Mathematical Model and Simulation of a Pneumatic Apparatus for In-Drilling Alignment of an Inertial Navigation Unit during Horizontal Well Drilling

Conventional methods in horizontal drilling processes incorporate magnetic surveying techniques for determining the position and orientation of the bottom-hole assembly (BHA). Such means result in an increased weight of the drilling assembly, higher cost due to the use of non-magnetic collars necessary for the shielding of the magnetometers, and significant errors in the position of the drilling bit. A fiber-optic gyroscope (FOG) based inertial navigation system (INS) has been proposed as an alternative to magnetometer -based downhole surveying. The utilizing of a tactical-grade FOG based surveying system in the harsh downhole environment has been shown to be theoretically feasible, yielding a significant BHA position error reduction (less than 100m over a 2-h experiment). To limit the growing errors of the INS, an in-drilling alignment (IDA) method for the INS has been proposed. This article aims at describing a simple, pneumatics-based design of the IDA apparatus and its implementation downhole. A mathematical model of the setup is developed and tested with Bloodshed Dev-C++. The simulations demonstrate a simple, low cost and feasible IDA apparatus.

利用遗传算法进行水平井水平段长度优化设计

在油藏开发过程中，随着水平井水平段长度的增加，水平井段与油藏的接触面也随之增加，同时井筒内流体的流动阻力也增加，从而导致水平井的产液量减少，即水平井的最终产量是2个相互制约的因素共同作用的结果。利用遗传算法全局寻优的特点，结合一种计算无限导流和有限导流情况下水平井产量的井筒／油藏耦合模型，提出了一种用于水平井水平段长度的优化设计方法。该方法可以在不同的油藏地质模型中使用。

西峰油田特低渗透油藏渗流机理及开发对策研究

Micro-pore-throat, micro-fracture and low permeability are the most obvious characters of Xifeng ultra-low permeability reservoir, and threshold pressure gradient and medium deformation during the period of oilfield developing results non-linear seepage feature of the formation liquid flowing in the porous medium underground. It is impossible to solve some problems in the ultra-low permeability reservoir development by current Darcy filtration theory and development techniques. In the view of the characters of ultra-low permeability and powerful-diagenesis and fracture up-growth, the paper quantitatively characterizes of through-going scope for reservoir parameters together with some materials such as similarity field outcrop, rock core, drilling, well logging and production dynamic, which provides geological base for further development adjustment. Based on the displacement experiment of different kinds of seepage fluid and oil-water two phases, this paper proves the relationship between threshold pressure gradient and formation permeability in experiment and theory, which is power function and its index is about -1. The variation rule and the mechanism of oil-water two phases threshold pressure gradient are studied. At the same time, based on the experiment of medium deformation, the variation rule of formation physical property parameters and the deformation mechanism are researched, and the influential factors on the medium deformation are analyzed systematically. With elastic unsteady filtration theory, nonlinear mathematical models of the steady and unsteady flow of single phase as well as horizontal well flow and oil-water two phases flow are deduced with the influence of nonlinear factors including threshold pressure gradient and media deformation. The influences of nonlinear factors upon well deliverability and reservoir pressure distribution as well as the saturation variation pattern of oil-water front are analyzed. By means of the researches such as reasonable well pattern, reasonable well array ration, artificial fracture length optimization advisable water flood timing and feasibility of advanced water flooding, it is necessary to find out effective techniques in order to improve development result of this kind of reservoir. This research result develops and improves on low-velocity nonlinear seepage theory, and offers ways to study similar kind of reservoir; it is meaningful to the development of the ultra-low permeability oil and gas reservoir.

孤岛油田曲流河微相单砂体储层建筑结构及挖潜方向研究

In the intermediary and later stage of oil field development, remaining oil disperses fiercely, the contradiction in the layer has become the main problem and the distribution of remaining oil is transforming to the difference of single sand-body. So, the fine description research of reservoir is becoming a tendency and the methods of remaining oil research need new developments. In the research of “The Single-sand-body Architectural Element and Potentiality Analysis Research of Meandering River, GuDao Oil Field”, the research principle is analytical hierarchy process and schema prescription what are reservoir fine description methods under the condition of dense well pattern. The knowledge of regional sedimentary system and sedimentary facies is the foundation of this research. According to the 3D distribution model of the microfacies sand-body of fluvial facies, stratigraphic unit classification & coenocorrelation of 154 wells are completed in the research of meandering river sand-body in Ng3-4. In this research, the 3D distribution of microfacies sand-body in the main layers are settled. The architectural element model of Ng4 point bar is analysed using the drill core and FMI data. According to the overgrow model of point bar, the surfaces of lateral accretion is traced and the architectural element model of point bar is settled. In the research, the control of micro-facies sand-body of meandering river to the distribution of remaining oil is analysed and the potential area is proposed. All these will play an important role in the development of GuDao oil field. In this research, abundant of logging data, drill core data and production performance data are used to analyse the contributing factor of single sand-body in the Ng3-4 meandering river. Using the technology of geological modeling, all that are researched including the 3D distribution scales of meandering river point bar, the control affection of inner lateral accretion layer to the distribution of oil & gas and remaining. Then, the way of remaining oil development in the sand-body of meandering river is improved. The innovation of the research technology includes (1) the presentation of the conception and research methods of micro-facies sand-body (2) enriching the content of reservoir architectural element research and (3) to renew the research method of remaining oil analysis. The research has practiced with obvious effect.(1)It is deepened into understand the river facies reservoir construction of Gudao oil field, By Building the reservoir construction and studying the effect of diffent deposit or geological interface to fluid partition and to the distribution of the remaining oil, we improved the understanding to the distribution of the remaining oil；(2)By building the distribution mod of the remaining oil in the reservoir construction and making the remaining oil description detailed,the development direction of old oil field is more clear；(3)Expanded the application scales of the horizontal well and enhanced the application effects of the horizontal well technique , we designed and drilled 23 ports horizontal wells in all , the cumulative hydrocarbon production is 10.6*104 t；(4) According to the findings of the internal building structure in reservoir of the fluvial facies in the region of interest, and uniting the injection/production corresponding states、the producing history and the dynamic monitoring documents of the oil/water wells in the flooding units , we researched the residual oil distribution in the point bar , and found the distribution regular patterns of the remaining oil, and comprehended the distribution of the remaining oil . In base of that , we proceeded the optimizing designs of the oil well potentialities , and advanced the effect of the treatment potentials . It is proved that , it was very important that internal building structure research of the single sand body of reservoir for guiding the high efficiency potentialities of the remaining oil in the high water cut stage .

孤岛油田中二北区Ng3～6储层建筑结构与油水分布规律研究

The reservoir of Zhongerbei region in Gudao Oilfield is a typical fluvial facies deposit, its serious heterogeneity of the reservoir caused the distribution of remaining oil in mature reservoirs is characterized by highly scattered in the whole field, and result to declination of production, tap potential and stabilize production is more difficult. Reservoir modeling based on lay scale can not fulfill requirement. How to further studied reservoir heterogeneity within the unit and establish the finer reservoir modeling is a valid approach to oil developing. The architectural structure elements analysis is the effectively method to study reservoir heterogeneity. Utilize this method, divide the reservoirs of Gudao Oilfield into ten hierarchies. The priority studying is sixth, seven hierarchies, ie single sand layers sand bodies By the identification of sixth, seven hierarchies, subdivide the reservoir to the single genetic unit. And to subdivide by many correlation means, such as isometry and phase transition, accomplish closure and correlation of 453 wells.Connectting fluvial deposit pattern, deposition characteristic with its log, build the inverting relation between “sedimentary facies” and “electrofacies” The process emphasize genetic communication and collocation structure of genetic body in space. By detailed architecture analyses sandbodies’ structure, this paper recognize seven structure elements, such as major channel, abandoned channel, natural levee, valley flat, crevasse splay, crevasse channel and floodplain fine grain.Combination identification of architectural structure elements with facieology and study of deposition characteristic, can further knowing genesis and development of abandoned channel. It boost the accuracy to separation in blanket channel bodies distribution, and provide reference to retrieving single channel boundary. Finally, establish fine plane and section construction. On basis architectural structure map, barrier beds and interbeds isopach map and mini-structure map, considering single thin layers to be construction unit, the main layer planimetric maps have drawn and the inner oil-water boundary have revealed. All account that architectural structure elements control remaining oil distribution in layer, and develop the study on architectural structure elements to direct horizontal well is succesful.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

Análise da trajetória de poços horizontais em reservatório de óleo pesado

The application of thermal methods, to increase the recovery of heavy oil in mature fields through drainage with multilateral and horizontal wells, has been thoroughly studied, theorically, experimentally, testing new tools and methods. The continuous injection of steam, through a steam injector well and a horizontal producer well in order to improve horizontal sweep of the fluid reservoir, it is an efficient method. Starting from an heterogeneous model, geologically characterized, modeling geostatistics, set history and identification of the best path of permeability, with seismic 3D, has been dubbed a studying model. It was studied horizontal wells in various directions in relation to the steam and the channel of higher permeability, in eight different depths. Into in the same area were studied, the sensitivity of the trajectories of horizontal wells, according to the depth of navigation. With the purpose of obtaining the highest output of oil to a particular flow, quality, temperature and time for the injection of steam. The wells studied showed a significant improvement in the cumulative oil recovery in one of the paths by promoting an alternative to application in mature fields or under development fields with heavy oil

Estudo comparativo da injeção de água usando poços verticais e horizontais

Oil recovery using waterflooding has been until now the worldwide most applied method, specially for light oil recovery, its success is mainly because of the low costs involved and the facilities of the injection process. The Toe- To-Heel Waterflooding TTHWTM method uses a well pattern of vertical injector wells completed at the bottom of the reservoir and horizontal producer wells completed at the top of it. The main producing mechanism is gravitational segregation in short distance. This method has been studied since the early 90´s and it had been applied in Canada with positive results for light heavy oils, nevertheless it hasn´t been used in Brazil yet. In order to verify the applicability of the process in Brazil, a simulation study for light oil was performed using Brazilian northwest reservoirs characteristics. The simulations were fulfilled using the STARS module of the Computer Modelling Group Software, used to perform improved oil recovery studies. The results obtained in this research showed that the TTHWTM well pattern presented a light improvement in terms of recovery factor when compared to the conventional 5- Spot pattern, however, it showed lower results in the economic evaluation

Estudo de simulação de reservatórios para o desenvolvimento de um campo do nordeste brasileiro

In the last 16 years emerged in Brazil a segment of independent producers with focus on onshore basins and shallow waters. Among the challenges of these companies is the development of fields with projects with a low net present value (NPV). The objective of this work was to study the technical-economical best option to develop an oil field in the Brazilian Northeast using reservoir simulation. Real geology, reservoir and production data was used to build the geological and simulation model. Due to not having PVT analysis, distillation method test data known as the true boiling points (TBP) were used to create a fluids model generating the PVT data. After execution of the history match, four development scenarios were simulated: the extrapolation of production without new investments, the conversion of a producing well for immiscible gas injection, the drilling of a vertical well and the drilling of a horizontal well. As a result, from the financial point of view, the gas injection is the alternative with lower added value, but it may be viable if there are environmental or regulatory restrictions to flaring or venting the produced gas into the atmosphere from this field or neighboring accumulations. The recovery factor achieved with the drilling of vertical and horizontal wells is similar, but the horizontal well is a project of production acceleration; therefore, the present incremental cumulative production with a minimum rate of company's attractiveness is higher. Depending on the crude oil Brent price and the drilling cost, this option can be technically and financially viable.

Análise da trajetória de poços horizontais em reservatório de óleo pesado

The application of thermal methods, to increase the recovery of heavy oil in mature fields through drainage with multilateral and horizontal wells, has been thoroughly studied, theorically, experimentally, testing new tools and methods. The continuous injection of steam, through a steam injector well and a horizontal producer well in order to improve horizontal sweep of the fluid reservoir, it is an efficient method. Starting from an heterogeneous model, geologically characterized, modeling geostatistics, set history and identification of the best path of permeability, with seismic 3D, has been dubbed a studying model. It was studied horizontal wells in various directions in relation to the steam and the channel of higher permeability, in eight different depths. Into in the same area were studied, the sensitivity of the trajectories of horizontal wells, according to the depth of navigation. With the purpose of obtaining the highest output of oil to a particular flow, quality, temperature and time for the injection of steam. The wells studied showed a significant improvement in the cumulative oil recovery in one of the paths by promoting an alternative to application in mature fields or under development fields with heavy oil

Estudo comparativo da injeção de água usando poços verticais e horizontais

Oil recovery using waterflooding has been until now the worldwide most applied method, specially for light oil recovery, its success is mainly because of the low costs involved and the facilities of the injection process. The Toe- To-Heel Waterflooding TTHWTM method uses a well pattern of vertical injector wells completed at the bottom of the reservoir and horizontal producer wells completed at the top of it. The main producing mechanism is gravitational segregation in short distance. This method has been studied since the early 90´s and it had been applied in Canada with positive results for light heavy oils, nevertheless it hasn´t been used in Brazil yet. In order to verify the applicability of the process in Brazil, a simulation study for light oil was performed using Brazilian northwest reservoirs characteristics. The simulations were fulfilled using the STARS module of the Computer Modelling Group Software, used to perform improved oil recovery studies. The results obtained in this research showed that the TTHWTM well pattern presented a light improvement in terms of recovery factor when compared to the conventional 5- Spot pattern, however, it showed lower results in the economic evaluation

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

Pupil shape as viewed along the horizontal visual field

Purpose: Changes in pupil size and shape are relevant for peripheral imagery by affecting aberrations and how much light enters and/or exits the eye. The purpose of this study is to model the pattern of pupil shape across the complete horizontal visual field and to show how the pattern is influenced by refractive error. Methods: Right eyes of thirty participants were dilated with 1% cyclopentolate and images were captured using a modified COAS-HD aberrometer alignment camera along the horizontal visual field to ±90°. A two lens relay system enabled fixation at targets mounted on the wall 3m from the eye. Participants placed their heads on a rotatable chin rest and eye rotations were kept to less than 30°. Best-fit elliptical dimensions of pupils were determined. Ratios of minimum to maximum axis diameters were plotted against visual field angle. Results: Participants’ data were well fitted by cosine functions, with maxima at (–)1° to (–)9° in the temporal visual field and widths 9% to 15% greater than predicted by the cosine of the field angle . Mean functions were 0.99cos[( + 5.3)/1.121], R2 0.99 for the whole group and 0.99cos[( + 6.2)/1.126], R2 0.99 for the 13 emmetropes. The function peak became less temporal, and the width became smaller, with increase in myopia. Conclusion: Off-axis pupil shape changes are well described by a cosine function which is both decentered by a few degrees and flatter by about 12% than the cosine of the viewing angle, with minor influences of refraction.