For unconventional reservoirs, it is very difficult to determine the values of key parameters or properties that govern fluid flow in the subsurface due to unknown fracture growth and rock properties. These parameters generally have quite large uncertainty ranges and need to be calibrated by available production data. Using an ensemble of history matched reservoir models to predict the Estimated Ultimate Recovery (EUR) is one of popular approaches when parallelized computing facilities become cheaper and cheaper to customers. The Randomized Maximum Likelihood (RML) method has been proved quite robust for generating multiple realizations by conditioning to production data. However, it is still expensive to apply traditional optimization algorithms to find a conditional realization by minimizing the objective function defined within a Bayesian framework, especially when adjoint-derivatives are unavailable. How to generate multiple conditional realizations efficiently is critically important but still a very challenging task for proper uncertainty quantification.
In this paper, a novel approach that hybrids the direct-pattern-search and the Gauss-Newton algorithm is developed to generate multiple conditional realizations simultaneously. The proposed method is applied to history match a real unconventional Liquid Rich Shale reservoir. The reservoir is stimulated by multiple stage hydraulic fractures. In this example, uncertainty parameters include those characterizing uncertainties of reservoir properties (including matrix permeability, permeability reduction coefficient, porosity, initial water saturation and pressure) and those for hydraulic fractures (height, width, length, and effective permeability of SRV zone). Uncertainty of production forecasts are quantified with both unconditional and conditional realizations.
The case study indicates that the new method is very efficient and robust. Uncertainty ranges of parameters and production forecasts before and after conditioning to production data are quantified and compared. The new approach enhances the EUR assessment confidence level and therefore significantly reduces risks for unconventional assets development.
For unconventional reservoirs, the key reservoir properties, such as effective flowing fracture length (Xf), effective fracture height (Hf), permeability and permeability reduction coefficient, fracture conductivity (FCD), drainage area (A) etc., that govern fluid flow in subsurface are very difficult to obtain due to unknown fracture growth in tight rock. Uncertainties associated with these parameters are usually quite large. Understanding the uncertainty of the subsurface model is helpful to define how to drill wells and determine fracture stages spacing or the number of wells. There are mainly three categories of Estimated Ultimate Recovery (EUR) prediction methodologies for unconventionals: