原文：
Quantitative Analysis of Mud Losses in Naturally Fractured Reservoirs: The Effect of Rheology
R. Majidi, SPE, S.Z. Miska, SPE, M. Yu, SPE, and L.G. Thompson, SPE, The University of Tulsa
Abstract
Significant fluid loss while drilling through fractured formations is a major problem for drilling operations. From field experience we know that the type and rheological parameters of the drilling fluid have a strong impact upon the rate and volume of losses.
In this work, a mathematical model for flow of Yield-Power-Law (Herschel-Bulkley) fluids in fractures is presented. The governing equation is derived using the principles of conservation of mass and linear momentum for transient radial flow in a fracture. Results are obtained based on numerical solutions and plotted in terms of mud loss volumes versus time for a given drilling fluid under certain operational conditions. Results show how the rheological properties of drilling fluid such as yield stress and flow behavior index ( shear-thinning/thickening effect ), influence mud losses in fractured formations. According to this model the yield stress of drilling fluids tremendously decreases the potential for mud losses. The effect of yield stress on reducing mud losses is the same as the effect of overbalance pressure on increasing losses. The shear thinning effect of drilling fluids can also greatly increase the rate of losses. Therefore, mud losses in fractures can be minimized by properly optimizing the rheology of the drilling fluid.
Using this model, quantitative analysis of losses that take into account fluid rheology in order to characterize the fracture can be achieved. One can obtain the hydraulic aperture of conductive fractures by continuously monitoring mud losses and fitting field
records of mud losses to the model. For general applications, type-curves are provided that describe drilling fluid loss of Yield-Power-Law fluids into fractures. Newtonian, Bingham Plastic and Power Law fluids are special cases. The proposed model is very useful not only for drilling applications but also for well completion design and fractured reservoir characterization.
Field data measurements are used to demonstrate the practical application of the proposed technique. Good agreement between the model and field data confirms the validity and applicability of the model.
Introduction
Drillers often encounter fractured formations which can either have positive or negative effects on the flow properties of the formations. But, large volumes of drilling fluid losses through these faults or fissures constitute severe problems due to improper functioning of the drilling fluids. Beside the problematic aspect of this issue and techniques to prevent losses such as under-balanced drilling or using the appropriate lost circulation materials, the industry has made several attempts to characterize the fractured formations by real-time monitoring of mud losses.
Dyke et al.(1995) reported that losses through the matrix permeability or fractures can be distinguished by the characteristis of the losses. Losses through pores start slowly and gradually increase whereas losses into fractures are associated with a rapid initiation followed by gradual decline with time. Different sources of information such as image logs, core data and using more accurate
flowmeters are suggested by several researchers to improve detection and characterization of the fractures1, 10.
However, quantitative analysis of mud losses is a more informative and reliable way of characterizing the fractures in terms of the flow properties of the fractures. Such an analysis should be based on mathematical model that describes the physical phenomenon and the mechanism under which flow within the fractures takes place.
Lavrov and Tronvoll(2004) developed a number oftheoretical models considering mud losses into a deformable fracture of finite length. Fracture opening/closing was the major mechanism for losses or gains. There are two analytical models in the literature,
developed to evaluate fracture hydraulic width from mud losses. Both models assume that the fracture width can be regarded as a slot of constant width and the mud propagates radially into the fracture. The models assume the validity of Poiseuille’s flow, so the fracture permeability is related to the fracture width or hydraulic aperture of the fracture.
The model developed by Sanfillippo et al.6is based on the pressure diffusivity equation and applies to radial mud flow into a fracture perpendicularly intersecting the wellbore. The final equation obtained is a measurement of circulation loss volume, and the width of the fracture is computed through numerical iteration. The assumption of Newtonian fluid is generally not feasible in he case of drling mud; therefore, the rheological model adopted by Sanfillippo et al. does not appear to be representative of real fluid behavior in the fracture.
However, the model is very flexible and can be applied to calculate the fracture width of either a local intensely
fractured rock or a single conductive fracture.
Lietard et al. developed a model based on the radial flow of Bingham-Plastic fluid into an unlimited extension fracture. The mud flow through the fracture is described by the local pressure drop due to laminar flow in a slot of width w. According to the linear momentum equation, pressure gradient and the average velocity are related as: where τy and µp are the yield point and plastic viscosity of
the fluid, respectively. Assuming that a constant overpressure is applied at the well, a relationship for mud invasion velocity versus time is obtained. Lietard showed that the mud losses will eventually stop due to the yield stress of drilling fluid. The ultimate volume of losses depends on the yield value of the drilling fluid and the amount of overpressure. The model proposed by Lietard et al. for Bingham-Plastic fluids reveals that the rheological behavior of drilling fluids considerably influences the rate and volume of losses.
Most drilling fluids show shear-thinning effect in addition to initial yield stress. Therefore, characterizing drilling fluids as Yield-Power-Law is more general and practical. Introducing a more realistic fluid rheological behavior to the model of mud losses in fractures enables us to investigate the effect of drilling fluid rheology on fluid losses in more detail.
翻译：
天然裂缝油藏中钻井液漏失量的数量分析：流变性的影响
摘要
在钻井作业中，当钻遇裂缝性地层时，显著的钻井液的漏失是一个主要问题。现场经验使我们认识到钻井液的类型和流变参数对漏失的体积和速度有极大影响。
在本文中，将提出一种符合带有动切力的幂律模式（赫—巴模式）的钻井液在裂缝中流动的数学模型。指导性方程由质量守恒定律和线性动量定律推得。结果在数值解的基础上取得，根据在一定的操作条件下，用给定钻井液的漏失量与时间的比来表示。结果表明了诸如屈服应力和流性指数（剪切稀释性）等钻井液的流变性对钻井液在裂缝地层中漏失量的影响程度。根据这个模型可以确定钻井液的屈服应力可以极大地降低钻井液的漏失能力。同过平衡压力可以增加钻井液的漏失量一样，屈服应力可以减少钻井液的漏失量。钻井液的剪切稀释性也可以极大的影响钻井液的漏失速度。因此，可以通过优化钻井液的性能来达到减少钻井液漏失的目的。
为了描述油藏的特征，利用这个模型，在考虑钻井液流变性的情况下可以得到对漏失量的数量分析。通过不断的监测钻井液的漏失量，得到一系列现场的记录数据，将这些数据与该模型进行比较，就能够得到有效裂缝的水力孔径。为了进行一般的应用，给出了一些用于描述符合赫—巴模式的钻井液在裂缝中漏失的曲线。
牛顿流体、宾汉塑性流体和假塑性流体属于特殊情况。该模型不仅在钻井中非常有用，同样也可用于完井设计和裂缝油藏的描述。
测得的现场数据展现了该技术的实际应用，现场数据同模型数据良好的一致性更加巩固了模型的正确性和实用性。
引言
钻井过程中常常会遇到钻遇裂缝性地层的情况，这些地层既会对钻井液在其中的流动产生积极的影响，也会产生消极的影响。但是，钻井液通过这些裂缝或断层会产生大量的漏失，这些钻井液不正常的活动会使正常的钻进过程产生严重的问题。除了一些仍然存在问题的诸如欠平衡压力钻井或使用合适的堵漏材料的理论和技术外，石油工业已经痛过实时的监测钻井液的漏失来尝试描述裂缝地层的特征。
Dyke[2]提出根据漏失特征的不同，可以将通过基质和裂缝的漏失区别开来。通过孔隙的漏失速度在开始一段时间很小，然后逐渐增大；而裂缝中的漏失有一个比较快的开始，然后随着时间的推移而会逐渐降低。一些学者主张使用不同的信息资料，如：图像测井、岩心数据或使用更加准确的流量计来改进对裂缝情况和特征的描述。然而，根据裂缝的渗流特征而提出的对钻井液漏失量的数量分析是进行裂缝特征描述的更加可靠和有价值的方法。这种数量分析应当有数学分析作为基础，这些模型描述的是裂缝中渗流的物理现象和机理。
Lavor和Tronvoll[3]-[5](2004)开发了一系列理论模型，这些模型考虑了有限大可变形裂缝中的漏失。裂缝的开启和关闭对于漏失或获得是一个重要机理。
在研究中总共提出了两种解析模型，它们可以根据钻井液的漏失量来估计裂缝的水力宽度。这两种模型都假设裂缝的宽度是不变的，钻井液径向流入裂缝中。模型假设泊肃叶定理的正确性，所以裂缝的渗透率与裂缝的宽度和水力孔径有关。
由Sanfillippo提出的模型以压力扩散方程为基础，适用于垂直于油井截面的钻井液的径向的流动。得到的最终方程衡量的是漏失的体积，裂缝的宽度由一系列的数学迭代计算出来。对钻井液来说，牛顿流体的假设是不适用的。因此，Sanfillippo的流变模式好像不能裂缝中流体流动的真实行为。然而，这个模型应用非常灵活，可以用来计算当地密集裂隙岩体和单一导电性裂缝的宽度。
Lietard[7][8]以无限延伸裂缝中的宾汉塑性流体的径向流动为基础提出了一种模型。钻井液沿着裂缝的流动以在宽度为 的狭槽中的层流所造成的压力降来描述。跟狙线性动量定理，压力梯度与平均速度的关系为：
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其中 和 分别为钻井液的动切力和塑性粘度。假设钻井使用的是一个不变的过平衡压力，钻井液侵入的时间和速度的关系就可以得到。Lietard认为由于屈服应力漏失最终将会停止。Lietard提出的针对宾汉塑性流体的模型揭示了钻井液的流变性对漏失的体积和速度有非常大的影响。
除了初始屈服应力外，大多数钻井液表现出剪切稀释性。因此，将钻井液描述为带有动切力的幂率模式更具普遍性和实用性[5]。将这种更加真实的钻井液的流变特性引入到漏失模型中使能我们更加详细的研究钻井液的流变性对漏失的影响。
