  Production forecast based on historical data provides essential value for
developing hydrocarbon resources. Classic history matching workflow is often
computationally intense and geometry-dependent. Analytical data-driven models
like decline curve analysis (DCA) and capacitance resistance models (CRM)
provide a grid-free solution with a relatively simple model capable of
integrating some degree of physics constraints. However, the analytical
solution may ignore subsurface geometries and is appropriate only for specific
flow regimes and otherwise may violate physics conditions resulting in degraded
model prediction accuracy. Machine learning-based predictive model for time
series provides non-parametric, assumption-free solutions for production
forecasting, but are prone to model overfit due to training data sparsity;
therefore may be accurate over short prediction time intervals.
  We propose a grid-free, physics-informed graph neural network (PI-GNN) for
production forecasting. A customized graph convolution layer aggregates
neighborhood information from historical data and has the flexibility to
integrate domain expertise into the data-driven model. The proposed method
relaxes the dependence on close-form solutions like CRM and honors the given
physics-based constraints. Our proposed method is robust, with improved
performance and model interpretability relative to the conventional CRM and GNN
baseline without physics constraints.
