IMPROVED CONVOLUTION ANALYSIS OF LATE WELLBORE STORAGE BUILDUP DATA OF GAS WELLS

Conventional pressure buildup tests of gas wells with wellbore storage have long been recognized as providing somewhat inaccurate estimates of the reservoir parameters. Also, the application of these tests to low permeability reservoirs is time consuming and impractical in some field practice. Moreover, these tests do not offer a straight forward method to determine of the rate-dependent skin factor of high-flow-rate wells.

This paper presents an extension of the convolution methods to analyze late wellbore storage buildup data of high-flow-rate gas wells. In addition of possessing all the advantages of the convolution techniques, the proposed extension offers a simple method that permits a direct estimation of the formation permeability, the mechanical and the rate-dependent skin factors, and the extrapolated reservoir pressure from three different analysis plots.     

关井早期采点密度与油藏模型识别

在关井压力恢复的早期阶段,一般地面所设置的压力计采点密度,难以适时的“捕捉”到井下由流动转入关井瞬间状态的早期压力恢复数据点。以实例验证关井早期压力恢复数据采样点加密前后,关井早期至油藏各个阶段的油藏模型拟合对比效果,关井早期采点密度对一般均质、非均质和裂缝性油藏模型的影响,以及识别具有裂缝性油藏特征试井资料的诊断分析。     

IMPROVED CONVOLUTION ANALYSIS OF LATE WELLBORE STORAGE BUILDUP DATA OF GAS WELLS

ABSTRACT

Conventional pressure buildup tests of gas wells with wellbore storage have long been recognized as providing somewhat inaccurate estimates of the reservoir parameters. Also, the application of these tests to low permeability reservoirs is time consuming and impractical in some field practice. Moreover, these tests do not offer a straight forward method to determine of the rate-dependent skin factor of high-flow-rate wells.

This paper presents an extension of the convolution methods to analyze late wellbore storage buildup data of high-flow-rate gas wells. In addition of possessing all the advantages of the convolution techniques, the proposed extension offers a simple method that permits a direct estimation of the formation permeability, the mechanical and the rate-dependent skin factors, and the extrapolated reservoir pressure from three different analysis plots.     

When does a longer shut-in lead to a larger radius of investigation?

While the concept of radius of investigation is better understood for drawdown tests, its applicability to buildup tests is less certain. For example, a rule of thumb is that “one cannot see a particular feature in a buildup unless the radius of investigation during the preceding flow period has seen that feature”. In this paper, we clearly illustrate that the radius of investigation of a buildup can be larger than that of its previous flow period.Another common contention is that the radius of investigation of a buildup is limited by noise dominating the late-time pressure behavior. Oliver [Oliver, D.S., 1990. The averaging process in permeability estimation from well-test data. SPEFE. pp. 319–324.] and later Thompson and Reynolds [Thompson, L.G. and Reynolds, A.C, 1997. Well testing for radially heterogeneous reservoirs under single and multiphase flow conditions. SPEFE. pp. 57–64.] defined the radius of investigation based on the distance from the well to the region of the reservoir which has the greatest impact on the pressure derivative. We have used this approach to calculate the derivative and show that the ratio of noise to the signal from the reservoir does not necessarily increase. While many situations exist when radius of investigation of a build-up test is limited by the preceding flow period and noise, we show that when data is sampled appropriately, the radius of investigation of a buildup can easily go beyond that of the preceding flow period, and demonstrate when this may remain unaffected by noise.     

低渗透应力敏感性油藏产能及影响因素

基于低渗透非达 西和变形介质拟稳态渗流理论及油相和水相相对流动能力方程,建立了低渗透应力敏感性油藏具有最大产量点的三相流流入动态曲线方程,据此可计算出油井或油藏的最低允许流动压力。在此基础上,结合大庆葡西油田生产数据,对影响油藏产能的油层启动压力梯度、变形系数、供给半径、平均地层压力和含水率进行了研究,结果表明,启动压力梯度、变形系数等因素对低渗透油藏产能和最低允许流压均有较显著的影响。该方法能有效评价和预测低渗透应力敏感性油藏的产能变化,也为油井合理工作制度的确定,充分发挥油井产能提供了依据。     

基于三参数非线性渗流的致密气藏数值试井分析

目前在低渗透储层的试井模型中,常采用具有平均启动压力梯度的拟线性渗流方程,然而拟线性渗流方程只能反映低渗透流动的启动压力梯度特征,不能描述流动的非线性特征。三参数非线性渗流方程既反映了启动压力梯度特征,也描述了非线性凹形曲线。为了提高致密气藏试井资料的解释精度,完善低渗透非线性试井理论,建立了一种基于三参数非线性渗流方程的致密气藏数值试井模型。利用有限差分方法求解模型,获得了井底压力响应曲线及储层压力分布。分析了压力响应曲线和压力分布特征,对比了三参数非线性模型与拟线性模型的结果,并研究了最小启动压力梯度和平均启动压力梯度的影响。研究结果表明：系统径向流阶段的压力导数曲线偏离0.5线,压降曲线的上翘幅度取决于平均启动压力梯度,压力恢复曲线的上翘幅度取决于平均启动压力梯度与最小启动压力梯度的差值。外边界响应的早晚和动边界扩展速度取决于最小启动压力梯度。     

用不稳定流动的压力和流量解释致密低渗气藏的地层参数

针对致密低渗气藏关井压力恢复很难达到径向流的特点,利用致密低渗气藏开井过程中气体的不稳定流动方程,推导出不稳定流动系数at与时间t的线性函数关系,结合修正等时测试不稳定流动段的井底流压数据,用最小二乘法分别计算出at和b,再利用直线段的斜率计算地层系数Kh和惯性系数D,利用同一直线段的截距计算气井开井的表皮系数S。通过大牛地气田几口井的实际测试数据进行解释表明,该方法可以用于现场解释。     

Analysis of pressure and pressure derivative without type-curve matching, 6. Horizontal well tests in anisotropic media

A new technique for interpreting pressure tests known as direct synthesis is proposed. This method couples the characteristic points and lines from a log-log plot of pressure and pressure derivative data with the exact analytical solution, consequently eliminating the need for multiple specialized plots or type curve matching.This paper concentrates on the interpretation of pressure tests in homogeneous and anisotropic porous media. The reservoir can be infinite or semi-infinite in areal extent and is bounded at the top and bottom boundaries. The pressure drop within the horizontal well is assumed to be negligible, i.e. infinite conductivity well condition.Step-by-step procedures to calculate reservoir parameters are presented for various pressure responses. Included are possible procedures to determine the effective horizontal wellbore length when sufficient characteristic points or lines are observed. This new technique is accurate because it uses the exact, analytical solutions to calculate reservoir parameters. Results are frequently verifiable from an independent source, e.g., another characteristic point or line. Application to pressure buildup and drawdown tests is illustrated by several examples which demonstrate the accuracy of the technique.     

低渗透油层测试资料解释方法

应用定产量压力导数方法、Peres卷积和反卷积方法对流动段压力资料进行解释,结果表明,在流动时间足够长的情况下,这3种方法能够求得可靠的地层参数。但Peres卷积和反卷积方法只适用于中期径向流动段,对受井筒储存和边界影响的早期和晚期资料无法分析;定产量压力导数方法的导数曲线通常未达到0.5水平线,多解性较严重。而恢复段的测试时间一般比流动段长,导数曲线比流动段完整,能够反映各种模型的流动特征。故提出一种新方法,即用拟稳定时间和拟稳定产量来等效开井流动过程,然后依据这两个参数采用典型曲线拟合和非线性回归分析方法对恢复段进行分析。应用新方法对10口井的恢复段压力资料进行了解释,并和直线分析方法（压力恢复方法一、二、三）以及平均产量方法进行了对比,结果表明,应用新方法能够求得准确可靠的参数,并能对各种边界情况做出判别。     

An Experimental Study of the Effect of the Water Injection Process on Rock Structure and Permeability Reduction

Abstract

The estimation and assessment of formation damage on reservoir core samples is an important measurement. Laboratory tests were set up to investigate the effects of injection pressure, flow rate, and induced fracture on the rock sample with respect to formation damage. In this research, selected rock samples from one of Iranian giant oil fields were used as the laboratory physical model. Permeability reduction was observed for unfractured samples: however, it was more interesting that no injection pressure buildup was detected in fractured samples. It appears that fractures in sandstones, especially with weak cementation, can play the role of an agent for particle movement and cause damage far from injection wells over a long period of time.     

溶解气驱油藏水平井IPR的数值模拟

目前,根据数值模拟计算,研究溶解气驱油藏水平井向井流动态关系时,都是沿用Vogel研究方法即制作一定采出程度下水平井IPR曲线,然后无因次化得到无因次IPR曲线。经研究发现溶解气驱油藏动态受生产过程的影响较大,即用不同的流压生产,当达到相同的采出程度时,油藏平均压力并不相等。故前人用数模制作无因次IPR曲线的方法存在较大的局限性,对此提出了用数模研究溶解气驱油藏水平井无因次IPR曲线时,应先制作油藏平均压力为定值时的IPR曲线, 然后再无因次化的新方法。按此方法对一系列溶解气驱油藏模型进行了三维流动模拟计算,总结出了无因次IPR曲线的曲度随油藏平均压力变化的规律,提出了描述溶解气驱油藏水平井无因次IPR曲线的新的统一方程。     

缝洞型碳酸盐岩储集层中气体流动新研究

建立了缝洞型碳酸盐岩油气藏多缝多洞复杂连通型储集层中气体流动的数学模型,得出了开井时压力降落阶段与关井后压力恢复阶段各溶洞内压力和各裂缝内气体流量的变化规律,并以六溶洞五裂缝复杂连通的储集层为例,进行了实例计算。发现压力下降阶段时,距离井筒越近的溶洞,压力下降越快;压力下降初期的气体产量主要由靠近生产井的溶洞供给,随着时间的增加远离生产井的溶洞才逐渐开始大量供给气体;压力恢复阶段中,由于缝洞的复杂连通性,各裂缝中流量变化比较复杂,部分裂缝中的流量在后期出现倒流现象。最后,研究了溶洞大小、裂缝长度和裂缝宽度对溶洞内压力与裂缝内气体流量变化的影响。     

确定裂缝性火山岩储集层孔隙容积的油藏工程实用方法

提出了应用试油阶段压力恢复试井和产量、流压矿场测试资料,采用Pollard-Pirson 方法和影响函数法,确定裂缝性火山岩油藏单井泄流范围内的裂缝、基质孔隙容积。提出的方法有效弥补了非均质性十分严重的裂缝性火山岩油藏现有确定裂缝、基质孔隙容积方法所存在的理论和技术上的局限性,对于进一步研究裂缝性火山岩油藏地质、油藏工程和产能特性有较好的理论和实际应用意义。     

A novel MLP-ANN approach to predict solution gas-oil ratio

Abstract

The better understanding and estimation of reservoir fluids properties have straight effects on accuracy of different processes such as simulation, well testing, and material balance calculations, so importance of accurate estimation of PVT properties such as solution gas-oil ratio is obvious. To this end, in the present paper, multilayer perceptron artificial neural network (MLP-ANN) is used as a novel predictive tool to estimate solution gas-oil ratio in terms of temperature, bubble point pressure, oil American Petroleum Institute gravity API, and gas specific gravity. Therefore, a total number of 1,137 experimental solution gas-oil ratios has been gathered from reliable databank for evaluation of model outputs. The different graphical and statistical analyses such as determination of average absolute relative deviation (AARD), the coefficient of determination (R²) and root mean square error (RMSE) were used to evaluate the performance of MLP-ANN algorithm. The comparisons show that MLP-ANN algorithm has great accuracy in prediction of solution gas-oil ratio, so it can be used as a simple tool to predict phase behavior of reservoir fluids.     

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提出了分形油藏中有限导流垂直裂缝井的非牛顿流的数学模型，用影响椭圆和平均值的方法求其近似解，分析计算了改变分维参数、幂律指数、弹性储量比、窜流系数、无量纲导流参数时的压力变化规律，其流态可分为４个阶段：开始时的裂缝内线性流；早期的双线性流；中期的质量交换压力平缓过渡阶段；晚期的平均双重介质径向流阶段。另外，得到了单重分形油藏中非牛顿幂律流的点源函数和有限导流垂直裂缝井的等流量解。     

试井车进行压力恢复测试的缺点探讨

长庆油田长期采用试井车下压力计的方法进行油井压力恢复测试。实际应用表明，该方法成功率低，存在很多缺点。如井筒续流效应严重，没有产量稳定性的监测记录，压力恢复曲线早期段数据丢失，关井时间长等。建议针对长庆油田储层实际，采用地层测试与抽汲联作技术，以取得可供解释的压力恢复资料。     

产水气井压力恢复特征的新认识

产水气井的压力恢复特征不同于纯气井。根据径向复合储层模型 ,将产水气井压力恢复曲线的上翘特征解释为气、水流度的变化 ,内区为气体流动 ,外区为水流动 ,代替了传统的边界效应解释 ,结合矿场实例 ,说明其适用性     

Application of TDS technique to developed reservoirs

Well test interpretation methods for a single well in infinite reservoirs may not be suitable for those wells when their pressure is affected by other wells operating in the same reservoir. This effect becomes more significant as both the flow rate and the test duration increase. It is observed in drawdown tests when the well experiences an additional pressure decline due to production from other wells and, also, when the well produces under pseudosteady state before shut-in it for a buildup test. When pressure data are interpreted as recorded, estimation of reservoir parameters may not be accurate. Slider1–3 introduced a technique for analyzing a pressure test that takes into account the effect of nearby active wells. Corrected or extrapolated pressures are obtained by applying the superposition principle to include the pressure decline contribution from the neighboring wells. Traditional semilog plots are then constructed and permeability and skin factor can be estimated, respectively, from the slope and intercept of their linear trend.A new technique, called TDS (Tiab's Direct Synthesis), was designed to analyze pressure and pressure derivative data without using type-curve matching. It uses characteristic features found on the derivative plot, so reservoir parameters are directly estimated. It depends upon how well the pressure derivative is calculated. If derivative is taken to the recorded pressure data the resulting curve will not be properly defined and the estimated parameters may be erroneous. Application of the TDS technique to wells in depleted reservoirs is presented here. The recorded pressure is extrapolated to include the contribution from other wells as suggested by Slider. Once the pressure derivative of the extrapolated data is taken, the TDS technique as discussed by Tiab [Tiab, D. 1993. Analysis of Pressure and Pressure Derivative without Type-Curve Matching: 1- Factor de daño and Wellbore Storage. J. Pet. Sci. Eng. 12 (1995), 171–181.] can be readily applied. It was successfully tested with synthetic and field examples. A comparative analysis was carried out to see the effects when derivative is taken to uncorrected pressure data and the estimation of permeability, skin factor and drainage area.     

气藏平均地层压力跟踪计算新方法

平均地层压力是产能评价和动态分析的基础，准确、快速获取平均地层压力对高效开发气藏意义重大。基于地层压力随时间变化的规律，分析了平均地层压力的变化规律。研究结果表明：平均地层压力等效点仅随时间发生改变，平均地层压力的下降速率等于或者近似等于井底流压的下降速率。从封闭弹性驱动气藏的物质平衡方程出发，考虑偏差系数和井底流压随平均地层压力的变化，推导建立了平均地层压力跟踪计算新方法，根据生产数据可迭代计算平均地层压力。方法验证结果显示，采气速度和采出程度共同影响模型的计算结果。应用实例表明，跟踪计算法与压力恢复试井和物质平衡法之间的相对误差均较小，满足工程计算精度要求，且跟踪计算法不需依托生产测试数据，节约了测试费用，避免了测试占产。