Analysis of flow characteristics of the dual media shale gas reservoir with the elastic outer boundary

In order to more accurately describe the seepage characteristics of shale gas reservoirs, in this paper, an elastic outer boundary condition is introduced, and a new dual-media shale gas seepage model is established to describe the seepage characteristics of shale gas reservoirs more accurately, while considering the adsorption and desorption process. Combining Laplace transformation and Similar Structure Method, the solution of the percolation model is obtained in Laplace space. Furthermore, the solutions are inverted into real space with the Stehfest numerical inversion method. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The results show that the conventional three kinds of outer boundary conditions (infinite, constant pressure and closed) are actually three special cases of elastic outer boundary. The introduction of elastic outer boundary conditions not only expands the scope of data interpretation, but also closer to the actual situation of the outer boundary of the reservoir. The theory of similar structure greatly simplifies the complex process of solving the model and will have a far-reaching impact on the development of well test analysis software in the future.

Experiment on Pressure Pulsation of Axial Flow Pump System with Different Runaway Head

The runaway condition is a damage condition for pumps and turbines which can induce the wake vortex, reverse flow, and severe pressure pulsation. This study aimed to research the characteristics of pressure pulsation of axial flow pumps under different runaway conditions, and the runaway model test was performed with different blade angles and heads. Moreover, four pressure sensors were uniformly arranged at the impeller inlet section to eliminate the random error. The time domain and frequency domain analysis were the main methods to obtain the change regulations. Results showed that the pressure pulsation under the runaway condition are mainly influenced by the rotation frequency, blade passing frequency, and wake vortex frequency. The dimensionless pressure pulsation coefficient of rotation frequency and wake vortex frequency increased obviously with the runaway head increasing, but changed little with different blade angles. In addition, the dimensionless pressure coefficient of wake vortex frequency of the sensors around the impeller inlet section differed a lot, which means that the wake vortex core is not in center of the rotation axis. The average dimensionless pressure pulsation coefficient of wake vortex frequency is higher than that of rotation frequency with the same runaway head, owing to the severer wake vortex.

Using Symbolic Regression Models to Predict the Pressure Loss of Non-Newtonian Polymer-Melt Flows through Melt-Filtration Systems with Woven Screens

When selecting a melt-filtration system, the initial pressure drop is a critical parameter. We used heuristic optimization algorithms to develop general analytical equations for estimating the dimensionless pressure loss of square and Dutch woven screens in polymer processing and recycling. We present a mathematical description – without the need for further numerical methods – of the dimensionless pressure loss of non-Newtonian polymer melt-flows through woven screens. Applying the theory of similarity, we first simplified, and then transformed into dimensionless form, the governing equations. By varying the characteristic independent dimensionless influencing parameters, we created a comprehensive parameter set. For each design point, the nonlinear governing equations were solved numerically. We subsequently applied symbolic regression based on genetic programming to develop models for the dimensionless pressure drop. Finally, we validated our models against experiments using both virgin and slightly contaminated in-house and post-industrial recycling materials. Our regression models predict the experimental data accurately, yielding a mean relative error of MRE = 13.7%. Our modeling approach, the accuracy of which we have proven, allows fast and stable prediction of the initial pressure drop of polymer-melt flows through square woven and Dutch weave screens, rendering further numerical simulations unnecessary.

Characteristics of Dimensionless Pressure Gradients and Derivatives of Horizontal and Vertical Wells Completed within Inclined Sealing Faults

Dimensionless pressure gradients and dimensionless pressure derivatives characteristics are studied for horizontal and vertical wells completed within a pair of no-flow boundaries inclined at a general angle ‘θ’. Infinite-acting flow solution of each well is utilized. Image distances as a result of the inclinations are considered. The superposition principle is further utilized to calculate total pressure drop due to flow from both object and image wells. Characteristic dimensionless flow pressure gradients and pressure derivatives for the wells are finally determined. The number of images formed due to the inclination and dimensionless well design affect the dimensionless pressure gradients and their derivatives. For n images, shortly after very early time for each inclination, dimensionless pressure gradients of 1.151(N+1)/LD for the horizontal well and 1.151(N+1) for vertical well are observed. Dimensionless pressure derivative of (N+1)/2LD are observed for central and off-centered horizontal well locations, and (N+1)/2 for vertical well are observed. Central well locations do not affect horizontal well productivity for all the inclinations. The magnitudes of dimensionless pressure drop and dimensionless pressure derivatives are maximum at the farthest image distances, and are unaffected by well stand-off for the horizontal well.

Flow Behavior of Horinzontal Well Cmpleted within Two Sealing Fauts Inclined at Right Angle

At inception of a production rate regime, a horizontal well is expected to sweep oil within its drainage radius until the flow transients are interrupted by an external boundary or an impermeable heterogeneity. If the interruption is an impermeable heterogeneity or sealing fault, then the architecture of the heterogeneity must be deciphered in order to be able to design and implement an effective work-over or well re-entry to boost oil production from the reservoir. In this paper, therefore, the behavior of a horizontal well located within a pair of sealing faults inclined at 90 degrees is investigated using flow pressures and their derivatives. It is assumed that the well flow pressure is undergoing infinite activity, and each fault acts as a plane mirror. The total pressure drop in the object well is calculated by superposition principle. Damage and mechanical skin and wellbore storage are not considered. The main objective of our investigation is to establish identifiable signatures on pressure-time plots that represent infinite flow in the presence of adjacent no flow faults inclined at 90degrees. Results obtained show that the flowing wellbore pressure is influenced strongly by object well design, object well distance from each fault, and distance of each image from the object well. Irrespective of object well distance from the fault, there are three (3) images formed. Central object well location yields a square polygon, with two image wells nearer to the object well at equidistance from the object well, and the farthest image well to be 2d2. From the object well For off-centered object well location within the faults, a rectangular polygon is formed, with each image at a different distance from one well to another. Dimensionless pressure and dimensionless pressure derivative gradients during infinite-acting flow are (4.6052/LD) and 2/LD, respectively for all well locations within the faults.

Full Three-Dimensional Inverse Design Method for S-Ducts Using a New Dimensionless Flow Parameter

In this study, a new inverse design method is proposed for the full 3-D inverse design of S-ducts using curvature-based dimensionless pressure distribution as a target function. The wall pressure distribution in a 3-D curved duct is a function of the centerline curvature and the cross-sectional profile and area. A dimensionless pressure parameter was obtained as a function of the duct curvature and height of the cross-sections based on the normal pressure gradient equation. The dimensionless pressure parameter was used to eliminate the effect of the cross-sectional area on the wall pressure distribution. Full 3-D inverse design of an S-shaped duct was carried out by substituting the 3-D duct with a large number of 2-D planar ducts. The ball-spine inverse design method with vertical spins was coupled with the dimensionless pressure parameter as a target function for the design of the planar ducts. The inverse design process was performed in two steps. First, the height of each cross-section was considered constant, and only the duct centerline was allowed to be deformed by applying the difference between the dimensionless pressure on the upper and lower lines of symmetry plane. Then, a constant curvature was considered for each centerline in the equation, and the difference between the current and the target dimensionless pressure was applied to each upper and lower line of the planar sections to correct the heights of the 2-D planar sections, separately. The method was validated by choosing a straight duct as an initial guess, which converges to the target S-shaped duct. The results showed that the method is an efficient physical-based residual-correction method with low computational cost and good convergence rate. The 3-D wall pressure distribution of a high-deflected 3-D S-shaped diffuser was modified to eliminate the separation, secondary flow, and outlet distortion. Finally, the geometry corresponding to the modified pressure was obtained by the proposed 3-D inverse design method, which revealed higher pressure recovery, lower total pressure loss, and lower outlet flow distortion and swirl angle.

Investigation on Reduction of Pressure Fluctuation for a Double-Suction Centrifugal Pump

Double-suction centrifugal pumps have been applied extensively in many areas, and the significance of pressure fluctuations inside these pumps with large power is becoming increasingly important. In this study, a double-suction centrifugal pump with a high-demand for vibration and noise was redesigned by increasing the flow uniformity at the impeller discharge, implemented by combinations of more than two parameters. First, increasing the number of the impeller blades was intended to enhance the bounding effect that the blades imposed on the fluid. Subsequently, increasing the radial gap between the impeller and volute was applied to reduce the rotor-stator interaction. Finally, the staggered arrangement was optimized to weaken the efficacy of the interference superposition. Based on numerical simulation, the steady and unsteady characteristics of the pump models were calculated. From the fluctuation analysis in the frequency domain, the dimensionless pressure fluctuation amplitude at the blade passing frequency and its harmonics, located on the monitoring points in the redesigned pumps (both with larger radial gap), are reduced a lot. Further, in the volute of the model with new impellers staggered at 12°, the average value for the dimensionless pressure fluctuation amplitude decreases to 6% of that in prototype pump. The dimensionless root-mean-square pressure contour on the mid-span of the impeller tends to be more uniform in the redesigned models (both with larger radial gap); similarly, the pressure contour on the mid-section of the volute presents good uniformity in these models, which in turn demonstrating a reduction in the pressure fluctuation intensity. The results reveal the mechanism of pressure fluctuation reduction in a double-suction centrifugal pump, and the results of this study could provide a reference for pressure fluctuation reduction and vibration performance reinforcement of double-suction centrifugal pumps and other pumps.

Pressure behaviour of a horizontal well sandwiched between two parallel sealing faults

Generally, reservoir fluid flow is governed by diffusivity equation and solution to this equation helps to investigate pressure behaviour under certain reservoir and wellbore boundary conditions. In this paper however, the analytical solution method of Green and Source function is deployed to determine the performance of a horizontal well located between two parallel sealing faults, assuming simple rectangular reservoir geometry. Also, the dimensionless pressure and derivative approach is applied for all computations as it prevents the problem of unit conversions, reduces longer expressions and it helps to handle numerical values. The pressure expression derived from this work reveals that a maximum of two flow periods occur for the stated reservoir model. It was found out that an inverse relationship exists between dimensionless pressure and dimensionless length while pressure increased with thickness. Also high vertical permeability shortens the effect of the early radial flow period experienced by the horizontal well, thereby increasing productivity index. Finally, it was discovered that increased perforation length reduces the production potential of the horizontal well. Keywords: Dimensionless pressure, pressure derivatives, heterogeneity, pressure performance, reservoir and wellbore characterization.

Pressure distribution of a horizontal well in a bounded reservoir with constant pressure top and bottom

The purpose of this study is to develop a mathematical model using Source and Green’s functions for a Horizontal Wells in a Bounded Reservoir with Constant Pressure at the Top and Bottom for the interpretation of pressure responses in the reservoir based on dimensionless pressure and pressure derivative. Reservoir and well parameters investigated revealed what sets of reservoir/ well parameters combination that will prolong infinite activity of the reservoir before steady state sets in. Results show that dimensionless lateral extent does not directly affect the dimensionless pressure and dimensionless pressure derivative for very short well lengths as used in this paper. Dimensionless pressure increases with reservoir pay thickness and delay the time for steady state conditions. In fact external fluid invasion is strongly affected by the size of the pay thickness, thus the minimum time for steady state period to set in is according to the relation TD ≥ LD/5. Keywords: Bounded, reservoir, steady-state conditions, horizontal well, constant pressure.

Assessment of Production Interference Level Due to Fracture Hits Using Diagnostic Charts

Summary The objective of this study is to develop a new method that leads to diagnostic charts that quantify the pressure response between two interfering wells. Analytical linear flow models for single hydraulic fracture are used to develop a fracture hit model, which is next verified with a numerical model for validity. An analytical two-fracture model is then developed to simulate flowing bottomhole pressure (BHP) of a shut-in well, which interferes with the other well through a fracture hit, during well-testing for a short-term period. From the insight of two-fracture analytical model, a dimensionless pressure scalar, which is proportional to square root of time, is proposed to summarize the interference level between two wells. Utilizing such proportionality between the defined dimensionless pressure scalar and square root of time, a diagnostic chart for quick assessment of the production interference level between wells is developed. Such diagnostic chart is also applied to interference caused by multifracture hits that a multistage fractured horizontal well with history match performed from the Eagle Ford formation is considered as a parent well for production interference quantification. A new identical horizontal well, which is just fractured but is not in production, is assumed parallel to the pre-existing well. The result shows that when the percentage of fracture connection increases, the slope of dimensionless pressure scalar vs. square root of time increases proportionally to the percentage of fracture connection. Because the slope of dimensionless pressure scalar vs. square root of time is between 0 and 1, it can be used to quantify the well production interference level under different situations.