Validity and Accuracy of Reservoir Simulation With A Two-Dimensional, Three-Phase, Unsteady-State Heterogeneous Matrix Computer Model

1967 ◽  
Author(s):  
J.E. Garrett
Keyword(s):  
Computer Model ◽  
Reservoir Simulation ◽  
Two Dimensional ◽  
Unsteady State ◽  
Three Phase ◽  
Heterogeneous Matrix

scholarly journals A New Approach to the Two-Dimensional Multiphase Reservoir Simulator

1966 ◽  
Vol 6 (02) ◽  
pp. 175-182 ◽  
Author(s):  
R.G. Fagin ◽  
C.H. Stewart
Keyword(s):  
Physical Properties ◽  
Digital Computer ◽  
Two Dimensional ◽  
Unsteady State ◽  
Pressure Data ◽  
Three Phase ◽  
Large Memory ◽  
Reservoir Simulator ◽  
Oil Gas ◽  
Gas Lift

Abstract A two-dimensional, three-phase reservoir simulator was programed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reservoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. Introduction This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section. SPEJ P. 175ˆ

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Reactive Power Compensation for Unbalanced Fluctuating Loads by Using Two-Dimensional Space Vector and a Static Var Compensator

2014 ◽  
Vol 533 ◽  
pp. 397-400 ◽  
Author(s):  
Chi Jui Wu ◽  
Yu Wei Liu ◽  
Shou Chien Huang
Keyword(s):  
Power Factor ◽  
Reactive Power ◽  
Dimensional Space ◽  
Measurement Data ◽  
Power Source ◽  
Active Power ◽  
Two Dimensional ◽  
Static Var Compensator ◽  
Space Vector ◽  
Three Phase

To modify the power factor and balance the three-phase currents simultaneously, this paper proposes the instantaneous compensator to calculate the compensation current. The instantaneous compensator utilizes two-dimensional instantaneous space vector and setting the active power as a constant for each cycle which can improve power quality effectively. Moreover, the instantaneous compensator requires an independent power source, whose capacity can be reduce by using a static var compensator (SVC). An SVC does not interfere with the capability of the instantaneous compensator. Field measurement data were analyzed. Simulation results confirmed the feasibility of correcting the power factor and balancing load currents simultaneously using the proposed method.

Quick Evaluation Method of Streak Line Pattern in Mixing Vessel Based on Unsteady State Two dimensional Analysis

2019 ◽  
Vol 45 (6) ◽  
pp. 211-218
Author(s):  
Kodai Oya ◽  
Shota Otani ◽  
Keisuke Suzuki ◽  
Kenji Ebisutani ◽  
Yuto Naito ◽  
...  
Keyword(s):  
Dimensional Analysis ◽  
Evaluation Method ◽  
Two Dimensional ◽  
Line Pattern ◽  
Unsteady State

A computer model for the analysis of DNA replication intermediates by two-dimensional agarose gel electrophoresis

Gene ◽  
1998 ◽  
Vol 217 (1-2) ◽  
pp. 41-49 ◽  
Author(s):  
E. Viguera ◽  
A. Rodrı́guez ◽  
P. Hernández ◽  
D.B. Krimer ◽  
O. Trellez ◽  
...  
Keyword(s):  
Dna Replication ◽  
Computer Model ◽  
Gel Electrophoresis ◽  
Agarose Gel ◽  
Two Dimensional ◽  
Agarose Gel Electrophoresis ◽  
Replication Intermediates

scholarly journals The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
J. M. Osborne ◽  
R. D. O’Dea ◽  
J. P. Whiteley ◽  
H. M. Byrne ◽  
S. L. Waters
Keyword(s):  
Shear Stress ◽  
Culture Medium ◽  
Porous Scaffold ◽  
Two Dimensional ◽  
Governing Equations ◽  
Long Wavelength ◽  
Wavelength Limit ◽  
Aspect Ratios ◽  
Three Phase ◽  
Tissue Construct

A three phase model for the growth of a tissue construct within a perfusion bioreactor is examined. The cell population (and attendant extracellular matrix), culture medium, and porous scaffold are treated as distinct phases. The bioreactor system is represented by a two-dimensional channel containing a cell-seeded rigid porous scaffold (tissue construct), which is perfused with a culture medium. Through the prescription of appropriate functional forms for cell proliferation and extracellular matrix deposition rates, the model is used to compare the influence of cell density-, pressure-, and culture medium shear stress-regulated growth on the composition of the engineered tissue. The governing equations are derived in O’Dea et al. “A Three Phase Model for Tissue Construct Growth in a Perfusion Bioreactor,” Math. Med. Biol., in which the long-wavelength limit was exploited to aid analysis; here, finite element methods are used to construct two-dimensional solutions to the governing equations and to investigate thoroughly their behavior. Comparison of the total tissue yield and averaged pressures, velocities, and shear stress demonstrates that quantitative agreement between the two-dimensional and long-wavelength approximation solutions is obtained for channel aspect ratios of order 10−2 and that much of the qualitative behavior of the model is captured in the long-wavelength limit, even for relatively large channel aspect ratios. However, we demonstrate that in order to capture accurately the effect of mechanotransduction mechanisms on tissue construct growth, spatial effects in at least two dimensions must be included due to the inherent spatial variation of mechanical stimuli relevant to perfusion bioreactors, most notably, fluid shear stress, a feature not captured in the long-wavelength limit.

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