考虑管线存储及表皮效应各向异性介质任意倾角下地层测试器流体分析(英文)

Formation Tester Flow Analysis in Anisotropic Media With Flowline Storage and Skin at Arbitrary Dip

设计一套融合正反演方法的地层测试分析工具,用于电缆和随钻地层测试硬件设计和压力瞬态解释。该方法基于达西流动方程,在可能条件下求得闭合解析解,在不同限定条件下进行反复验证以保证其一致性和精确度。考虑管线存储效应及表皮效应,在各向异性介质中任意倾角下地层测试器流体压力响应瞬态问题,早期通过假设椭圆抽吸探针(用复数余误差函数)已求得闭合解析精确解,现被用来推导出当抽吸探针、观测探针压降值及倾斜角度给定时的多个渗透率反演精确解。对恒定抽吸流量下零表皮效应稳态正演解的评价。推导出各种水平、垂直渗透率及其倾角下的反演公式。该方法运用正演模拟计算出任意倾角下压降值,再通过推导方程来预测正演所假设的水平及垂直渗透率,给出现场解释验证结果。在预测各向异性介质时如忽视倾角会引起极大误差。存在多个反演解的问题:对于1组给定的压降值,求得3对渗透率解需要其他测井数据来确定。对恒定抽吸流量下带表皮效应稳态正演解的评价。该解生成的方程将抽吸探针压降、观测探针压降、垂直渗透率、水平渗透率及表皮因子相关联。两探针压降已知可推导出任意倾角下的各向异性渗透率及表皮因子任意解算法。该算法只假设了2个压力数据点,需额外的测井资料来确定特定点值。采用观测探针处持续时间很短的脉冲干扰法来确定地层各向异性,这在扩散占主导的低渗透率地层中具有明显优势。这些高频短脉冲可提供详细的地层信息。多脉冲波串具有不同的流速、脉冲宽度和脉冲间隔,在不要求使用新硬件情况下在钻井现场实现多个快速测试,降低仪器在致密岩层遇卡风险。阐述类似电磁波测井的相延迟法预测渗透率。抽吸探针出现正弦压力瞬态波,由一个或多个观测探针测得这些压力波的波幅及相位,并用达西解析模型进行解释。与脉冲干扰法一样,相延迟法也因测试时间短而具有高效、安全、信噪比高的特点。给出一个全方位三维水平井模型,适用于层状介质中带有实际心轴的单探针、双探针、双封隔器及加长极板的仪器;计算结果显示方位和层边界对压力响应以及渗透率预测的影响。抽吸探针模型要求使用双探针数据来实现反演,采用全方位的的三维模型来适用于单探针随钻测井仪器FTWD(测量方位压力)来获取与渗透率、各向异性及层厚相关的数据。讨论随钻地层测试的实时地层压力及可动性预测,这是钻井安全及快速经济评价的关键,其包含由管线存储效应引起的瞬态数据失真,采用最少的压力数据来尽可能求出正确的预测值。开发的有理多项式展开法,无需使用指数函数、实数或复数余误差函数,不用回归或最小二乘平滑滤波这些超出达西流动方程隐含会引起扩散假设的方法。快速分析功能使随钻仪器的微处理器能腾出更多的空间来容纳钻井过程中所需的其他重要的控制及解释功能。

We describe a comprehensive set of integrated formation testing forward and inverse analysis tools developed for wireline and ＂while drilling＂ （FTWD） applications in hardware design and pressure transient interpretation. The methods based on rigorous Darcy {low formulations are solved analytically in closed form whenever possible and cross-checked in different limits to ensure physical consistency and accuracy. The transient problem for formation tester liquid pressure response in anisotropic media with flowline storage and skin at arbitrary dip, earlier solved in exact, closed analytical form assuming ellipsoidal sources, is used to derive exact solutions to several inverse problems where permeabilities are sought when dip angle and source and observation probe pressure drops are given. First, the zero-skin forward solution is evaluated in the steady-state limit for constant rate pumping. Explicit inverse formulas are derived for all horizontal and vertical permeabilities and dip angles. With pressure drops computed at various dip angles from the forward simulation, derived formulas are used to predict both assumed permeabilities, demonstrating their utility in field interpretation. Neglect of dip angle can lead to significant errors in anisotropy prediction. Moreover, multi-valued inverse solutions exist： for a given set of pressure drops, three permeability pairs are found which require resolution from additional log data. .Second, the ＂with-skin＂ forward solution is evaluated at steady-state for constant rate pumping to develop formulas relating source and observation probe pressure drop, vertical and horizontal permeabilities and skin factor. An algorithm giving possible solutions for both permeabilities and skin at any dip angle when both pressure drops we known is derived. Because only two pressure data points are assumed, additional logging information is needed to render a unique determination. Third, short- duration ＂pulse interactions＂ at the observation probe are used to determine anisotropy. These are the strongest and most advantageous at low permeabilities where diffusion predominates. Short pulses with high frequency content provide detailed information. Multi-pulse wave-trains with different flow rates, pulse durations and separations enable multiple fast test suites at the rigsite without requiring new hardware. They are accurate, economical and reduce tool sticking risks in tight zones. Fourth, ＂phase delay＂ approaches for permeability prediction analogous to electromagnetic logging methods are described. Sinusoidal pressure transients are created at the pumping probe. Their amplitudes and phases are measured at one or more observation probes. These are interpreted using Darcy analysis models. As with pulse interaction methods, phase delay approaches allow short-duration tests that are economical, safe and characterized by high signal-to-noise ratios. Fifth, a full 3D horizontal well model for single probe, dual-probe, dual-packer and elongated pad tools with real mandrels in layered media is given, with computations showing effects of azimuth and bed boundary on pressure response and their implications on permeability prediction. While source models require dual-probe data for inverse application, full 3D models can be used with single-probe FTWD tools （measuring azimuthal pressures） to provide clues related to permeability, anisotropy and bed thickness. Finally, real-time FTWD pore pressure and mobility prediction is discussed. Such problems, key to drilling safety and rapid economic evaluation, involve transient data distorted by flowline storage effects. Accurate predictions are possible using a minimum of pressure data. We develop rational polynomial expansion methods that do not require exponential, real or complex complementary error functions, and moreover, do not use regression or least-squares smoothing filters that introduce diffusive assumptions beyond those implicit in Darcy＇s laws. Rapid analysis frees microprocessor resources for other important control and interpretation functions needed during drilling.