Optimization of integrated geological-engineering design of volume fracturing with fan-shaped well pattern

According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method(FEM) based fluid-solid coupling, an integrated geological-engineering method of volume fracturing for fan-shaped well pattern is proposed considering the geomechanical modeling, induced stress calculation, hydraulic fracturing simulation, and post-frac productivity evaluation. Besides, we propose the differential fracturing design for the conventional productivity-area and the potential production area for fan-shaped horizontal wells. After the fracturing of the conventional production area for H1 fan-shaped well platform, the research shows that the maximum reduction of the horizontal principal stress difference in the potential productivity-area is 0.2 MPa, which cannot cause the stress reversal, but this reduction is still conducive to the lateral propagation of hydraulic fractures. According to the optimized fracturing design, in zone-Ⅰ of the potential production area, only Well 2 is fractured, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage;in zone-Ⅱ, Well 2 is fractured before Well 3, with a cluster spacing of 30 m and an injection rate of 12 m^(3)/min per stage. The swept area of the pore pressure drop in the potential production area is small, showing that the reservoir is not well developed. The hydraulic fracturing in the toe area can be improved by, for example, properly densifying the fractures and adjusting the fracture distribution, in order to enhance the swept volume and increase the reservoir utilization.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Wigner function and density operator of the photon-subtracted squeezed thermal state

By using the technique of integration within an ordered product of operators, the normal ordered density operator of the photon-subtracted squeezed thermal state （PSSTS） is derived. Then the corresponding Wigner function is presented by using the coherent state representation of the Wigner operator. The nonclassical properties of the PSSTS are discussed based on the negativity of the Wigner function.

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We derive some new generating function formulae of the two-variable Hermite polynomials, such as ∞∑n=0tm/m!Hn,2m（x）,∞∑n=0sntm/n!m!H2n,2m（x,y）,and ∞∑n=0sntm/n!m!H2n＋l,2m＋k（x,y）.We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Wigner functions and tomograms of the even and odd binomial states

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

胜利油田低渗透油藏压驱工程方案优化及矿场应用

为解决低渗透油藏压驱过程中存在的油井见效方向明显、压力下降快、含水上升快等开发难题,基于低渗透油藏压驱地质特征,抽提压驱开发工程问题,建立耦合渗流-应力-损伤(H-M-D)的低渗储层压驱数学模型,开展“压-闷-采”一体化压驱数值模拟,建立压驱工程参数优化图版。结果表明:以3 a累计经济净现值为目标,优化单层压驱注入量为3.0×10^(4)~3.5×10^(4)m^(3),压驱注入速度为1000~1200 m^(3)/d,闷井时间为20~30 d,驱油剂体积分数为0.15%~0.20%;优化后的低渗透油藏目标方案区BN1区块压驱缝网长度、宽度及高度较未优化的相邻BN0区块分别提高19.4%、27.3%、11.3%;与未优化的相邻BN2区块相比,BN1区块井口油压相当,日产液量降低42.4%,日产油量增加163.6%,含水率降低62.3%。研究成果能有效指导低渗透油藏压驱工程方案优化与现场实施。

塔里木盆地顺北油气田少井高产地质工程一体化做法与关键技术

塔里木盆地顺北油气田埋藏深度为7300~9000m,脆性地层破碎形成的缝洞型储层沿高陡走滑断裂带发育,断裂破碎带内部非均质性极强,且流体性质差异大。面对这类超深复杂的断控缝洞型油气藏,高效成井面临世界级挑战,单井费用高,效益开发难度大,没有现成的经验、技术可借鉴。顺北油气田以项目管理为抓手,建立了独有的“五有五提升”地质工程一体化管理模式,创新形成了“少井高产”七要素关键技术。近几年,少井高产地质工程一体化实现了质的飞跃,落实了4号、8号断裂带2个亿吨级资源阵地,新增石油探明储量为1.53×10^(8)t、天然气探明储量为1620×10^(8)m^(3),4号断裂带共部署井位20口,两年建成了130×10^(4)t油当量产能阵地。与2016年开发动用的1号断裂带相比,高产井成功率提升了35%、单井产能提升了316%、单井发现探明储量提升了55%,实现了高效勘探,效益开发,其经验对其他同类型油藏开发具有较好的借鉴意义。

考虑气水两相流动的页岩气井压裂-生产一体化数值模拟

基于位移不连续法和离散裂缝统一管网模型,采用顺序迭代数值模拟方法,构建了考虑气水两相流动的页岩气井压裂-生产一体化数值模型。模型考虑了天然裂缝、基质物性对压裂过程的影响,且直接将压裂后地层压力及含水饱和度分布用于后续焖井、生产模拟,可以更准确地实现压裂-生产一体化模拟。模拟结果表明:储层物性参数对裂缝扩展有较大影响,合理预测压裂结束后地层压力及储层流体分布是准确预测页岩气井产气量、产液量的关键;相较于常规方法,提出的模型同时考虑压裂对基质压力及含水饱和度的影响,可以更准确地模拟产水量、产气量。将建立的模型应用于实际页岩气压裂水平井的压裂-生产一体化模拟,模拟结果与实际生产数据吻合程度较好,验证了模型的准确性。

裂缝-孔隙型枯竭气藏储气库一体化注采运行评价

为诊断评价裂缝-孔隙型枯竭气藏储气库注采运行状况及单井注采能力,针对中原油田储气库,建立考虑应力敏感的裂缝-孔隙型储层-井筒-地面一体化模型,以一体化模拟为手段,以地层压力、注采气量界限为约束,分析储气库注采能力影响因素,诊断储气库注采运行制约瓶颈,评价储气库系统注采能力。研究表明:井口和井底压力、油管尺寸等对储气库注采气量影响较大;储气库气藏压力低于27 MPa,所受应力超过50 MPa,采气指数明显下降,应力敏感性更强;低压时可能存在临界携液情况,但无冲蚀影响;压力下合理注气量为71×10^(4)m^(3)/d,合理采气量43×10^(4)m^(3)/d。此研究可为裂缝-孔隙型储气库注采运行评价提供参考。

鄂尔多斯盆地神府区块深部煤层气体积压裂实践与认识

鄂尔多斯盆地东缘神府深煤层大气田探明地质储量超千亿方,实现该地区深部煤层气高效开发对保障国家能源供应具有重要意义。但是,由于深煤层地质环境复杂,具有高地应力、中高温度、特低渗透、强非均质性、割理/裂隙发育等特点,导致现有中浅煤层压裂改造技术难以完全适用于深煤层,其施工规模与参数仍处于探索阶段。为了探究与深煤层地质条件相适应的增产改造技术,以鄂尔多斯盆地神府区块为地质背景,以深煤层大规模体积压裂为工程实践,围绕“极限动用+均衡扩展+有效支撑”的设计理念,提出“少段多簇适度密切割+等孔径深穿透限流射孔+复合液造缝(高黏液体破岩+低黏液体造复杂缝)+大排量高强度加砂+前置酸液降低破裂压力+多粒径组合支撑剂”为核心的体积压裂技术,并引入地质−工程−智能一体化压后评估方法,通过压裂−产能双重智能拟合校正,精细刻画了储层改造体积(SRV)和气体泄流体积(DRV),预测了不同压裂规模及井型条件下的最终可采储量EUR。最后,通过统计神府区块深煤层压裂井地质、工程和产量特征数据,采用随机森林算法量化分析了影响深部煤层气产能的主控因素。实践结果表明:采用上述大规模体积压裂技术,已投产的直/定向井最高日产气量超过1×10^(4) m^(3),水平井最高日产气量超过2×10^(4 )m^(3),说明深煤层可压性良好、开发潜力巨大;深部煤层气峰值产气量的主要影响因素为:煤层含气量、煤层厚度和加砂强度;累积产气量的主要影响因素为:煤层含气量、加砂强度和总砂量。

海上深层潜山长裸眼地层测试技术

为安全高效评价渤海油田深层潜山油气藏,从长裸眼段测试工艺、管柱、安全控制、压井技术等方面开展了细化研究。通过对比不同工艺优选出了“坐套测裸”+“生产测井”潜山测试工艺;引入RD试压阀与RD旁通替液阀,优化试压替液一体化测试管柱,在传统测试管柱的基础上增加了试压、替液的功能;选用PDF-HSD无固相测试液体系,引进含砂实时监测装置,通过控制压差有效地控制地层出砂;引进有毒有害气体实时监测技术并在流程中加装实时除硫装置,达到安全监控及除硫的目的;长裸眼段测试压井技术有效保障了施工后的井控安全。经渤海油田3口井应用,有效保障了作业安全,均达到工业油气流,成功获取地层测试资料,顺利评价所在区域油气藏。该技术为类似深层潜山长裸眼储量解放提供了借鉴思路。

New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems

By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.

Four-mode continuous-variables entangled state:generation from beam splitter,a parametric down-conversion and a polarizer

We introduce a new kind of four-mode continuous variable entangled state in Fock space. The completeness relation and the partly nonorthonormal property of such a state are proven. The scheme to generate this state is presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. After making a single-mode quadrature amplitude measurement, the remaining three modes are kept in entanglement. And its applications are also discussed.

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation （EFFT） and derive the transformation kernel. The EFFT＇s additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Evolution of quantum states via Weyl expansion in dissipative channel

Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation,we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator.It is shown that they can be related by a transformation matrix corresponding to the unitary evolution.In addition,for any density operator going through a dissipative channel,the evolution formula of the Wigner function is also derived.As applications,we considered further the two-mode squeezed vacuum as inputs,and obtained the resulted Wigner function and density operator within normal ordering form.Our method is clear and concise,and can be easily extended to deal with other problems involved in quantum metrology,steering,and quantum information with continuous variable.

ANTI-PLANE CRACK MOVING ALONG THE INTERFACE OF DISSIMILAR PIEZOELECTRIC MATERIALS

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result far the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.

Some applications of a new coherent-entangled state in two-mode Fock space

Using the technique of integration within an ordered product of operators, we find a new kind of coherent-entangled state （CES）, which exhibits both coherent and entangled state properties. The set of CESs makes up a complete and partly nonorthogonal representation. Using a beam splitter, we propose a simple experimental scheme to produce the CES. Finally~ we present some applications of CESs in quantum optics.

The s-parameterized Weyl-Wigner correspondence in the entangled form and its applications

Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.