Methods and system for modeling wellbore treatment operations in which the flow of treatment fluids may be diverted are provided. In one embodiment, the methods comprise: receiving, at a processing component, one or more treatment operation inputs characterizing a treatment operation for a wellbore system comprising a wellbore penetrating at least a portion of a subterranean formation and a treatment fluid comprising a diverter, wherein at least one of the one or more treatment operation inputs comprises the inlet concentration of the diverter in the treatment fluid; and using the processing component to determine a wellbore system pressure distribution and a wellbore system flow distribution based, at least in part, on the one or more treatment operation inputs and a diversion flow model, wherein the diversion flow model captures an effect of the diverter on fluid flow in the wellbore system.

Methods and system for modeling wellbore treatment operations in which the flow of treatment fluids may be diverted are provided. In one embodiment, the methods comprise: receiving, at a processing component, one or more treatment operation inputs characterizing a treatment operation for a wellbore system comprising a wellbore penetrating at least a portion of a subterranean formation and a treatment fluid comprising a diverter, wherein at least one of the one or more treatment operation inputs comprises the inlet concentration of the diverter in the treatment fluid; and using the processing component to determine a wellbore system pressure distribution and a wellbore system flow distribution based, at least in part, on the one or more treatment operation inputs and a diversion flow model, wherein the diversion flow model captures an effect of the diverter on fluid flow in the wellbore system.

A computer-implemented numerical simulation method for studying a physical system governed by at least one differential equation such as a fluid in motion. The simulation is launched, making it possible to define a simulation domain. In the computation step, a machine learning algorithm is implemented to predict a global solution to the equation in the simulation domain. The computation step includes n consecutive sequences, each sequence includes cutting a piece in the simulation domain followed by predicting a local solution in the piece on the basis of local boundary conditions, n being an integer strictly greater than 1. The prediction step being carried out by a machine learning model, as input, global boundary conditions on the simulation domain.

A computer-implemented numerical simulation method for studying a physical system governed by at least one differential equation such as a fluid in motion. The simulation is launched, making it possible to define a simulation domain. In the computation step, a machine learning algorithm is implemented to predict a global solution to the equation in the simulation domain. The computation step includes n consecutive sequences, each sequence includes cutting a piece in the simulation domain followed by predicting a local solution in the piece on the basis of local boundary conditions, n being an integer strictly greater than 1. The prediction step being carried out by a machine learning model, as input, global boundary conditions on the simulation domain.

A smoothed-particle hydrodynamics (SPH)-based fluid analysis simulation apparatus comprises: an input unit for receiving, as an input, data about a plurality of particles, for a fluid analysis simulation; a space formation unit that divides, into a plurality of cells, the space in which the plurality of particles are present, and generates cell indexes on the basis of the locations of the cells in the space where the plurality of particles are present; a particle search unit for searching for at least one neighboring particle that neighbors a target particle, on the basis of particle reference information about the plurality of particles and cell reference information about the plurality of cells; and a flow data calculation unit that calculates flow data between the target particle and the at least one neighboring particle, and performs a fluid simulation on the basis of the flow data for the plurality of particles.

A smoothed-particle hydrodynamics (SPH)-based fluid analysis simulation apparatus comprises: an input unit for receiving, as an input, data about a plurality of particles, for a fluid analysis simulation; a space formation unit that divides, into a plurality of cells, the space in which the plurality of particles are present, and generates cell indexes on the basis of the locations of the cells in the space where the plurality of particles are present; a particle search unit for searching for at least one neighboring particle that neighbors a target particle, on the basis of particle reference information about the plurality of particles and cell reference information about the plurality of cells; and a flow data calculation unit that calculates flow data between the target particle and the at least one neighboring particle, and performs a fluid simulation on the basis of the flow data for the plurality of particles.

A method for stimulation of a well in a material formation which includes a workflow for the design of hole-size distribution in the liner of a LEL liner system is modelled, wherein a solution strategy for providing an initial estimate of the number of holes per segment honours the acid coverage per segment and the drop in pressure (dp) across the last one of the holes, where the initial estimate can be found from the relationship between interstitial velocity, pump rate, and total cross-sectional hole area for a particular discharge coefficient and liner configuration.

A method for stimulation of a well in a material formation which includes a workflow for the design of hole-size distribution in the liner of a LEL liner system is modelled, wherein a solution strategy for providing an initial estimate of the number of holes per segment honours the acid coverage per segment and the drop in pressure (dp) across the last one of the holes, where the initial estimate can be found from the relationship between interstitial velocity, pump rate, and total cross-sectional hole area for a particular discharge coefficient and liner configuration.

An apparatus and methods are provided for a suppressor to be coupled with a muzzle end of a barrel of a firearm to reduce muzzle blast and muzzle flash. The suppressor comprises a housing having a proximal end and a distal end. A front portion within the housing comprises a series of cylindrical gas expansion chambers for attenuating the temperature and energy of propellant gases accompanying a projectile fired from the firearm. An annular gas expansion chamber surrounds the cylindrical gas expansion chambers and directs a portion of the propellant gases from a rear portion of the suppressor to peripheral vents disposed at the distal end. Lateral chambers within the rear portion deflect and rebound a portion of the propellant gases before passing them into the annular gas expansion chamber. Ledges within the annular gas expansion chamber direct the propellant gases distally through suppressor toward the peripheral vents.

Assemblies and methods to enhance a fluid catalytic cracking (FCC) process associated with a refining operation, during the FCC process, may include supplying a hydrocarbon feedstock to first processing units associated with the refining operation. The assemblies and methods also may include conditioning a hydrocarbon feedstock and unit material samples, and analyzing the samples via one or more spectroscopic analyzers. The assemblies and methods further may include prescriptively controlling, via one or more FCC process controllers, based at least in part on the hydrocarbon feedstock properties and the unit material properties, the FCC processing assembly, so that the prescriptively controlling results in causing the FCC process to produce intermediate materials, the unit materials, and/or the downstream materials having properties within selected ranges of target properties, thereby to cause the FCC process to achieve material outputs that more accurately and responsively converge on one or more of the target properties.