Multigrid Methods for Three-Dimensional Petroleum Reservoir Simulation

1989 ◽  
Author(s):  
J.E. Dendy ◽  
S.F. McCormick ◽  
J.W. Ruge ◽  
T.F. Russell ◽  
S. Schaffer
Keyword(s):  
Reservoir Simulation ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Petroleum Reservoir

Numerical studies of a class of linear solvers for fine-scale petroleum reservoir simulation

2016 ◽  
Vol 18 (2-3) ◽  
pp. 93-102 ◽  
Author(s):  
Zheng Li ◽  
Shuhong Wu ◽  
Chen-Song Zhang ◽  
Jinchao Xu ◽  
Chunsheng Feng ◽  
...  
Keyword(s):  
Reservoir Simulation ◽  
Fine Scale ◽  
Petroleum Reservoir ◽  
Linear Solvers ◽  
Numerical Studies

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Gravity Segregation in Two-Phase Displacement Processes

1974 ◽  
Vol 14 (06) ◽  
pp. 619-632 ◽  
Author(s):  
Allan Spivak
Keyword(s):  
Reservoir Simulation ◽  
Three Dimensional ◽  
Mobility Ratio ◽  
Two Dimensional ◽  
Two Phase ◽  
Gravity Segregation ◽  
Reservoir Performance ◽  
Phase Displacement ◽  
Gravity Effects ◽  
Displacement Processes

Spivak, Allan,* Member SPE-AIME, Chevron Oil Field Research Co., La Habra, Calif. Abstract This paper describes a study of gravity segregation (underrun or override of injected fluids) in two-phase, secondary recovery displacement processes. Reservoir simulation was used to investigate the factors that influence gravity segregation and the magnitude of gravity effects for both water floods and gas floods. The degree of segregation for a given set of conditions was determined bycomparing the results of two-dimensional cross-sectional with one-dimensional horizontal calculations, andcomparing the results of three-dimensional vs two-dimensional a real calculations. The degree of segregation is quantitatively described by the dimensionless number E defined as (Rbt)no gravity -(Rbt)gravity E =, (Rbt)no gravity where Rbt is recovery at breakthrough. Gravity segregation effects in two-phase displacement processes were found to increase withincreasing processes were found to increase withincreasing permeability (either horizontal or vertical),permeability (either horizontal or vertical),increasing density difference,increasing mobility ratio,decreasing production rates. anddecreasing level of viscosity for a fixed viscosity ratio. A series of calculations was made in which the parameters that affect gravity segregation were varied. The effect of each parameter on the degree of gravity segregation was observed. The effect of both stratified and random heterogeneity was also studied. A correlation between the degree of gravity segregation and the dimensionless groups G = 0.00633 and M = mobility ratio was established. This correlation is based on the results of the simulator calculations and a detailed analysis of the equations for three-dimensional, two-phase. immiscible, incompressible flow. The correlation can be used to determine qualitatively whether gravity segregation will be a significant factor in a given flooding process. It can also be used to determine whether the assumption of vertical equilibrium is valid in the simulation by a two-dimensional a real simulation model of reservoirs where fluid saturations vary significantly in the vertical direction. Introduction For many years, gravity segregation in reservoir processes was not accounted for because it could processes was not accounted for because it could not be adequately handled in reservoir engineering calculations. The advent of reservoir simulation provided the capability to handle gravity, and it provided the capability to handle gravity, and it became apparent that gravity effects could significantly affect reservoir performance. This paper describes a study in which a three-dimensional paper describes a study in which a three-dimensional (3-D), two-phase, incompressible simulator was used to look at gravity effects in displacement processes. The objectives of this study wereto processes. The objectives of this study wereto determine what factors influence gravity segregation and in what way;to look at the magnitude of gravity segregation effects;to compare reservoir performance calculations with and without gravity performance calculations with and without gravity effects. PREVIOUS WORK ON GRAVITY PREVIOUS WORK ON GRAVITY SEGREGATION IN DISPLACEMENT PROCESSES Craig et al. did experimental work to study the effects of gravity segregation during water, gas, and solvent flooding. As a result of their studies, they concluded that segregation of fluids due to gravity effects could result in oil recoveries at breakthrough as low as 20 percent of those otherwise expected. They also concluded that performance may in some cases be influenced to a greater degree by heterogeneity than by gravity effects. They were not able to directly compare performance under a given set of conditions with and without gravity. SPEJ p. 619

scholarly journals Assessing the Needs to Incorporate Completion Details in a Petroleum Reservoir Simulation Model

2015 ◽  
Vol 8 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Liang-Biao Ouyang
Keyword(s):  
Fluid Flow ◽  
Simulation Model ◽  
Simulation Study ◽  
Reservoir Simulation ◽  
High Rate ◽  
Petroleum Reservoir ◽  
Well Performance ◽  
Well Completion ◽  
Reservoir Permeability ◽  
Reservoir Simulation Model

Most of the current research and commercial reservoir simulators lack the capability to handle complex completion details like perforation tunnels in a simulation study. In most common applications, the simplified handling of completion complexity in reservoir simulations is not expected to introduce significant error in simulation results. However, it has been found that under certain circumstances, especially in high rate wells that have become more and more common in deepwater oil and profilic gas development, exclusion of the complex completion details in a reservoir simulation model would lead to nontrivial errors. New equations have been proposed to assess the needs to incorporate completion details in a reservoir simulation study based on the understanding of the fluid flow in a formation, the fluid flow along a wellbore and the fluid flow through perforation tunnels if exist. A series of sensitivity studies with different completion options under different flow and reservoir environments has been conducted to provide some guidance to improve well performance prediction through reservoir simulation. Impacts of key parameters like perforation density, perforation diameter, perforation length, wellbore length, borehole diameter, well completion configuration, well placement, reservoir permeability, reservoir heterogeneity, pressure drawdown, etc, have also been investigated.

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