Obtaining Transient Local Two-Phase Flow Data from Periodic Oscillations and Its Uncertainty Quantification

Uncertainty quantification of two-phase flow in porous media via the Coupled-TgNN surrogate model

A new hybrid CRWENO-MWENOZ-adaptive moving mesh method for cavitating two-phase compressible fluid flow simulation

Numerous graphical pre- and post-processors have been developed for numerical modeling. Many of these systems support numerical models that can be used for both steady state and transient simulations. Dealing with transient data can be particularly difficult in such an environment due to the differing time scales and units associated with transient field data and boundary conditions. A data model and a set of functions are presented in this paper as a simple, yet powerful strategy for managing temporal data in a comprehensive modeling environment. The strategy makes it possible to seamlessly integrate multiple types of transient data and convert the data to the appropriate values at the desired computational time intervals. In addition to simplifying the creation of transient models, the strategy makes it possible to automate much of the data manipulation required for model calibration.

During the past twenty years multiphase flow technology has become increasingly important for the economic transportation of well streams from reservoir to process. In particular, production offshore, where the trend is to develop numerous small fields by transporting untreated fluids Via existing infrastructures, imposes high demands on the multiphase science and technology required to ensure economic and safe operation. This paper addresses the state of the art in the development of multiphase production systems and highlights future trends. It subsequently scrutinizes the reliability of models and techniques currently available and identifies issues in the area of multiphase flow technology that need to be addressed. Typical aspects that will be covered are steady and transient two-phase pipe flow modelling, the effect of water on oil/gas flow, multiphase metering and multiphase boosting, and the use of trunkline management systems in multiplatform production schemes.

The interaction between natural events and technological installations involves complex mechanisms which have the potential to affect simultaneously more critical systems, nullifying the redundancy measures common to industrial safety systems and endangering the integrity of facilities. The concerns related to this kind of events are far from being restricted to a merely economic or industrial nature. On the contrary, due to the sensitivity of most processes performed in industrial plants and the negative consequences of eventual releases of hazardous materials, the impact of simultaneous failures embraces also the environment and population surrounding the installations. The risk is further widened by the trend of climate extremes: both observations over the past century and projections for next decades suggest an increase of the severity of extreme weather events and their frequency, both on local and global scales. The rise of sea water levels together with the exacerbation of extreme winds and precipitations, enlarge the geographic area of risk and rise the likelihood of accidents in regions historically susceptible to natural hazards. The prevention of technological accidents triggered by natural hazards lies unavoidably with the development of efficient theoretical and computational tools for the vulnerability assessment of industrial installations and the identification of effective strategies to tackle the growing risks to which they are subject. In spite of the increasing trend of the risk and the high-impact consequences, the current scientific literature still lacks robust means to tackle these issues effectively. The research presented in this dissertation addresses the critical need for novel theoretical and computational methods tailored for the risk assessment of complex systems threaten by extreme natural events. The specific requirements associated with the modelling of the interaction between external hazards and engineering systems have been determined, resulting in the identification of two main bottlenecks. On the one hand, this kind of analysis has to deal with the difficulty of representing accurately the complexity of technological systems and the mutual influence among their subsystems. On the other, the high degree of uncertainty affecting climate variables (due to their inner aleatory nature and the restricted information generally available), strongly bounds the accuracy and credibility of the results on which risk-informed decisions must be made. In this work, well-known traditional approaches (such as Bayesian Networks, Monte Carlo methods etc.) as well as cutting-edge methods from different sectors of the scientific literature have been adopted and integrated in order to obtain a novel theoretical strategy and computational tool able to overcome the limitations of the current state of the art. The result of the research is a complete tool for risk assessment and decision making support, based on the use of probabilistic graphical models and able to fully represent a wide spectrum of variables types and their uncertainty, to provide the implementation of flexible computational models as well as their computation and uncertainty quantification.

A partial differential equation was developed and programed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious diminution in delivery capacity. The pressure differential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. Introduction A computing program developed by the authors to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, (1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(PD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville for computing multicomponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(PD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. SPEJ P. 125ˆ

A fully implicit EOS based compositional two-phase transient flow simulator in wellbores

Hydraulic tomography, a procedure involving the performance of a suite of pumping tests in a tomographic format, provides information about variations in hydraulic conductivity at a level of detail not obtainable with traditional well tests. However, analysis of transient data from such a suite of pumping tests represents a substantial computational burden. Although steady state responses can be analyzed to reduce this computational burden significantly, the time required to reach steady state will often be too long for practical applications of the tomography concept. In addition, uncertainty regarding the mechanisms driving the system to steady state can propagate to adversely impact the resulting hydraulic conductivity estimates. These disadvantages of a steady state analysis can be overcome by exploiting the simplifications possible under the steady shape flow regime. At steady shape conditions, drawdown varies with time but the hydraulic gradient does not. Thus transient data can be analyzed with the computational efficiency of a steady state model. In this study, we demonstrate the value of the steady shape concept for inversion of hydraulic tomography data and investigate its robustness with respect to improperly specified boundary conditions.

To protect a pressurized system from overpressure, one of the most established strategies is to install a Pressure Safety Valve (PSV). Therefore, the excess pressure of the system is relieved through a vent pipe when PSV opens. The vent pipe is also called “PSV Outlet Header”. After the process starts, a transient two-phase flow is formed inside the outlet header consisting of high speed pressurized gas interacting with existing static air. The high-speed jet compresses the static air towards the end tail of the pipe until it is discharged to the ambiance and eventually, the steady state is achieved. Here, this transient process is investigated both analytically and numerically using the method of characteristics. Riemann’s solvers and Godunov’s method are utilized to establish the solution. Propagation of shock waves and flow property alterations are clearly demonstrated throughout the simulations. The results show strong shock waves as well as high transient pressure take place inside the outlet header. This is particularly important since it indicates the significance of accounting for shock waves and transient pressure, in contrast to commonly accepted steady state calculations. More precisely, shock waves and transient pressure could lead to failure, if the pipe thickness is chosen only based on conventional steady state calculations.

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

In this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions. The parameters include values and directions of principal hydraulic conductivities (or transmissivities) in anisotropic media, specific storage (or storativity), interior and boundary recharge or leakage rates, coefficients of head‐dependent interior and boundary sources, and boundary heads. In transient situations, the initial head distribution can also be estimated if the system is originally at a steady state. Paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters. The inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters. Since not all the factors which contribute to the prior errors can be quantified statistically at the outset, the covariance matrices of these errors are expressed in terms of several parameters which, if unknown, can be estimated jointly with the hydraulic parameters by a stagewise optimization process. When transient head data are separated by a fixed time interval, the temporal structure of these data is approximated by a lag‐one autoregressive model with a correlation coefficient that can be treated as another unknown parameter. Estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace. Paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature, all of which are based on the maximum likelihood concept, might be useful for selecting the best groundwater model (or the best method of parameterizing a particular model) among a number of given alternatives.

Transient Boiling Two-Phase Flow with a sudden decrease of flow rate

A series of techniques is proposed for volumetric air flow measurements that are based upon the principles of particle image velocimetry (PIV). The proposed techniques fall in two categories; part 1 of this dissertation considers measurement data processing using constitutive laws and part 2 focuses on development of a coaxial volumetric flow measurement system that uses helium filled soap bubbles (HFSB) as tracer particles. In part 1, first a technique is proposed to measure instantaneous volumetric pressure using a low repetition rate tomographic PIV system. Instead of time-resolved measurement of the flow temporal evolution, which typically required for pressure-from-PIV procedures, the required temporal information is obtained by solution of the incompressible Navier-Stokes equations in vorticity-velocity formulation using the spatial information available from the instantaneous measurements. The reverse is proposed for cases where temporal resolution is more abundant, but spatial resolution is limited. The vorticity transport equation is leveraged to couple temporal information with instantaneous velocity data in the proposed VIC+ framework, in an attempt to obtain a dense velocity field at high spatial resolution. The governing principle is that by using the flow governing equations, the data ensemble used for interpolation is increased beyond instantaneous velocity measurements only. The technique is demonstrated to allow for measurement of vorticity and dissipation in a real-world experiment, which would otherwise be underestimated by more than 40% using the established tomographic PIV approach. The proposed VIC+ technique uses a data ensemble for dense velocity interpolation consisting of the instantaneous velocity and material derivative measurements obtained from Lagrangian particle tracking velocimetry. An extension of the VIC+ framework that uses a measurement time-segment instead of instantaneous data only is shown to potentially improve the measurement fidelity further, when a cost-effective three-dimensional implementation can be realized. An uncertainty quantification technique is proposed for future developments of such dense interpolation techniques. It is shown that the results from Lagrangian particle tracking measurements can be directly used for uncertainty quantification of dense interpolations and no independent measurement data is required. In part 2 of this dissertation, a technique is first proposed for large-scale volumetric pressure measurement. The method follows recent developments of large-scale measurements using HFSB tracer particles, in combination with Lagrangian particle tracking and ensemble bin-averaging. This allows for evaluation of accurate velocity statistics and in turn the time-averaged pressure field. The dissertation concludes with the proposal of the coaxial volumetric velocimeter (CVV). The CVV brings imaging and illumination together in a compact box, viewing and illuminating a measurement volume from a single viewing direction. The theoretical background that is derived shows that measurements in air using the CVV are only possible using tracer particles that scatter significantly more light than traditional micron sized tracer particles. Here, HFSB tracer particles are used. Due to the small solid angle of the imaging system, tracer particles need to be imaged over an extended number of snapshots to increase particle positional accuracy, making use of particle trajectory regularization. A prototype CVV has been realized, which is first used to confirm that the flow around a sphere is measured with acceptable correspondence to a potential flow solution. Second, in the case of the flow around a cyclist, the CVV is shown to allow for measurements near both concave and convex surfaces within one measurement volume. This allows for flow analysis using skin-friction lines. In addition, the compact nature of the CVV allows mounting on a robotic arm for time-averaged of a large and complex wind tunnel model. The full-scale measurement of the flow around Giro d’Italia cyclist Tom Dumoulin shown using the CVV is an example of the latter.

A major concern with hydraulic fracturing in tight formation is the fracturing fluid-induced formation damage (FFIFD) for the high capillary pressure and the presence of water-sensitive clays. Analytical models are good choices for formation damage evaluation comparing to computationally expensive numerical simulations. However, many analytical models are limited to single-phase flow and the FFIFD is seldom addressed. This paper presents a semi-analytical model for this problem with the consideration of both two-phase flow and FFIFD. A triple-porosity model is modified to capture the formation damage caused by fracturing fluid, and mainly two modifications are made. First, two-phase flow is assumed in the fractures to capture the choking effects. In addition, a low permeability fracturing fluid invasion layer (FFIL) is used to characterize leakoff caused clay swelling and polymer adsorption in the matrix pores. The analytical solution is obtained in the Laplace domain, and a successive iteration is used to update the dynamic parameters by coupling the flowing material balance equations. The precision of the semi-analytical model is validated using the commercial numerical simulator Eclipse. Several synthetic cases and a field case are studied, the results show that gas production is greatly affected by FFIFD. The effect of two-phase flow on gas production is mainly within the early several days. The permeability and width of FFIL have a significant effect on gas production. Gas production rate in the early hundreds of days will be much larger with thinner FFIL and larger permeability, but it will decline sharper later for the faster depletion. The field case shows that different models can match the production data, but the interpreted parameters and the physical meaning are totally different. In addition, a good match will be obtained with FFIFD and two-phase flow effects considered in the model. A simple yet versatile semi-analytical model is proposed in this paper for production prediction and analysis with the consideration of both FFIFD and two-phase flow. It is a quite comprehensive model to allow for a seamless way to analyze production data in the flow-back and production stage. It can also serve as an alternative to computationally expensive numerical simulations to evaluate the formation damage for unconventional reservoirs.

This paper presents a new method of analyzing the performance of a flowing well. The method employs a thermodynamic property known as the Availability Function. The advantage of the availability function method of analysis is that it allows for the calculation of the thermodynamic efficiency of all processes, including not only those that are large work producers or consumers but also those that do not have work production or consumption as their goal. The efficiency of a process indicates how close the process is to its ultimate possible performance. It can be used as a way of comparing various processes and to make a sound decision as to where improvements are possible. In order to simulate the fluid flow behavior, a transient, two-phase flow model was developed in both the reservoir and the wellbore. A one-dimensional flow was assumed for the wellbore model while a radial flow was assumed for the reservoir system. The equations governing the fluid flow behavior in both systems are: (1) mass, (2) momentum, (3) energy, and (4) entropy balance equations. The wellbore model includes heat transfer in the wellbore and heat conduction in the formation. Finite difference approximation was used in solving the fluid flow equations. The model developed in this study is capable of handling a single component, single phase (oil or gas) or two-phase (oil and gas) flow. The fluid flow equations provide the thermodynamic properties – energy, enthalpy, entropy, and the fluid velocity for use in the calculations of the maximum reversible (theoretical possible) work, the useful energy utilized in the lifting of the hydrocarbon fluid from the bottom of the well to the surface and the energy lost due to irreversibilities. The thermodynamic efficiency of production is obtained from the ratio of the actual work obtainable to the reversible maximum work that could have been obtained in the absence of irreversibilities. The thermodynamic derivatives and phase properties were predicted by using the multiparameter equation of state which was a modification of the BWR equation of state of Lee and Kesler. Results obtained from this study show that: Thermodynamic efficiency of hydrocarbon fluid production increases as production rate increases. A considerable fraction of the fluid energy is lost due to irreversibilities, especially at the early stages of production. The thermodynamic efficiency of fluid production would be greatly improved by minimizing wellbore heat loss. Irreversibilities associated with frictional losses between the fluid and the interior pipe wall do not affect the thermodynamic efficiency of production. A transient model is essential in analyzing the fluid flow behavior, especially at the early stages of production.