Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Ultrasonic method for measuring water holdup of low velocity and high-water-cut oil-water two-phase flow

Oil reservoirs with low permeability and porosity that are in the middle and late exploitation periods in China＇s onshore oil fields are mostly in the high-water-cut production stage.This stage is associated with severely non-uniform local-velocity flow profiles and dispersed-phase concentration（of oil droplets） in oil-water two-phase flow,which makes it difficult to measure water holdup in oil wells.In this study,we use an ultrasonic method based on a transmission-type sensor in oil-water two-phase flow to measure water holdup in lowvelocity and high water-cut conditions.First,we optimize the excitation frequency of the ultrasonic sensor by calculating the sensitivity of the ultrasonic field using the finite element method for multiphysics coupling.Then we calculate the change trend of sound pressure level attenuation ratio with the increase in oil holdup to verify the feasibility of the employed diameter for the ultrasonic sensor.Based on the results,we then investigate the effects of oildroplet diameter and distribution on the ultrasonic field.To further understand the measurement characteristics of the ultrasonic sensor,we perform a flow loop test on vertical upward oilwater two-phase flow and measure the responses of the optimized ultrasonic sensor.The results show that the ultrasonic sensor yields poor resolution for a dispersed oil slug in water flow（D OS/W flow）,but the resolution is favorable for dispersed oil in water flow（D O/W flow） and very fine dispersed oil in water flow（VFD O/W flow）.This research demonstrates the potential application of a pulsed-transmission ultrasonic method for measuring the fraction of individual components in oil-water two-phase flow with a low mixture velocity and high water cut.

An Experimental Study on the Flow Characteristics of OilWater Two-Phase Flow in Horizontal Straight Pipes

The flow patterns and their transitions of oil-water two-phase flow in horizontal pipes were studied. The experiments were conducted in two kinds of horizontal tubes, made of plexiglas pipe and stainless steel pipe with 40 mm ID respectively. No. 46 mechanical oil and tap water were used as working fluids. The superflcial velocity ranges of oil and water were: 0.04-1.2m·s-1 and 0.04-2.2m·s-1, respectively. The flow patterns were identified by visualization and by transient fluctuation signals of differential pressure drop. The flow patterns were defined according to the relative distribution of oil and water phases in the pipes. Flow pattern maps were obtained for both pipelines. In addition, semi-theoretical transition criteria for the flow patterns were proposed, and the proposed transitional criteria are in reasonable agreement with available data in liquid-liquid systems.

Oil–water two-phase flow pattern analysis with ERT based measurement and multivariate maximum Lyapunov exponent

Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.

Partial phase flow rate measurements for stratified oil-water flow in horizontal wells

To accurately measure and evaluate the oil-water production profile of horizontal wells, a dynamic measurement experiment of oil-water two-phase flow in horizontal wells and numerical simulation were combined to establish a method for measuring the partial phase flow rate of oil-water two-phase stratified flow in horizontal wells. An experimental work was performed in horizontal oil-water two-phase flow simulation well using combination production logging tool including mini-capacitance sensor and mini-spinner. The combination tool provides a recording of holdup and velocity profiles at five different heights of the borehole cross-section. The effect of total flow rate and water-cut on the response of spinner and capacitive sensor at five measured positions were investigated. The capacitance water holdup interpolation imaging algorithm was used to determine the local fluid property and oil-water interface height, and the measured local fluid speed was combined with the numerical simulation result to establish an optimal calculation model for obtaining the partial phase flow rate of the oil-water two-phase stratified flow in the horizontal well. The calculated flow rates of five measured points are basically consistent with the experimental data, the total flow rate and water holdup from calculation are in agreement with the set values in the experiment too, suggesting that the method has high accuracy.

Multifractal analysis of inclined oil-water countercurrent flow

Characterizing countercurrent flow structures in an inclined oil-water two-phase flow from one-dimensional measurement is of great importance for model building and sensor design.Firstly,we conducted oil-water two-phase flow experiments in an inclined pipe to measure the conductance signals of three typical water-dominated oil-water flow patterns in inclined flow,i.e.,dispersion oil-in-water pseudo-slug flow （PS）,dispersion oil-in-water countercurrent flow （CT）,and transitional flow （TF）.In pseudo-slug flow,countercurrent flow and transitional flow,oil is completely dispersed in water.Then we used magnitude and sign decomposition analysis and multifractal analysis to reveal levels of complexity in different flow patterns.We found that the PS and CT flow patterns both exhibited high complexity and obvious multifractal dynamic behavior,but the magnitude scaling exponent and singularity of the CT flow pattern were less than those of the PS flow pattern; and the TF flow pattern exhibited low complexity and almost monofractal behavior,and its magnitude scaling was close to random behavior.Meanwhile,at short time scales,all sign series of two-phase flow patterns exhibited very similar strong positive correlation; at high time scales,the scaling analysis of sign series showed different anti-correlated behavior.Furthermore,with an increase in oil flow rate,the flow structure became regular,which could be reflected by the decrease in the width of spectrum and the difference in dimensions.The results suggested that different oil-water flow patterns exhibited different nonlinear features,and the varying levels of complexity could well characterize the fluid dynamics underlying different oil-water flow patterns.

Simulation of Oil-Water Flow in Shale Oil Reservoirs Based on Smooth Particle Hydrodynamics

A Smooth Particle Hydrodynamics(SPH)method is employed to simulate the two-phase flow of oil and water in a reservoir.It is shown that,in comparison to the classical finite difference approach,this method is more stable and effective at capturing the complex evolution of this category of two-phase flows.The influence of several smooth functions is explored and it is concluded that the Gaussian function is the best one.After 200 days,the block water cutoff for the Gaussian function is 0.3,whereas the other functions have a block water cutoff of 0.8.The effect of various injection ratios on real reservoir production is explored.When 14 and 8 m^(3)/day is employed,the water breakthrough time is 130 and 170 days,respectively,and the block produces 9246 m^(3) and 6338 m^(3) of oil cumulatively over 400 days.

Simulation of Oil-Water Flow in a Shale Reservoir Using a Radial Basis Function

Due to the difficulties associated with preprocessing activities and poor grid convergence when simulating shale reservoirs in the context of traditional grid methods,in this study an innovative two-phase oil-water seepage model is elaborated.The modes is based on the radial basis meshless approach and is used to determine the pressure and water saturation in a sample reservoir.Two-dimensional examples demonstrate that,when compared to the finite difference method,the radial basis function method produces less errors and is more accurate in predicting daily oil production.The radial basis function and finite difference methods provide errors of 5.78 percent and 7.5 percent,respectively,when estimating the daily oil production data for a sample well.A sensitivity analysis of the key parameters that affect the radial basis function’s computation outcomes is also presented.

Two Phase Flow Simulation of Fractal Oil Reservoir Based on Meshless Method

The reservoir is the networked rock skeleton of an oil and gas trap,as well as the generic term for the fluid contained within pore fractures and karst caves.Heterogeneity and a complex internal pore structure characterize the reservoir rock.By introducing the fractal permeability formula,this paper establishes a fractal mathematical model of oil-water two-phase flow in an oil reservoir with heterogeneity characteristics and numerically solves the mathematical model using the weighted least squares meshless method.Additionally,the method’s correctness is verified by comparison to the exact solution.The numerical results demonstrate that the fractal oil-water two-phase flow mathematical model developed using the meshless method is capable of more accurately and efficiently describing the flow characteristics of the oil-water two-phase migration process.In comparison to the conventional numerical model,this method achieves a greater degree of convergence and stability.This paper examines the effect of varying the initial viscosity of the oil,the initial formation pressure,and the production and injection ratios on daily oil production per well,water cut in the block,and accumulated oil in the block.For 10 and 60 cp initial crude oil viscosities,the water cut can be 0.62 and 0.80,with 3100 and 1900 m^(3)cumulative oil production.Initial pressures have little effect on production.In this case,the daily oil production of well PRO1 is 1.7 m^(3)at 7 and 10 MPa initial pressure.Block cumulative oil production is 3465.4 and 2149.9m^(3)when the production injection ratio is 1.4 and 0.8.The two-phase meshless method described in this paper is essential for a rational and effective study of production dynamics patterns in complex reservoirs and the development of reservoir simulations of oil-water flow in heterogeneous reservoirs.