New models for heater wells in subsurface simulations, with application to the in situ upgrading of oil shale

Downhole electrical heating can be used to achieve the high temperatures required for in situ upgrading of oil shale or oil sands. Heater-well models are needed if this process is to be simulated accurately. The traditional Peaceman approach used for fluid injection and production wells may not be applicable because it does not capture transient effects, which can be important in downhole heater models. Standard models also neglect the effects of heterogeneity and temperature dependence in the rock properties. Here, we develop two new models for representing heater wells in reservoir simulators. The first model is applicable for homogeneous systems with properties that are not temperature dependent. For such cases, we develop a semi-analytical procedure based on Green's functions to construct time-dependent heater-well indexes and heater-block thermal transmissibilities. For the general case, which can include both fine-scale heterogeneity and nonlinearity due to the temperature dependence of rock properties, we present a numerical procedure for constructing the heater-well model. This technique is essentially a near-well upscaling method and requires a local fine-scale solution in the near-well region. The boundary conditions are determined using a local-global treatment. The accuracy of the new heater-well models is demonstrated through comparison to reference solutions for example problems. The approach is then applied for the coarse-scale modeling of the in situ upgrading of oil shale, which entails a thermal-compositional simulation with chemical reactions. The model is shown to provide an accurate and efficient solution for this challenging problem.