Method system and program storage device for simulating a multilayer reservoir and partially active elements in a hydraulic fracturing simulator

A system, comprising:

• an Earth formation comprising multiple layers;
• a wellbore intersecting the multiple layers, the wellbore including a perforated interval;
• at least one fracturing pump fluidly connected to the wellbore;
• a computing device including a program storage device readable by the computing device tangibly embodying a program of instructions executable by the computing device to perform a simulation method comprising:
• simulating a hydraulic fracture in an Earth formation, the formation including a multilayered reservoir, wherein a mesh overlays the hydraulic fracture thereby defining a plurality of fracture elements;
• calculating and determining an influence coefficient matrix having spatially related indices,
• wherein the spatially related indices relate influence coefficient matrix elements to corresponding fracture elements;
• wherein the mesh overlays the hydraulic fracture in a plurality of layers of the multilayered reservoir;
• and
• wherein the calculating and determining an influence coefficient matrix having spatially related indices comprises:
• determining spectral coefficients corresponding to each layer of the multilayered reservoir, wherein the spectral coefficients do not include a time dependency;
• performing an exponential approximation to determine exponential expansion coefficients;
• and
• assembling the influence coefficient matrix according to the exponential expansion coefficients.

A method comprising:

• simulating a hydraulic fracture in an Earth formation, the formation including a multilayered reservoir, wherein a mesh overlays the hydraulic fracture thereby defining a plurality of fracture elements;
• calculating and determining an influence coefficient matrix having spatially related indices, wherein the spatially related indices relate influence coefficient matrix elements to corresponding fracture elements using a computing device including a program storage device readable by the computing device tangibly embodying a program of instructions executable by the computing device;
• and
• wherein the mesh overlays the hydraulic fracture in a plurality of layers of the multilayered reservoir;
• and
• wherein the calculating and determining an influence coefficient matrix having spatially related indices comprises:
• determining spectral coefficients corresponding to each layer of the multilayered reservoir, wherein the spectral coefficients do not include a time dependency;
• performing an exponential approximation to determine exponential expansion coefficients;
• and
• assembling the influence coefficient matrix according to the exponential expansion coefficients.