Inverse modeling
  1. Using the Markov Chain Monte Carlo method (MC2)
  2. Saturated flow with measurements of hydraulic conductivity (Lu, Z., D. Higdon, and D. Zhang, 2004)
  3. Unsaturated media, i.e, estimating van Genuchten parameters using measurements of pressure head, moisture content, and solute concentration (manuscript in preparation)

    4.
  4. Data assimilation based on KL decomposition(Zhang, D., Lu, Z. , and Y. Chen, SPE Journal, 2007)

    The traditional Kalman filter reuires computing and storing the covariance matrix of state variables, which is computationally expensive for large-scale problems with millions of gridblocks. In this study, we propose an efficient, dimension-reduced Kalman filtering scheme based on Karhunen-Loeve and other orthogonal polynomial decompositions of the state vector. We consider flow in heterogeneous reservoirs with spatially variable permeability. The reservoir responses such as pressure head are measured at some locations at various time intervals. The aim is to dynamically characterize the reservoir properties and to predict the reservoir performance and its uncertainty at future times. In our scheme, the covariance of the reservoir properties is approximated by a small set of eigenvalues and eigenfunctions using the Karhunen-Loeve (KL) decomposition, and reconstruction of this covariance from the KL decomposition can be done whenever needed. In each update, the forward problem is solved using the KL-based moment method, giving a set of functions from which the mean and covariance of the state vector can be constructed, when needed.

  5. Parameter Identification using the Level Set Method(Lu, Z., and B. Robinson, movie1, movie2, Geophy. Res. Letts, 2006).

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