Joint Inversion of Production and Temperature Data for Identification of Permeability Distribution with Depth in Deep Reservoirs

Characterization of permeblity variation with depth in compartmentalized deep aquifers, geothermal and hydrocarbon reservoirs is important for prediction of flow and transport in complex subsurface environments and directly affects the development of natural and energy resources. In deep formations, temperature gradient can be significant and temperature data can provide valuable information about fluid displacement and conductivity in the vertical extent of the formation. This paper examines the importance of temperature data in resolving permeability distribution with depth by integrating flow and temperature data jointly and individually. We show that incorporation of temperature data in model calibration of deep aquifers can increase the resolution of permeability distribution profile with depth. To illustrate the importance of temperature measurements, we adopt a coupled heat and fluid flow model as a forward model to predict the heat and fluid transport in an a deep reservoir and perform a series of numerical experiments for integration of flow data alone, temperature data alone, and flow and temperature data jointly. For model calibration, we use the Maximum A-Posteriori (MAP) estimation approach and for uncertainty quantification we apply the Randomized Maximum Likelihood (RML). We develop an adjoint model for the coupled fluid and heat flow system of equations to compute the required gradients for model calibration. Investigation of the sensitivity of temperature and production data to the distribution of permeability shows that while fluid flow rate data can primarily resolve the distribution of permeability in the lateral extent of the reservoir, the fluid temperature data, even when measured at the surface, show sensitivity to permeability variability with depth, allowing for a higher resolution profiling of the permeability map. The results elucidate the value of temperature data in enhancing the resolution of the estimated aquifer permeability maps with depth. Introduction Numerical simulation of flow and transport processes in porous media is widely used to predict the fluid flow behavior in complex geologic formations. Accurate predictions hinges on reliable knowledge of rock hydraulic properties such as permeability. Since direct measurement of rock hydraulic properties is often not feasible, these properties are usually estimated from interpolation of scattered static data and low resolution seismic maps. Incorporation of aquifer dynamic response into prior aquifer model is often carried out through inverse modeling. In model calibration, it is common to use well flow rate and head measurements to estimate reservoir properties. However, the limitation in available observations complicates the estimation of reservoir properties, especially when heterogeneity is taken into account. In deep hydrocarbon and geothermal reservoirs, temperature variations with depth can be quite significant (Hutchinson et al. 2007; Arnold et al. 2010). Due to this temperature gradient, the fluids produced from different layers of the reservoir have different temperatures (higher temperatures with depth). Thus, the flowing fluid temperature is expected to carry information about flow-related property distributions with depth. In addition, modern monitoring technologies such as distributed permanent down-hole gauges (down-hole fiber optic temperature sensors) offer relatively inexpensive continuous measurements of pressure and temperature at various depths in the borehole (Fryer et al., 2005; Nath et al., 2006). Fiber optic sensors are used in both oil and gas reservoirs and geothermal reservoirs (Kragas, Williams et al. 2001; IKEDA