A Numerical Solution to the Unsteady-State Partial-Water-Drive Reservoir Performance Problem

1961 ◽  
Vol 1 (03) ◽  
pp. 184-194
Author(s):  
Walter L. Henson ◽  
Paul L. Wearden ◽  
John D. Rice
Keyword(s):  
Digital Computer ◽  
Analogue Computer ◽  
Reservoir Pressure ◽  
Unsteady State ◽  
Aquifer Parameters ◽  
Pressure Behavior ◽  
Reservoir Performance ◽  
Performance Problem ◽  
Partial Water ◽  
Digital Computers

Abstract Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Schilthuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co.'s Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir performance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method.

The Estimation of Aquifer Properties From Reservoir Performance in Water-Drive Fields

1977 ◽  
Vol 99 (2) ◽  
pp. 345-352 ◽  
Author(s):  
A. T. Chatas
Keyword(s):  
Least Squares ◽  
Material Balance ◽  
Dimensionless Form ◽  
Simultaneous Solution ◽  
Method Of Least Squares ◽  
Normal Equations ◽  
Aquifer Parameters ◽  
Reservoir Performance ◽  
Analytical Functions ◽  
Aquifer Properties

The purpose of this paper is to indicate a method for estimating values of specified aquifer parameters from an investigation of the reservoir performance of an associated oilfield. To achieve this objective an analysis was made of the simultaneous solution of the material-balance and diffusivity equations, followed by an application of the method of least squares. Three analytical functions evolved, which in dimensionless form were numerically evaluated by computer and tabulated herein. Application of the proffered method requires the simultaneous solution of the three normal equations developed in the paper.

Computer analysis of curves from an infrared CO2 analyzer and screen-type airflow meter

1963 ◽  
Vol 18 (1) ◽  
pp. 149-157 ◽  
Author(s):  
F. E. Noe
Keyword(s):  
Computer Analysis ◽  
Dead Space ◽  
Digital Computer ◽  
Breath Holding ◽  
Analogue Computer ◽  
Schematic Diagram ◽  
Practical Applications ◽  
Obese Subjects

Curves from an infrared CO2 analyzer and a screen-type airflow meter were analyzed with a digital computer, and new curves were obtained. Practical applications are illustrated for the data and curves from the computer, and the significance of differences is discussed for the curves from normal, emphysematous, and obese subjects. Curves are shown for breaths with added dead space and for breaths after various periods of breath holding. Also included is a schematic diagram for an analogous analogue computer. Submitted on October 26, 1961

Analysis of Pressure Data for Fractured Wells: The Constant-Pressure Outer Boundary

1978 ◽  
Vol 18 (02) ◽  
pp. 139-150 ◽  
Author(s):  
R. Raghavan ◽  
Nico Hadinoto
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Reservoir Pressure ◽  
Pressure Gradients ◽  
Pressure Data ◽  
Pressure Behavior ◽  
Fracture Length ◽  
Infinite Conductivity ◽  
Production Pattern ◽  
Fractured Well

Abstract Analysis of flowing and shut-in pressure behavior of a fractured well in a developed live-spot fluid injection-production pattern is presented. An idealization of this situation, a fractured well located at the center of a constant pressure square, is discussed. Both infinite-conductivity and uniform-flux fracture cases are considered. Application of log-log and semilog methods to determine formation permeability, fracture length, and average reservoir pressure A discussed. Introduction The analysis of pressure data in fractured wells has recovered considerable attention because of the large number of wells bat have been hydraulically fractured or that intersect natural fractures. All these studies, however were restricted to wells producing from infinite reservoirs or to cases producing from infinite reservoirs or to cases where the fractured well is located in a closed reservoir. In some cases, these results were not compatible with production performance and reservoir characteristics when applied to fractured injection wells. The literature did not consider a fractured well located in a drainage area with a constant-pressure outer boundary. The most common example of such a system would be a fractured well in a developed injection-production pattern. We studied pressure behavior (drawdown, buildup, injectivity, and falloff) for a fractured well located in a region where the outer boundaries are maintained at a constant pressure. The results apply to a fractured well in a five-slot injectionproduction pattern and also should be applicable to a fractured well in a water drive reservoir. We found important differences from other systems previously reported. previously reported. We first examined drawdown behavior for a fractured well located at the center of a constant-pressure square. Both infinite-conductivity and uniform-flux solutions were considered. The drawdown solutions then were used to examine buildup behavior by applying the superposition concept. Average reservoir pressure as a function of fracture penetration ratio (ratio of drainage length to fracture length) and dimensionless time also was tabulated. This represented important new information because, as shown by Kumar and Ramey, determination of average reservoir pressure for the constant-pressure outer boundary system was not as simple as that for the closed case since fluid crossed the outer boundary in an unknown quantity during both drawdown (injection) and buildup (falloff). MATHEMATICAL MODEL This study employed the usual assumptions of a homogeneous, isotropic reservoir in the form of a rectangular drainage region completely filled with a slightly compressible fluid of constant viscosity. Pressure gradients were small everywhere and Pressure gradients were small everywhere and gravity effects were neglected. The outer boundary of the system was at constant pressure and was equal to the initial pressure of the system. The plane of the fracture was located symmetrically plane of the fracture was located symmetrically within the reservoir, parallel to one of the sides of the boundary (Fig. 1). The fracture extended throughout the vertical extent of the formation and fluid was produced only through the fracture at a constant rate. Both the uniform-flux and the infinite-conductivity fracture solutions were considered. P. 139

Can Digital Computers Think? (1951)

2004 ◽  
Author(s):  
Alan Turing
Keyword(s):  
Human Brain ◽  
Digital Computer ◽  
Extreme Case ◽  
Turing Test ◽  
The Brain ◽  
Digital Computers

The lecture ‘Can Digital Computers Think?’ was broadcast on BBC Radio on 15 May 1951, and was repeated on 3 July of that year. (Sara Turing relates that Turing did not listen to the Wrst broadcast but did ‘pluck up courage’ to listen to the repeat.) Turing’s was the second lecture in a series with the general title ‘Automatic Calculating Machines’. Other speakers in the series included Newman, D. R. Hartree, M. V. Wilkes, and F. C. Williams. Turing’s principal aim in this lecture is to defend his view that ‘it is not altogether unreasonable to describe digital computers as brains’, and he argues for the proposition that ‘If any machine can appropriately be described as a brain, then any digital computer can be so described’. The lecture casts light upon Turing’s attitude towards talk of machines thinking. In Chapter 11 he says that in his view the question ‘Can machines think?’ is ‘too meaningless to deserve discussion’ (p. 449). However, in the present chapter he makes liberal use of such phrases as ‘programm[ing] a machine . . . to think’ and ‘the attempt to make a thinking machine’. In one passage, Turing says (p. 485): ‘our main problem [is] how to programme a machine to imitate a brain, or as we might say more briefly, if less accurately, to think.’ He shows the same willingness to discuss the question ‘Can machines think?’ in Chapter 14. Turing’s view is that a machine which imitates the intellectual behaviour of a human brain can itself appropriately be described as a brain or as thinking. In Chapter 14, Turing emphasizes that it is only the intellectual behaviour of the brain that need be considered (pp. 494–5): ‘To take an extreme case, we are not interested in the fact that the brain has the consistency of cold porridge. We don’t want to say ‘‘This machine’s quite hard, so it isn’t a brain, and so it can’t think.’’ ’ It is, of course, the ability of the machine to imitate the intellectual behaviour of a human brain that is examined in the Turing test (Chapter 11).

Direct Printout X-Ray Pole Figures from Digital Computers

1968 ◽  
Vol 12 ◽  
pp. 391-403 ◽  
Author(s):  
Hung-Chi Chao
Keyword(s):  
Computer Program ◽  
Pole Figure ◽  
Sheet Metal ◽  
Digital Computer ◽  
Stereographic Projection ◽  
X Ray Diffraction ◽  
X Ray ◽  
Pole Figures ◽  
Time Required ◽  
Digital Computers

AbstractThe texture of sheet metal Is best described, by means of pole figures, which are very expensive and time-consuming to prepare. About 8 to 12 hours of effort by a specially trained, and. highly skilled technician are needed to prepare each pole figure. Accordingly, pole figures are not used as extensively in research studies as they would, be if they could be obtained more easily.A method has been developed for automatically producing pole figures by printing results directly from a digital computer. This method does not require the use of additional plotting attachments and, is therefore less expensive and time consuming than other methods. With this method, any laboratory with access to a digital computer can produce pole figures automatically.X-ray diffraction intensities are recorded on punched tape or on punched cards and are fed into the digital computer. A computer program corrects X-ray data obtained, by either transmission or reflection X-ray techniques, maps the stereographic projection, and prints pole figures directly. The time required, to prepare an accurate pole figure is reduced from 8 to 12 hours to 20 minutes or less depending on the type of digital computer used.

CO 2 dissolution and its impact on reservoir pressure behavior

2015 ◽  
Vol 43 ◽  
pp. 115-123 ◽  
Author(s):  
E. Peters ◽  
P.J.P. Egberts ◽  
D. Loeve ◽  
C. Hofstee
Keyword(s):  
Reservoir Pressure ◽  
Pressure Behavior

scholarly journals RESERVOIR PERFORMANCE ANALYSIS USING MATERIAL BALANCE METHOD IN GAS FIELD

2021 ◽  
Vol 2 (2) ◽  
pp. 68
Author(s):  
Indah Widiyaningsih ◽  
Panca Suci Widiantoro ◽  
Suwardi Suwardi ◽  
Riska Fitri Nurul Karimah
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Material Balance ◽  
Gas Production ◽  
Recovery Factor ◽  
Reservoir Pressure ◽  
Gas Flow Rate ◽  
Reservoir Performance ◽  
Cumulative Production ◽  
Material Balance Method

The RF reservoir is a dry gas reservoir located in Northeast java offshore that has been produced since 2018.  The RF reservoir has produced 2 wells with cumulative production until December 2019 is 31.83 BSCF. In January 2018 the gas production rate from the two wells was 36 MMSCFD and the reservoir pressure at the beginning of production was 2449.5 psia, peak production occurred in April 2019 with a gas flow rate of 98 MMSCFD but in December 2019 the gas production rate from both wells decreased to 30 MMSCFD with reservoir pressure decreased to 1607.8 psia. Changes in gas flow rate and pressure in the RF reservoir will affect changes in reservoir performance, so it is necessary to analyze reservoir performance to determine reservoir performance in the future with the material balance method. Based on the results the initial gas in place (IGIP) is 80.08 BSCF. The drive mechanism worked on the RF reservoir until December 2019 was a depletion drive with a recovery factor up to 88% and a current recovery factor (CRF) is 40%. The remaining gas reserves in December 2019 is 39 BSCF and the reservoir will be made a production prediction until December 2032. Based on production predictions of the four scenarios, scenario 2 was chosen as the best scenario to develop the RF reservoir with a cumulative production is 66.1 BSCF and a recovery factor of 82.6%.

scholarly journals Simulation of Genetic Systems by Automatic Digital Computers IV. Selection Between Alleles at a Sex-Linked Locus

1958 ◽  
Vol 11 (4) ◽  
pp. 613 ◽  
Author(s):  
JSF Barker
Keyword(s):  
Life Cycle ◽  
Digital Computer ◽  
Genetic Systems ◽  
Digital Computers

A programme simulating selection between two alleles at a sex�linked locus has been developed for an automatic digital computer (the SILLIAC). It introduces selection and chance effects at four stages of the life cycle.

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

Sign in / Sign up

Export Citation Format

Share Document