Determining performance data for hydrocarbon reservoirs using diffusive time of flight as the spatial coordinate

A non-transitory computer readable medium encoded with a computer program for determining a performance data for a hydrocarbon reservoir that when executed by one or more processors perform the steps comprising:

• obtaining a heterogeneous multi-dimensional model of at least a portion of the hydrocarbon reservoir divided into cells, each cell having a volume and one or more other attributes;
• calculating a diffusive time of flight based upon the heterogeneous multi-dimensional model;
• transforming the heterogeneous multi-dimensional model to an equivalent homogeneous one-dimensional model by defining the diffusive time of flight as a spatial variable;
• determining the performance data for the hydrocarbon reservoir based on the equivalent homogeneous one-dimensional model;
• and
• providing the performance data to an output device.

An apparatus for determining a performance data for a hydrocarbon reservoir comprising:

• a data storage;
• an output device;
• and
• one or more processors communicably coupled to the data storage and the output device, the one or more processors:
• obtain a heterogeneous multi-dimensional model of at least a portion of the hydrocarbon reservoir divided into cells, each cell having a volume and one or more other attributes;
• calculate a diffusive time of flight based upon the heterogeneous multi-dimensional model;
• transform the heterogeneous multi-dimensional model to an equivalent homogeneous one-dimensional model by defining the diffusive time of flight as a spatial variable;
• determine the performance data for the hydrocarbon reservoir based on the equivalent homogeneous one-dimensional model;
• and
• provide the performance data to the output device.