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首页> 外文期刊>Applied Mathematical Modelling >Generalized analytical model of Transient linear flow in heterogeneous fractured liquid-rich tight reservoirs with non-static properties
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Generalized analytical model of Transient linear flow in heterogeneous fractured liquid-rich tight reservoirs with non-static properties

机译：非静态非均质裂隙富液致密油藏瞬态线性流动的广义解析模型

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摘要

The industry is increasingly reliant on rate-transient analysis (RTA) to extract valuable information about the reservoir and hydraulic fractures. However, the application of current, commercially-available RTA models can lead to incorrect estimates of reservoir/fracture properties, potentially causing costly mistakes to be made in capital planning and reserve estimation. The root cause of these errors is that currently-available analytical solutions used in RTA models largely ignore reservoir heterogeneities, and assume static reservoir properties.In this work, a new transient linear flow is rigorously modeled in unconventional reservoirs with (1) pressure-dependent rock and fluid properties and (2) both continuous and discontinuous (heterogeneous) porosity and permeability. To achieve this, new transformations of pseudo-pressure, pseudo-time and pseudo-distance are first introduced to reduce the temporal and spatial non-linear diffusivity equation to that with approximately constant coefficients. Both a Laplace-domain solution and approximate analytical solution to the diffusivity equation are verified against a series of fine-grid numerical simulations for the assumption of fractal-based reservoir heterogeneity (over a wide range of stress dependent rock and fluid properties). The results indicate that reservoir heterogeneity can result in nonlinear square-root-of-time plots. Further, rock and fluid pressure-dependencies act to decrease the slope of the square-root-of-time plot and affect reservoir/fracture property evaluations.Three liquid-rich shale (LRS) field examples in North America are analyzed to demonstrate the practical applicability of the new RTA models. Additional value of new RTA models over the sophisticated numerical simulation is to provide us an improved backforward-analysis workflow that can be used to quantify both effective fracture half-length and non-uniform permeability distribution around the fractures.The major contribution of this work is the introduction of a new analytical model for evaluating the transient linear flow period for the cases of arbitrary reservoir heterogeneity and non-static reservoir properties. This new approach is particularly useful for evaluating the effectiveness of hydraulic fracturing operations by extracting the spatial variability of reservoir quality within the stimulated reservoir volume (SRV). (C) 2019 Elsevier Inc. All rights reserved.
机译：该行业越来越依赖速率瞬变分析（RTA）来提取有关储层和水力压裂的有价值的信息。但是，当前商业上可买到的RTA模型的应用可能导致对储层/裂缝特性的错误估计，从而可能导致在资本计划和储量估计中犯下代价高昂的错误。这些错误的根本原因是RTA模型中使用的当前分析解决方案在很大程度上忽略了油藏的非均质性，并假定了静态油藏属性。在这项工作中，在非常规油藏中严格建模了一种新的瞬态线性流，其（1）依赖于压力岩石和流体性质以及（2）连续和不连续（非均质）孔隙率和渗透率。为此，首先引入伪压力，伪时间和伪距离的新变换，以将时间和空间非线性扩散系数方程式简化为系数近似恒定的方程。针对一系列基于分形储层非均质性假设的细网格数值模拟，验证了扩散系数方程的Laplace域解和近似解析解（在很大范围内取决于应力的岩石和流体性质）。结果表明，储层非均质性可导致非线性时间平方根图。此外，岩石和流体压力的依赖性降低了时间平方根图的斜率并影响了储层/裂缝性评价。分析了北美的三个富液页岩（LRS）油田实例，以证明其实用性。新RTA模型的适用性。与复杂的数值模拟相比，新的RTA模型的附加价值是为我们提供了一种改进的后向分析工作流程，可用于量化有效裂缝的半长和裂缝周围渗透率的不均匀分布。引入了一种新的分析模型，用于评估任意储层非均质性和非静态储层特性情况下的瞬态线性流动周期。通过提取受激储层体积（SRV）内储层质量的空间变异性，这种新方法对于评估水力压裂作业的有效性特别有用。 （C）2019 Elsevier Inc.保留所有权利。

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