Numerical solution of the problem was implemented in Frost 3D Universal software, with a computational mesh of 58.5 million nodes, to predict ground thaw under the influence of the pipeline. A 2-year simulation of the ground thaw around the pipeline was performed. The computation in Frost 3D Universal software on a quad-core CPU took approximately 70 hours and used 17 GB of RAM. We had already simulated this model before with less detailed discretization: the mesh consisted of 22.3 million nodes and this wasn’t enough to enable us to factor in small elements such as thin heat insulators. Using an NVIDIA Titan graphics accelerator, the prediction of ground thaw over a 20-year period took about 7 hours.
The model of a lengthy section of a gas pipeline
The specific nature of the current problem – simulation of the ground thaw formation along a 500-meter section of the oil pipeline, 1.2 meters in diameter – rendered a large computational mesh necessary. This section is characterized by a complex geological-lithological structure of grounds, which also includes layers of ice deposits. A total of 21 ground typologies with various thermophysical properties were revealed in this section alone. Altitude differences in the daylight surface of 35 meters were also taken into account.
Complex geological-lithological structure of grounds beneath oil pipeline
Thus, in order to obtain a quality, detailed discretization of the pipeline while also taking into account both the complex geological-lithological structure of the grounds and the fine heat insulation material, we built a large computational mesh with 58.5 million nodes.
Detail of computational mesh near pipeline and penoplex
Discretization of geological layer and altitude difference on section with oil pipeline
There is a high demand on the market for solutions to such challenging problems as these, and we responded by implementing conceptually new plug-in architecture for Frost 3D Universal, capable of handling computational meshes of hundreds of millions of nodes. Our new architecture enabled a significant reduction in the demand placed on application memory by performing a functional division of the software into logical parts (plugins), each of which is then loaded individually and independently into RAM. This approach enables the independent upgrade of each plugin without modifying the application itself.
Thaw bulb of frozen ground beneath oil pipeline
Frozen ground thaw due to heated oil flowing through pipeline
In order to save RAM and Video memory, we have developed innovative solutions for implementing the more resource-intensive software modules in the Frost 3D Universal package:
1) In the mathematical solver, arithmetic operations with floating-point numbers are now performed with a single precision (float type is used instead of double). In order avoid reduced precision in comparison with double precision computations, the computed target value (such as temperature) is transformed from the whole range of single precision floating-point numbers into a subset, where it is changed as the problem is being solving.
2) The computational mesh module, developed for 64-bit CPU architecture, is now based on:
a) the most recent algorithms for determining the occupancy of mesh cells by source objects;
b) faster determination and resolution of collisions;
c) optimized mechanism for liminal memory selection and cleaning.
3) The 3D visualizer of computational results, developed for 64-bit CPU architecture and graphics cards, now preprocesses the computational mesh by forming a hash data structure. This has enabled significant reduction in graphics memory overheads without impacting display quality. In addition, the latest NVIDIA graphics accelerator instructions and point buffers are used, enabling over 300 fps when displaying multi-million meshes.
Thermal distribution in permafrost ground near oil pipeline