薄差储层有效驱替理论与应用

应用油藏工程方法,综合考虑驱替压力梯度和启动压力梯度的影响对薄差储层有效驱替理论进行研究.根据不等产量一源一汇驱替压力梯度公式,分别得到地层压力、注入压力、井底流压以及井距变化时的驱替压力梯度图版,并分析其变化规律;根据岩心水动力实验结果,建立启动压力梯度与渗透率的关系,分析有效驱动不同渗透率的储层所需要的驱替压力梯度临界值.研究表明:驱替压力梯度大于最大启动压力梯度是薄差储层有效驱替的必要条件;小井距是薄差层有效驱动的最优选择;可以通过措施和注采压力系统调整达到驱替压力梯度高于最大启动压力梯度的目的,从而有效驱动薄差储层.研究对薄差储层开采具有重要的指导意义,并在矿场试验中得到了有效论证.     

水湿储层水驱油微观驱替特征的网络模拟研究

应用逾渗理论,基于计算机随机建模方法,建立了水湿储层三维网络模型.模型的孔隙喉道半径采用截断式威布尔分布随机产生,通过与实际岩心相渗曲线的拟合,验证了模型的有效性.计算了形状因子、孔隙度、导流率等参数,为模拟过程提供基础数据.应用建立的网络模型,模拟了饱和油和水驱油两个驱替过程,分析了孔隙特性参数对相对渗透率及驱替效率的影响.结果表明:随着孔喉比的降低、配位数的增加、形状因子的增加(在一定范围内),水相渗透率降低,油相渗透率升高,残余油饱和度降低,驱替效率增大.与其他理想模型相比,模型可以更真实地研究油水两相流动特征.     

一种基于相渗资料与动态数据的裂缝和基质水驱动用程度计算方法

利用水驱油机理研究裂缝性油藏注水开发过程中裂缝系统、基质系统产量贡献与采收率变化规律,对制定油田开发技术政策具有重要意义.根据注采守恒原理和渗吸机理,利用Welge水驱方程,推导了水驱开发过程中裂缝系统、基质系统的产油量、采出程度计算方法.该方法基于相渗资料和动态数据,利用Welge水驱方程通过产出端含水率计算裂缝系统含水饱和度,采用注采守恒原理计算裂缝系统、基质系统的存水量,根据渗吸机理计算裂缝系统、基质系统水驱储量采出程度,最终计算得到水驱开发过程中裂缝系统、基质系统的含水饱和度、含水率、产油量与采出程度变化情况.实例计算表明,该方法能够表征裂缝性油藏水驱开发过程中裂缝系统、基质系统的含水变化特征与水驱开发规律,可为制定该类油田开发技术政策提供依据.     

多孔介质中两相不可压混溶驱替的差分流线扩散法及其误差分析

多孔介质中两相不可压混熔驱替问题可描述为椭圆和抛物耦合的非线性偏微分方程组，对椭圆方程采用混合元方法，而对抛物方程采用差分流线扩散法，本文构造了求解该问题的差分流线扩散-混合元格式，最后，给出所构造格式按L^∞(L^2）模的拟最优误差阶估计。     

三维油水运移聚集数值模拟的交替方向格式和分析

研究油气运移聚集史的数值模拟,其数学模型是三维非线性偏微分方程组的初进值问题．我们从实际出发,考虑了重力、毛管力和浮力的作用,同时考虑到三维问题大规模科学和工程计算的特征,提出对流动方程采用大步长的混合元法,而对三维饱和度方程的计算,采用一类交替方向特征有限元法．将其化为连续解三个一维问题,使工程数值计算成为可能．应用张量积计算．负模估计和先验估计理论,得到最佳阶Ｌ~２误差估计．     

三维油水运移聚庥数值模拟的交替方向格式和分析

研究油气运移聚集史的数值模拟,其数学模型是三维非线性偏微分方程组的初边值问题,我们从实际出发,考虑了重力、毛管力浮力的作用,同时考虑到三维总理２大规模科学和工程计算的特征,提出对流动方程采用大步长的混合元法,而对三维饱和度方程的计算,采用一类交替方向特征有限元法,钭其化主国连续解三个一维问题,使工程数值计算成为可能,应用张量积计算,负模估计和先验估计理论,得到最佳阶Ｌ＾２误差估计。     

考虑接触角滞后性多孔介质内非混相驱替研究

接触角滞后性表现为前进和后退接触角不同,其是润湿表面上两相流动中的重要现象.该文采用改进的伪势格子Boltzmann(LB)两相模型,并与几何润湿边界条件相结合,研究了接触角滞后性、毛细数以及几何结构对多孔介质内不混溶驱替过程的影响.数值结果表明:单渗透性多孔介质内相同毛细数下,保持后退角一定,驱替效率随着前进角的增大而增大;疏水和中性接触角滞后性窗口中,驱替效率随滞后性窗口大小增大而减小.在亲水接触角滞后性窗口中,接触角滞后性大小作用不明显;同等窗口大小下,所有选取的亲水滞后性窗口驱替效率大于中性滞后性窗口,中性滞后性窗口驱替效率大于疏水滞后性窗口.单渗透性多孔介质内相同接触角滞后性条件下,毛细数C_a越大,驱替相在多孔介质内的指进现象越明显,驱替效率越小.另外,双渗透多孔介质中驱替相更易在高渗透性区域流动并率先突破边界,驱替效率较单渗透性显著下降.     

非牛顿流体的二相驱替问题

本文考虑非牛顿流体的二相驱替问题.假设石油是非牛顿流体,满足带有初始压力梯度的直线渗透定律,对于一维问题推导了孔隙介质以及裂缝-孔隙介质中水驱非牛顿石油问题的基本方程,并且求得了数值解.通过和牛顿流情况的比较,揭示了水驱非牛顿石油的基本规律.     

油水两相渗流对称性特征研究与应用

通过岩心相渗资料分析,发现在一定条件下,油水相对渗透率比值随归一化饱和度变化呈现对称性.针对这一现象,结合实际岩心驱替和数字岩心的实验结果,考虑水驱油过程中的优势相和弱势相的转换,构建了新的油水渗流关系,即油、水相对渗透率比与归一化弱势相饱和度的幂指函数关系.设计了不同条件下水驱油实验,探讨了水驱油时对称性特征产生条件,并分析了其对水驱特征曲线的影响.最后利用对应条件下的油藏实际数据,验证了对称性的存在及双对数水驱特征曲线的适应性.表明考虑弱势相转换的幂指关系较好的表征了凹型水驱特征全生命周期的变化,丰富了油水两相渗流基础理论,对水驱特征曲线的研究和应用具有一定借鉴意义.     

随机分数阶微分方程初值问题基于模拟方程法的数值求解

基于模拟方程法,提出了一种求解随机分数阶微分方程初值问题的数值方法.考虑含两个分数阶导数项的微分方程,引入两个线性的、非耦合的随机模拟方程,利用它们解构原方程,借助Laplace变换及逆变换,得到方程解的积分表达式,同时建立起两个模拟方程之间的联系,结合初始状态,得到求解随机微分方程初值问题的数值迭代算法.作为特例,对于含两个分数阶导数项线性常微分方程的初值问题,给出了基于模拟方程法的数值解法的显式结果.该方法是稳定的,它的误差仅存在于积分近似时的截断误差和计算软件的舍入误差.应用实例说明了数值方法在确定和随机情形的有效性和准确性.     

Approximations for the delay probability in the M/G/s queue

This paper develops approximations for the delay probability in an M/G/s queue. For M/G/s queues, it has been well known that the delay probability in the M/M/s queue, i.e., the Erlang delay formula, is usually a good approximation for other service-time distributions. By using an excellent approximation for the mean waiting time in the M/G/s queue, we provide more accurate approximations of the delay probability for small values of s. To test the quality of our approximations, we compare them with the exact value and the Erlang delay formula for some particular cases.     

A note on the optimality of the N- and D-policies for the M/G/1 queue

This note considers the N- and D-policies for the M/G/1 queue. We concentrate on the true relationship between the optimal N- and D-policies when the cost function is based on the expected number of customers in the system.     

Analysis of the queue-length distribution for the discrete-time batch-service Geo/G/1/K queue

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary ‘rate-in = rate-out’ arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end.     

On the Transient Behavior of the M/M/1 and M/M/1/M Queues

This paper gives a transient analysis of the classic M/M/1 and M/M/1/K queues. Our results are asymptotic as time and queue length become simultaneously large for the infinite capacity queue, and as the system’s storage capacity K becomes large for the finite capacity queue. We give asymptotic expansions for p_n(t), which is the probability that the system contains n customers at time t. We treat several cases of initial conditions and different traffic intensities. The results are based on (i) asymptotic expansion of an exact integral representation for p_n(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of p_n(t).     

Dimension of the crown Skn

In 1941, Dushnik and Miller introduced the concept of the dimension of a poset (X, P) as the minimum number of linear extensions of P whose intersection is exactly P. Although Dilworth has given a formula for the dimension of distributive lattices, the general problem of determining the dimension of a poset is quite difficult. An equally difficult problem is to classify those posets which are dimension irreducible, i.e., those posets for which the removal of any point lowers the dimension. In this paper, we construct for each n≥3, k≥0, a poset, called a crown and denoted S^k_n, for which the dimension is given by the formula $\text{2?(n+k)}\text{(k+2)}$. Furthermore, for each t≥3, we show that there are infinitely many crowns which are irreducible and have dimension t. We then demonstrate a method of combining a collection of irreducible crowns to form an irreducible poset whose dimension is the sum of the crowns in the collection. Finally, we construct some infinite crowns possessing combinatorial properties similar to finite crowns.     

On the Queue Length Distribution for the GI/G/1/K/VM Queue

Abstract

We present a transform-free distribution of the steady-state queue length for the GI/G/1/K queueing system with multiple vacations under exhaustive FIFO service discipline. The method we use is a modified supplementary variable technique and the result we obtain is expressed in terms of conditional expectations of the remaining service time, the remaining interarrival time, and the remaining vacation, conditional on the queue length at the embedded points. The case K → ∞ is also considered.     

Proof of the impossibility of the fermat equation Xp + Yp = Zp for special values of p and of the more general equation bXn + cYn = dZn

This paper continues the search to determine for what exponents n Fermat's Last Theorem is true. The main theorem and Corollary 1 consider the set of prime exponents p for which mp + 1 is prime for certain even integers m and prove the truth of FLT in Case 1 for such primes p. The remaining theorems prove the inequality of the more general Fermat equation bXⁿ + cYⁿ = dZⁿ.     

Comparison conjectures about the M/G/s queue

We conjecture that the equilibrium waiting-time distribution in an M/G/s queue increases stochastically when the service-time distribution becomes more variable. We discuss evidence in support of this conjecture and others based partly on light-traffic and heavy-traffic limits. We also establish an insensitivity property for the case of many servers in light traffic.     

On the M/G/1 queue with D-policy

This paper deals with the M/G/1 queue with D-policy, i.e., the server is turned off at the end of a busy period and turned on when the cumulative amount of work firstly exceeds some fixed value D. We first concentrate on the computation of the steady-state probabilities. The first moments and relationships among the busy period, the number of customers served and other performance measures are investigated. Some variants of the main model and the special case of the M/M/1 are also studied.     

On the Relative Waiting Times in the GI/M/s and the GI/M/1 Queueing Systems

The expected steady-state waiting time, Wq(s), in a GI/M/s system with interarrival-time distribution H(·) is compared with the mean waiting time, Wq, in an "equivalent" system comprised of s separate GI/M/1 queues each fed by an interarrival-time distribution G(·) with mean arrival rate equal to 1/s times that of H(·). For H(·) assumed to be Exponential, Gamma or Deterministic three possible relationships between H(·) and G(·) are considered: G(·) can be of the "same type" as H(·); G(·) can be derived from H(·) by assigning new arrivals to the individual channels in a cyclic order; and G(·) may be obtained from H(·) by assigning customers probabilistically to the different queues. The limiting behaviour of the ratio R = Wq/Wq(s) is studied for the extreme values (1 and 0) of the common traffic intensity, ρ. Closed form results, which depend on the forms of H(·) and G(·) and on the relationships between them, are derived. It is shown that Wq is greater than Wq(s) by a factor of at least (s + 1)/2 when ρ approaches one, and that R is at least s(s!) when ρ tends to zero. In the latter case, however, R goes to infinity (!) in most cases treated. The results may be used to evaluate the effect on the waiting times when, for certain (non-queueing) reasons, it is needed to partition a group of s servers into several small groups.