We proposed a modified Green element method based on edge-based element concept. Unknowns and matrix dimension are reduced. Then, a local grid refinement method is proposed based on the improved Green element, which ensures precision in early flow regimes for fractured horizontal wells with complex fractured networks. Solution of a degradation model solved with the method is compared with solutions obtained with a semianalytical model and numerical simulation. It verifies accuracy and efficiency of the improved Green element method based on local grid refinement. Finally, effects of model parameters on transient behavior is analyzed. It shows that the Green element method is a high precision dynamic simulation method, which improves computational efficiency of dynamic simulation of fractured horizontal well by setting node on edge of grid. In addition, local grid refinement method applied to the modified Green element method is based on superposition principle, in which interpolation approximation is not needed. The method is of high accuracy. Under same grid systems, local grid refinement based on improved Green element method is better than using finite difference. On the other hand, conductivity of complex fracture, permeability and size of stimulated reservoir volume have great influence on transient behavior of fractured horizontal wells. These effects should be taken into consideration and interpreted in transient behavior analysis.

With analyses of field production data and numerical simulations,solvent-enhanced steam flooding (SESF) production process is divided into three stages. By integrating mass conservation equation, energy conservation equation, motion equation and diffusion equation, a mathematical model was obtained to describe steam front development.The expression is a typical Volterra integral function of the second kind and could be transformed by Laplace transformation.It is solved by discretizing time and space into small intervals. With comparison of calculated results and those of STARS, relative error of less than 4% for whole process is found. The model provides an accurate and quick method for analyzing effects of solvent properties and injection strategies on SESF production process.

Dissipative particle dynamics (DPD) is modified by introducing attractive force. Attractive interaction of liquid and solid and micro-scale flow in nano throats is simulated to discuss mechanism of boundary layer. It is found that thermal motion affects velocity significantly in molecular scale while pressure gradient is leading function as greater than molecular scale. However, thermal motion cannot change integral moving direction. As throat radius becomes larger, parabola shape of velocity distribution becomes more and more obvious. Boundary layer thickness is affected by pressure gradient, throat radius and fluid viscosity. As pressure gradient increases and fluid viscosity decreases, boundary layer thickness decreases. As throat radius decreases, boundary layer thickness increases first and then decreases. Boundary layer is essential reason of nonlinear flow behavior and thickness of boundary layer increasing makes nonlinear flow behavior more obvious.

For reservoirs with high rock brittleness coefficient and uniform development of natural fractures, three basic modes are developed to characterize fracture network created by volume fracturing in horizontal wells. Flow from reservoir to wellbore is divided to two parts:reservoir flow and network flow. Principle of potential superposition is used to derive reservoir flow equation. Finitedifference method is adopted to establish flow equation within finite conductivity network. Star-Delta transformation is used to tackle interplay of flow between hydraulic and natural fractures. A comprehensive flow model is presented by coupling matrix equations of two flows. It indicates that as stimulated horizontal length is kept constant, effect of quantity of fracture stages and perforation clusters in each stage on production is more significant than that of half-length and flow conductivity of hydraulic fracture, which is, in turn, more dominant than that of density and flow conductivity of natural fractures. Finally, a field example shows that little difference exists between measured and calculated results.

With Green function and Laplace transformation, one-dimensional element is established considering effect of permeability tensor of anisotropic reservoir. Inflow of fracture is obtained by linear interpolation of endpoints and flow in fracture is treated with linear integral of flow rate. Coupling flow in formation and fractures, calculating method for bottom-hole pressure is formed semi-analytically. It shows that there are three flow regimes including fracturing linear flow, formation linear flow and system radial flow. The more the fractures, the less the dimensionless pressure and number of factures has significant impact on flow rate. With increase of fractures increasing rate is dropping in the same time. Fracture length and conductivity have similar characteristics. Flow rate is improving as angle between fracture and wellbore is increasing. Flow rate reaches maximum as fracture is perpendicular to wellbore, and vice versa. Angle between maximum permeability and fracture has similar impact on production. In summary, production rate reach maximum as fracture is perpendicular to wellbore and direction of maximum permeability.

A model to calculate stress sensitivity is established based on theory of accumulation of geology, geomechanics and theory of flow through porous media. Compared with experimental results, the model is accurate and reliable. Distribution range of tight oil reservoir in Daqing Field is narrower than that of Changqing Field. It results in that stress sensitivity of Daqing Field is severer than that of Chaingqing Field. And productivity of Daqing Field is lower than that of Changqing Field. We make a quantitative description on mechanism of stress sensitivity in tight oil reservoirs.

Based on two annular pressure buildup mechanisms, coupling of wellbore heat transfer and formation heat transfer and coupling of gas temperature and gas pressure, we build a calculation model for critical rate in deep high temperature high pressure( HT/HP) gas wells. It takes account of influence of gas well profile, string assembly and fluid properties. The model is solved with programm based on iterative method. Finally, it is applied to a deep HT/HP gas well in Tarim oilfield. Critical rate under several operational modes are calculated and they provide basis for optimum allocation in deep HT/HP gas wells.

Based on analyses of SAGD field production data and numerical simulations,SAGD production process in thin heavy oil reservoirs was divided into periods: steam chamber horizontal expansion period and steam chamber downwards migration period. A model was built,which includes mass conservation equation,energy conservation equation and heat loss equation. A comprehensive mathematical expression was obtained to describe steam chamber development process. The expression is a typical Volterra integral function of the second kind,which could be solved by Laplace transformation. Comparisons were made between the model and CMG Stars'. A small relative error,less than 5% for the whole SAGD production process,was found. The model provides an accurate and quick method for determination of limited reservoir properties and proper production parameters for SAGD production.

We focus on anisotropic reservoir with natural fractures,and simulate distribution of natural fracture with Monte Carlo. It characterizes natural fracture parameters from the perspective of statistics. Coupled natural and artificial fractures are considered as independent sources. A formula of steady production is derived according to potential superposition principle. It shows that Monte Carlo simulations of natural fractures reflect trends of productivity from a statistical point of view. It analyzes quickly steady productivity of fractured directional well.

Considering artificial fracture,inclined wellbore and formation coupling flow,flow to directional well is divided into three parts： Flow from reservoir to fracture,flow in fracutre and variable mass flow in production pipe. Principles of potential superposition and mirror reflection as well as the concept of infinitesimal line congruence are used to model flow from reservoir to fracture and potential distribution in reservoir. By discreting fracuture to 2D grid,boundary theory is used to couple flow dynamics in fracture with variable mass flow in inclined pipe. A comprehensive coupling model for finite-conductivity fractured directional well is shown.Iteration method is used to solve the model. A practical case shows that for vertical fracutre result of coupling model agrees with that of Prats method. Fracture conductivity and inclined angle have great effects on productivity and pressure.

Traditional equation of steam quality is improved based on definition. Rate of wellbore heat loss is calculated with both depth step and time step. Drift-flux model of two-phase flow by Hasan is used to estimate pressure drop in wellbore. It indicates that results of modified model and new algorithm agree well with field date. They are more accurate than Beggs-Brill method. In addition, steam pressure, temperature and quality are almost unchanged at the same depth. However, rate of wellbore heat loss decreases with injection time. The algorithm provides a reference for accurate calculation of wellbore heat loss.

A mathematical model for transient flow of non-Newtonian heavy oil with dynamic radius and variable viscosity is established.The non-Newtonian transient pressure distribution of heavy oil is obtained with time and space.It shows that under same production,dynamic radius is closer to the well as threshold pressure gradient increases.The greater the threshold pressure gradient, the greater the pressure drop neflr the well.We combine dynamic radius and viscosity to avoid shortcomings of existing non-Newtonian heavy oil flow model.

Based on flow characteristics of horizontal wells in naturally fractured reservoirs,vadose area is divided into two zones: near wellbore zone and far wellbore zone.The far wellbore zone is featured by its continuous homogeneity.In near wellbore zone,a coupling model is established considering fluid flow in fracture and horizaontal well simultaneously.Principles of potential superposition and mirror reflection as well as the concept of infinitesimal line congruence are used in the model.Combining flow characteristics of the far and near wellbore zones,a comprehensive computational method for fractured hoizontal well productivity is presented.A practical case is used to verify this method.Computational result shows that productivity of horizontal well calculated with this method is closer to actual flow rate than theoretical formula.Productivity of horizontal well increases as fracture density rises,but increment of productivity decreases as fracture density increases.

An unsteady model of fractured horizontal wellbore coupling with a box-shaped reservoir is constructed with consideration of anisotropy in a low permeability reservoir. Solution of the model is shown. Pressure drops of friction and acceleration are considered under different types of constraints. Flow condition in fractured horizontal well is divided into early transient period and pseudo-steady period. In transient period, the output from each fracture differs little, and total production rate increases linearly with fracture number. In pseudo-steady phase, production rate of fractures at the toe and heel is higher than that in the middle. Fractures in symmetrical position have different yield due to frictional and accelerational pressure drops. Pressure loss along the wellbore results in decrease of production in horizontal well and non-uniform distribution of pressure in wellbore. Under constant flow rate followed by constant bottom-hole pressure constraints, production plateau stays longer with increase of fracture number.