Carbon Dioxide (CO2) storage and sequestration in unconventional shale resources has been attracting interest since last couple of years due to the very unique characteristics of such formations have made them a feasible option for this object. Shale formations are found all around the world and the conventional assets are easily accessible, and also the huge move of operators toward developing unconventional reservoirs during past years leaves many of such formations ready for sequestering CO2. Today, the use of long horizontal wells that are drilled on a pad has the lowest amount of environmental footprint in which for storage and sequestration purpose also provides much more underground pore spaces available for CO2. In this paper we study the state of the art of the technology of CO2 storage and sequestration and provide different and fresh look for its complex phenomena from a mathematical modeling point of view. Moreover, we hope this study provides valuable insights into the use of depleted shale gas reservoirs for carbon sequestration, which as a result, a cleaner atmosphere will be achieved for the life of our next generations. Also, we present that the depleted shale gas reservoirs are very adequate for this purpose as they already have much of the infrastructure required to perform CO2 injection available in sites.

Modeling and simulation of unconventional reservoirs are much more complicated than the conventional reservoir modeling, because of their complex flow characteristics. Mechanisms, which control the flow in the reservoir, are still under the investigation of researchers. However, it is important to investigate applications of mechanisms which are present to our knowledge. This paper presents the theory and applications of flow mechanisms in unconventional reservoir modeling. It is a well-known fact that most of the reservoir flow problems are non-linear due to pressure dependency of particular parameters. It is also widely accepted that fully numerical solutions are costly both computational and time wise. Therefore, the presented model in this paper follows semi-analytical solution methods. Gas adsorption in unconventional reservoirs is the major pressure dependent mechanism; in addition existence of natural fractures is also taken considerable attention. This paper aims to investigate combined effect of existence of natural fractures gas adsorption, and gas slippage effect while keeping the computational effort in acceptable range. Unlike the existing literature (Langmuir is widely used), BET multi-layer isotherm employed in this paper for gas adsorption modeling. A modified dual porosity modeling is used for natural fracture and gas slippage effect modeling. For model verification purposes a history matched is performed with real field data from Marcellus shale. The proposed model in this paper shows a good agreement with the field data. It is observed that BET isotherm models early time production performance more accurately than Langmuir isotherm. It is also concluded that gas adsorption significantly improves the production performances of unconventional reservoirs, with natural fractures. In addition, gas slippage has a slight effect in long term production.

Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydrocracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.

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