Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Format

Subjects

Date

Availability

1-4 of 4

Keywords: derivative

Close
**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 14–17, 2019

Paper Number: PSIG-1923

... the above method requires that we solve a nonlinear system at each time step. In these situations, it may be useful to use an affine method: = + where is the

**derivative**of evaluated at In this case we need only solve a linear system for SDoLE & ASDoLE methods To have a second-order correct method...
Abstract

ABSTRACT This paper defines and studies a simple, efficient method for discretizing pipeline equations in time. In many ways the solutions of pipe flow equations look like the solutions of nonlinear diffusion equations, so it is natural that schemes that work well for diffusion problems might have analogs for pipe flow problems. The method presented here is based on backward Euler (BE). To advance the solution from time t to time t+dt it uses a single step of BE with step size dt and two steps of BE with step size ????/2. The results are then combined to give a second-order correct scheme. This process is called step doubling with local extrapolation (SDoLE) and has been rigorously analyzed for nonlinear diffusion problems in the context of Galerkin spatial discretizations. [1] Here a collocation scheme is the underlying discretization in space and time. The backward Euler that forms the basis of this method is done using a linearization technique instead of solving a nonlinear system. This is extended to minimize the computational costs associated with evaluation of the nonlinearities in the equations. The resulting discretization technique is called affine step doubling with local extrapolation (ASDoLE). The properties of the method are explained by looking first at a scalar ODE and then by presenting examples based on pipeline operation. A single pipe case is given followed by a simple gun barrel example.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 14–17, 2019

Paper Number: PSIG-1932

... of the laboratory data matches values calculated using Ref. 1. The most significant difference is in the

**derivative**of isothermal bulk modulus with pressure which we will discuss at some length. Sonic velocity can be computed directly as the square root of the adiabatic bulk modulus divided by the...
Abstract

ABSTRACT Ultrasonic flow meters, in addition to calculating flow rate, measure the speed of sound in the fluid at the local fluid pressure and temperature. It is desirable to be able to compute the crude oil specific gravity at base (i.e. standard temperature and pressure) conditions from this measurement. However, there is no straightforward way to do this, in large part because there is no accepted standard for computing crude oil sonic velocity as a function of pressure, temperature, and base density. The authors develop an approach for computing sonic velocity for crude oil. Using this as a foundation, they propose a calculation approach to compute crude oil specific gravity as a function of observed speed of sound, pressure, and temperature. OVERVIEW The motivation for this work was to be able to compute crude oil density from sonic velocity, pressure, and temperature. Pipeline companies often have ultrasonic flow meters at pump stations that, as part of measuring flow, compute sonic velocity. Because of cost, densitometers are usually much more sparsely spaced. Since elevation head depends directly on density, a measurement of fluid density can improve hydraulic modeling calculations.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 12–15, 2015

Paper Number: PSIG-1508

... Abstract This paper proposes a novel model-based leak location method for pipelines. We first formulate the leak location problem into an optimization problem under certain conditions. Then we develop a

**derivative**-based search algorithm to solve that optimization problem. The**derivative**will...
Abstract

Abstract This paper proposes a novel model-based leak location method for pipelines. We first formulate the leak location problem into an optimization problem under certain conditions. Then we develop a derivative-based search algorithm to solve that optimization problem. The derivative will be calculated from an approximate of the underlying mathematical model that describes the dynamics of pipeline systems, by means of discretization and linearization. Results of simulation and tests using real pipeline data show that this proposed method is accurate, timely, and computationally effective. Introduction Pipelines are one of the major transportation means in oil and gas industry. Leakage remains one of the concerns for pipeline operators. Once a leak occurs, it is important to detect and locate it quickly and accurately in order to minimize potential economic loss and/or environmental damage. Thus leak detection and location is an indispensable technology for managing pipelines smoothly and safely. In this note we are only concerned about leak location, assuming that an existing leak has been detected. Despite the fact that many techniques have been developed in order to address this issue, locating a leak timely and accurately remains a challenging problem both in industry and in academia, see and references therein. One of the conventional methods for leak location is the pressure-gradient method which utilizes the fact that the leak outflow changes the steady pressure-gradients for the sections before and after the leak, respectively. Thus the intersection of those two gradient lines represents the true leak location. This method assumes that the pipeline system is in steady state, which however is a quite stringent condition since in practice most pipelines contain rich transients all the time.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 30–31, 1986

Paper Number: PSIG-8603

... rate contracts. optimization problem pump schedule constraint water system cost savings operation

**derivative**reservoir level duty cycle algorithm procedure peak period control variable penalty function optimization algorithm artificial intelligence gradient search method...
Abstract

An Optimization Algorithm for Looped Water Networks This paper contains the results, and represents the culmination of a six month study of the procedures and techniques for the optimization of operation of the City of Albuquerque Water System. 1.0 OVERVIEW 1.1 Primary Purpose of the Optimization Subsystem The optimization subsystem for the AUTO 8 system has as its objective to deliver water to the Water System customers at the lowest possible cost to the city while maintaining reliability-of its components and certain safety standards. These safety standards include minimum levels in each of the reservoirs which must be maintained to insure adequate water for fighting fires. 1.2 Inherent Problems With a network as complicated as a city water distribution system must necessarily be, there are many difficulties with designing a straightforward optimal solution to a pzoblem such as getting water from the ground to the ultimate users. A problem that any mathematical method for optimization will encounter with a system such as a municipal water system is the heavy degree of looping of the network. This redundancy of paths is necessary to ensure adequate channels for water to any portion of the system for safety and reliability reasons. The result is a problem that is very non-linear. In the design of a procedure for optimal control, this non linearity must be taken into consideration. The Albuquerque water network is made up of trunks which extend from the lower elevations in the Rio Grande Valley up toward the higher elevations o f the Sandia Mountains on the East side and toward the upper valley on the West. The trunks are connected by large intertrunk transfer lines which are connected to the distribution networks within the system. The network is divided into zones of elevation with each zone representing approximately 115 feet of elevation. The system is gravity fed from reservoirs in each zone. The Albuquerque system has many sources of water at least in the lower zones. Water may be pumped directly from wells which are local to the reservoirs in the lowest four zones, or boosted from the zone below, or in any combination. Each of the well fields and booster stations contains multiple pumps. Each of the pumps within the system has a different pumping rate and cost of pumping water. Therefore the well pumps located at one reservoir represent a source of water for that reservoir, and, through the boosters located at the site, can be considered a source for the reservoir on the same trunk in the zone above. In addition, because of the intertrunk transfer lines, sources for one reservoir may serve to some degree as sources for other reservoirs within the same zone on parallel trunks. The City currently has a contract with the power company which charges for electricity on a peak / off peak basis. The optimization algorithm must not only take this cost structure into consideration, but must also provide the flexibility for adaptation to future rate contracts.