Numerical Calculation of Flows and Long-Range Transport of Contaminants in Lowland River Reservoirs

Flows and contaminant transport in the Novosibirsk reservoir are calculated on the basis of a two-dimensional (plane) nonstationary model with Saint Venant's equations. The model allows for the presence of a large number of islands. Coefficients of horizontal exchange (dispersion) are calculated by the formula taking into account dynamic velocity at the bottom. Numerical implementation of the model employs a semi-implicit conservative finite-difference TVD scheme on a distributed grid and procedures allowing for the flow past these islands. Model examples of calculations and computation results for dynamics of long-range transport of contaminants along the Novosibirsk reservoir are given.     

Calculation of tracer travel times in fractured geothermal reservoirs

A new method is presented for calculating the time taken for tracer to move between wells in a fractured geothermal reservoir. The reservoir model considered is a two-dimensional confined layer, but many wells and a background regional flow can be included. Also, either a straight or dog-leg, finite length, high permeability fracture can be included. The fracture can alternatively be considered as a barrier to lateral flow. The flow field is represented by complex potentials which are used to accurately calculate the streamline locations and tracer travel times are evaluated by numerical integration along the streamlines. The methods developed are used to model the dispersion of tracer produced by large-scale differences in the flow paths along which the tracer travels from the release well to the observation well(s).Notation C _d concentration, kg m^-3 - C dimensionless concentration - C _obs dimensionless concentration at the observation well - f dimensionless distance between the injection and production wells - h _d fracture half length, m - h dimensionless fracture half length - H reservoir thickness, m - Ln(·) complex algorithm - M mass of tracer released, kg - n porosity, dimensionless - N _b number of streamlines calculated for blob release - N _f number of subdivisions for the high permeability fracture - N _w number of streamlines calculated for injection well release - ¢P _d complex potential, m² s^-1 - P dimensionless complex potential - Q _c characteristic well volume flow rate, m³ s^-1 - q _p production well volume flow rate, m³ s^-1 - R _c characteristic length, m - t _d time, s - t _b dimensionless response start time - t dimensionless time - t _td tracer travel time (without dispersion), s - t _t dimensionless tracer travel time - u average fluid velocity, ms^-1 - v _d background fluid speed, m s^-1 - v dimensionless background fluid speed - x _d Cartesian coordinate, m - x dimensionless Cartesian coordinate - y _d Cartesian coordinate, m - y dimensionless Cartesian coordinate - (·) Dirac delta distribution - _d velocity potential, m² s^-1 - dimensionless velocity potential - angle from the positive x axis to the direction of the background flow - _d stream function, m² s^-1 - dimensionless stream function - complex number - circle mapped to the fracture by the Joukowski transformation - region occupied by the blob - complex number - p production/observation well - r release well     

Analytic Analysis for Oil Recovery During Counter-Current Imbibition in Strongly Water-Wet Systems

We study counter-current imbibition, where a strongly wetting phase (water) displaces non-wetting phase spontaneously under the influence of capillary forces such that the non-wetting phase moves in the opposite direction to the water. We use an approximate analytical approach to derive an expression for saturation profile when the viscosity of the non-wetting phase is non-negligible. This makes the approach applicable to water flooding in hydrocarbon reservoirs, or the displacement of non-aqueous phase liquid (NAPL) by water. We find the recovery of non-wetting phase as a function of time for one-dimensional flow. We compare our predictions with experimental results in the literature. Our formulation reproduces experimental data accurately and is superior to previously proposed empirical models.     

Numerical Simulation of Single-Phase and Multiphase Non-Darcy Flow in Porous and Fractured Reservoirs

A numerical method as well as a theoretical study of non-Darcy fluid flow through porous and fractured reservoirs is described. The non-Darcy behavior is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The non-Darcy flow through a fractured reservoir is handled using a general dual-continuum approach. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in petroleum and geothermal reservoirs.     

Travel-time analysis of tracer tests in two geothermal fields

The most important results from a tracer test are whether or not tracer is detected at each observation well and the travel times to the wells that respond. A method developed by the authors for accurately calculating travel times for tracer movement in general flow fields enables the locations of major fractures in a reservoir to be deduced from the travel-time data. The procedure is applied here to data from Wairakei, New Zealand, and Palinpinon, Philippines.Notation H reservoir thickness, m - porosity, dimensionless - Q _c characteristic well volume flow rate, m³ s^-1 - R _c characteristic length, m - t _d time, s - t dimensionless time - t _td tracer travel time (without dispersion), s - t _t dimensionless tracer travel time - v _d background fluid speed, m s^-1 - v dimensionless background fluid speed - x _d Cartesian coordinate, m - x dimensionless Cartesian coordinate, m - y _d Cartesian coordinate, m - y dimensionless Cartesian coordinate     

Stress-induced fluid flow anisotropy in fractured rock

Anisotropic stress states are common in the upper crust and result in fracture apertures being dependent on fracture orientation. Fractured rocks should therefore display an anisotropic permeability determined by the aperture, length, and orientation of those fractures remaining open. In this paper, a numerical study of this effect is made for a rock containing two orthogonal fracture sets subject to a uniaxial compressive stress applied perpendicular to one of the sets. With increasing compressive stress, the decreasing aperture of fractures orientated perpendicular to the stress axis leads to a decrease in permeability both parallel and perpendicular to the stress. For flow parallel to the stress direction, this is a consequence of the finite length of the fractures, flow in fractures perpendicular to the stress being required to connect fractures orientated parallel to the stress direction. As the number of fractures is decreased towards the percolation threshold, the average permeability tensor is found to become increasingly isotropic. This behaviour results from the highly tortuous nature of the flow paths just at the percolation threshold.     

裂隙岩体中非饱和渗流与运移的概念模型及数值模拟

探讨了裂隙岩体中非饱和地下水渗流与溶质运移的几种概念模型的构造及数值模拟问题 ,如裂隙网络模型、连续体模型、等效连续体模型、双孔隙度 (单渗透率 )模型、双渗透率模型、多组份连续体模型等。在裂隙岩体中 ,非饱和地下水的渗流可能只局限于岩体中的岩石组份、或裂隙网络 ,也可能在裂隙和岩石中同时发生 ;对前一种情形只需考虑单一连续体中的流动 ,而后一种情况则需要包括地下水在岩石和裂隙之间的交换。岩体中的裂隙网络往往是溶质运移的主要通道 ;但当溶质在裂隙与岩石之间的渗透和扩散是重要的运移机制时 ,就需要考虑岩石与裂隙界面处的溶质交换。为了模拟岩石与裂隙之间地下水和溶质的交换 ,就需要了解岩石与裂隙之间相互作用的模式和范围 ,使得这类问题的概念模型较单一连续体模型多了一层不确定性、其数值模拟也变得更为困难。因为在实际问题中不易、甚至根本不能判别非饱和渗流的实际形态 ,具体采用哪种模型主要取决于分析的目的和对现场数据的掌握程度。不论哪种模型都会受到模型及参数不确定性的影响 ,因此必须考虑与其他辅助模型的比较.     

一种超支化疏水缔合聚合物的制备与性能评价

首先制备了疏水单体2-丙烯酰胺基十四烷磺酸,在此基础上又以改性Si O2功能单体为反应核制备了超支化疏水缔合聚合物(HBPAM),结构经红外光谱(FTIR)和核磁共振氢谱(1H NMR)表征证实。HBPAM在低浓度时主要是分子内缔合,表观黏度低,随着浓度的增加,分子内缔合逐渐变为分子间缔合,又因其独特的三维立体网状结构,溶液黏度显著增加。与梳形KYPAM相比,HBPAM在耐温抗盐及抗剪切方面有较高的优势:升温到85℃时黏度保留率为62.2%;100000mg·L-1Na Cl、150000 mg·L-1Na Cl、500 mg·L-1Mg Cl2、1000 mg·L-1Mg Cl2、500 mg·L-1Ca Cl2、1000 mg·L-1Ca Cl2时的黏度保留率分别为233.0%、132.9%、64.4%、26.1%、66.2%、15.7%;3400rpm/min剪切30s后HBPAM的黏度保留率为69.8%,比KYPAM高10.9%。在60℃烘箱中的30d老化实验证明,HBPAM比KYPAM有明显抗老化能力,尤其是在高矿化度条件下优势更明显。     

Pressure transient response of stochastically heterogeneous fractured reservoirs

A stochastic model for flow through inhomogeneous fractured reservoirs of double porosity, based on Barenblattet al.'s continuum approach, is presented. The fractured formation is conceptualized as an interconnected fracture network surrounding porous blocks, and amenable to the continuum approach. The block permeability is negligible in comparison to that of the fractures, and therefore the reservoir permeability is represented by the permeability of the fracture network. The fractured reservoir inhomogeneity is attributed to the fracture network, while the blocks are considered homogeneous. The mathematical model is represented by a coupled system of partial differential random equations, and a general solution for the average and for the correlation moments of the fracture pressure are obtained by the Neumann expansion (or Adomian decomposition). The solution for pressure is represented by an infinite series and an approximate solution for radial flow, is obtained by retaining the first two terms of the series. The purpose of this investigation is to get an insight on the pressure behavior in inhomogeneous fractured reservoirs and not to obtain type curves for determination of reservoir properties, which owing to the nonuniqueness of the solution, is impossible. For the present analysis we assumed an ideal reservoir with cylindrical symmetric inhomogeneity around the well. Fractured rock reservoirs being practically inhomogeneous, it is of interest to compare the pressure behavior of such reservoirs, with Warren and Roots's solution for (ideal) homogeneous reservoirs, used as a routine for determining the fractured reservoir characteristic parameters and, using the results of well tests. The comparison of the results show that inhomogeneous and homogeneous reservoirs exhibit a similar pressure behavior. While the behavior is identical, the same drawdown or a build-up pressure curve may be fitted by different characteristic dimensionless parameters and, when attributed to an inhomogeneous or a homogeneous reservoir. It is concluded that the ambiguity in determining the fractured reservoir and, makes questionable the usefulness of determination of these parameters. Computations were also carried out to determine the correlation between the fracture pressure at the well and the fracture pressure at different points.     

Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media

In this article, the numerical simulations for one-dimensional three-phase flows in fractured porous media are implemented. The simulation results show that oil displacement in matrix is dominated by oil–water capillary pressure only under certain conditions. When conditions are changed to decrease the amount of water entering into the fractured media from the boundary of the flow field, water in fracture may be vaporized to superheated steam. In these cases, the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture, which results in oil flowing from matrix to fracture. Assuming that oil is wetting to steam, the matrix steam–oil capillary pressure will decrease the matrix oil-phase pressure as the matrix steam saturation increases. After the steam–oil capillary pressure finally exceeds the pressure difference due to the appearance of superheated steam in fracture, the oil displacement in matrix will stop. It is also shown that variations of the water relative permeability curve in matrix do not result in different mechanisms for oil displacement in matrix. The simulation results suggest that the amount of liquid water supply from the boundary of flow field fundamentally influence the mechanisms for oil displacement in matrix.