Wormhole Propagation Behavior and Its Effect on Acid Leakoff under In Situ Conditions in Acid Fracturing

In acid fracturing, excessive acid leakoff is thought to be the main reason that limits fracture propagation and live acid penetration distance. Although acid leakoff has been studied under experimental conditions, the acid leakoff theory developed under experimental conditions cannot be extended to in situ conditions because the injection rate or pressure drop across a core plug is fixed in the experiments. In this paper, we used a model that couples a two-scale continuum model simulating wormholing in the invaded zone and a reservoir flow model for the compressed zone to simulate acid leakoff process under in situ conditions. Based on this model, we investigated wormhole propagation behavior and its effect on acid leakoff under in situ conditions. The study shows different wormhole propagation behavior under in situ conditions from that under experimental conditions. Wormholes grow fast at the beginning and slow down at later time due to the rise of reservoir pressure caused by the leakoff and the growth of the invaded zone. In oil reservoirs, wormholing has minor effect on acid leakoff because of small compressibility and relatively high reservoir fluid viscosity, but in gas reservoirs, the influence of wormholing on acid leakoff becomes significant due to large compressibility and low reservoir fluid viscosity. Acid viscosity has more notable influence on acid leakoff in gas reservoirs than in oil reservoirs.     

Modeling the acidizing of a carbonate formation

Two approaches to the determination of the optimum conditions of the well bottom zone treatment in a carbonate formation are considered and compared. The first, bench approach is based on the investigation of the process of wormhole formation in rock cores, while the second approach is the mathematical modeling of the process within the framework of mechanics of multi-component seepage flows using averaged values of the reservoir porosity and permeability. A mathematical model of the process, that takes account for fluid flow and the chemical reaction between the acid and the rock matrix proceeding in the kinetic regime, is presented. Both approaches indicate the existence of an optimum rate of acid solution injection into the formation at a certain given value of the dimensionless Damköller number.     

Analytical Modeling of Flow Behavior for Wormholes in Naturally Fractured–Vuggy Porous Media

Acidizing technology has been widely applied when developing naturally fractured–vuggy reservoirs. So testing and evaluating acidizing wells’ pressure behavior become necessary for further improving the wells’ performance. Analyzing transient pressure data can estimate some key reservoir parameters. Generally speaking, carbonate minerals are usually composed of dolomite and calcite which are easy to be dissolved by hydrochloric acid which is often used to react with the rock to create a high conductivity channel, namely wormhole. Pressure transient behavior in fractured–vuggy reservoirs has been studied for many years; however, the models of acidizing wells with wormholes were not reported in previous studies. This article presented an analytical model for wormholes in naturally fractured–vuggy carbonate reservoirs, and wormholes solutions were obtained through point sink integral method. The results were validated accurately by comparing with previous results and numerical simulation. Then in this paper, type curves were established to recognize the flow characteristics, and flow was divided into six flow regimes comprehensively. The calculative results showed that the characteristics of type curves were influenced by inter-porosity flow factor, wormhole number, fluids capacitance coefficient. We also showed that the pressure behavior was affected by the angles between wormholes, and the pressure depletion increased as the angle decreased, because the wormholes were closer, their interaction became stronger. At the end, a reservoir example was showed to demonstrate the methodology of new type curve analysis.     

Modeling the acidizing of carbonate formations with account for the occurrence of wormholes

he results of an investigation of hydrochloric acid treatment on micro and macroscales are presented. A petrophysical permeability-porosity dependence used in the averaged mathematical model and taking account of the wormhole formation effect on the level of individual pores is proposed. The values of the surface reaction rate on carbonate rock dissolving in hydrochloric acid are given from the results of laboratory studies. An optimum rate of hydrochloric acid plug injection is estimated and the constraints due to possible transition of the acidizing in the acid breaking of the formation are discussed.     

Modeling of Wormhole Growth in Cold Production

Cold production is a non-thermal process in which sand is intentionally produced with the oil in order to enhance oil recovery. Two experiments were performed to investigate the effect of producing large quantities of sand on the overall permeability of a formation. A large high porosity channel (wormhole) was observed in both experiments. A model of wormhole growth was successfully tested in two sand production experiments simulating the growth of a wormhole from a perforation in a vertical well. The produced volumes of oil, sand and gas, the pressure distribution along the pack and the final length of the wormholes were well predicted. The two sand packs had significantly different cohesive strengths. The strength of the sand did not have a significant effect on the growth of the wormholes. The formation of tensile failure bands at the wormhole surface, as observed in the experiments, may weaken the sand and allow it to be fluidized more easily. This weakening effect would explain the lower pressure gradients calculated at the surface of the wormhole while it developed compared to the critical pressure gradient for sand production predicted by Bratli and Risnes (1981).     

Flow Modeling of Well Test Analysis for Porous–Vuggy Carbonate Reservoirs

Porous–vuggy carbonate reservoirs consist of both matrix and vug systems. This paper represents the first study of flow issues within a porous–vuggy carbonate reservoir that does not introduce a fracture system. The physical properties of matrix and vug systems are quite different in that vugs are dispersed throughout a reservoir. Assuming spherical vugs, symmetrically distributed pressure, centrifugal flow of fluids and considering media that is directly connected with wellbore as the matrix system, we established and solved a model of well testing and rate decline analysis for porous–vuggy carbonate reservoirs, which consists of a dual porosity flow behavior. Standard log–log type curves are drawn up by numerical simulation and the characteristics of type curves are analyzed thoroughly. Numerical simulations showed that concave type curves are dominated by interporosity flow factor, external boundary conditions, and are the typical response of porous–vuggy carbonate reservoirs. Field data interpretation from Tahe oilfield of China were successfully made and some useful reservoir parameters (e.g., permeability and interporosity flow factor) are obtained from well test interpretation.     

The Use of Fractal Geostatistics and Artificial Neural Networks for Carbonate Reservoir Characterization

In this study, a carbonate oil reservoir located in the southeast part of Turkey was characterized by the use of kriging and the fractal geometry. The three-dimensional porosity and permeability distributions were generated by both aforementioned methods by using the wireline porosity logs and core plug permeability measurements taken from six wells of the field. Since classical regression (lognormal or polynomial) and geostatistical techniques (cross variograms) fail to estimate permeability from wireline log-porosity data, the use of artificial neural networks (ANNs) is proposed in this study to generate permeability data at uncored intervals of porosity logs. For both of the methods, kriging and fractal techniques, the validation of the estimated/simulated data with known wellbore data resulted with acceptable agreements, especially for porosity. Also the comparison of both methods at unsampled locations show better agreements for porosity than permeability.     

Acid Leakoff Mechanism in Acid Fracturing of Naturally Fractured Carbonate Oil Reservoirs

In acid fracturing, excessive acid leakoff is thought to be the main reason that limits fracture propagation and live acid penetration distance. Since most carbonates are naturally fractured, we developed a new model in this paper to simulate acid leakoff into a naturally fractured carbonate oil reservoir during acid fracturing. Our model incorporates the acid-rock reaction, fracture width variation due to rock dissolution on the fractured surfaces, and fluid flow in naturally fractured carbonate oil reservoirs. Given the information of the reservoir, injected acid, and pressure in the hydraulic facture and the reservoir, the model predicts acid leakoff with time. In this study, we found that acid leakoff mechanism in naturally fractured carbonates is much different from that in reservoirs without natural fractures. Widened natural fractures by acid-rock reaction act as high-conductivity conduits allowing leakoff acid to penetrate deeper into the formation, resulting in serious leakoff. Wide natural fractures have a dominant effect on acid leakoff compared to micro-fractures and matrix.     

CO<Subscript>2</Subscript> injection into saline carbonate aquifer formations I: laboratory investigation

Although there are a number of mathematical modeling studies for carbon dioxide (CO₂) injection into aquifer formations, experimental studies are limited and most studies focus on injection into sandstone reservoirs as opposed to carbonate ones. This study presents the results of computerized tomography (CT) monitored laboratory experiments to analyze permeability and porosity changes as well as to characterize relevant chemical reactions associated with injection and storage of CO₂ in carbonate formations. CT monitored experiments are designed to model fast near well bore flow and slow reservoir flows. Highly heterogeneous cores drilled from a carbonate aquifer formation located in South East Turkey were used during the experiments. Porosity changes along the core plugs and the corresponding permeability changes are reported for different CO₂ injection rates and different salt concentrations of formation water. It was observed that either a permeability increase or a permeability reduction can be obtained. The trend of change in rock properties is very case dependent because it is related to distribution of pores, brine composition and thermodynamic conditions. As the salt concentration decreases, porosity and the permeability decreases are less pronounced. Calcite deposition is mainly influenced by orientation, with horizontal flow resulting in larger calcite deposition compared to vertical flow.     

Permeability Changes During the Evolution of a Geothermal Field Due to the Dissolution and Precipitation of Quartz

The changes in permeability and porosity associated with quartz deposition in an evolving geothermal reservoir are investigated. We review the processes associated with permeability changes in a geothermal reservoir and also review recent work on quartz solubility and deposition rates. Porosity and permeability changes are calculated for two reservoir models. The first is a generic model of a Taupo Volcanic Zone geothermal reservoir and the second is based on the model of the deep circulation system at Kakkonda published by Hanano. We find that when a reservoir experiences BPD conditions during part of its lifetime the lower reservoir becomes impermeable and a hydrothermal circulation system is only present in the upper part of the reservoir.     

裂缝性低渗透油藏流固耦合渗流分析

在低渗透油田的开发过程中，油藏流体渗流和储层岩土之间存在明显的耦合作用。本文首先研究给出了低渗裂缝性储层孔渗参数的等效方法，然后将渗流力学和岩土力学相结合，给出了低渗透裂缝性储层流固耦合渗流的数学模型，该模型不仅可以反映基质孔渗参数在开发中的变化，而且更能反映裂缝开度变化所引起的渗透率变化，而这对于低渗透裂缝性油田而言十分重要。最后对一实际井网进行了流固耦合油藏数值模拟，给出了开发过程中孔渗参数的变化及其耦合效应对油田开发的影响．     

页岩气藏的双重介质-离散裂缝模型

考虑页岩气藏开发中渗流的多尺度效应,提出了一个基于裂缝-孔隙双重介质的离散裂缝模型．在该模型中,基质、天然裂缝和人工压裂裂缝采用各自控制方程独立计算,不同介质之间通过流量交换相互关联．为分析模型可靠性,分别和基于渗透率粗化及压裂裂缝导流能力无穷大的模型对比．数值算例显示,伴随着网格细分,该模型与精确渗透率粗化模型具有相同计算精度,两者收敛速度均较快,但该模型易推广到多相流动问题,而等压模型对产量将有所高估．研究了地质参数和工艺参数对气井产量的影响规律．计算结果表明天然裂缝渗透率及基质孔隙扩散系数对产气速率有着重要影响,产气速率伴随着人工压裂裂缝导流能力、长度以及数目的增加而增加,但是增加幅度会逐步趋缓．     

缝洞型油藏三维离散缝洞数值试井模型

缝洞型碳酸盐岩油藏发育着大尺度的溶洞和裂缝,非均质性极强,缝洞型碳酸盐岩油藏问题的研究成为了世界级难题之一.由于大尺度溶洞和裂缝对储层的流体流动起主导作用,因此,基于连续介质理论的双重介质或三重介质模型已不适合其中流体流动的描述.根据大型缝洞分布地质特征,探索性地提出了一种板块组合的复合架构离散缝洞模型描述该类油藏中的流体流动,将三维空间大裂缝用板块描述,溶洞用高渗透率和高孔隙度不规则多面体团块描述.将裂缝面用二维三角形单元离散, 溶洞和基质用三维四面体离散, 利用三维混合单元有限元法对建立的不定常渗流模型进行求解,得到了三维渗流条件下的试井理论曲线及压力场分布.通过对试井理论曲线特征的分析, 获得了各敏感参数对试井曲线的影响规律.通过对1口井的实际测试资料解释结果的分析,并与实际地震反射资料及生产实际资料的对比,发现本文所建立的模型可以较好地反映裂缝和溶洞的地质动态状况,并与实际生产状况具有较好的一致性.这一结果说明了所建模型的正确性以及测试资料分析结果的可靠性.      

A Semi-analytical Model for Pressure-Dependent Permeability of Tight Sandstone Reservoirs

In tight gas reservoirs, permeability is pressure dependent owing to pore pressure reduction during the life of the reservoir. Empirical models are commonly used to describe pressure-dependent permeability. In this paper, it was discussed a number of issues which centered around tight sandstone pressure-dependent permeability experiment, first to apply core aging on permeability test and then to develop a new semi-analytical model to predict permeability. In tight sandstone permeability test experiment, the microinterstice between core and sleeves resulted in over estimation of dependency of permeability on pressure. Then, a new semi-analytical model was developed to identify the relation between permeability and fluid pressure in tight sandstone, which indicates there is a linear relation between pore pressure changes and the inverse of permeability to a constant power. Pressure-dependent permeability of 8 tight sandstone core samples from Ordos Basin, China, was obtained using the modified procedure, and results were perfectly matched with the proposed model. Meanwhile, the semi-analytical model was also verified by pressure-dependent permeability of 16 cores in the literature and experiment results of these 24 cores were matched by empirical models and the semi-analytical model. Compared with regression result of commonly used empirical models, the semi-analytical model outperforms the current empirical models on 8 cores from our experiment and 16 cores from the literature. The model verification also indicates that the semi-theoretical model can match the pressure-dependent permeability of different rock types. In addition, the permeability performance under reservoir condition is discussed, which is divided into two stages. In most tight gas reservoirs, the permeability performance during production is located in stage II. The evaluation result with proposed experiment procedure and the stress condition in stage II will reduce permeability sensitivity to stress.     

储层微观参数对宏观参数影响的网络模拟研究

储层宏观参数是储层微观参数的宏观体现.以孔隙度、绝对渗透率、相对渗透率等宏观参数作为约束条件,拟合生成网络模拟模型,在此基础上讨论了孔喉半径、喉道半径均质系数、孔喉比、孔喉润湿性、孔喉形状和配位数等微观参数的变化对孔隙度、绝对渗透率和相对渗透率等宏观参数的影响.在影响因素敏感性分析的基础上,确定了引起储层宏观参数变化的...     

Co-history Matching: A Way Forward for Estimating Representative Saturation Functions

Core-scale experiments and analyses would often lead to estimation of saturation functions (relative permeability and capillary pressure). However, despite previous attempts on developing analytical and numerical methods, the estimated flow functions may not be representative of coreflood experiments when it comes to predicting similar experiments due to non-uniqueness issues of inverse problems. In this work, a novel approach was developed for estimation of relative permeability and capillary pressure simultaneously using the results of “multiple” corefloods together, which is called “co-history matching.” To examine this methodology, a synthetic (numerical) model was considered using core properties obtained from pore network model. The outcome was satisfactorily similar to original saturation functions. Also, two real coreflood experiments were performed where water at high and low rates were injected under reservoir conditions (live fluid systems) using a carbonate reservoir core. The results indicated that the profiles of oil recovery and differential pressure (dP) would be significantly affected by injection rate scenarios in non-water wet systems. The outcome of co-history matching could indicate that, one set of relative permeability and capillary pressure curves can reproduce the experimental data for all corefloods.     

Analytical Solution to Subsurface Air Pressure in a Three-Layer Unsaturated Zone with Atmospheric Pressure Changes

In this study, a solution to one-dimensional vertical airflow induced by the time-dependent atmospheric pressure fluctuations is developed in a three-layer unsaturated zone. The discrete atmospheric pressure data are transformed into a continuous boundary condition using the Fourier series analysis. The solution is applied to interpret the field air pressure data in a three-layer unsaturated zone reported in previous studies. The new solution improves the previous solution by reducing the required data measurement and input. The new solution is found to be accurate enough for the purpose of this study by comparing with a numerical solution developed in COMSOL Multiphysics. Given the necessary hydrogeological parameters, the new solution is capable of calculating the air permeability of each layer above a specified depth where the air pressures are known. Sensitivity analysis of the new solution shows that location, thickness, and air permeability of the less permeable layer impose large influence on the propagation of the atmospheric pressure fluctuations. Variations of air-filled porosity in soil layers in/below the less permeable layer may lead to greater amplitude attenuation and phase lag of air pressure than those in soil layers above the less permeable layer.     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

Numerical characterization of micro heat exchangers using experimentally tested porous aluminum layers

A microporous heat exchanger device is being developed for cooling high-power electronics. The device uses a mechanically compressed aluminum porous layer to improve the heat transfer at the coolant/solid interface and to provide more uniform cooling of the electronics. The hydraulic characteristics (porosity, permeability, and Forchheimer coefficient) of nine distinct compressed layers are obtained experimentally. These layers have porosity from 0.3 to 0.7 and permeability from 1.8 × 10⁻¹⁰ m2 to 1.2 × 10⁻⁹ m2. The inertia coefficient varies from 0.3 to 0.9. These hydraulic characteristics are used in the numerical simulations of a real microporous heat exchanger for cooling phased-array radars in development. Thermal and hydraulic performances are illustrated in terms of total pressure drop across the heat exchanger, maximum temperature difference in the direction transverse to the electronic modules, and maximum temperature within the coolant passage. Results indicate that the proposed design is capable of achieving a maximum transverse temperature difference of 2°C using polyalphaolephin as coolant.     

Experimental Study of Fracture Permeability for Stimulated Reservoir Volume (SRV) in Shale Formation

“Stimulated reservoir volume”(SRV) makes shale gas production economic through new completion techniques including horizontal wells and multiple hydraulic fractures. However, the mechanism behind these treatments that provide sufficient permeability is not well understood. The effects of different stimulation treatments need to be further explored. To understand the effects of fracture surface roughness, fracture registration, confining pressure, proppant type and distribution mode, fiber and acidizing treatment on fracture permeability, a series of laboratory permeability experiments were performed on fractured cores from shale formation of Shengli Oilfield. The results of this study demonstrate that sedimentary bedding of shale has important influence on matrix permeability. At 35 MPa confining pressure, the permeability of aligned fracture (unpropped and without fracture offset) can increase about 1–3 orders of magnitude over shale matrix. The permeability of displaced fracture can increase about 1–2 orders of magnitude over the aligned fracture. The permeability of fracture propped with proppant can increase about 2–4 orders of magnitude over unpropped fracture. The greater the fracture surface roughness, the higher the permeability. The increasing degree of displaced fracture permeability is not proportional to the amount of fracture offset. In the microfracture of shale, the effect of ceramic proppant is still better than that of quartz sand, and the permeability of a centralized fairway distribution of proppant is about 1.2 times better than an even monolayer distribution of proppant. Under high pressure, proppant is easy to cause the break of fracture faces of brittle shale, and increase local fracture permeability to some extent. However, quartz sand are more easily broken to embed and block microcracks just made, which results in fracture permeability lower than that of ceramic proppant. At the same time, the argillation phenomenon is easy to happen on propped fracture faces of shale, which is one of the main factors that leads to a substantial decline in fracture permeability. The permeability of displaced fracture propped with proppant is greater than that of aligned fracture propped with proppant. Because of added fiber presence, the permeability of microfractures presented in SRV is greatly reduced. The pressure dependence of aligned fractures in shale obeys Walsh’s theory, but the pressure dependence of propped and displaced fractures in shale obeys Walsh’s law over a limited range of pressures. Deviations reflect proppant seating, proppant embedding and breaking. For shale formation with the high carbonate content, acidizing treatment should be carefully implemented. Experimental results may provide more valuable information for effective design of hydraulic fracturing in shale reservoir.