonate Gas Reservoirs

This paper develops a model of the multi-wing finite-conductivity fractures considering stress sensitivity for low-permeability bi-zone composite gas reservoirs. A new semi-analytical solution in the Laplace domain is presented. The main solution includes the theory of source function, Laplace integral transformation, perturbation technique, and Stehfest numerical inversion. Wellbore pressure is obtained by coupling solutions of reservoirs and fractures. The results showed that the pressure and derivative curves generated by this model include a bi-linear flow stage. The model was validated by comparing its results with Wang’s results and the commercial well-test simulator; the results showed excellent agreement. This model illustrated the seepage characteristic of acid fracturing stimulated wells during refracturing treatment and how they are influenced by reservoir and hydraulic fractures parameters (asymmetrical factor and fractures distribution, etc.). The model is suitable to solve the solution of arbitrary-angle hydraulic fracture in refracturing and helpful to understand the transient production rate characteristic of the multi-wing fracturing well.

Numerical study on the transient pressure response of the vug in carbonate reservoirs

Vugs are usually distributed in carbonate reservoirs, which have an important contribution to oil reserves. The number, size, distribution mode, and distance from the well of vugs are important factors affecting the transient pressure response, which cannot be fully described by continuum mode. Therefore, a discontinuum single-phase oil model which treat the vug as an aquifer is proposed to study the effect of vugs on transient pressure response. Four oilfield cases are used to calibrate and validate the proposed model and code. After verifying the model, a vertical well model is established to conduct the sensitivity study. We found that the larger the vug, the greater the number of vugs and the closer the distance between the vug and the well, the greater the effect. When multiple vugs are symmetrically distributed around the well and the formation is isotropic, it can be equivalent to a large vugs which means that the derivative curve of pressure can only reflect the characteristics of one vug but not all vugs. The findings of this study can help for better understanding of effect of vugs on the transient pressure response and have great significance for further exploration and development of carbonate reservoir.

The Catalytic Effect of Iron and Alkali and Alkaline Earth Metal Sulfates Loading Series on the Conversion of Cellulose-Derived Hydrochars and Chars.

The catalytic effect of minerals on biomass conversion was studied focusing on Fe as well as alkali and alkaline earth metals as the metallic inorganic elements typically present in minerals found in biomass. A mineral-free reference hydrochar and an analogous char material based on cellulose were systematically doped with sulfates of the different metallic inorganic elements in various amounts via impregnation, thereby excluding differences originating from the counterion and the carbon matrix. Thermogravimetric reactivity measurements were performed in diluted O2 and CO2, and the derivative thermogravimetry curves were fitted using the random pore model. This procedure enabled a quantification of the apparent activation energy decrease due to doping as well as the influence of doping on the carbon structural parameter. Fe sulfate was always among the most active minerals, and alkali metal sulfates were typically more active than alkaline earth metal sulfates. The only exception was the high activity of very small Ca sulfate loadings during gasification. A saturation behavior of the kinetic parameter upon increasing the mineral loading was observed. The Langmuir-type modeling of this dependence further revealed that catalytically influenced devolatilization results in a char with higher oxidation reactivity, whereas for gasification, thermal annealing dominates. The systematically derived parameters provide a comprehensive description of catalytic effects, taking into account the type of mineral, the applied loading, the used atmosphere, and the fuel morphology. The derived activation energies can be used to include catalytic effects into combustion models.

Transient Flow Performance of a Vertical Well With Multiple Varying Conductivity Fractures in a Tight Oil Reservoir

Summary Due to uneven proppant distribution and varied proppant sizes during hydraulic fracturing, artificial fractures of varying length, asymmetry, and varying conductivity are easily formed near the wellbore. The principal focus of this work is to investigate the pressure transient performance of a vertical well penetrated by multiple asymmetrical fractures with varying lengths and varying conductivities in a tight oil reservoir. A novel fracture flow equation was developed specifically to describe the flow behavior inside the complex artificial fractures mentioned above. By combining with the point source solution of the tight oil reservoir, a semianalytical solution was further obtained to analyze the pressure transient behavior of a vertical well with multiple varying-conductivity fractures in a tight oil reservoir. The accuracy and reliability of the newly-developed solution were verified by comparing with the result of a numerical model. With this new solution, fracture flux distribution for different conductivity modes, namely, linearly declining mode, exponentially declining mode, and elliptically declining mode, shows that the near-wellbore fracture flux of the exponential mode is greater than that of the other two modes, but the flux distribution near the fracture tips is on the contrary. Meanwhile, the transient flow characteristics under the above varying conductivity modes indicate that the exponentially varying conductivity has a significant influence on the early linear flow regimes, while the linear and elliptical mode only has a slight influence on the bilinear flow regime under high conductivity. Parameter sensitivity analysis reveals that the obvious inversion point occurring in the pressure derivative curves of uniform conductivity fractures disappears on the pressure derivative curves of varying conductivity fractures, and a weaker asymmetry, a greater adjacent fracture angle, and a larger fracture number and fracture length ratio are conducive to improve the fracturing stimulation effect. This study deepens our understanding of the transient flow performance of vertically fractured wells and helps to estimate artificial fracture properties and evaluate hydraulic fracturing performance.

Pressure-Transient Analysis for Waterflooding with the Influence of Dynamic Induced Fracture in Tight Reservoir: Model and Case Studies

Summary It is well known that waterflooding will create fractures. The created fractures are divided into hydraulic fractures (artificial fractures with proppant) and induced fractures (formed during waterflooding without proppant). There is no proppant in the induced fracture, so it will close as the pressure decreases and extend as the pressure increases. We call it a dynamic induced fracture (DIF). Because of reduced pressure, the DIF will be closed during the shut-in pressure test (well testing). The current conventional well-testing model cannot describe the dynamic behavior of the DIF, resulting in obtaining unreasonable parameters. Thus, this work proposes a DIF model to characterize the DIF behavior during well testing (the injection well will shut in, resulting in a reduction in bottomhole pressure and induced-fracture closure). It is worth noting that a high-permeability zone (HPZ) will be formed by long-time waterflooding and particle transport. The HPZ radius will be greater than or equal to the DIF half-length because the waterflooding pressure can move particles but not necessarily expand the fracture. The point source function method and Duhamel principle are used to obtain the bottomhole pressure response. Numerical simulation methods are used to verify the accuracy of the model. Field cases are matched to demonstrate the practicability of the DIF model. Results show a straight line with a slope greater than the unit, a peak, a straight line with a slope less than one-half, and an upturned straight line on the pressure derivative curve. This peak can move up, down, left, and right to characterize the induced fracture’s dynamic conductivity (DC). The straight line with a slope greater than the unit can illustrate a fracture storage effect. The straight line with a slope less than one-half can describe the closed induced-fracture (CIF) half-length. The upturned straight line can describe the HPZ and reservoir permeability. The obtained parameters will be inaccurate if they are incorrectly identified as other flow regimes. Field cases are matched well to illustrate that identifying the three innovative flow regimes can improve the parameters’ accuracy. In conclusion, the proposed model can characterize the dynamic behavior of induced fracture, better match the field data, and obtain more reasonable reservoir parameters. Finally, two field cases in tight reservoir are discussed to prove its practicality.

Transient pressure analysis of polymer flooding fractured wells with oil-water two-phase flow

The oil-water two-phase flow pressure-transient analysis model for polymer flooding fractured well is established by considering the comprehensive effects of polymer shear thinning, shear thickening, convection, diffusion, adsorption retention, inaccessible pore volume and effective permeability reduction. The finite volume difference and Newton iteration methods are applied to solve the model, and the effects of fracture conductivity coefficient, injected polymer mass concentration, initial polymer mass concentration and water saturation on the well-test type curves of polymer flooding fractured wells are discussed. The results show that with the increase of fracture conductivity coefficient, the pressure conduction becomes faster and the pressure drop becomes smaller, so the pressure curve of transitional flow goes downward, the duration of bilinear flow becomes shorter, and the linear flow appears earlier and lasts longer. As the injected polymer mass concentration increases, the effective water phase viscosity increases, and the pressure loss increases, so the pressure and pressure derivative curves go upward, and the bilinear flow segment becomes shorter. As the initial polymer mass concentration increases, the effective water phase viscosity increases, so the pressure curve after the wellbore storage segment moves upward as a whole. As the water saturation increases, the relative permeability of water increases, the relative permeability of oil decreases, the total oil-water two-phase mobility becomes larger, and the pressure loss is reduced, so the pressure curve after the wellbore storage segment moves downward as a whole. The reliability and practicability of this new model are verified by the comparison of the results from simplified model and commercial well test software, and the actual well test data.

Study of MFL signal identification in pipelines based on non-uniform magnetic charge distribution patterns

Magnetic flux leakage (MFL), a pipeline internal detection, is the mainstream technology for international oil and gas pipeline safety maintenance. To address the problem of large errors in the assessment of defects in pipeline inspection by existing theoretical analysis models, this paper introduces the charge density parameter to establish a mathematical model of non-uniform magnetic charge for pipeline leakage detection and calculates the non-uniform distribution pattern of magnetic charge on the defect side wall. The contour plot method is proposed to visually analyze the size of defects. To compare the error between uniform and non-uniform models, and verify the correctness of the theoretical model, experiments were systematically conducted on the X70 pipeline with internal MFL technology. The results show that: the magnetic charge distribution curve is symmetrically shaped at the center of the defect, with a valley at the center and two peaks at the defect edge. As the defect depth and width increase, the magnetic charge density increases sharply near the surface and edge. The peak-to-valley spacing and peak-to-valley values in the contour map of the MFL signal can directly reflect the location and size of defects. The signal characteristic values follow the trend of a first-order decreasing exponential function as the value of the lift-off increases. The first-order derivative of the signal characteristic value tends to decrease and then increase as the mesh size decreases, and the extreme point of the derivative curve is the best mesh size.

A Semianalytical Mathematical Model and Seepage Characteristics of Off‐Center Fractured Vertical Wells with Multiwing Asymmetrical Fractures

The complexity of formation conditions leads to multiwing asymmetric fractures after large‐scale fracturing. According to a well pattern model and reservoir characteristics, a testing well is away from the center of the reservoir, and the existing well‐test mathematical model cannot meet the field data analysis demand. Therefore, the mathematical model for the fractured wells with multiwing asymmetrical fractures is established. The model solution of the Laplace domain is obtained by the Laplace transform, nonuniform fracture discretization, and pressure drop superposition principle. The model is compared with the numerical model in this paper, and the result shows that the presented semianalytical model and the calculation method are correct. The eight main flow stages are divided according to pressure derivative characteristics and the seepage process of off‐center fractured vertical wells with multiwing asymmetrical fractures. The larger off‐center distance will lead to higher pressures and derivative curves. Larger fracture asymmetry factors are higher pressures and derivative curves during bilinear and linear flow regimes. The field data show that the model is applicable and that the model can give the guidance of fractured well formation evaluation.

Thermal dehydration of D-glucose monohydrate in solid and liquid states.

The physico-geometrical reaction pathway and kinetics of the thermal dehydration of D-glucose monohydrate (DG-MH) dramatically alter by the melting of the reactant midway through the reaction. By controlling the reaction conditions, the thermal dehydration of DG-MH was systematically traced by thermoanalytical techniques in three different reaction modes: (1) solid-state reaction, (2) switching from a solid- to liquid-state reaction, and (3) liquid-state reaction. Solid-state thermal dehydration occurred under isothermal conditions and linear nonisothermal conditions at a small heating rate (β ≤ 1 K min-1) in a stream of dry N2. The kinetic behavior comprised the presence of an induction period and a sigmoidal mass loss process characterized by a derivative mass loss curve with a symmetrical shape under isothermal conditions, resembling the autocatalytic reaction in homogeneous kinetic processes. When DG-MH was heated at a larger β (≥2 K min-1), the melting of DG-MH occurred midway through the thermal dehydration process, by which a core-shell structure of molten DG-MH and surface product layer of crystalline anhydride was produced. Subsequently, thermal dehydration proceeded as a complex multistep process. Furthermore, the thermal dehydration initiated at approximately the melting point of DG-MH upon the application of a certain water vapor pressure to the reaction atmosphere, and proceeded in the liquid-state, exhibiting a smooth mass loss process to form crystalline anhydride. The reaction pathway and kinetics of the thermal dehydration of DG-MH and the corresponding changes with the sample and reaction conditions are discussed on the basis of the detailed kinetic analysis.

Thermogravimetric analysis for the characterization and comparative analysis of polyvinyl chloride (PVC) wall panel

In this paper, thermogravimetric analysis of different types/grades of polyvinyl chloride (PVC) wall panel is carried out using thermogravimetric analyzer. The data output from the analyzer is subjected to data analysis software i.e., OriginPro 2018, from which thermal attributes are find out for different grades of PVC wall panel i.e., soft PVC, hard PVC, WPVC and SPVC. The thermogravimetric attributes i.e., onset degradation temperature Ti, final degradation temperature Tf,, reaction interval and the peak temperature TP from the derivative thermogravimetric curve for the four basic types of PVC were comparatively analyzed for the characterization purpose. Beside the thermal characterization, the thermogravimetric analysis also disclosed the compositional attributes of the four types of PVC wall panel. The analysis in this paper characterized the SPVC as the most thermally stable PVC wall panel followed by hard, soft and WPVC.

Establishment of Unstable Flow Model and Well Testing Analysis for Viscoelastic Polymer Flooding

At present, the polymer solution is usually assumed to be Newtonian fluid or pseudoplastic fluid, and its elasticity is not considered on the study of polymer flooding well testing model. A large number of experiments have shown that polymer solutions have viscoelasticity, and disregarding the elasticity will cause certain errors in the analysis of polymer solution seepage law. Based on the percolation theory, this paper describes the polymer flooding mechanism from the two aspects of viscous effect and elastic effect, the mathematical model of oil water two-phase three components unsteady flow in viscoelastic polymer flooding was established, and solved by finite difference method, and the well-test curve was drawn to analyze the rule of well test curve in polymer flooding. The results show that, the degree of upward warping in the radial flow section of the pressure recovery curve when considering polymer elasticity is greater than the curve which not considering polymer elasticity. The relaxation time, power-law index, polymer injection concentration mainly affect the radial flow stage of the well testing curve. The relaxation time, power-law index, polymer injection concentration and other polymer flooding parameters mainly affect the radial flow stage of the well testing curve. The larger the polymer flooding parameters, the greater the degree of upwarping of the radial flow derivative curve. This model has important reference significance for well-testing research in polymer flooding oilfields.

A HYBRID NUMERICAL/ANALYTICAL MODEL OF TRANSIENT SEEPAGE FOR VERTICAL FRACTURED WELL IN TIGHT GAS RESERVOIR BY USE OF FRACTAL THEORY AND CONFORMAL MAPPING METHOD

Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

Novel Method to Detect Pitfalls of Intracoronary Pressure Measurements by Pressure Waveform Analysis.

Potential pitfalls of fractional flow reserve (FFR) measurements are well-known drawbacks of invasive physiology measurement, e.g., significant drift of the distal pressure trace may lead to the misclassification of stenoses. Thus, a simultaneous waveform analysis of the pressure traces may be of help in the quality control of these measurements by online detection of such artefacts as the drift or the wedging of the catheter. In the current study, we analysed the intracoronary pressure waveform with a dedicated program. In 130 patients, 232 FFR measurements were performed and derivative pressure curves were calculated. Local amplitude around the dicrotic notch was calculated from the distal intracoronary pressure traces (δdPn/dt). A unidimensional arterial network model of blood flow was employed to simulate the intracoronary pressure traces at different flow rates. There was a strong correlation between δdPn/dt values measured during hyperaemia and FFR (r = 0.88). Diagnostic performance of distal δdPn/dt ≤ 3.52 for the prediction of FFR ≤ 0.80 was 91%. The correlation between the pressure gradient and the corresponding δdPn/dt values obtained from all measurements independently of the physiological phase was also significant (r = 0.80). During simulation, the effect of flow rate on δdPn/dt further supported the close correlation between the pressure ratios and δdPn/dt. Discordance between the FFR and the δdPn/dt can be used as an indicator of possible technical problems of FFR measurements. Hence, an online calculation of the δdPn/dt may be helpful in avoiding some pitfalls of FFR evaluation.

A Semi-Analytical Model of an Off-Center Multi-Wing Fractured Well in a Low-Permeability Gas Reservoir

Summary Since there are several hydraulic fractures around a wellbore after a large-scale hydraulic fracturing and the well is not in the center of the reservoir, no corresponding semianalytical model for wellbore pressure analysis has been proposed. To bridge this gap, this paper aims to present a semianalytical model of the off-center multiwing fractured well. With consideration of permeability stress sensitivity, the reservoir model and hydraulic fracture model are established, respectively. The coupling approach of the reservoir model and hydraulic fracture model is used to obtain the wellbore pressure solution. Meanwhile, the off-center multiwing fractured well is verified with a numerical solution. The seven flow regimes can be distinguished according to the characteristics of the pressure derivative curve. Furthermore, the effect of different fracture distributions on wellbore pressure and the derivative curve is discussed and analyzed. Assuming that the fracture wing number is equal to the average length of all fracture wings, the wellbore pressure is lowest before the radial flow regime when the fracture wing has a uniform distribution around the angle and all fracture wings are equal in length. Besides, the influence of other important parameters (fracture wing number, off-center distance, etc.) is discussed. According to the analysis, we conclude that fracture wing number has a significant influence on the pressure and derivative curves before the radial flow regime. The off-center distance has no influence on the pressure and derivative curve before the radial flow regime, but it has an obvious influence on arc boundary reaction time. Finally, the advantages of the semianalytical solution are fast calculation speed and high calculation accuracy (especially in the early flow regime).

A Method for Evaluating the Dominant Seepage Channel of Water Flooding in Layered Sandstone Reservoir

A method for evaluating the dominant seepage channel (DSC) water flooding in a layered sandstone reservoir is proposed and applied in an oilfield based on the water-cut derivative. The water-cut derivative curve of the reservoir with DSC shows double peaks. Therefore, based on the analysis of geology and production characteristics, the evaluation method of DSC is established. The evaluation index is proposed to quantitatively characterize the development degree of DSC and determine its distribution in a water-flooding reservoir. The test data validate that the proposed method can not only accurately determine the DSC and quantitatively evaluate its development degree, but also show its dynamic change. This method will be a powerful guide for water controlling and oil stabilizing in the adjustment stage of sandstone reservoirs.

Fast and Stable Iterative Algorithm for Searching Wheel–Rail Contact Point Based on Geometry Constraint Equations

Abstract This paper proposes a fast and stable iterative algorithm for wheel–rail contact geometry based on constraint equations, which can be implemented in dynamic wear simulations that real-time profile updating is needed. Further, critical factors that determine convergence and iteration stability are analyzed. A B-spline is adopted for wheel–rail profile modeling because it does not contribute to changes in the global shape of curves. It is found that the smoothness of the first and second derivative curves significantly affects the numerical stability of the Jacobian matrix, which determines the increments in iterations. Moreover, a damped Newton's iteration formula with a scaling factor of 0.5 is proposed considering the convergence rate and out-of-bound issues for the updated step. The influence of the initial iteration parameters on the convergence is studied using Newton fractals. The range within ±3 mm, centered on the target contact point, is found to be an unconditionally stable domain. The proposed method could achieve convergence within 10 and 30 steps under thread and flange contact conditions, respectively.

Flow diagnosis in variable bottom hole pressure multi-well horizontal pad with well interference using rate/pressure transient analysis

Horizontal multi-well pads are frequently used in unconventional reservoirs. Along with infill wells and hydraulic fracturing, interference between multiple multi-fractured horizontal wells (MFHWs) has become a major concern. The current rate transient analysis (RTA) makes the assumption that the unconventional formation contains a single MFHW. This study introduces a novel multi-MFHW solution and associated analysis methodology for analyzing the performance of targeted well rates in a multi-MFHW system.The constant bottom-hole pressure (BHP) condition and the Laplace transform can be used to obtain multi-MFHW solutions for transient flow. We investigated interference between various fractures and MFHWs using the superposition of various constant BHP solutions. The variable BHP of the targeted well is calculated using a variable dimensionless BHP function in the Laplace domain without performing any convolution or deconvolution. The proposed method is rigorously validated using a commercial numerical simulator for cases involving offset MFHWs and multi-MFHW with variable BHP. With this multi-MFHW analysis, we can analyze a target well in the pad using the total material balance of the multi-MFHW system. Offset well interference frequently occurs following the onset of infinite-acting radial flow (IARF) in the target well's hydraulic fracture. It results in an increase in the pressure derivative curves for elliptical flow and IARF, as well as the rate-normalized pressure (RNP) derivative. Inverse semi-log derivatives exhibit the inverse trend. The proposed deviation pressure integral and RNP can be used to diagnose the flow region caused by the offset well's flow rate in a unique manner, displaying the horizontal line, V-shaped dip, and unit slope, respectively, during IARF, cross flow, and boundary-dominated flow (BDF). Sensitivity analysis of well spacing demonstrates that as well spacing increases, the “transition flow” between wells transitions from elliptical to formation linear flow and can exhibit transitional flow characteristics in more common cases.

A dynamic fracture model combining with Laplace transform and synchronous iteration method for transient behavior analysis of a four-zone system

A robust and generic semi-analytical model with the capture of dynamic fracture behaviors under long-term pumping rate condition is developed for transient flow analysis in this four-zone system. To characterize the variations of fracture length, the improved pressure-dependent dynamic fracture factor is introduced and incorporated into this model. The Laplace domain with predetermined time discretization and synchronous iteration technique are deployed to obtain the solutions of pressure and pumping rate with the least computational burden. Meanwhile, the stability and convergence of this semi-analytical model can be met within the discrete time. Furthermore, the pressure and pumping rate solutions of this model under the static fracture condition are in good agreement with those of the constant length fracture, which verifies the reliability of this model.The dynamic fracture model with the four -zone system develops five flow stages on the dimensionless pressure and its derivative curves: fracture bilinear flow, dynamic fracture flow, inner area linear flow, transitional flow and boundary-dominated flow. The dynamic fracture behavior is mainly reflected in the obviously positive upwards and pressure derivative curve presents a higher than unit slope. Moreover, the significant decrease of flow rate indicates that fracture closure could result in a rapid decline in pumping rate, which might be the reason why the pumping rate decrease quickly during the long-term pumping period. As the shrinkage coefficient increases, fractures are closed from abruptly to gradually, and typical signatures of fracture closure may be hidden if the shrinkage factor is too small, which may be caused by the instantaneous pressure depletion in the fractures. With the decrease of retained fracture coefficient, there is greater in the positive upward of transient pressure behavior and a lower in pumping rate. As a result, the flow rate will be seriously overestimated if the fracture closure is not considered especially for the tight formation.

Analytical model for transient pressure analysis in a horizontal well intercepting with multiple faults in karst carbonate reservoirs

In recent years, the Shunbei karst-carbonate reservoirs becomes a huge productivity oilfield, which produced over one million tonnes crude oil annually. However, there are difficulties in understanding production contribution of each fault-karst branch in reservoirs, which significantly impacts the efficient development. Multibranched fault-karst reservoirs in the Shunbei have an obvious tree-shaped geostructure, in which the natural fractures and eroded cave develop along multiple large-scale faults. The existing models for pressure transient analysis (PTA) were mainly established for fracture-cave reservoirs only with single fault, which cannot be applicable to characterize the multibranched fault-karst reservoir. To fill this gap, a novel analytical PTA model for horizontal commingled production well in the multibranched fault-karst reservoir was established to describe pressure response and identify flow regimes. First, our model includes the Darcy flow with the fluid compressibility effect in fracture region, and the large-scale vertical storage flow in cave region as well as the horizontal laminar flow in the horizontal wellbore. Then, the accuracy of this PTA model is verified by comparing it with the existing single branch fault-karst pressure model. Further, we applied the model to analyze the Shunbei oilfield case data. Last, the effect of boundary type, fluid compressibility effect, fracture physical properties, and cave spatial distribution on the pressure response are discussed in detail. The sensitivity analysis results show (a) the cave storage flow regime exhibits an obvious unit-slope-line on pressure derivative curve, at the time the skin transient flow constitutes a V-shape characteristic. (b) The number of fracture-cave branches can be directly obtained by counting the number of V-shaped appearances on the pressure derivative curve. (c) The fluid compressibility effect leads to an upward trend on the pressure and its derivative, reservoir engineers should be cautious to explain that characteristic as a closed boundary effect. (d) The cave volume and cave position control the timing of the V-shape occurring. As the cave volume increases, the linear flow regime lasts longer and the V-shaped feature becomes apparent. With the cave distance and cave depth increasing, the V-shape characteristic comes later. This work can provide technical support for accurate characterization of multibranched fault-karst reservoirs, and give a type curve analysis method for rapidly diagnosing the spatial location of each karst cavity by analyzing bottom-hole pressure.