A Method for Determining the Optimum Location of Wells in a Reservoir Using Mixed-Integer Programming

1974 ◽  
Vol 14 (01) ◽  
pp. 44-54 ◽  
Author(s):  
Gary W. Rosenwald ◽  
Don W. Green
Keyword(s):  
Mathematical Model ◽  
Gas Flow ◽  
Demand Curve ◽  
Gas Storage ◽  
Mixed Integer ◽  
Trial And Error ◽  
Flow Rates ◽  
Storage Reservoir ◽  
Reservoir Simulator ◽  
Production Demand

Abstract This paper presents a mathematical modeling procedure for determining the optimum locations of procedure for determining the optimum locations of wells in an underground reservoir. It is assumed that there is a specified production-demand vs time relationship for the reservoir under study. Several possible sites for new wells are also designated. possible sites for new wells are also designated. The well optimization technique will then select, from among those wellsites available, the locations of a specified number of wells and determine the proper sequencing of flow rates from Those wells so proper sequencing of flow rates from Those wells so that the difference between the production-demand curve and the flow curve actually attained is minimized. The method uses a branch-and-bound mixed-integer program (BBMIP) in conjunction with a mathematical reservoir model. The calculation with the BBMIP is dependent upon the application of superposition to the results from the mathematical reservoir model.This technique is applied to two different types of reservoirs. In the first, it is used for locating wells in a hypothetical groundwater system, which is described by a linear mathematical model. The second application of the method is to a nonlinear problem, a gas storage reservoir. A single-phase problem, a gas storage reservoir. A single-phase gas reservoir mathematical model is used for this purpose. Because of the nonlinearity of gas flow, purpose. Because of the nonlinearity of gas flow, superposition is not strictly applicable and the technique is only approximate. Introduction For many years, members of the petroleum industry and those concerned with groundwater hydrology have been developing mathematical reservoir modeling techniques. Through multiple runs of a reservoir simulator, various production schemes or development possibilities may be evaluated and their relative merits may be considered; i.e., reservoir simulators can be used to "optimize" reservoir development and production. Formal optimization techniques offer potential savings in the time and costs of making reservoir calculations compared with the generally used trial-and-error approach and, under proper conditions, can assure that the calculations will lead to a true optimum.This work is an extension of the application of models to the optimization of reservoir development. Given a reservoir, a designated production demand for the reservoir, and a number of possible sites for wells, the problem is to determine which of those sites would be the best locations for a specified number of new wells so that the production-demand curve is met as closely as possible. Normally, fewer wells are to be drilled than there are sites available. Thus, the question is, given n possible locations, at which of those locations should n wells be drilled, where n is less than n? A second problem, that of determining the optimum relative problem, that of determining the optimum relative flow rates of present and future wells is also considered. The problem is attacked through the simultaneous use of a reservoir simulator and a mixed-integer programming technique.There have been several reported studies concerned with be use of mathematical models to select new wells in gas storage or producing fields. Generally, the approach has been to use a trial-and-error method in which different well locations are assumed. A mathematical model is applied to simulate reservoir behavior under the different postulated conditions, and then the alternatives are postulated conditions, and then the alternatives are compared. Methods that evaluate every potential site have also been considered.Henderson et al. used a trial-and-error procedure with a mathematical model to locate new wells in an existing gas storage reservoir. At the same time they searched for the operational stratagem that would yield the desired withdrawal rates. In the reservoir that they studied, they found that the best results were obtained by locating new wells in the low-deliverability parts of the reservoir, attempting to maximize the distance between wells, and turning the wells on in groups, with the low-delivery wells turned on first.Coats suggested a multiple trial method for determining well locations for a producing field. SPEJ P. 44

Model Study of Foam as a Sealant for Leaks in Gas Storage Reservoirs

1970 ◽  
Vol 10 (01) ◽  
pp. 9-16 ◽  
Author(s):  
George G. Bernard ◽  
L.W. Holm
Keyword(s):  
Gas Flow ◽  
Pore Space ◽  
Economic Loss ◽  
Gas Storage ◽  
Flow In Porous Media ◽  
Underground Gas Storage ◽  
Foaming Agents ◽  
Storage Reservoir ◽  
Gas Leakage ◽  
Storage Reservoirs

Abstract Previous studies have shown that foam, because of its unique structure, reduces gas flow in porous media. This blocking action of foam appears to be especially suitable for sealing leaks in underground gas storage reservoirs. Such reservoirs often have permeable areas in the overlying caprock that allow permeable areas in the overlying caprock that allow vertical migration of gas from the storage zone to the upper formations. The escaped gas represents both a safety hazard and an economic loss. Our objectives in this study were to evaluate the effectiveness of foam in preventing the escape of gas from a leaky gas storage reservoir and to find the foaming agents that were most suitable for this purpose. We simulated the behavior of a leaky gas reservoir with a sandstone model and found that foam was 99-percent effective in reducing leakage of gas through the model. The amount of foaming agent required to seal a leak depends on the adsorption-desorption properties of the agent. After testing many foaming agents, we concluded that best results are obtained with certain modified anionic esters of relatively low molecular weight. Less than 0.3 lb of such agents is required per barrel of pore space in Berea sandstone. This study indicates that foam generation should be an effective and economical method for reducing or stopping gas leakage from an underground storage reservoir. Introduction The practicality of underground gas storage is greatly dependent upon the confinement that the caprock provides for the formation to be used as a storage reservoir. In spite of numerous precautions, several gas storage projects are plagued by vertical migration of gas from the intended storage zone to upper formations. Such gas leaks pose a safety hazard and represent an economic loss. If leakage is very high, the storage operation may be uneconomical. In at least one cases the leak problem is minimized by periodically collecting the escaped gas from the upper formation and reinjecting it into the storage reservoir. While such a solution is feasible, it is economically unattractive because the leak limits pressures and gas injection rates. Furthermore, energy must be expended in order to circulate the escaped gas. Recent studies have shown that foam, because of its unique structure, reduces gas flow in porous media. This blocking action of foam appears to be uniquely suitable for sealing leaks in underground gas storage reservoirs. Our objectives in this study were to determine the effectiveness of foam in reducing gas flow in a model of a "leaky" gas storage reservoir and to find foaming agents most suitable for this purpose. APPARATUS AND PROCEDURE PREPARATION OF THE MODEL PREPARATION OF THE MODELA laboratory model representing an estimated area of gas leakage in an Illinois gas storage reservoir was constructed of 24-in. × 6-in. × 1-in. Berea sandstone (See Fig. 1). The model was coated with Hysol plastic. The model represented an area of the reservoir approximately 600 ft wide, 2,400 ft long and 100 ft thick. The section contained about 2,000,000 bbl of pore space. The major portion of the reservoir is upstream of the inlet to this estimated area of leakage. The model, then, was geometrically scaled to this area of leakage in the reservoir. Distribution channels were installed on both ends of the model to permit linear gas flow through its entire width and thickness. Three injection wells were drilled into the model about one-third the distance from the inlet to the outlet. SPEJ P. 9

Convection Effects in Epitaxial Reactors: an Experimental and Theoretical Study

1988 ◽  
Vol 144 ◽  
Author(s):  
P. B. Chinoy ◽  
P. D. Agnello ◽  
S. K. Ghandhia
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Energy Transfer ◽  
Natural Convection ◽  
Gas Flow ◽  
Theoretical Study ◽  
Excellent Correlation ◽  
Flow Rates ◽  
Wide Range ◽  
Experimental Vehicle

ABSTRACTAn experimental and theoretical study has been undertaken of the effects of natural and forced convection in horizontal epitaxial reactors. The epitaxial growth of GaAs was used as the experimental vehicle for this study. A mathematical model for mass, momentum and energy transfer in the reactor was developed. Excellent correlation between modeled and experimental results was demonstrated over a wide range of reactor pressures and susceptor geometries. Recirculation of hot gases, caused by natural convection, was found to result in a strong pressure dependence of growth rate at higher susceptor slopes. Low reactor pressures have been shown to be a more effective way to eliminate recirculation than high gas flow rates.

scholarly journals Underground Gas Storage Process Optimisation with Respect to Reservoir Parameters and Production Equipment

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4324
Author(s):  
Vladislav Brkić ◽  
Ivan Zelenika ◽  
Petar Mijić ◽  
Igor Medved
Keyword(s):  
Mathematical Model ◽  
Pressure Drop ◽  
Gas Storage ◽  
Production Equipment ◽  
Base Case ◽  
Hydraulic Loss ◽  
Storage Facility ◽  
Underground Gas Storage ◽  
History Match ◽  
Storage Reservoir

The storage of natural gas in geological structures such as depleted fields, aquifers and salt caverns plays an important role in a gas supply system as it balances the fluctuation of gas demand and price. Hydraulic loss due to fluid flow through gas storage production equipment and an interfering effect from nonequal productivity index of storage wells may have an important influence on gas storage performance. An integrated mathematical model is developed based on underground gas storage facility production data. Using this model, the hydraulic loss is determined. A real test case that consists of a gas storage reservoir linked to the surface facility is analysed. The mathematical model uses an experimentally determined pressure drop coefficient in chokes. The base case scenario created using real gas storage facility data enables the achievement of a good history match with the given parameters of the gas storage reservoir. Using the history match simulation case as an initial scenario (a base case), two different scenarios are created to determine the injection and withdrawal performance of the gas storage field. The results indicate that the pressure drop in chokes, when fully open as a constraints in an underground gas storage facility, has a significant impact on gas storage operations and deliverability.

scholarly journals A mathematical model for designing a reliable cellular hybrid manufacturing-remanufacturing system considering alternative and contingency process routings

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Amirreza Hooshyar Telegraphi ◽  
Akif Asil Bulgak
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Manufacturing Systems ◽  
Closed Loop ◽  
Sustainable Manufacturing ◽  
Critical Issue ◽  
Economic Benefits ◽  
Mixed Integer ◽  
Hybrid Manufacturing ◽  
Closed Loop Supply Chain

AbstractDue to the stringent awareness toward the preservation and resuscitation of natural resources and the potential economic benefits, designing sustainable manufacturing enterprises has become a critical issue in recent years. This presents different challenges in coordinating the activities inside the manufacturing systems with the entire closed-loop supply chain. In this paper, a mixed-integer mathematical model for designing a hybrid-manufacturing-remanufacturing system in a closed-loop supply chain is presented. Noteworthy, the operational planning of a cellular hybrid manufacturing-remanufacturing system is coordinated with the tactical planning of a closed-loop supply chain. To improve the flexibility and reliability in the cellular hybrid manufacturing-remanufacturing system, alternative process routings and contingency process routings are considered. The mathematical model in this paper, to the best of our knowledge, is the first integrated model in the design of hybrid cellular manufacturing systems which considers main and contingency process routings as well as reliability of the manufacturing system.

scholarly journals Analysis of Performance of the Wind-Driven Pulverizing Aerator Based on Average Wind Speeds in the Conditions of Góreckie Lake

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2796
Author(s):  
Andrzej Osuch ◽  
Ewa Osuch ◽  
Stanisław Podsiadłowski ◽  
Piotr Rybacki
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Water Pump ◽  
Average Wind Speed ◽  
Flow Rates ◽  
Wind Speeds ◽  
Average Wind ◽  
Flow Through ◽  
Analysis Of Performance ◽  
Research Period

In the introduction to this paper, the characteristics of Góreckie lake and the construction and operation of the wind-driven pulverizing aerator are presented. The purpose of this manuscript is to determine the efficiency of the pulverizing aerator unit in the windy conditions of Góreckie Lake. The efficiency of the pulverization aerator depends on the wind conditions at the lake. It was necessary to conduct thorough research to determine the efficiency of water flow through the pulverization segment (water pump). It was necessary to determine the rotational speed of the paddle wheel, which depended on the average wind speed. Throughout the research period, measurements of hourly average wind speed were carried out. It was possible to determine the efficiency of the machine by developing a dedicated mathematical model. The latest method was used in the research, consisting of determining the theoretical volumetric flow rates of water in the pulverizing aerator unit, based on average hourly wind speeds. Pulverization efficiency under the conditions of Góreckie Lake was determined based on 6600 average wind speeds for spring, summer and autumn, 2018. Based on the model, the theoretical efficiency of the machine was calculated, which, under the conditions of Góreckie Lake, amounted to 75,000 m3 per year.

scholarly journals Evaluation of a Humidified Nasal High-Flow Oxygen System, Using Oxygraphy, Capnography and Measurement of Upper Airway Pressures

2011 ◽  
Vol 39 (6) ◽  
pp. 1103-1110 ◽  
Author(s):  
J. E. Ritchie ◽  
A. B. Williams ◽  
C. Gerard ◽  
H. Hockey
Keyword(s):  
Healthy Volunteers ◽  
Airway Pressure ◽  
Gas Flow ◽  
Air Entrainment ◽  
High Flow ◽  
Positive Pressure ◽  
Mean Airway Pressure ◽  
Flow Rates ◽  
Oxygen Fraction ◽  
Airway Pressures

In this study, we evaluated the performance of a humidified nasal high-flow system (Optiflow™, Fisher and Paykel Healthcare) by measuring delivered FiO2 and airway pressures. Oxygraphy, capnography and measurement of airway pressures were performed through a hypopharyngeal catheter in healthy volunteers receiving Optiflow™ humidified nasal high flow therapy at rest and with exercise. The study was conducted in a non-clinical experimental setting. Ten healthy volunteers completed the study after giving informed written consent. Participants received a delivered oxygen fraction of 0.60 with gas flow rates of 10, 20, 30, 40 and 50 l/minute in random order. FiO2, FEO2, FECO2 and airway pressures were measured. Calculation of FiO2 from FEO2 and FECO2 was later performed. Calculated FiO2 approached 0.60 as gas flow rates increased above 30 l/minute during nose breathing at rest. High peak inspiratory flow rates with exercise were associated with increased air entrainment. Hypopharyngeal pressure increased with increasing delivered gas flow rate. At 50 l/minute the system delivered a mean airway pressure of up to 7.1 cmH2O. We believe that the high gas flow rates delivered by this system enable an accurate inspired oxygen fraction to be delivered. The positive mean airway pressure created by the high flow increases the efficacy of this system and may serve as a bridge to formal positive pressure systems.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

Activation of Nanoflows for Fuel Cells

2012 ◽  
Vol 3 (2) ◽  
Author(s):  
Z. Insepov ◽  
R. J. Miller
Keyword(s):  
Carbon Nanotubes ◽  
Fuel Cells ◽  
Surface Waves ◽  
Traveling Waves ◽  
Gas Flow ◽  
Atomic Mass ◽  
Flow Rates ◽  
Selective Filter ◽  
Phase Velocities ◽  
Dynamics Simulations

Propagation of Rayleigh traveling waves from a gas on a nanotube surface activates a macroscopic flow of the gas (or gases) that depends critically on the atomic mass of the gas. Our molecular dynamics simulations show that the surface waves are capable of actuating significant macroscopic flows of atomic and molecular hydrogen, helium, and a mixture of both gases both inside and outside carbon nanotubes (CNT). In addition, our simulations predict a new “nanoseparation” effect when a nanotube is filled with a mixture of two gases with different masses or placed inside a volume filled with a mixture of several gases with different masses. The mass selectivity of the nanopumping can be used to develop a highly selective filter for various gases. Gas flow rates, pumping, and separation efficiencies were calculated at various wave frequencies and phase velocities of the surface waves. The nanopumping effect was analyzed for its applicability to actuate nanofluids into fuel cells through carbon nanotubes.

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