Zheng Shen

Determining Coefficient of Quadratic Term in Forchheimer Equation

Forchheimer equation takes non-Darcy flow effect into account in the event of high flow velocity in porous media. Its application requires both permeability, which is in linear term, and Beta factor, which is in quadratic term. Permeability and Beta factor are determined by rock type, textural of rock, effective porosity, pore throat size, geometry of the pore, and connection and distribution of pores. Beta factor comes into play when the fluid flow rate is high and the flow rate deviates from Darcy’s law. Non-Darcy flow is described by Forchheimer equation. Usually the coefficient of non-Darcy flow term is hard to be determined. Existing approaches are core measurement and empirical correlations. To the best of our knowledge there is no theoretical equation available. To get an accurate estimation of flow rate or pressure drop in the reservoir, we need a method that has solid theoretical basis. The deficiency triggered our study. Starting from multiple-capillary tubes concept, we derived a rigorous relationship between pores geometry and pressure drop required for fluid flow through the pores. Through this correlation pressure drop can be calculated from known pores geometry. Since pores geometry can be often obtained from lab experiment or well logging, the new correlation also provides a unique approach to quantify the coefficient of quadratic term in Forchheimer equation. In this study we developed a governing equation through a rigorous theoretical derivation. With this equation the non-Darcy flow coefficient in Forchheimer equation can be calculated. The required input data for the new equation are readily obtained from well log interpretation. The new equation is a powerful tool in the event of no experimental measured non-Darcy flow coefficient available. It eliminates the errors or the arbitrary content in the empirical correlations.

A rigorous method to calculate the rising speed of gas kick

The rising speed of gas kick is an important parameter in well control operation. The position of the gas kick dictates the pressure at the casing shoe, which is usually the weakest point in the openhole section, and the wellhead pressure, which is one of the key factors affecting the blowout preventer and choke folder. In this research, we derived a rigorous model to estimate the rising speed of gas kick. Starting from the force analysis and mass conservation, we developed equations to calculate the forces exerting on the gas kick. With the mass of the gas kick, the rising speed of the gas kick is calculated. The effect of wellbore temperature profile on the rising of the gas kick is taken into account in the derivation. Before the development of this model, the estimation of gas kick position is commonly based on experience. In many cases, the experience alone is not good enough for well control. The proposed model provides a new approach with solid theoretical base to characterize the rising of gas kick in the hole. It makes the procedure of the well control simple and makes drilling engineers feel more comfortable to control the well. The new model can be combined with engineers experience to predict the downhole situation, shut-in casing pressure, and mud rate as a functions of position of gas kick. Any deviation from the forecast indicates accidents or downhole problems. Therefore, the proposed model is a valuable tool to diagnose the problems in well control.

The Mechanism of Wellbore Weakening in Worn Casing-Cement-Formation System

Maintaining casing integrity, in terms of downhole zonal isolations and well stability, is extremely important in oil/gas wells. Casing wear occurs not only in directional drilling, but also in vertical drilling with a slight deviation angle. In most hydrocarbon wells, deteriorated casing was reported from the onset of casing wear by the presence of friction force during the rotation of drillpipe. The friction force against the casing wall causes the reduction of casing strength. Furthermore, the rotation of drillpipe combined with corrosive drilling fluids could dramatically degrade the casing strength. We used a finite element analysis to focus on the stress evolution in worn casings. Comparison study between worn casing and perfect casing was conducted. Our study showed that the thermal load significantly increases the stress concentration of the worn casing in the wellbore. Finite element solutions indicated that the radial stress of the worn casing is not affected as much as the hoop stress. Along with the increased burst pressure or the elevated temperature, the unworn portion of the casing also suffers from severe compression stress. This work is important to broadening the understanding of well engineers through addressing the true stress profile of worn casing in cemented wellbore.