Horizontal Permeability Anisotropy Research Articles

Analyzing the relationship between doublet lifetime and thermal breakthrough at the Dogger geothermal exploitation site in the Paris basin using a coupled mixed-hybrid finite element model

Reinjection of produced water is a critical aspect of managing geothermal reservoirs. The sustainability of extracted thermal energy relies on the performance of well doublets, which in turn is linked to the hydrothermal properties of the reservoir, the thermal characteristics of confining layers, and operating conditions. This study presents an advanced mixed-hybrid finite element simulator that solves coupled hydrothermal equations on unstructured grids. The model is favorably compared with the conforming finite element method at a geothermal power plant site that exploits the Dogger reservoir in the Paris basin. The study also includes a parametric sensitivity analysis, using an ensemble simulation to assess doublet lifetime, thermal breakthrough, and their ratio as performance metrics. Our findings emphasize the significant influence of horizontal permeability anisotropy and production flow rate on doublet performance, with doublet orientation relative to the principal axes of the areal permeability tensor as a key control parameter. Other influential factors include the thermal conductivity of the confining beds, while longitudinal thermal dispersivity and the total productive thickness of the reservoir are less critical. We establish, for the first time, a simple relationship between doublet lifetime and thermal breakthrough, indicating that the former is twice as long as the latter. This underscores the importance of long-term monitoring to sustain geothermal exploitation. This relationship can inform enhanced management of the Dogger reservoir at the basin scale.

Effects of vertical anisotropy on optimization of multilateral well geometry

Multilateral wells have been increasingly used in recent years by different industries such as the oil- and gas industry (incl. coal-bed methane (CBM)) and geothermal energy production. The common purpose of these wells in the oil industry and partially in the geothermal industry is to achieve a higher production rate per well without increasing the hydraulic gradient significantly. In geothermal systems the ultimate objective is to improve heat extraction performance by enhancing productivity but also by increasing the heat transfer area. Optimal design of multilateral wells has been the focus of numerous publications in CBM and unconventional oil- and gas production, but as a result of cross-fertilization and technology-transfer among different sectors in the energy industry in the last few years, the focus of research on multilateral wells has turned to enhanced geothermal systems (EGS). Recently, several papers have been published on the use of multilateral wells in deep geothermal reservoirs. Coaxial closed-loop geothermal systems with multilateral wells utilize only the increased heat transfer area due to the laterals while EGS's with multilateral injection and production wells also benefit from the hydrodynamic advantages of such well configurations. However, substantial emphasis is – understandably – placed on the effect of artificial and natural fracture networks of EGS reservoirs and less focus is devoted to the impact of vertical permeability anisotropy which can seriously influence the flow pattern of a given configuration. Similarly, in CBM-related studies, the effect of horizontal permeability anisotropy along the face cleats to the butt cleats on multilateral well-design was investigated and vertical permeability anisotropy was not considered. In the current work we present a generalized approach for evaluating the effects of vertical permeability anisotropy on multilateral well geometry by numerical hydrodynamic modelling in an idealized, homogeneous hydrogeological setting. Current paper proposes an alternative modelling approach for representing the non-horizontal branches of multilateral wells by introducing a thin layer for the laterals with the same inclination as the well branches. This approach is then is used to investigate the effect of anisotropy on the flow pattern and near-wellbore drawdown and hydraulic gradient in the case of different branch deviations. Results suggest that the benefits of highly deviated or horizontal laterals emerge when vertical anisotropy is high. Evaluation of branch deviation vs. anisotropy indicates that above approx. 60° there is no significant benefit in increasing deviation which implies that very highly deviated or horizontal laterals might not necessarily pay off the associated technical challenges and extra costs.

Improving the geological and hydrodynamic model of a carbonate oil object by taking into account the permeability anisotropy parameter

Significant share of the developed oil assets related to carbonate complex-built objects has formidably increased in Russia, including the Perm Region. Reliable knowledge of the parameters for the cavern-pore type of the reservoir allows clarifying the existing geological and hydrodynamic models (GHM), selecting a rational development system, regulating the development processes and providing optimal geological and technical measures for this formation. In the construction and adaptation of GHM for oil fields, especially those related to complex-built carbonate reservoirs, knowledge of both horizontal and vertical permeability (anisotropy parameter) is important. When creating GHM of carbonate objects in Perm Region deposits, vertical permeability is often taken to be zero, although this is far from being the case. Determining the vertical permeability (anisotropy parameter), its dynamics when changing the formation and bottomhole pressures and using it in GHM is an urgent task that will improve the quality and reliability of using digital models to calculate and predict the oil production process.
 Article describes the methodology for determining permeability anisotropy according to the interpretation of hydrodynamic investigations of wells. Proposed methodology for determining the anisotropy parameter processed the results of more than 200 studies conducted on production and injection wells of the Famennian deposit at the Gagarinskoye field. For each lithological-facies zone, dependence of the permeability anisotropy index on the bottomhole pressure is constructed. To predict and evaluate the effectiveness of the applied geological and technical measures and technological development indicators, author modified the geological and hydrodynamic model taking into account the obtained dependencies on the change in the anisotropy parameter.
 Using a modified hydrodynamic model, it was possible to significantly improve the adaptation of both production and injection wells. Thus, the quality and reliability of the digital model of the Famennian deposit at the Gagarinskoye field for calculating and predicting the oil production process has improved.

УЧЕТ ПАРАМЕТРА АНИЗОТРОПИИ ПРОНИЦАЕМОСТИ В ГЕОЛОГО-ГИДРОДИНАМИЧЕСКИХ МОДЕЛЯХ КАРБОНАТНЫХ ОБЪЕКТОВ (НА ПРИМЕРЕ ГАГАРИНСКОГО МЕСТОРОЖДЕНИЯ)

Актуальность работы. Значительная доля разрабатываемых нефтяных активов, приуроченных к карбонатным сложнопостроенным объектам, заметно возросла как на территории России, так и в Пермском крае. Достоверное знание параметров трещинно-порового типа коллектора позволяет уточнить действующие геолого-гидродинамические модели, подобрать рациональную систему разработки, регулировать процессы разработки и обеспечить для данного пласта оптимальные геолого-технические мероприятия. При построении и адаптации геолого-гидродинамических моделей нефтяных месторождений, особенно относящихся к сложнопостроенным карбонатным коллекторам, важное значение имеет знание как горизонтальной, так и вертикальной проницаемости (параметра анизотропии). При создании геолого-гидродинамических моделей карбонатных объектов месторождений Пермского края зачастую вертикальную проницаемость принимают равной нулю, хотя это далеко не так. Определение вертикальной проницаемости (параметра анизотропии), ее динамика при изменении пластового и забойного давлений и использование в геолого-гидродинамических моделях является актуальной задачей, которая позволит повысить качество и достоверность использования цифровых моделей для расчета и прогнозирования процесса добычи нефти. Цель: совершенствование геолого-гидродинамических моделей с учетом использования показателя анизотропии проницаемости. Объект: карбонатная фаменская залежь Гагаринского месторождения. Методы:обработка данных геолого-промысловых исследований; использование гидродинамического симулятораTempest версии 8.3.1 компании Roxar. Результаты. По предложенной в статье методике определения параметра анизотропии обработаны 252 исследования, проведенные на добывающих и нагнетательных скважинах фаменской залежи Гагаринского месторождения. Для каждой литолого-фациальной зоны построена зависимость показателя анизотропии проницаемости от забойного давления. Для прогнозирования и оценки эффективности применяемых геолого-технических мероприятий и технологических показателей разработки авторами статьи модифицирована геолого-гидродинамическая модель с учетом полученных зависимостей об изменении параметра анизотропии. С помощью модифицированной гидродинамической модели удалось значительно улучшить адаптацию как по добывающим, так и по нагнетательным скважинам. Таким образом, повысилось качество и достоверность цифровой модели фаменской залежи Гагаринского месторождения для расчетов и прогнозирования процесса добычи нефти.

Analysis of Spatial Distribution Pattern of Reservoir Petrophysical Properties for Horizontal Well Performance Evaluation-A Case Study of Reservoir X

Introduction:Building a large number of static models to analyze reservoir performance is vital in reservoir development planning. For the purpose of maximizing oil recovery, reservoir behavior must be modelled properly to predict its performance. This requires the study of the variation of the reservoir petrophysical properties as a function of spatial location.Methods:In recent times, the method used to analyze reservoir behavior is the use of reservoir simulation. Hence, this study seeks to analyze the spatial distribution pattern of reservoir petrophysical properties such as porosity, permeability, thickness, saturation and ascertain its effect on cumulative oil production. Geostatistical techniques were used to distribute the petrophysical properties in building a 2D static model of the reservoir and construction of dynamic model to analyze reservoir performance. Vertical to horizontal permeability anisotropy ratio affects horizontal wells drilled in the 2D static reservoir. The performance of the horizontal wells appeared to be increasing steadily as kv/kh increases. At kv/kh value of 0.55, a higher cumulative oil production was observed compared to a kv/kh ratio of 0.4, 0.2, and 0.1. In addition, horizontal well length significantly affects cumulative oil production of the petroleum reservoir studied.Results:At kv/kh of 0.55, the results of the analysis showed a rapid decrement in cumulative oil production as the horizontal well length decreases. Considering horizontal well length of 3000 ft, 2000 ft, and 1500 ft, a minimum cumulative oil production was obtained from a horizontal well length of 1500 ft.Conclusion:The geostatistical and reservoir simulation methods employed in this study will serve as an insight in analyzing horizontal well performance.

Well-flow behavior of reorientation fracture considering permeability anisotropy

PurposeIn petroleum industry, hydraulic fracturing is essential to enhance oil productivity. The hydraulic fractures are usually generated in the process of hydraulic fracturing. Although some mathematical models were proposed to analyze the well-flow behavior of conventional fracture, there are few models to depict unconventional fracture like reorientation fracture. To figure out the effect of reorientation fracture on production enhancement and guide the further on-site operating, this paper aims to investigate the well-flow behavior of vertical reorientation fracture in horizontal permeability anisotropic reservoir.Design/methodology/approachBased on the governing equation considering horizontal permeability anisotropy, the mathematical models for reorientation fractures in infinite reservoir are developed by using the principle of superposition. Furthermore, a rectangular closed drainage area is also considered to investigate the well-flow behavior of reorientation fracture, and the mathematical models are developed by using Green’s and source functions.FindingsComputational results indicate that the flux distribution of infinite conductivity fracture is uniform at very early times. After a period, it will stabilize eventually. High permeability anisotropy and small inclination angle of reorientation will cause significant end point effect in the infinite conductivity fracture. The reorientation fractures with small inclination angle in high anisotropic reservoir are capable of improving 1-1.5 times more oil productivity in total.Originality/valueThis paper develops the mathematical methods to study the well-flow behavior for unconventional fracture, especially for reorientation fracture. The results validate the production enhancement effect of reorientation fracture and identify the sensitive parameters of productivity.

Permeability evolution of anthracite coal considering true triaxial stress conditions and structural anisotropy

It is critical to understand the gas flow behavior in coal under a reservoir stress condition for coal bed methane production, underground coal mining, and CO2-sequestration in deep coal seams. With respect to coal seams, the in-situ stress is anisotropic and generally exists under true triaxial stress (σ1 > σ2 > σ3) conditions. Additionally, the flow channels determining the permeability of coal are also anisotropic. This dual anisotropy produces difficulties in replicating the gas transport characteristics of coal at the laboratory scale, and there is a paucity of relevant studies. In this study, we performed a series of permeability measurements using cubic anthracite coal samples and changing the principal stresses and flow directions under various true triaxial stress conditions. The coal permeability exhibited greater anisotropy in the vertical direction as a result of the presence of minerals in cleats across the bedding plane. After each principal stress compression at a differential stress of 20 MPa, the permeability in each direction decreased by an order of magnitude. With an increase in the intermediate stress parameter, the permeability values of two horizontal cleats experienced higher decreasing rates compared with the vertical bedding permeability. This increased the significance of the horizontal permeability anisotropy. With respect to the true triaxial stress condition with a higher horizontal principal stress (σH > σh > σv), a higher permeability reduction was observed during the principal stress loading period. The butt cleat plane was more sensitive to changes in the principal stress because of the lower connectivity of the flow channels induced by the closure of the face cleat that acted as a cross-linked pathway. The anisotropic permeability data measured under true triaxial stress conditions were well expressed by an exponential equation containing different mean cleat compressibility and stress terms. The cleat compressibility values in different directions were obtained by data fitting.

Pressure-transient analysis for a vertically fractured well at an arbitrary azimuth in a rectangular anisotropic reservoir

The principal focus of this paper is on pressure-transient analysis for a finite-conductivity fracture at an arbitrary azimuth in a rectangular anisotropic reservoir. An analytical solution is derived by spatial integration of point-source along the direction of the fracture for a fracture at an arbitrary azimuth in a rectangular reservoir. Furthermore, type curves are generated to investigate the influence of the main parameters on transient pressure behavior, including permeability anisotropy, azimuth of the fracture, reservoir's outer boundary, and fracture conductivity. Strong effects of horizontal permeability anisotropy and azimuth of a fracture on transient responses can be observed. The more the fracture deviates from the direction of maximum horizontal permeability, lesser the drawdown needed to maintain constant flow rate. Therefore, it seems that the optimum orientation for the hydraulic fracture is perpendicular to the direction of maximum horizontal permeability. Outer boundary size dominates pseudo-steady-state flow and aspect ratio mainly affects the periods of radial flow and compound-linear flow. The existence and duration of bilinear flow and formation linear flow are mainly determined by dimensionless fracture conductivity. This paper provides a theoretical basis for well pattern deployment and fracture configuration in anisotropic reservoirs.

Effect of heterogeneity on the productivity of vertical, deviated and horizontal wells in water drive gas reservoirs

Gas recovery from water drive gas reservoirs depends on many engineering and geologic factors. Type of well completion, reservoir heterogeneity and layering pattern are typical factors which determine the ultimate gas recovery. This paper presents the effect of heterogeneity on performance of water drive gas reservoirs by considering recovery factor and cumulative water production. In this regard, Design of Experiments (DOE) and Response Surface Methodology (RSM) are used to investigate the simultaneous effect of effective parameters using a reservoir simulation model. Box–Behnken design (BBD) is applied to implement reservoir simulator. Factors that have been inspected include well inclination angle (Ө), layers permeability distribution (LPD), geometric mean of reservoir horizontal permeability (KG), permeability anisotropy (Kv/Kh), production rate (Qg) and level of heterogeneity in terms of Dykstra–Parsons coefficient (VDP). Three different permeability distribution of increasing downward, random and increasing upward have been considered. In simulation tests with systematic distribution of increasing upward, the permeability of layers increases within lower part towards the upper layer. However in cases with systematic distribution of increasing downward, the layers permeability increases from upper to the bottom layer of the model. Also in random distribution, the layers have random values of permeability.Results indicate that distribution of layers permeability controls the effect of other factors on water drive gas reservoirs performance. For random and systematic distribution of increasing upward, three factors namely geometric mean of reservoir horizontal permeability, permeability anisotropy and level of heterogeneity play an important role on gas productivity. In terms of contribution to total variance, level of heterogeneity for random and increasing upward distribution cases has effect of 3.7% and 41.7% respectively. Increasing level of heterogeneity increases recovery factor by 8.6%–16.2% for the base case. However, in the case of systematic distribution of increasing downward, the level of heterogeneity has very weak effect on objective functions and, could be truly ignored during reservoir performance predictions.

A Novel Integrated Approach to Modelling of Depletion-Induced Change in Full Permeability Tensor of Naturally Fractured Reservoirs

More than half of all hydrocarbon reservoirs are Naturally Fractured Reservoirs (NFRs), in which production forecasting is a complicated function of fluid flow in a fracture-matrix system. Modelling of fluid flow in NFRs is challenging due to formation heterogeneity and anisotropy. Stress sensitivity and depletion effect on already-complex reservoir permeability add to the sophistication. Horizontal permeability anisotropy and stress sensitivity are often ignored or inaccurately taken into account when simulating fluid flow in NFRs. The aim of this paper is to present an integrated approach for evaluating the dynamic and true anisotropic nature of permeability in naturally fractured reservoirs. Among other features, this approach considers the effect of reservoir depletion on reservoir permeability tensor, allowing more realistic production forecasts. In this approach the NFR is discretized into grids for which an analytical model yields full permeability tensors. Then, fluid flow is modelled using the finite-element method to obtain pore-pressure distribution within the reservoir. Next, another analytical model evaluates the change in the aperture of individual fractures as a function of effective stress and rock mechanical properties. The permeability tensor of each grid is then updated based on the apertures obtained for the current time step. The integrated model proceeds according to the next prescribed time increments.

Integrated reservoir characterization and simulation of a shallow, light-oil, low-temperature reservoir: Umiat field, National Petroleum Reserve, Alaska

Umiat field in northern Alaska is a shallow, light-oil accumulation with an estimated original oil in place of more than 1.5 billion bbl and 99 bcf associated gas. The field, discovered in 1946, was never considered viable because it is shallow, in permafrost, and far from any infrastructure. Modern drilling and production techniques now make Umiat a more attractive target if the behavior of a rock, ice, and light oil system at low pressure can be understood and simulated. The Umiat reservoir consists of shoreface and deltaic sandstones of the Cretaceous Nanushuk Formation deformed by a thrust-related anticline. Depositional environment imparts a strong vertical and horizontal permeability anisotropy to the reservoir that may be further complicated by diagenesis and open natural fractures. Experimental and theoretical studies indicate that there is a significant reduction in the relative permeability of oil in the presence of ice, with a maximum reduction when connate water is fresh and less reduction when water is saline. A representative Umiat oil sample was reconstituted by comparing the composition of a severely weathered Umiat fluid to a theoretical Umiat fluid composition derived using the Pedersen method. This sample was then used to determine fluid properties at reservoir conditions such as bubble point pressure, viscosity, and density. These geologic and engineering data were integrated into a simulation model that indicate recoveries of 12%–15% can be achieved over a 50-yr production period using cold gas injection from five well pads with a wagon-wheel configuration of multilateral wells.

Chemo-poroelastic analysis of pore pressure and stress distribution around a wellbore in swelling shale: effect of undrained response and horizontal permeability anisotropy

The aim of this paper is to study the effect of undrained response and horizontal permeability anisotropy on transient changes in pore pressure and stress state of surrounding area to wellbores drilled in swelling shales. For this purpose a finite element model of coupled chemo-hydro-mechanical processes is developed and used. Super convergent patch recovery method is employed to accurately evaluate time dependent stress tensor. From the results of this study it was found that at any time and radial position around the wellbore, change in pore pressure, thus effective stress, depends on horizontal permeability anisotropy, which influences three main contributing processes namely hydraulic flow, chemical effect and undrained response. It was also revealed that at a given time after shale is exposed to the mud, maximum change in pore pressure, thus in effective stress, can take place at different radial distances from the wellbore along different directions due to permeability anisotropy.

An Enhanced Potential Fluid Theory Approach for Horizontal-well Productivity Calculations

Horizontal wells have emerged as a new alternative to vertical wells for optimal reservoir exploitation. The vertical to horizontal permeability anisotropy is a crucial variable in deciding which configuration can provide the best performance. This work presents the derivation of an improved equation using potential-fluid theory to calculate the productivity of horizontal wells. Furthermore, a production potential assessment of horizontal wells in comparison to vertical wells by productivity indices using the proposed equation is presented. The results show that a horizontal well could produce oil at a rate two to six times greater than an unstimulated vertical well, assuming the same pressure drawdown.

Horizontal permeability anisotropy: Effect upon the evaluation and design of primary and secondary hydraulic fracture treatments in tight gas reservoirs

Numerous field trials have shown that fracturing and refracturing of tight sands have improved the economics of gas production from these reservoirs. In order to evaluate and design hydraulic stimulation in these reservoirs, it is essential to implement a holistic approach in which conducting a secondary fracture treatment after a primary production period from an initial hydraulic fracture is considered as an option. In such an approach, the optimal design is determined based on the combined performance of primary and secondary hydraulic fractures. In this paper we show that horizontal permeability anisotropy significantly affects productivity of both fracture and refracture as well as the potential length of a re-oriented secondary fracture and the optimal time for refracture treatment. For this purpose a numerical model is used to simulate fully coupled gas flow and stress changes from a hydraulically fractured and refractured tight gas reservoir. Results of this study have shown that horizontal permeability anisotropy is a key parameter in the holistic design of hydraulic fracture treatment. In particular, results of this study show that refracture treatment has a high potential to increase production when parallel component of horizontal permeability to the primary fracture is greater than the orthogonal component. We have also shown that horizontal permeability anisotropy controls the optimal time for conducting refracture treatment.

Determination of horizontal permeability from the elliptical flow of horizontal wells using conventional analysis

Besides the regular four flow regimes normally seen during a pressure test of horizontal wells, it is possible, under special circumstances, to observe such additional flow regimes as spherical, hemi-radial, linear (reservoir channel) and elliptical. The last flow regime is characterized by a slope of 0.36 of the pressure derivative curve and occurs between the early linear flow and the pseudo-radial flow periods. This may have been overlooked in horizontal well test analysis, because it is often masked by the other flow regimes, unless the conditions are just right. The elliptical flow regime has been previously mentioned by very few researchers, Issaka et al. [Issaka, M.B., Zaoral, K., Ambastha, A.K. and Mattar, L., 2000: “Determination of Horizontal Permeability Anisotropy from Horizontal Well Tests,” SPE Saudi Arabia Section Technical Symposium, Dhahran, Saudi Arabia, 21–23 October.], Chacon et al. [Chacon, A., Djebrouni, A. and Tiab, D., 2004. “Determining the Average Reservoir Pressure from Vertical and Horizontal Well Test Analysis Using Tiab's Direct Synthesis Technique”. SPE 88619, Proceedings, SPE Asia Pacific Oil & Gas Conf. & Exhibition, Perth, Australia, 18–20 October.] and Escobar et al. [Escobar, F.H., Munoz, O.F., and Sepulveda, J.A., 2004. “Horizontal Permeability Determination from the Elliptical Flow Regime for Horizontal Wells”. CT&F — Ciencia, Tecnología y Futuro. Vol. 2 Num. 5. p. 83–95. Dec.]. A methodology for its characterization has been also introduced using the pressure derivative concept and TDS technique [Escobar, F.H., Munoz, O.F., and Sepulveda, J.A., 2004. “Horizontal Permeability Determination from the Elliptical Flow Regime for Horizontal Wells”. CT&F — Ciencia, Tecnología y Futuro. Vol. 2 Num. 5. p. 83–95. Dec.]. However, conventional analysis for the characterization of this has not yet been reported in the literature. This flow regime is very useful to estimate the horizontal permeability, especially, when the pseudo-radial flow is very short or unclear, or simply, when it is desired to verify that estimation. In this paper, equations for the estimation of the horizontal permeability and elliptical skin factor are developed for both gas and oil horizontal wells, so that the mentioned parameters can be estimated, respectively, from the slope and intercept of linear plot of pressure versus time to the power 0.36. The equations were successfully tested with two field examples previously worked in the literature.

The winds of change

Editor's note: This article is the first of two parts that together form an abbreviated version of the Fall 2004 SEG/AAPG Distinguished Lecture. A PowerPoint presentation of this material is posted on the SEG Web site. “The winds of change” refer to much more than just anisotropic rocks whose seismic anisotropy provides insight into horizontal permeability anisotropy. The way we view our planet is changing. The planet is now being studied as the interaction of four interlocking systems—the hydro-sphere, the atmosphere, the lithosphere, and the biosphere—as all absorb energy from our sun and change. The planet and all its subsystems, like geology or climate, are explicitly evaluated as interdependent and interacting within the context of the local community. The heterogeneity at the surface of our planet and the recycling of compounds and elements (water, nitrogen, sulfur, etc.) enable our planet to support life. My earth science career has spanned two revolutions: the plate-tectonic revolution during the 1970s, and today's profound reevaluation of “how our planet works” and our roles as planet-dwellers. The rocks that are the primary focus of most of our studies are best understood as, firstly, the result of the interactions of the climate, the water conditions, the depositional setting, the biosphere, and the provenance of the sediments, and secondly, the lithification and geologic history they have undergone. The biosphere shows up in our rocks both as fossils (a key means of dating rocks!) and as liquid or solid organic remains. We understand any given stratigraphic facies in the context of its spatial neighbors—its community—and its plate-tectonic setting. The climate includes the actions of gravity, sunlight, and atmosphere, but it is affected by where the land masses are and how they are linked together. Oil industry geoscientists are uniquely placed, via access to important data and sophisticated tools, …

Analytical And Statistical Analyses of Pseudo Skin Factors For Horizontal Wells

Abstract The pressure behaviour of horizontal wells in bounded anisotropic reservoirs has been investigated in this paper. New equations for calculating the effective length of the horizontal well, mechanical skin factor, shape factor, and productivity index of horizontal wells are presented. It is determined that the performance of a horizontal well of half-length Xf1 with mechanical skin can be replaced by the performance of an equivalent horizontal well of half-length Xf2 with no mechanical skin. The statistical analysis showed that pseudo skin factor for a horizontal well in a given drainage area can be directly correlated with formation thickness, and natural logarithms of horizontal well half-length and permeability anisotropy. These statistical correlations can easily be used to predict skin damage around horizontal wellbores, to evaluate stimulation treatment of horizontal wells, and to compare their performance with unstimulated vertical wells without the need to use complex numerical and/or analytical solutions which require extensive computer use. Introduction The growing interest in field development using horizontal well drilling necessitates development of new concepts for improved performance prediction of these wells. To predict the productivity index of horizontal wells requires the determination of the pressure drop due to formation damage around such wells. Long duration of formation exposure to drilling fluids may be the main reason for the unexpected failure of some horizontal wells(1, 2) drilled in favourable reservoirs. The combined effect of the formation damage and the presence of impermeable barriers and low permeability regions in the vicinity of some sections of the horizontal wellbore will manifest itself as mechanical skin damage in well test analysis if the total drilled (or perforated) length of the horizontal section is used in the calculations. The total skin factor obtained from a well test is the summation of the mechanical skin factor and pseudo skin factor. The purpose of this paper is to present new analytical equations for calculating pseudo skin factor and mechanical skin factor for horizontal wells during the unsteady state and pseudo steady state flow periods. The ne\v equations can be used to determine:the fraction of horizontal well length contributing to unrestricted production, andhorizontal well productivity index based on the equivalent non-damaged length of the horizontal wellbore. Furthermore, statistical correlations for pseudo skin factor, mechanical skin factor, and the fraction of horizontal well length contributing to unrestricted production are presented that can be used to evaluate the performance of horizontal wells without the need to use complex numerical and/or analytical solutions. Determination of Horizontal Well Productivity Index Malekzadeh and Abdelgawad(3) presented the dimensionless wellbore pressure, pseudo skin factor, and effective horizontal well length for horizontal wells in bounded anisotropic reservoirs, shown in Figure 1, as: Equation 1 (available in full paper) where the dimensionless parameters are defined as: Equation 2–12 (available in full paper) The late time approximation to the full solution, Equation (1) was derived as(3): Equation 13 (available in full paper)

Effect of In Situ Stress and Production-Induced Changes in Stress on Permeability of Naturally Fractured Reservoirs: ABSTRACT

Fractures are present in almost all hydrocarbon reservoirs, but it is only when fractures form an interconnected network that their effect on fluid flow becomes important. Fractures not only enhance the overall permeability of many reservoirs, they also create significant permeability anisotropy. Knowledge of the orientation and magnitude of permeability anisotropy has major economic importance in developing and managing a reservoir. It is commonly assumed that the horizontal permeability anisotropy of a naturally fractured reservoir will be elongate along the dominant trend of subsurface natural fracture systems. Although this can be demonstrated to apply in many simple geologic settings, this predictive concept must commonly be modified for stress changes caused by post-fracture geologic history of the reservoir, including local variations in stress magnitude and orientation caused by structures. In cases where the local stresses and fractures are superimposed on regional stresses and fractures, the fractures that are parallel to the in situ maximum horizontal stress may provide the dominant control on reservoir permeability anisotropy. Fracture reservoir permeability may also change over the life of a reservoir because peturbations in stress state, caused by drilling, production, and waterflood activities, create changes in the three-dimensional effective stress field, and thus in fracturemore » conductivity. High angle fractures aligned with the local maximum horizontal stress will have the smallest decline in conductivity as the reservoir is produced. These conclusions are supported by core analyses, in situ stress measurements, well tests, and production histories of clastic and carbonate reservoirs.« less

Horizontal Permeability Anisotropy Developed from the Upscaling of Anisotropic Facies Patterns: ABSTRACT

Traditionally, the size and shape of grid blocks owe more to the limitations of numerical simulation procedures than to any consideration of geological heterogeneity. Geological systems, and hence associated permeability and porosity fields, are inherently complex, being characterized by nested levels of heterogeneity. Moreover, for directionally dependent variables, such as permeability, a heterogeneous nature at small scales will lead directly to anisotropy in average (or measured) values at larger scales. The representation of geologically complex volumes as individual horizontal and vertical permeability values has long been recognized as a necessary simplification. Recent advances in stochastic modeling have vastly improved the representation of complex geology in unknown interwell regions. The high level of detail provided by such models often requires several million grid blocks. This degree of detail cannot, however, be used in flow simulations, and hence, scaling up is necessary. The difficulties in scaling up of rock-property data are based on the conflicting requirements of significantly reducing the number of grid blocks, while maintaining a reasonable degree of detail in the representation of heterogeneity. To analyze whether grid blocks adequately represent complex heterogeneities the authors constructed complex, geologically realistic channel-levee complexes, using an object-modeling (Boolean) approach. This approach has themore » advantage over reservoir, or outcrop, derived data in so much as the 3-D architecture is fully known. The disadvantages are that the realizations are too simplistic, not necessarily geologically realistic, and contain only one scale of heterogeneity. In the present context, however, simplification of both geological and scale-related heterogeneities can be seen as advantageous in the interpretation of the results.« less

Well Imaging and Fault Detection In Anisotropic Reservoirs

Flow-confining image well location in both isotropic and anisotropic reservoirs can be reduced to one general equation. The equation is presented here, along with analyses of fault-location errors that result presented here, along with analyses of fault-location errors that result from conventional pressure transient studies applied to anisotropic systems. Introduction Engineers and geologists have long been aware of the directional flow properties of natural rocks. Permeabilities measured across the bedding are usually much Permeabilities measured across the bedding are usually much less than those along the bedding. Moreover, a change in flow direction along the plane of bedding will often show a significant change in horizontal permeability. This anisotropic behavior of natural permeability. This anisotropic behavior of natural rocks can pose some major problems for efficient reservoir exploitation. Some degree of horizontal permeability anisotropy is believed to be present, with few exceptions, in bedded rocks and limestones. In general, sandstones do not exhibit permeability ratios, k /k, in excess of 2.0. Homogeneous fractured reservoirs, such as the Spraberry trend field, however, may exhibit ratios as high as 144. In about half of some 10 limestone cores analyzed, Hutchinson reported significant permeability ratios averaging about 16. Arnold et al. and Elkins and Skov developed steady-state and transient pressure methods to evaluate horizontal, anisotropic media. Both the orthogonal permeability ratio and the orientation of the principal permeability ratio and the orientation of the principal axes can be determined by suitable well tests. The effect of anisotropy upon secondary recovery flood patterns has been studied by a number of patterns has been studied by a number of investigators. They conclude that the ease of flow or transmissibility of the fluid in one preferential direction causes premature water breakthrough and poor sweep efficiency with improper choice of pattern geometry and orientation. The combined effects of inhomogeneity and horizontal anisotropy have not been studied extensively. Greenkorn et al. extended the tensor theory of permeability to include heterogeneity for the case of flow permeability to include heterogeneity for the case of flow parallel to the plane of bedding. Merrick considered parallel to the plane of bedding. Merrick considered both anisotropy and stratification in evaluating recovery from gas cycling projects in bounded systems, using steady-state streamline flow solutions. Transient pressure buildup and drawdown tests used to define linear discontinuities within a reservoir should also be affected by anisotropy. Conventional methods of analysis us in their mathematical development the principles of superposition and direct mirror imaging of wells - principles applicable to isotropic systems only. The purpose of this study, therefore, was to:develop a valid technique for well imaging in anisotropic media,verify its use by a study of steady-state streamline patterns about a single well in the vicinity of a linear sealing boundary,devise methods for fault detection and location in anisotropic media, andinvestigate the error incurred by use of isotropic methods of fault location when applied to anisotropic reservoirs. JPT P. 1317