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  本文選題：自適應(yīng)網(wǎng)格法 + 油藏數(shù)值模擬�。� 參考：《中國科學(xué)技術(shù)大學(xué)》2015年博士論文

【摘要】：稠油由于其豐富的儲量在碳氫能源領(lǐng)域占據(jù)的地位越來越重要。蒸汽注采作為稠油開采的主要工藝,其數(shù)值模擬研究也引起了學(xué)者們的重視。該類問題是一種帶有相變的多孔介質(zhì)多相流動問題,滲流流場內(nèi)存在變化劇烈且狹窄的溫度與飽和度鋒面,為了準確模擬流場變化動態(tài),鋒面附近網(wǎng)格的尺度必須足夠小,若直接對全場采用均勻網(wǎng)格,龐大的網(wǎng)格數(shù)據(jù)與計算量是難以承受的�？紤]于此,可以動態(tài)追蹤流場鋒面的自適應(yīng)網(wǎng)格法成為本文的主要研究對象。該方法在流場內(nèi)的網(wǎng)格結(jié)構(gòu)會隨著注采過程推進而實時變化,在物理量變化劇烈的區(qū)域采用細網(wǎng)格而在物理量變化緩慢的區(qū)域采用粗網(wǎng)格,從而大幅度降低計算規(guī)模并提高計算速度。 由于地質(zhì)模型與數(shù)值模型在尺度上存在較大差異,地質(zhì)參數(shù)一般需要進行粗化,并產(chǎn)生滲透率張量,因而需要單獨處理網(wǎng)格界面的流量。借助各網(wǎng)格內(nèi)壓力線性分布的假設(shè)以及流量守恒,本文介紹了張量滲透率下網(wǎng)格界面上的流量求解方法,同時結(jié)合二維油藏的自適應(yīng)網(wǎng)格法,研究了絕對滲透率為張量時的自適應(yīng)網(wǎng)格法。對于自適應(yīng)網(wǎng)格法中相鄰不同層次的網(wǎng)格,由于它們的空間尺度不同,本文引入粗網(wǎng)格的子網(wǎng)格使其與相鄰網(wǎng)格層次匹配,從而有效解決了不同層次網(wǎng)格界面上的流量求解問題。通過張量滲透率下的二維蒸汽驅(qū)以及注蒸汽輔助重力泄油的具體算例驗證了自適應(yīng)網(wǎng)格法的準確性與高效性。 實際油藏往往包含多種流動單元,即分布著不同輸運性質(zhì)的巖石,不同巖石對應(yīng)不同的相對滲透率、毛管力函數(shù)、殘余油水飽和度以及初始油水飽和度,這些因素導(dǎo)致相飽和度在跨越不同巖石界面時產(chǎn)生間斷,從而給自適應(yīng)網(wǎng)格法的網(wǎng)格劃分以及粗細化操作帶來較大困難。本文對于此類油藏數(shù)值模擬的自適應(yīng)網(wǎng)格法展開研究：當重力可忽略,且毛管力梯度影響不大時,根據(jù)網(wǎng)格界面處流量守恒的條件,推導(dǎo)出在同一個粗網(wǎng)格內(nèi)都連續(xù)的變量一一不同相相對滲透率的比值,進而給出自適應(yīng)網(wǎng)格法的網(wǎng)格劃分以及粗細化操作的具體方案。二維水平剖面下的蒸汽驅(qū)算例驗證了理論推導(dǎo)的合理性,并說明了自適應(yīng)網(wǎng)格法的準確性與高效性；當重力不可忽略時,三相區(qū)內(nèi)油氣毛管力在同一個粗網(wǎng)格內(nèi)保持連續(xù),且油水相對滲透率之比在同一個粗網(wǎng)格內(nèi)也是不依賴于巖石種類的。借助于該相對滲透率之比以及油氣毛管力,本文解決了自適應(yīng)網(wǎng)格法在考慮重力的多種巖石蒸汽注采問題中網(wǎng)格劃分與粗細化等主要難點。二維下的注蒸汽輔助重力泄油算例表明自適應(yīng)網(wǎng)格法較精細網(wǎng)格法在該類問題中的速度優(yōu)勢。 上述蒸汽注采問題中,本文假設(shè)各流動單元毛管力總體相差不大,并忽略了毛管力梯度的影響。但是對于某些特殊情況,毛管力在不同介質(zhì)中可能會存在較大差異,例如裂縫性油藏中的裂縫與基質(zhì),此時界面上毛管力梯度較大。本文對包含有兩種巖石且一側(cè)考慮毛管力一側(cè)不考慮毛管力的多孔介質(zhì)進行了研究。考慮到不同巖石界面處毛管力函數(shù)關(guān)系的不同,本文給出了該界面需要滿足的條件,包括流量守恒以及與毛管力相關(guān)的條件,針對上述界面條件做出了基于控制方程的數(shù)學(xué)證明,同時發(fā)現(xiàn)在界面上有時會有飽和度梯度發(fā)散或者毛管力間斷的特殊現(xiàn)象。為了解界面處的流動特性,本文初步研究了相應(yīng)的數(shù)值算法,在巖石界面附近進行了穩(wěn)態(tài)假設(shè)下的解析求解,并基于該局部近似解構(gòu)造了流量的離散格式。數(shù)值結(jié)果表明毛管力的非均質(zhì)性會影響界面處的流動特性,當含有毛管力的巖石位于上游,不含有毛管力的巖石位于下游時,界面上的毛管力可以保持連續(xù),但是在含毛管力側(cè)的巖石界面處,潤濕相飽和度會趨向于1.0,且其梯度趨于無窮大；相反,不含有毛管力的巖石位于上游時,若毛管力不能進行匹配,會出現(xiàn)毛管力間斷的現(xiàn)象,此時潤濕相壓力間斷,非潤濕相壓力連續(xù)。 綜上,本文主要對滲透率張量下多種巖石油藏蒸汽注采問題的自適應(yīng)網(wǎng)格法進行了研究,解決了自適應(yīng)網(wǎng)格法在該類應(yīng)用中遇到的一系列問題。相應(yīng)的蒸汽驅(qū)以及注蒸汽輔助重力泄油的算例表明自適應(yīng)網(wǎng)格法在保證計算精度的同時,較精細網(wǎng)格法有巨大的計算速度優(yōu)勢。同時本文還對毛管力非均質(zhì)的一維不可壓縮不混溶兩相流問題進行了研究,給出了相應(yīng)的界面條件以及數(shù)值算法。文中的數(shù)值算例也說明了巖石界面上的流動特性。
[Abstract]:Heavy oil is becoming more and more important in the field of hydrocarbon energy because of its rich reserves. As the main process of heavy oil mining, the numerical simulation of steam injection has also aroused the attention of scholars. This kind of problem is a multi-phase flow problem with a porous medium with phase change, and there is a severe and narrow temperature in the flow field. With the saturation front, in order to simulate the dynamics of flow field, the scale of the grid near the front must be small enough. If a uniform grid is used directly to the whole field, the large grid data and calculation are difficult to bear. Considering this, the adaptive mesh method that can dynamically track the front of the flow field is the main object of this paper. The grid structure in the flow field will change in real time as the injection and production process advance, and the coarse grid is adopted in the area with intense physical quantity, and the coarse mesh is adopted in the region of slow change of physical quantity, which greatly reduces the calculation scale and improves the calculation speed.
Due to the large difference between the geological model and the numerical model on the scale, the geological parameters generally need to be coarsened and the permeability tensor is generated. Therefore, the flow of the grid interface needs to be treated separately. With the assumption of the linear distribution of pressure in each grid and the conservation of flow, the flow solution on the mesh interface under the tensor permeability is introduced. At the same time, combining the adaptive grid method of two dimensional reservoir, the adaptive mesh method of the absolute permeability as the tensor is studied. For the grid adjacent to the different layers in the adaptive grid method, because of the different spatial scales, this paper introduces the coarse mesh subgrid to match the adjacent grid layer, thus effectively solving the different layers. The accuracy and efficiency of the adaptive mesh method are verified by a specific example of two dimensional steam flooding and steam injection assisted gravity drainage under the tensor permeability.
The actual reservoir often contains a variety of flow units, that is, the distribution of different transport properties of rock. Different rocks correspond to different relative permeability, capillary force function, residual oil water saturation and initial oil water saturation. These factors cause phase saturation to produce discontinuity across different rock boundaries, thus giving the mesh of adaptive grid method. In this paper, the adaptive grid method for numerical simulation of such reservoirs is studied in this paper. When gravity is negligible and the influence of the capillary force gradient is small, according to the condition of the flow conservation at the grid interface, the relative permeability of the successive variables in the same coarse grid is derived. The ratio is then given to the specific scheme of the grid division and the coarse and fine operation from the adaptive grid method. The steam flooding example under the two-dimensional horizontal section proves the reasonableness of the theoretical deduction and illustrates the accuracy and efficiency of the adaptive grid method. When the gravity can not be ignored, the oil and gas force in the three phase region is in the same coarse grid. The ratio of the relative permeability of oil and water is not dependent on the type of rock in the same coarse mesh. With the aid of the ratio of the relative permeability and the oil and gas capillary force, the paper solves the main difficulties of the grid division and the coarse refinement of the adaptive grid method in the problem of various rock steam injection and production in the consideration of gravity. An example of steam assisted gravity drainage shows that the adaptive grid method is superior to the refined grid method in this kind of problem.
In the above problem of steam injection and production, this paper assumes that the overall difference of capillary force in each flow unit is small and neglects the influence of Mao Guanli gradient. However, for some special cases, there may be great differences in the capillary force in different media, such as cracks and foundations in fractured reservoirs, and the capillary force gradient is larger at this time. A porous medium containing two kinds of rocks and one side considering the force of capillary force is studied. Considering the difference of the capillary force function at different rock interfaces, this paper gives the conditions that the interface needs to be satisfied, including the conservation of flow and the conditions related to the capillary force, which is based on the interface conditions. In order to understand the flow characteristics at the interface, the corresponding numerical algorithm is preliminarily studied in order to understand the flow characteristics at the interface. In order to find out the solution of the solution under the steady state assumption near the rock interface, the flow rate is built on the basis of the local approximate deconstruction. The numerical results show that the heterogeneity of the capillary force affects the flow characteristics at the interface. When the rock with Mao Guanli is located upstream and the rock without the capillary force is located downstream, the capillary force on the interface can be kept continuous, but the wetting phase saturation will tend to 1 at the rock interface with the force side of the capillary force. The gradient tends to infinity; on the contrary, when the rock does not contain the capillary force on the upper reaches, if the capillary force can not be matched, the capillary force discontinuous will occur, at this time the wetting phase pressure discontinuous and the non wetting phase pressure is continuous.
To sum up, this paper mainly studies the adaptive grid method of steam injection and production in various rock reservoirs under permeability tensor, and solves a series of problems encountered in this kind of application by adaptive grid method. The calculation examples of the corresponding steam flooding and steam injection assisted gravity discharge show that the adaptive grid method is at the same time guaranteeing the accuracy of the calculation. The finer grid method has a huge computational speed advantage. At the same time, this paper also studies the one-dimensional incompressible immiscible incompressible two-phase flow problem of the capillary force heterogeneity, and gives the corresponding interface conditions and numerical algorithms. The numerical examples in this paper also show the flow characteristics on the rock interface.

【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TE319

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