Numerical solution of non-isothermal flow in oil reservoirs using OpenACC

Modelling and analysis of tracer flow in oil reservoirs

▪ Abstract Efficiently and accurately solving the equations governing fluid flow in oil reservoirs is very challenging because of the complex geological environment and the intricate properties of crude oil and gas at high pressure. We present these challenges and review successful and promising solution approaches. We discuss in detail the modeling of fluid flow in reservoirs with strongly varying rock properties. This requires subgrid-scale models that accurately represent the flow physics due to fine-scale fluctuations. A second focus is on the complex multiphase, multicomponent systems that describe miscible gas injection processes for enhanced oil recovery and CO2 sequestration.

An approach to modeling the processes of non-isothermal multiphase flow in oil reservoir is considered. The approach is based on implicit calculation of pressure using the finite element method and explicit calculation of phase saturations. The considered computational scheme for calculating the temperature field makes it possible to simulate the flow of a fluid mixture in oil reservoirs, accompanied by thermal processes, and to consider both heat transfer between phases and heat transfer of a fluid mixture and rock. The proposed approach also takes into account the effect of the temperature field on the properties of phases and provides for the possibility of heat sources/sinks in the reservoir. Numerical experiments are carried out on a model of a real field with a large number of wells and a high heterogeneous porous medium. Based on the calculation results with hot water injection into a well, the applicability of the considered scheme for solving oil production problems using thermal recovery methods is demonstrated.

Published in Petroleum Transactions, AIME, Volume 201, 1954, pages 217–229. Abstract One of the most important problems of reservoir mechanics is the prediction of the behavior of a gas and oil producing reservoir for a variety of production programs. In the absence of a knowledge of the behavior of even idealized systems, it has been difficult, if not impossible, to determine which production program would yield maximum economic recovery. The problem was formulated mathematically many years ago, but a solution of the equations had never been obtained because of their extreme complexity. The solution of the problem became possible, however, with the advent of modern computing machines. This paper describes a digital method of solving the problem and discusses some of the results which have been obtained to date. The IBM Type 701 Electronic Data Processing Machines located at IBM's New York Scientific Computing Service were used successfully to perform the computations. The flow of gas and oil through a reservoir can be described mathematically by two second-order, nonlinear partial differential equations which must be solved simultaneously. All derivatives were replaced by finite differences to bring the equations into a form suitable for digital calculations. A number of finite difference formulations were investigated and one form was found which resulted in stable, convergent solutions. This form was used to obtain solutions for both radial and linear systems producing by solution gas drive. The results presented in this paper are:saturation profile within the hypothetical reservoir vs. time,pressure profile within the hypothetical reservoir vs. time,gas-oil ratio vs. cumulative recovery, andultimate recovery. The saturation profile clearly shows the effect of critical gas saturation. The saturation near the wellbore drops quickly to the critical gas saturation and remains essentially at that value until the remainder of the reservoir also has dropped to the critical gas saturation. The pressure profile shows a smooth variation of pressure across the reservoir. The gas-oil ratio drops slightly during the early stage of production until the critical gas saturation is reached, rises rapidly from then on and eventually passes through a sharp maximum just before the economic limit of production is reached. For the radial example presented in this paper, the average oil saturation of the reservoir at a time corresponding to the limit of economic production was 56.5 per cent and the ultimate recovery was 6.86 per cent. The difference between change in saturation and ultimate recovery is caused by shrinkage of the oil phase.

Simulation-assisted gas tracer test study of Tarim Yaha gas-condensate reservoir in China

One of the key problems in modelling flow in oil reservoirs is our lack of precise knowledge of the variations in flow properties across the field. At best we can infer the statistics of these variations from field observations. The challenge is to determine the statistics of the flow itself (flow rates, pressures etc.) from the statistics of the permeability variations. Conventional simulations are computationally very expensive unless smart sampling techniques or surrogate models are used. In this paper we demonstrate the use of a path integral formulation for this problem. To demonstrate how this methods works, we start with the one dimensional Darcy flow problem: q(x)=-K(x)dp(x)/dx where p(x) is the pressure, q(x) is the flow rate and K(x) is the rock permeability. The randomness of the porous medium is modelled by regarding K as a stochastic quantity which is assumed to follow Gaussian statistics. Because of the randomly varying rock structure, there is a variety of conceivable pressure realisations p(x). The path integral Z is an integral over all realisations with an appropriate probability measure. Once Z is evaluated, either analytically, or by standard Monte Carlo methods, any observable of interest, including pressure correlations can be easily obtained.

An adaptive time stepping algorithm for IMPES with high order polynomial extrapolation

Introduction. The analysis and interpretation of hydrodynamic research data are based on theoretical models and computational algorithms. Despite the demand for this topic, numerous issues related to unsteady fluid flows in oil reservoirs still require solutions. Therefore, mathematical setting of problems related to the account of unsteady fluid flow, the development of effective numerical methods and algorithms, their solution using modern web technologies are pressing. This study is aimed at developing a web application for mathematical modeling of the process of fluid filtration in single- porosity reservoirs when conducting a hydrodynamic study at a production well.Materials and Methods. To solve the problem, the methods of continuum mechanics and computational mathematics were applied. A model of oil flow in a single-porosity reservoir was presented. Python and JavaScript programming languages were used in the development of the application. The calculation results were stored in a relational database implemented using PostgreSQL tools.Results. A new web application has been developed for modeling the oil filtration process in single- porosity reservoirs. It is applicable for studying fluid dynamic processes and can be used to predict flowrates, production and calculation of optimal well operation modes.Discussion and Conclusion. The developed web application provides for building pressure and temperature fields in the reservoir near a flowing and shut-in production well and at various distances from it. This information makes it possible to urgently assess the duration of hydrodynamic studies, as well as to regulate the operation of wells. The application can be deployed in an existing network infrastructure and use all the functionality by connecting to a remote server. It is optimized for use on various platforms and has broad prospects for further development.

A Fast Method for Computing Tracer Flow in Oil Reservoirs J.M. Guevara-Jordan J.M. Guevara-Jordan Universidad Central de Venezuela Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad and Tobago, April 2003. Paper Number: SPE-81153-MS https://doi.org/10.2118/81153-MS Published: April 27 2003 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Guevara-Jordan, J.M. "A Fast Method for Computing Tracer Flow in Oil Reservoirs." Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, Trinidad and Tobago, April 2003. doi: https://doi.org/10.2118/81153-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Latin America and Caribbean Petroleum Engineering Conference Search Advanced Search AbstractThis paper describes a new and fast numerical scheme for computing tracer flow in oil reservoirs. It combines the f undamental s olution m ethod (FSM) and the s treamline a pproach (SA) to obtain a very efficient algorithm. The FSM is based on the method of images and the singular value decomposition technique to compute the pressure and velocity fields. The SA uses the time of flight notion along the streamlines to obtain very accurate tracer concentration. Applications of the new scheme to a quarter five spot, arbitrary shaped and multiple wells reservoir problems show that it is faster than boundary and finite element methods.IntroductionThe numerical simulation of tracer flow in oil reservoir and aquifers is probably one of the most basic and important problems in reservoir engineering1. A new generation of streamline reservoir simulators has emerged in last ten years2,3. It is based on very efficient numerical schemes for tracer flow problems4. These reservoir simulators are very general because they use extremely fine grid and multigrid solvers in their implementation5. However, they may not be the best choice to simulate every type of reservoir. If the reservoir is homogeneous, sectionally homogeneous, fracturated or it has barriers and faults then a mesh free reservoir simulator, which uses boundary techniques in its implementation, are a better choice6,7,8 because it requires less data and its results are more accurate.Recently a new kind of mesh free method for tracer flow problems was introduced in the petroleum engineering literature9. It combines the FSM10 and a streamtube model11 to obtain a numerical scheme that allows tracer flow simulations in homogeneous reservoirs with horizontal wells and very thin permeability barriers. The FSM uses a s ingular v alue d ecomposition12 (SVD) solver to determine the streamline distribution needed in the streamtube model. The main advantages of the new scheme are: zero numerical diffusion, easy implementation and high precision in its results.An original extension and modification of the numerical method described in the last paragraph is presented in this paper. It combines an extension of the FSM to heterogeneous reservoir13 and a SA based on the time of flight concept2,3,4, instead of streamtube model, into a very efficient algorithm. The new scheme was tested on a set of standard reservoir engineering problems and the results were validated against analytical solutions and numerical solutions produced by a commercial reservoir simulator on a very fine grids. It addition, a CPU time study, which compare the new scheme against standard numerical methods, gives evidence of its fast execution times.This article is distributed in four sections. The first section sets down the tracer flow equations used in this work. The second section provides a short description of the new numerical method. The third section develops and analyzes the test problems used in the evaluation of the new method. One of these problems includes a CPU time comparative study. Finally, section four has the conclusions, discussions and recommendations.Mathematical ModelThe system of equations for the tracer flow in a two dimensional reservoir is composed by three equations. They are the concentration equationEquation 1Darcy's lawEquation 2and the continuity equationEquation 3In these equations the main variables are: C the tracer concentration, p the reservoir pressure, (xi,yi) the i well position, qi the i well rate, n the number of wells, K the isotropic permeability, (vx,vy) the velocity field, f the porosity, µ fluid viscosity, and d the Dirac's delta function14. Keywords: streamline distribution, concentration, tracer concentration, equation, imaginary well, production well, subregion, spe 81153, fluid dynamics, tracer flow Subjects: Reservoir Fluid Dynamics, Reservoir Simulation, Flow in porous media This content is only available via PDF. 2003. Society of Petroleum Engineers You can access this article if you purchase or spend a download.

Current microprocessors aggressively exploit instruction-level parallelism (ILP) through techniques such as multiple issue, dynamic scheduling, and non-blocking reads. Recent work has shown that memory latency remains a significant performance bottleneck for shared-memory multiprocessor systems built of such processors.This paper provides the first study of the effectiveness of software-controlled non-binding prefetching in shared memory multiprocessors built of state-of-the-art ILP-based processors. We find that software prefetching results in significant reductions in execution time (12% to 31%) for three out of five applications on an ILP system. However, compared to previous-generation system, software prefetching is significantly less effective in reducing the memory stall component of execution time on an ILP system. Consequently, even after adding software prefetching, memory stall time accounts for over 30% of the total execution time in four out of five applications on our ILP system.This paper also investigates the interaction of software prefetching with memory consistency models on ILP-based multiprocessors. In particular, we seek to determine whether software prefetching can equalize the performance of sequential consistency (SC) and release consistency (RC). We find that even with software prefetching, for three out of five applications, RC provides a significant reduction in execution time (15% to 40%) compared to SC.

The study and development of high-order discretization techniques for the modeling and simulation of multiphase flows in petroleum reservoirs are still a challenge from the computational viewpoint due to the difficulty posed by some physical features such as heterogeneity and anisotropy of the medium, that are of paramount importance in this class of applications. In this paper, we present a preliminary investigation of the very high order Spectral Finite Volume Method (SFVM) for the discretization of the saturation equation that describes the 1-D Oil-Water displacement through porous media. In this equation, the hyperbolic term is discretized using a high order SFVM, the capillary term is approximated using a second order CVFD (Control Volume Finite Difference) method and the integration in time is carried out using a third-order Runge–Kutta method. On the other hand, to prevent numerical oscillations near shocks, that are typical from higher order schemes, a slope limiter procedure is used in the reconstruction stage. To evaluate the performance of the SFVM some simple model problems, including capillarity and gravity, are solved, yielding accurate and efficient results. The use of very high order formulations can be of utmost importance, particularly for multidimensional and real large-scale applications with complex wave structures.

A parallel rough set based dependency calculation method for efficient feature selection

Modern computational workloads demand exceptional performance and efficiency, necessitating the effective utilization of advanced CPU features such as SIMD (Single Instruction Multiple Data), instruction-level parallelism (ILP), and branch prediction. This paper explores optimization techniques that address inefficiencies at the algorithmic, architectural, and system levels, enabling software to align with hardware capabilities. Key techniques include resolving data dependencies, enhancing memory locality, utilizing compiler intrinsics,applying tail call optimizations, and employing strategies like loop unrolling, blocking, vectorization, and function inlining. Tail call optimization and breaking dependency chains are analyzed to improve parallelism and reduce processing overhead. Both manual and compiler-driven approaches are evaluated, providing insights into their trade-offs and synergies. Experimental results from benchmarks, such as matrix multiplication and particle simulations, demonstrate significant gains, with up to a 3x increase in instructions per cycle (IPC) and a 40% reduction in execution time. These findings highlight the critical role of optimizing software for architectural features like cache hierarchies, pipelining, and vector widths. This study provides techniques to maximize CPU efficiency, bridging the gap between hardware potential and software performance. Future directions include extending these methodologies to hybrid architectures like GPUs and integrating machine learning models for dynamic runtime optimization.

The protein threading problem is the problem of determining the three-dimensional structure of a given but arbitrary protein sequence from a set of known structures of other proteins. This problem is known to be NP-hard and current computational approaches to threading are time-consuming and data-intensive. In this paper, we propose an evolution strategy for protein threading. We also developed two parallel approaches for fast threading. We have obtained at least better results than current comparable approaches, as well as significant reduction in execution time.

Thermal transients during nonisothermal fluid injection into oil reservoirs