DYNAMIC DATA INTEGRATION FOR TRANSPORT USING STATISTICAL MOMENT EQUATIONS A REPORT SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE By Pipat Likanapaisal

Only limited information is usually available about the properties (e.g., permeability) of oil reservoirs, which are usually heterogeneous with high variability levels and complex spatial correlation structures. Incomplete knowledge about these heterogeneous natural systems leads to uncertainty in the reservoir description model (i.e., permeability distribution). The uncertainty in the reservoir description (input), leads to uncertainty in predictions of flow performance (output). Available information (e.g., measurements of permeability, pressure, saturation, and production rate) can be used to reduce the level of uncertainty in both the input and output parameters. We describe an inversion algorithm for integrating saturation measurements directly into the Statistical Moments Equations (SME) of immiscible twophase flow in heterogeneous porous media. The approach employs a geostatistical (Kriging) scheme and makes use of an existing SME simulator of the forward problem for two-phase flow and transport. We demonstrate the iterative sequential algorithm using simple examples for the quarter of a five-spot geometry. The behavior of the first two conditional moments of log-permeability and predicted saturation due to the presence of saturation measurement is analyzed.