Weighted material point method for managing fluid flow in pipes

A method of managing a pumping rate with the aid of a fluid flow data analysis system, the method comprising:

• obtaining data related to an initial state of a plurality of pipe elements and a plurality of fluid pads within the pipe elements;
• generating a pumping schedule with the fluid flow data analysis system for the plurality of fluid pads through the plurality of pipe elements, the pumping schedule being adjusted based on an estimated pressure at a location in the pipe elements, the pressure being estimated by:
• initializing models of the fluid pads and of the pipe elements with the obtained data, the models of the fluid pads comprising material points;
• for each of the material points, determining:
• an integration weight;
• and
• a material state;
• (a) for each of the fluid pads, discretizing governing fluid flow equations on a numerical grid, wherein the numerical grid is constrained to the pipe elements;
• (b) solving the discretized equations to generate nodal solutions;
• (c) constructing material point solutions from the nodal solutions;
• updating the models of the fluid pads with the material point solutions;
• and
• adjusting the pumping rate based on the updated models.

A fluid flow data analysis system comprising:

• a processor;
• and
• a display configured to display graphical representations of a fluid flow model, wherein the system is configured to:
• initialize models of at least two fluid pads and of one or more pipe elements, the models of the fluid pads comprising material points;
• for each of the material points, determine:
• an integration weight;
• and
• a material state;
• (a) discretize governing equations on a numerical grid, wherein the numerical grid is constrained within the pipe elements;
• (b) solve the discretized equations to generate nodal solutions;
• (c) construct material point solutions from the nodal solutions;
• update the models of the fluid pads with the material point solutions;
• estimate a pressure at a wellbore location represented by the models of the pipe elements based on the updated models;
• and
• cause a pumping rate to be adjusted based on the estimated pressure.