Local direct sampling method for conditioning an existing reservoir model

A method for computer modeling a reservoir using multiple-point statistics from non-stationary training images, comprising:

• a) identifying a path via a computer processing machine to visit all nodes of a simulation field;
• b) setting a template for searching data event in the simulation field and for searching data event replicates in the non-stationary training image;
• c) defining a neighborhood in which the training image is sampled;
• d) formulating a kernel function that gσ(d) that decreases from 1 to 0 when distance d increases from 0 to infinity;
• e) for the current node in the simulation field, identifying the data event covered by the template;
• f) randomly sampling the training image in the neighborhood of corresponding node in the training image until an exact or approximate replicate of the data event is found;
• g) computing d between central node of the replicate and simulation node;
• h) computing the kernel function;
• i) drawing a random number u between 0 and 1;
• j) assigning value of central node of the replicate to the simulation node if gσ(d) is greater than u;
• and
• k) repeating steps f) to j) if gσ(d) is not greater than u.
• l) repeating steps e) to k) until all simulation nodes are visited and simulated.

A method for computer modeling a reservoir using multiple-point statistics from non-stationary training images, comprising:

• a) identifying a path via a computer processing machine to visit all nodes of a simulation field;
• b) setting a template for searching data event in the simulation field and for searching data event replicates in the non-stationary training image;
• c) defining a neighborhood in which the training image is sampled;
• d) formulating a kernel function that gσ(d) that decreases from 1 to 0 when distance d increases from 0 to infinity, wherein gσ(d) is a Gaussian kernel function defined as gσ(d)=exp (−d2/2σ2);
• e) for the current node in the simulation field, identifying the data event covered by the template;
• f) randomly sampling the training image in the neighborhood of corresponding node in the training image until an exact or approximate replicate of the data event is found;
• g) computing d between central node of the replicate and simulation node;
• h) computing the kernel function;
• i) drawing a random number u between 0 and 1;
• j) assigning value of central node of the replicate to the simulation node if gσ(d) is greater than u;
• and
• k) repeating steps f) to j) if gσ(d) is not greater than u.