O uso de modelos ocultos de Markov no estudo do fluxo de rios intermitentes

In this work, we present our understanding about the article of Aksoy [1], which uses Markov chains to model the flow of intermittent rivers. Then, we executed an application of his model in order to generate data for intermittent streamflows, based on a data set of Brazilian streams. After that, we build a hidden Markov model as a proposed new approach to the problem of simulation of such flows. We used the Gamma distribution to simulate the increases and decreases in river flows, along with a two-state Markov chain. The motivation for us to use a hidden Markov model comes from the possibility of obtaining the same information that the Aksoy’s model provides, but using a single tool capable of treating the problem as a whole, and not through multiple independent processes

Análise de viabilidade de injeção de fluidos alternativos ao vapor em reservatórios de óleo pesado

Many of hydrocarbon reserves existing in the world are formed by heavy oils (°API between 10 and 20). Moreover, several heavy oil fields are mature and, thus, offer great challenges for oil industry. Among the thermal methods used to recover these resources, steamflooding has been the main economically viable alternative. Latent heat carried by steam heats the reservoir, reducing oil viscosity and facilitating the production. This method has many variations and has been studied both theoretically and experimentally (in pilot projects and in full field applications). In order to increase oil recovery and reduce steam injection costs, the injection of alternative fluid has been used on three main ways: alternately, co-injected with steam and after steam injection interruption. The main objective of these injection systems is to reduce the amount of heat supplied to the reservoir, using cheaper fluids and maintaining the same oil production levels. This works discusses the use of carbon dioxide, nitrogen, methane and water as an alternative fluid to the steam. The analyzed parameters were oil recoveries and net cumulative oil productions. The reservoir simulation model corresponds to an oil reservoir of 100 m x 100 m x 28 m size, on a Cartesian coordinates system (x, y and z directions). It is a semi synthetic model with some reservoir data similar to those found in Brazilian Potiguar Basin. All studied cases were done using the simulator STARS from CMG (Computer Modelling Group, version 2009.10). It was found that waterflood after steam injection interruption achieved the highest net cumulative oil compared to other fluids injection. Moreover, it was observed that steam and alternative fluids, co-injected and alternately, did not present increase on profitability project compared with steamflooding

Incorporação do vínculo de suavidade no ajuste de histórico de reservatórios de petróleo

The history match procedure in an oil reservoir is of paramount importance in order to obtain a characterization of the reservoir parameters (statics and dynamics) that implicates in a predict production more perfected. Throughout this process one can find reservoir model parameters which are able to reproduce the behaviour of a real reservoir.Thus, this reservoir model may be used to predict production and can aid the oil file management. During the history match procedure the reservoir model parameters are modified and for every new set of reservoir model parameters found, a fluid flow simulation is performed so that it is possible to evaluate weather or not this new set of parameters reproduces the observations in the actual reservoir. The reservoir is said to be matched when the discrepancies between the model predictions and the observations of the real reservoir are below a certain tolerance. The determination of the model parameters via history matching requires the minimisation of an objective function (difference between the observed and simulated productions according to a chosen norm) in a parameter space populated by many local minima. In other words, more than one set of reservoir model parameters fits the observation. With respect to the non-uniqueness of the solution, the inverse problem associated to history match is ill-posed. In order to reduce this ambiguity, it is necessary to incorporate a priori information and constraints in the model reservoir parameters to be determined. In this dissertation, the regularization of the inverse problem associated to the history match was performed via the introduction of a smoothness constraint in the following parameter: permeability and porosity. This constraint has geological bias of asserting that these two properties smoothly vary in space. In this sense, it is necessary to find the right relative weight of this constrain in the objective function that stabilizes the inversion and yet, introduces minimum bias. A sequential search method called COMPLEX was used to find the reservoir model parameters that best reproduce the observations of a semi-synthetic model. This method does not require the usage of derivatives when searching for the minimum of the objective function. Here, it is shown that the judicious introduction of the smoothness constraint in the objective function formulation reduces the associated ambiguity and introduces minimum bias in the estimates of permeability and porosity of the semi-synthetic reservoir model

Análise de viabilidade de injeção de fluidos alternativos ao vapor em reservatórios de óleo pesado

Many of hydrocarbon reserves existing in the world are formed by heavy oils (°API between 10 and 20). Moreover, several heavy oil fields are mature and, thus, offer great challenges for oil industry. Among the thermal methods used to recover these resources, steamflooding has been the main economically viable alternative. Latent heat carried by steam heats the reservoir, reducing oil viscosity and facilitating the production. This method has many variations and has been studied both theoretically and experimentally (in pilot projects and in full field applications). In order to increase oil recovery and reduce steam injection costs, the injection of alternative fluid has been used on three main ways: alternately, co-injected with steam and after steam injection interruption. The main objective of these injection systems is to reduce the amount of heat supplied to the reservoir, using cheaper fluids and maintaining the same oil production levels. This works discusses the use of carbon dioxide, nitrogen, methane and water as an alternative fluid to the steam. The analyzed parameters were oil recoveries and net cumulative oil productions. The reservoir simulation model corresponds to an oil reservoir of 100 m x 100 m x 28 m size, on a Cartesian coordinates system (x, y and z directions). It is a semi synthetic model with some reservoir data similar to those found in Brazilian Potiguar Basin. All studied cases were done using the simulator STARS from CMG (Computer Modelling Group, version 2009.10). It was found that waterflood after steam injection interruption achieved the highest net cumulative oil compared to other fluids injection. Moreover, it was observed that steam and alternative fluids, co-injected and alternately, did not present increase on profitability project compared with steamflooding

Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process