Computer Codes for Oilwell-Perforator Design
- J.A. Regalbuto (Halliburton Explosive Products Center) | B.C. Gill (Halliburton Explosive Products Center)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- September 1997
- Document Type
- Journal Paper
- 188 - 195
- 1997. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 1.14 Casing and Cementing, 1.2.3 Rock properties, 1.8 Formation Damage, 5.2.2 Fluid Modeling, Equations of State, 2.2.2 Perforating, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.6 Drilling Operations
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This paper presents three computer codes used to analyze and design oilwell perforators that are specifically tailored to hydrocarbon-bearing formations. The codes are a Lagrangian, finite-element code; a Eulerian, finite-difference code; and a coupled Lagrangian/analytical code.
Applications of the codes involve charge-to-charge interference effects, estimation of penetration and hole size, explanation of charge/gun-system behavior, and perforator-design optimization.
Analysis of an existing six-shot/ft system, which showed charge-to-charge interference, is presented. The solution, which eliminated the interference and increased overall performance, involved charge-case modification. Topics discussed include the following.
Initial correlations between experimental and calculated penetrations and hole size in steel and cement.
The mechanism of producing burr-free holes in casing, explained by modeling the perforation system.
An example of perforator-performance improvement by determination of discrete jet properties.
Expanding the application of the codes by enlarging the equation-of-state database to include fluid-filled porous media.
The interaction of the shaped-charge jet with fluid-filled porous media is a phenomenon of basic importance to oilwell completion. The 40-year history of the use of shaped charges to perforate oil-bearing rock is notable by the minimal work done to enhance the understanding of the basic penetration mechanism by high-velocity jets.
The oilwell-perforator developmental efforts over the years have been characterized by design improvements to increase penetration in specified targets,1,2 some of which have properties of interest to petroleum engineers and some of which do not. In 1963, Venghiattis3 sought to relate perforator performance to measurable in-situ acoustic rock properties. The next effort in this area was made in 1991 by Halleck et al.4 They made correlations between penetration of a specific charge and the acoustic and density characteristics of specific rock types.
Other recent studies5-15 have attempted to establish the extent of the damaged zone around the perforation tunnel and its modification by the pressure fields existing at or after the time of perforation. To date, an analytical model describing the physics of penetration into porous rock does not exist. Experimental techniques to study the effects of pressure fields on the damaged zone lack a true surge capability that closely resembles real situations.
All in all, the current capability to estimate perforator performance from shaped-charge jet properties and measurable formation properties is at a very low level. New finite-element and finite-difference computer codes and shaped-charge diagnostic techniques appear to offer the potentials needed to increase our level of understanding of the jet-vs.-formation interaction.
The work described and recommended here is a small but important step toward formulation of a better understanding of perforation dynamics in hydrocarbon-bearing media.
Relevance to the Industry
When the basic perforation mechanism becomes clear and substantiated by experiment, the completion engineer can design the best perforation technique for each specific well. The perforator manufacturer can devote design efforts toward perforators with jet properties tailored to more specific hydrocarbon-bearing formations rather than, for example, designing for maximum penetration in cement, from which very few hydrocarbons are produced.
The Lagrangian code used in this work is a vectorized, explicit, two-dimensional, axisymmetrical, and plane strain finite-element code for analyzing the large-deformation dynamic and hydrodynamic response of inelastic solids. The basic feature of a Lagrangian code is that the computational grid is fixed in the material and moves with it. (See Fig. 1a.) Lagrangian methods have several advantages, including the following.
The codes use a relatively less-complicated computational algorithm because no convective terms are required to represent mass flow in the coordinate frame; i.e., the frame moves with the mass. Fewer computations per cycle mean faster running times for a given problem.
Boundary conditions and interfaces between materials can be sharply defined and treated in a straightforward fashion.
Materials with properties exhibiting time/history behavior are easily accommodated.
In summary, the Lagrangian code will run quickly. A typical shaped-charge problem run on a 486/66 MHz personal computer requires a few minutes of real time to reach 20 microseconds of problem time. Generally the distortions in the jet will terminate the problem, requiring rezoning to continue the problem further in time. This limits its applicability to the initial stages of jet formation, for example, without extensive rezoning.
In the Eulerian approach, the computational grid is fixed in space while the material moves through it. (See Fig. 1b.) Thus, a convective term must be included in the computational algorithm. Interfaces between materials are harder to define than in the Lagrangian method. Material surfaces and interfaces are defined only to within one mesh width, and special computational schemes must be used to prevent the material from diffusing throughout the computational grid. Computations take longer than the Lagrangian method; however, large distortions are easily handled. This chief shortcoming of the Lagrangian method is overcome, and (for example) jet formation and interaction with a target can be followed as far as desired, consistent with the available computing time. A typical penetration problem performed on an IBM work station may consume 24 to 96 hours of central-processing-unit time.
Coupled Lagrangian/Analytical Code.
A technique used since the 1970's to mitigate the restrictions imposed by the severe distortions that occur during jet formation and stretching is to couple an analytical model with the finite-element code. The finite-element code is used to model the liner collapse. The conditions in the liner at collapse are then input to an analytical jetting model; e.g. Pugh-Eichelberger-Rostoker, to compute jet properties. This approach produces important jet properties such as jet velocity, momentum, and kinetic energy in short computational times. Consequently, many variations in charge configuration can be analyzed quickly for their effects on jet characteristics.
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