Optimization of shut-in time based on saturation rebalancing in volume-fractured tight oil reservoirs

Based on imbibition replacement of shut-in well in tight oil reservoirs, this paper expounds the principle of saturation rebalancing during the shut-in process after fracturing, establishes an optimization method for shut-in time after horizontal well volume fracturing with the goal of shortening oil breakthrough time and achieving rapid oil breakthrough, and analyzes the influences of permeability, porosity, fracture half-length and fracturing fluid volume on the shut-in time. The oil and water imbibition displacement in the matrix and fractures occurs during the shut-in process of wells after fracturing. If the shut-in time is too short, the oil-water displacement is not sufficient, and the oil breakthrough time is long after the well is put into production. If the shut-in time is too long, the oil and water displacement is sufficient, but the energy dissipation in the formation near the bottom of the well is severe, and the flowing period is short and the production is low after the well is put into production. A rational shut-in time can help shorten the oil breakthrough time, extend the flowing period and increase the production of the well. The rational shut-in time is influenced by factors such as permeability, porosity, fracture half-length and fracturing fluid volume. The shortest and longest shut-in times are negatively correlated with porosity, permeability, and fracture half-length, and positively correlated with fracturing fluid volume. The pilot test in tight oil horizontal wells in the Songliao Basin, NE China, has confirmed that the proposed optimization method can effectively improve the development effect of horizontal well volume fracturing.

Effects of Physical Parameters and Time-Delay Coefficients on the Amplitude and Frequency Bandwidth of Saturation Controller for a Beam Vibration

In this paper, the influence of physical parameters on the width of saturated control frequency band and the influence of time delay parameters on the stability of saturated control system are studied. The analytical solution of the motion equation of the system when the main resonance and the 1:2 internal resonance occur simultaneously is obtained by multiple scale method, experimentally measured natural frequencies of nonlinear beams. The effects of excitation amplitude, delay feedback coefficients and nonlinear coefficients on saturation control are investigated. The results of the study show that the bandwidth of the saturation control can be increased by increasing the value of the external excitation, the nonlinear coefficients enhance the nonlinear phenomena of the system.

Robust stabilization of state delayed discrete-time Takagi-Sugeno fuzzy systems with input saturation via an anti-windup fuzzy design

We consider the robust stabilization problem for discrete-time Takagi-Sugeno （T S） fuzzy systems with time- varied delays subjected to input saturation. We design static and dynamic anti-windup fuzzy controllers to ensure the convergence of all admissible initial states within the domain of attraction. Based on the project lemma and classical sector conditions, the conditions for the existence of solutions to this problem are obtained and expressed in terms of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.

A Delay-Dependent Anti-Windup Compensator for Wide-Area Power Systems With Time-Varying Delays and Actuator Saturation

In this paper, a delay-dependent anti-windup compensator is designed for wide-area power systems to enhance the damping of inter-area low-frequency oscillations in the presence of time-varying delays and actuator saturation using an indirect approach. In this approach, first, a conventional wide-area damping controller is designed by using output feedback with regional pole placement approach without considering time-varying delays and actuator saturation. Then to mitigate the effect of both time-varying delays and actuator saturation, an add-on delay-dependent anti-windup compensator is designed. Based on generalized sector conditions, less conservative delay-dependent sufficient conditions are derived in the form of a linear matrix inequality(LMI) to guarantee the asymptotic stability of the closedloop system in the presence of time-varying delays and actuator saturation by using Lyapunov-Krasovskii functional and Jensen integral inequality. Based on sufficient conditions, the LMI-based optimization problem is formulated and solved to obtain the compensator gain which maximizes the estimation of the region of attraction and minimizes the upper bound of-gain. Nonlinear simulations are performed first using MATLAB/Simulink on a two-area four-machine power system to evaluate the performance of the proposed controller for two operating conditions, e.g.,3-phase to ground fault and generator 1 terminal voltage variation. Then the proposed controller is implemented in real-time on an OPAL-RT digital simulator. From the results obtained it is verified that the proposed controller provides sufficient damping to the inter-area oscillations in the presence of time-varying delays and actuator saturation and maximizes the estimation of the region of attraction.

Finite-time Stabilization of the Double Integrator Subject to Input Saturation and Input Delay

The time-optimal control design of the double integrator is extended to the finite-time stabilization design that compensates both input saturation and input delay. With the aid of the Artstein's transformation, the problem is reduced to assigning a saturated finite-time stabilizer.

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.

Heat Saturation Time of Solid Spherical Regenerator of HTAC

In order to control the heat saturation time, the temperature field of the regenerators of high temperature air combustion （HTAC） technology after reheating furnace was studied. A one-dimensional unsteady mathematical model was established and discretized through finite difference method. The relationship between the heat saturation time and some factors was determined through the calculation of a program developed by language C. The heat saturation time decreases with the increase of heat convection coefficient, however, the increase of heat capacity, density and radius of regenerator all increase the heat saturation time approximately linearly.

Determining the degree of saturation of rocks as a function of time:A case study from mountainous area of Turkey

The aim of this study is to scrutinize whether, in terms of saturation, the 48 hour duration suggested by ISRM(International Society for Rock Mechanics) methods and ASTM(American Society for Testing and Materials) standard in rocks is sufficient or not, and to examine how the degree of saturation of rocks may be determined as a function of time. For this purpose, samples from five different rock groups including igneous(andesite, granite, andesitic tuff) and sedimentary(limestone, sandstone) exposed in Gümü?hane city which is from mountainous area of north-eastern Turkey, have been compiled. Measurements were taken on the samples left for saturation under laboratory conditions as a result of which the degree of saturation values at the end of these time periods were determined. Similarly, at the end of 48 hours, the samples were left to dry under atmospheric conditions in the laboratory environment and their time dependent degree of saturation were also calculated at different times. The changes as a function of time in the degree of saturation were then examined mathematically using non-linear, exponential and logarithmic functions. Graphs and equations related with the acquired time-degree of saturation values and the correlation coefficient(r) values for these equalities have indicated a high accordance between time and degree of saturation for the studied rock groups. The applied methodology will be beneficial for determining the degree of saturation based on time for engineering studies that will be carried out in similar lithologies.

Assessment of residual oil saturation with time-differentiated variable multiple material balance model

This study aims to improve the evaluation of residual oil saturation in water flooded zones based on the material balance model(MBM)with variable multiple for injected water.We investigated the change patterns of rock-electro parameters during waterflooding through the analysis of displacement tests.Our work differentiated the waterflooding into numerous displacement processes and accordingly propose an improved time-differentiated variable multiple MBM.The calculation results of the improved model are more consistent with the displacement experiment data of cores.Furthermore,the improved method was integrated into the comprehensive interpretation platform of offshore logging to analyze water flooded zones of a well in the A oilfield.As a result,the residual oil saturation calculated is in close agreement with the results of experiments on cores.Our results indicate that the time-differentiation and variable multiplier for injected water can effectively enhance the assessment accuracy of the residual oil saturation of water-flooded zones.

Robust Predictive Control for Polytopic Uncertain Systems with Time-delay Subjected to Actuator Saturation

Robust predictive control algorithms were presented for polytopic uncertain linear discrete systems with time-delay subjected to actuator saturation. In the first algorithm, the parameter dependent state feedback model predictive control (MPC) law was obtained from minimizing the upper bound of the cost function subjected to several linear matrix inequality constraints. In order to reduce computation burden, a second robust MPC algorithm based on nominal performance cost was presented. The feasibility of the optimization problems guarantees that the algorithms are robustly stable. The simulation results verify the effectiveness of the proposed algorithms.

TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR DYNAMIC ANALYSES IN SATURATED PORO-ELASTO-PLASTIC MEDIUM

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

Delay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators

This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

Finite-time Feedback Stabilization of a Class of Input-delay Systems With Saturating Actuators via Digital Control

In this paper, the problem of making an input-delay system with saturating actuators finite-time stable by virtue of digital control is investigated. A digital state feedback controller and digital observer-controller compensator are designed for two cases: when the state of the input-delay system are available or when it is unavailable. Sufficient conditions which guarantee finite-time stability of a closed-loop input-delay system are given and the proof procedure is presented in a heuristic way by constructing appropriate comparison functions. The condition can be transformed into the intersection of two curves satisfying some constraints, which reveals the relationship between designed parameters clearly. Finally, simulation results are presented to validate the method proposed in this paper.

Dynamic failure of dry and fully saturated limestone samples based on incubation time concept

This paper outlines the results of experimental study of the dynamic rock failure based on the comparison of dry and saturated limestone samples obtained during the dynamic compression and split tests. The tests were performed using the Kolsky method and its modifications for dynamic splitting. The mechanical data(e.g. strength, time and energy characteristics) of this material at high strain rates are obtained. It is shown that these characteristics are sensitive to the strain rate. A unified interpretation of these rate effects, based on the structuraletemporal approach, is hereby presented. It is demonstrated that the temporal dependence of the dynamic compressive and split tensile strengths of dry and saturated limestone samples can be predicted by the incubation time criterion. Previously discovered possibilities to optimize(minimize) the energy input for the failure process is discussed in connection with industrial rock failure processes. It is shown that the optimal energy input value associated with critical load, which is required to initialize failure in the rock media, strongly depends on the incubation time and the impact duration. The optimal load shapes, which minimize the momentum for a single failure impact, are demonstrated. Through this investigation, a possible approach to reduce the specific energy required for rock cutting by means of high-frequency vibrations is also discussed.

Dynamic Stress and Pore Pressure Around Circular Cavity in Saturated Porous Elastic Half-space Under Harmonic Plane Dilatational Waves

Dynamic stress concentration and pore pressure concentration around an infinitely long cylindrical cavity of circular cross-section subjected to harmonic plane dilatational waves in fluid-saturated porous elastic half-space were obtained by a complex function method based on potential function and multi-polar coordinate. The steady state Biot’s dynamic field equations of porous elastic solid with a viscous liquid were uncoupled into Helmholtz equations via given potential functions. A circular cavity with large radius is used to replace the straight boundary of the saturated porous elastic half-space. The stresses and pore pressures were obtained by using complex functions in multi-polar coordinates with certain boundary conditions of the solid matrix and the fluid matrix. The approximate solutions were compared to existing numerical solutions. Then the variations of the coefficients of dynamic stress concentration and the pore pressures concentration on boundaries of the cavity were discussed with different parameter conditions. The results of the given numerical example indicate that the method used is useful and efficient to the scattering and dynamic stress concentration of plane dilatational waves in saturated porous elastic half-space.

Solution of a Green's function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green＇s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters （permeability, frequency, etc.） under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner＇s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two- phase saturated medium in engineering.

Modeling of Surface Waves in a Fluid Saturated Poro-Elastic Medium under Initial Stress Using Time-Space Domain Higher Order Finite Difference Method

In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).