No abstract

No abstract

No abstract

No abstract

No abstract

Many empirical and analytical models were developed to forecast oil production. Empirical models (including data-driven models) can, for example, find correlations between oil cut and production, but they lack explicit knowledge of the physical behavior. Classic analytical models are loyal to reservoir physics. Nevertheless, they often require estimation of water saturation as a function of time, which is difficult to obtain for multiwell reservoirs. It is desirable to combine advantages of both empirical and analytical models and develop a physical-model-based method that uses field data to infer oil rate.In this paper, we propose to infer fractional-flow models from field data by use of the Koval (1963) theory. We inversely solved the Koval fractional-flow equation to obtain a relationship between water cut and dimensionless time. By history matching field water-cut data, two model parameters, the Koval factor and the producer-drainage volume, are estimated. Nevertheless, it is challenging to use the Koval approach as a predictive model directly because the injection contribution into each producer in a future-time horizon must be evaluated first.To address this issue, we combine the Koval approach with the capacitance/resistance model (CRM), which characterizes the injector/producer connectivities and response time. The material balance of fluids is established in a producer-based drainage volume to consider the contributions from nearby injectors and the time lag in production caused by reservoir/fluids compressibility. A regression approach is simultaneously advanced to minimize the model error. Because of robustly integrating the reservoir physical behavior and the data-driven approach, the combination of the Koval theory and the CRM can result in a synergy that leads to accurate oil-rate predictions.We validated this integrated method in synthetic homogeneous and heterogeneous reservoirs to test its reliability, and further applied it to a field case in western Venezuela. Case studies demonstrate that one can use this integrated model as a real-time tool to characterize interwell connection and to predict future oil production accurately.

Summary Gas adsorption, stress dependence, non-Darcy flow, and surface diffusion of the adsorbed layer are significant mechanisms in shale-gas reservoirs. However, the volume occupied by the adsorbed layer is generally overlooked by current industry standards and numerical models. In addition, stress dependence of matrix pores does not draw as much attention as hydraulic fractures, and surface diffusion has not been included in commercial simulators. Moreover, all these effects significantly affect each other, which can lead to additional complexity of gas transport and production. Therefore, development of an integrative model with consideration of these complicated mechanisms is needed. In this paper, we develop such a fully coupled model for shale-gas-reservoir simulations. We present the derivation of models reflecting the time-dependence effects of gas adsorption/desorption upon original gas in place (OGIP) and petrophysical properties. In particular, both the Langmuir and Brunauer, Emmett, and Teller (BET) (Brunauer et al. 1938) isotherms are included by use of a unified formula. Surface diffusion of adsorbed layer is also added to this model on the basis of rigorous derivation. More features, such as non-Darcy flow and stress dependence in matrix, natural fractures, hydraulic fractures, and leakage effect between matrix and natural fractures, are incorporated. After that, we present an implicit numerical algorithm to solve the model. Numerical simulations were performed in both 1D and 3D cases and compared with two sets of experimental data and three sets of production data in Marcellus and Barnett shale-gas fields. The simulations indicated that the new simulator cannot only lead to consistent results with these data, but also gives an accurate estimation of OGIP, which traditional models failed to do. It is noted that the model parameters we used for the simulations were close to the values suggested by the literature, if available. By use of this validated simulator, we demonstrated applications with respect to real shale reservoirs, studied the effects of the model parameters upon the gas transport and production, and achieved a variety of new insights.

The capacitance resistance model (CRM) has become a popular complement to real time reservoir analysis and improved oil recovery in water and CO2 floods. However, the current CRM model is based on a material balance of the total fluid and only the pressure propagation equation is considered. Saturation changes are also important, especially when the water cut is small. To overcome this limitation, this paper proposes a coupled CRM model based on two-phase flow by incorporating an oil material balance and fractional flow theories. In the coupled CRM model, we construct material balances on both total fluid and oil. Pressure and saturation equations are updated at each time step to account for changes of total mobility. By semi-analytically coupling the pressure and saturation in a producer-based control volume and using constrained multivariate nonlinear regression, the new coupled model can quantify the inter-well connection as well as the oil saturation. As a result, the coupled CRM model can be applied to the whole time frame of water and gas floods, not limited to late time (large water cut) cases as was the current CRM model. This new CRM model is validated in heterogeneous synthetic fields using a conventional reservoir simulator. Case studies show that the saturation profile from the coupled CRM model matches very well with the simulation results. The connectivities obtained from the coupled CRM model correspond well with the field geology and the time constant for each producer is also changing reasonably with the total mobility. Validation of both total production and oil production rates showed that relative errors are very small. With estimated parameters from a waterflood, the model found an optimal injection strategy to maximize the field total oil production. By incorporating the saturation variations to model two-phase flow, the coupled CRM model successfully overcomes the limitation of the previous version. It is able to extend the CRM model from mature water floods to immature water floods, which makes the CRM model more adaptable to different field cases. The coupled CRM model also improves the quality of the prediction of the oil rate significantly, especially for immature water floods. This work can lead to a more informed workflow of optimizing injection scheme, and serve the goal of improving ultimate oil recovery.