Reservoir Boundaries Research Articles

Transient pressure behavior of horizontal well in gas reservoirs with arbitrary boundary

Transient pressure analysis is a crucial tool to forecast the production performance during the exploration and production process in gas reservoirs. Usually, a regular shaped outer boundary is assumed in previous studies for well-testing analysis, which is just a simplification of practical cases and cannot reflect the actual boundaries of reservoirs. In this paper, a mathematical model is established to analyze the transient pressure behaviors of a horizontal well in an arbitrarily shaped gas reservoir. Dimensionless treatment, Laplace transformation, and boundary element method are applied in solving the model, which is verified by comparing with the results from the source function method. Based on the Stehfest numerical inversion method, the models of single-porosity media and dual-porosity media are solved respectively. Then, the time-domain curves of pseudo pressure and its derivative are obtained, and the flow regimes are identified. Finally, the impacts of some critical parameters on pressure transient behaviors are analyzed, including storativity ratio, interporosity coefficient, well length, and well orientation. This paper presents an effective way to handle complex external boundary problems in gas reservoirs.

Lithology‐dependent seismic anisotropic amplitude variation with offset correction in transversely isotropic media

ABSTRACTAnalysis of amplitude variation with offset is an essential step for reservoir characterization. For an accurate reservoir characterization, the amplitude obtained with an isotropic assumption of the reservoir must be corrected for the anisotropic effects. The objective is seismic anisotropic amplitude correction in an effective medium, and, to this end, values and signs of anisotropic parameter differences (Δδ and Δε) across the reflection interfaces are needed. These parameters can be identified by seismic and well log data. A new technique for anisotropic amplitude correction was developed to modify amplitude changes in seismic data in transversely isotropic media with a vertical axis of symmetry. The results show that characteristics of pre‐stack seismic data, that is, amplitude variation with offset gradient, can be potentially related to the sign of anisotropic parameter differences (Δδ and Δε) between two layers of the reflection boundary. The proposed methodology is designed to attain a proper fit between modelled and observed amplitude variation with offset responses, after anisotropic correction, for all possible lithofacies at the reservoir boundary. We first estimate anisotropic parameters, that is, δ and ε, away from the wells through Backus averaging of elastic properties resulted from the first pass of isotropic pre‐stack seismic inversion, on input data with no amplitude correction. Next, we estimate the anisotropic parameter differences at reflection interfaces (values and signs of Δδ and Δε). We then generate seismic angle gather data after anisotropic amplitude correction using Rüger's equation for the P‐P reflection coefficient. The second pass of isotropic pre‐stack seismic inversion is then performed on the amplitude‐corrected data, and elastic properties are estimated. Final outcome demonstrates how introduced methodology helps to reduce the uncertainty of elastic property prediction. Pre‐stack seismic inversion on amplitude‐corrected seismic data results in more accurate elastic property prediction than what can be obtained from non‐corrected data. Moreover, a new anisotropy attribute (ν) is presented for improvement of lithology identification.

Transition zone diagnosis in finite fractured reservoirs

A major part of world hydrocarbon resources is located in fractured reservoirs. The identification of fractured reservoir parameters is essential for their optimal production. The Warren-Root model is one of the most fundamental models for fluid flow in fractured reservoirs. The simplified assumption of the Warren-Root model is not applicable for a finite reservoir, and transition zone cannot be detected in finite fractured reservoirs. In this study, the significance of the fractured reservoir boundary effect in the Warren-Root equation is investigated. Also, the numerical solutions of the Warren-Root model are proposed for all types of boundary conditions. Results show that in some cases, it is impossible to diagnose the transition zone in fractured reservoirs from dimensionless curves due to the transition zone and boundary effect interference. This interference is specifically observed in finite fractured reservoirs and it is a function of the interprosity parameter (λ) and reservoir dimensionless radius (rDe). This functionality is presented and discussed in the cases of constant production rate and constant pressure production conditions. The proposed equations are applicable to all types of boundary conditions.

A new accuracy evaluation method for water body extraction

ABSTRACT This paper employs the Normalized Difference Water Index (NDWI), Automated Water Extraction Index (AWEI), Modified Normalized Difference Water Index (MNDWI) and Near-Infrared (NIR) threshold methods to extract the boundaries of Hongjiannao Lake, Zasak reservoir and Changjiagou reservoir. The real boundary of the water bodies was obtained by visual interpretation from high-resolution imagery. The Digital Shoreline Analysis System (DSAS) is further used to calculate the net shoreline movement (NSM) between the real lake boundary and the lake boundary extracted by the NDWI, AWEI, MNDWI and NIR threshold methods. We quantitatively evaluated the accuracy of each water body extraction method by NSM, which was competed with kappa coefficient (κ) and edge detection. The results showed that the average of the |NSM| of the NDWI, MNDWI, AWEI and NIR threshold methods are 12.77 m, 16.76 m, 28.65 m and 31.43 m, respectively. The κ is 0.9869, 0.9855, 0.9747 and 0.9736, respectively and the correct extracted (T) ratios for the edge detection are 84.06%, 82.68%, 56.8% and 53.52%, respectively. The mean value of |NSM| for NDWI is the smallest, while κ and T are the highest. It indicates that the accuracy of NDWI is the highest in Hongjiannao lake. The smaller the |NSM| is, the larger κ and the higher T are. This shows that the |NSM| is consistent with the commonly used accuracy verification method such as κ and edge detection. The results of water extraction from the other two reservoirs also support this conclusion. Therefore, the accuracy verification of NSM can reflect the spatial position information and has reliability. It provides a new approach in verifying the accuracy of water body extraction methods. The optimum water extraction index for different study areas is different. The NIR band threshold method and AWEI can accurately extract water boundaries with a small amount of aquatic vegetation. However, NDWI and MNDWI are more suitable for extracting water bodies located in complex terrains.

Fracture mechanics approach to the problem of subsidence induced by resource extraction

A new area of application of Fracture Mechanics methods is proposed: the determination of surface deformation induced by internal volume change (e.g. due to underground hydrocarbon extraction). The finite layer-like zone of volume alteration is modelled as a crack, that is as a continuous distribution of dislocation loops. This approach allows the determination of surface deformation and can serve as the basis for monitoring of the volume alteration from surface measurements. In a limiting case of nearly uniform deformation of the reservoir boundaries the model consists of a single dislocation loop (an inserted cylindrical body of a constant height) in half-space and results in simple approximate expressions for the normal and tangential displacement components of the free surface. For the example of subsidence in the Groningen gas field the proposed method produces more realistic results describing reality better than the traditional models based on representing the reservoir as a collection of independent dilation centres. Also, analytical expressions are proposed for the nuclei – the basic Green’s function type expressions that allow representation of a planar horizontal reservoir layer of an arbitrary shape as a distribution of infinitesimal dislocation loops. For the case of a cylindrical reservoir, the nuclei integration recovers the exact distribution of the surface displacements.

Determination of in-situ elastic properties and reservoir boundary conditions

The elastic properties of reservoir formation are usually measured through laboratory triaxial tests or are estimated from empirical correlations obtained from well logs. Both approaches have similar limitation of the estimated value being representative of near-wellbore region. The former, however, has the further limitations of being costly and the unavailability of core samples for having a reliable estimate. In this paper, a new methodology is presented to determine the in-situ elastic properties (Poisson's ratio-PR- and Young's modulus) using pressure transient testing. Adopting the poroelasticity theory, a generalized diffusivity equation is formulated incorporating reservoir deformations into the fluid flow. By applying different boundary conditions, namely generalized plane stress, plane strain, and uniaxial strain, several analytical solutions were developed to obtain the PR from well testing. It shall be noted that the Young's modulus can be estimated given PR and bulk modulus. Two field data sets were used to implement and validate the proposed methodology for estimation of the PR (a build-up test data-set from a limestone oil reservoir and an interference drawdown well testing data-set from a sandstone aquifer). Results indicate that indeed the PR is a strong function of the reservoir deformational behavior. Moreover, estimation of PR under different boundary conditions provide a tool to identify the dominant reservoir deformational conditions. This was identified for the first data set by having the sonic well log data available and for the second data set by comparing the pressure-time measurements with their counterparts obtained from fully coupled fluid flow/geomechanics simulations. Moreover, once the validity of the output is confirmed by comparison with the available PR from well logging and/or coupled flow/geomechanics simulations, the proposed protocol can be re-used multiple times during reservoir life to estimate the elastic properties under the appraised BCs, without the necessity to run new well logs or lab tests.

The performance of complex-structure fractured reservoirs considering natural and induced matrix block size, shape, and distribution

This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media.The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration.The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.

Effects of reservoir size and boundary conditions on pore-pressure buildup and fault reactivation during CO2 injection in deep geological reservoirs

The excessive burning of the fossil fuels has caused severe global climatic changes such as increasing the global temperature, causing initiation of the wild fire, rising the sea level, increasing the floods, storms, amount of rain and snow. One of the effective global mitigation strategies is sequestration of huge quantity of CO2 deep below the ground level for a long period of time. An important issue is to ensure the permanency and safety of the sequestration process due to the associated pore-pressure buildup. It is necessary to have correct estimates of the pore-pressure buildup, ground uplift and re-activation of any existing fault during the process of CO2 injection and long-term storage. In this investigation, the effects of reservoir size and boundary conditions are investigated by means of geomechanical modeling of the deep Biyadh sandstone reservoir in Saudi Arabia. Currently, carbon dioxide is not injected into the actual Biyadh reservoir. In this investigative modeling, CO2 is injected for an injection period of ten years using a single injection well at the center of the reservoir. The developed modeling scheme for a single injection well has been extended further to include multiple injection wells. For multiple injection wells, the reservoir size and locations of injection wells are varied to evaluate their effect on the pore-pressure buildup and ground uplift. The reservoir stability analysis has been performed using Mohr–Coulomb failure criterion for both small and large reservoir models, with the same injection parameters. The simulation results demonstrated that pressure buildup and ground uplift are relatively higher for reservoirs with small sizes and closed boundaries; while in the case of large sizes and open boundaries, the pore-pressure buildup and ground uplift are relatively lower. Moreover, the effect of the reservoir size and boundary conditions on the reactivation of faults during CO2 injection has been evaluated. The stability analysis performed in this study shows that injecting CO2 into larger size reservoir is safer as compared to smaller size reservoir. Injecting CO2 with multiple injection wells will cause pore-pressure buildup of huge magnitudes. The modeling results show that suggesting a representative volume for the reservoir during CO2 injection can under-estimate the pore-pressure buildup and fault re-activation that can cause the reservoir failure and leakage of the stored CO2.

Seismic analysis of damaged concrete gravity dams subjected to mainshock-aftershock sequences

The current study aims at seismic analysis of damaged concrete gravity dams subjected to aftershocks loading of earthquake. Dams’ sliding behaviour is also discussed to shed light on the issue. For the purpose of the study, a cracked concrete gravity dam was modelled, and zero thickness contact elements were used to model the contact between the main body and the separated damaged parts of the dam. The augmented Lagrangian method, considering frictional sliding and opening of contact joints, was used in non-linear analyses. Fluid-structure-interaction, considering fluid compressibility and absorptive boundary of reservoir, was also taken into account. The damage model of ‘Konya’ and ‘Manjil’ dams comprised our case study. Non-linear dynamic analyses were done based on both models. Stiffness and damping coefficients effect on the seismic response of dam were examined. Dam, foundation and reservoir interaction effects were also included. The results were compared to the results obtained from other methods, which showed adequate similarities. The differences between damages caused by aftershocks are discussed, and it is pinpointed that the stability of dam during aftershocks is not compromised. It is demonstrated that top block slides during each aftershock and finally incurs some permanent sliding which may destroy the dam.

A COMPREHENSIVE MODEL FOR OIL–WATER RELATIVE PERMEABILITIES IN LOW-PERMEABILITY RESERVOIRS BY FRACTAL THEORY

Oil–water relative permeability curve is an important parameter for analyzing the characters of oil and water seepages in low-permeability reservoirs. The fluid flow in low-permeability reservoirs exhibits distinct nonlinear seepage characteristics with starting pressure gradient. However, the existing theoretical model of oil–water relative permeability only considered few nonlinear seepage characteristics such as capillary pressure and fluid properties. Studying the influences of reservoir pore structures, capillary pressure, driving pressure and boundary layer effect on the morphology of relative permeability curves is of great significance for understanding the seepage properties of low-permeability reservoirs. Based on the fractal theory for porous media, an analytically comprehensive model for the relative permeabilities of oil and water in a low-permeability reservoir is established in this work. The analytical model for oil–water relative permeabilities obtained in this paper is found to be a function of water saturation, fractal dimension for pores, fractal dimension for tortuosity of capillaries, driving pressure gradient and capillary pressure between oil and water phases as well as boundary layer thickness. The present results show that the relative permeabilities of oil and water decrease with the increase of the fractal dimension for tortuosity, whereas the relative permeabilities of oil and water increase with the increase of pore fractal dimension. The nonlinear properties of low-permeability reservoirs have the prominent significances on the relative permeability of the oil phase. With the increase of the seepage resistance coefficient, the relative permeability of oil phase decreases. The proposed theoretical model has been verified by experimental data on oil–water relative permeability and compared with other conventional oil–water relative permeability models. The present results verify the reliability of the oil–water relative permeability model established in this paper.

An Interpretation Method for a Gas Production Profile Based on the Temperature and Pressure Behavior of Low-Permeability Gas Reservoirs

This study aims to interpret the temperature and pressure behavior of an open-hole horizontal gas well (OHHGW) in a low-permeability gas reservoir in order to obtain the permeability and production profile of the OHHGW. First, the mathematical model, which is comprised of viscous dissipation, friction, the Joule–Thomson effect, and several other micro-thermal effects, was developed under a single-phase condition. Second, during the process of solving the numerical model, the drilling skin, heterogeneity, and non-Darcy effect were taken into consideration. In addition, the reservoir and wellbore models were coupled. Third, the testing temperature and pressure data were inverted using the Levenberg–Marquardt (LM) or Markov Chain simulated annealing algorithms, and the permeability and production profiles of the wellbore were obtained. The synthetic cases demonstrate the models’ ability to predict the temperature profile, and the results show the following: (a) The inversion results are in good agreement with the actual data, that is, the model can provide effective guidance for horizontal well development. (b) The wellbore temperature is lower than that of the reservoir boundary, so the micro-thermal effects for the horizontal gas well cannot be ignored during production. (c) As the gas production, the relative density of the gas, and the drilling skin factor increase, the wellbore temperature profile gradually decreases. The wellbore temperature increases with increasing horizontal permeability. (d) The trend of the temperature profile is contrary to the flow path of the wellbore fluid. (e) Reservoir heterogeneity has a significant influence on the temperature profile.

Depositional and diagenetic controls on reservoir quality: Example from the upper Cretaceous Mishrif Formation of Iraq

The Cenomanian-Turonian Mishrif Formation at the H field in southeastern Iraq displays a wide range of rock fabrics that result in highly variable reservoir quality and flow properties. Reservoir quality in this field is controlled by the complex interplay of depositional and diagenetic factors. Depositionally, seven main productive facies are recognized, which are organized into six sequences; reservoir quality occurs primarily in the grain dominated high energy shoal, shallow open marine, and rudist biostrome facies. A major change in stratigraphic style occurs midway through the reservoir, with a lower portion that is dominated by laterally continuous upward shoaling cycles (that are often shoal or tidal flat capped) and an upper part that is more heterogeneous and dominated by lagoonal and back-shoal facies. While diagenesis has overprinted and altered this initial framework, karsting - resulting in both enhanced reservoir quality due to leaching and reduced reservoir quality due to cementation, brecciation and fines infiltration - associated with sequence boundaries within and at the top of the Mishrif Formation represents the major flow-significant diagenetic effect in the reservoir. Here, diagenesis has followed the stratigraphic pattern established at the time of deposition, and reinforced its impact on reservoir quality. Mishrif reservoir quality is ultimately controlled by sea-level history, in that high energy, grain dominated textures and facies associated with sea-level highstands have the best reservoir quality, while meteoric diagenesis has produced low reservoir quality (and reservoir boundaries) at karsted exposure surfaces that formed during sea-level falls. Recognition that reservoir quality, both good and bad, results from congruent depositional and diagenetic effects ultimately driven by the sea-level history of the succession provides an important key to understanding and predicting reservoir quality in the H field and in other carbonate fields with similar depositional and diagenetic histories.

ОЦЕНКА ОХВАТА ПЛАСТА СИСТЕМОЙ РАЗРАБОТКИ С ПОМОЩЬЮ РАДИУСА ДРЕНИРОВАНИЯ СКВАЖИН

Актуальность исследования.В гидродинамических симуляторах фильтрация флюидов описывается с помощью законов сохранения массы, в результате чего может оказаться, что значительная часть объекта разработки вовлечена в процесс дренирования. Данный подход может не вполне корректно оценить область притока жидкости к добывающей скважине. Зоны притока жидкости к скважине (зоны дренирования)часто схематизируют в виде концентричной к скважине окружности с радиусом, равным половине расстояния между забоями скважин. Данный подход не учитывает различие линий тока, границы пласта, его неоднородность и другие факторы. Значение радиуса дренирования особенно изменчиво в карбонатных коллекторах при изменении пластового давления. Достоверная оценка размера зоны дренирования скважин позволит более точно оценить степень охвата залежи разработкой, особенно в карбонатном коллекторе. Цель: исследовать возможность охвата залежи нефти системой разработки с помощью оценки фактических радиусов дренирования скважин;определить наиболее эффективные технологии увеличения радиуса дренирования скважин. Объект: Башкирская залежь на месторождении нефти в Соликамской депрессии. Средняя обводненность продукции скважин на залежи составляет 39,2%.На залежи отмечается существенная зависимость фильтрационных параметров горных пород от пластовых и забойных давлений. Методы: определение значений коэффициентов проницаемости и пьъезопроводности на основе обработки результатов гидродинамических исследований. Результаты. На текущий момент времени залежь нефти охвачена разработкой по площади на 40%. На радиус дренирования скважин существенное влияние оказывает коэффициент проницаемости. На рассматриваемом объекте отмечена сильная взаимосвязь между коэффициентом проницаемости и энергетическим состоянием залежи. Понижение значения радиусов дренирования скважин может существенно уменьшить охват залежи системой разработки и увеличить сроки выработки извлекаемых запасов нефти. На рассматриваемом объекте разработки наиболее эффективные методы увеличения радиусов дренирования скважин – кислотные гидроразрывы и комбинированные с другими технологиями кислотные обработки.

Pressure behaviour of a horizontal well sandwiched between two parallel sealing faults

Generally, reservoir fluid flow is governed by diffusivity equation and solution to this equation helps to investigate pressure behaviour under certain reservoir and wellbore boundary conditions. In this paper however, the analytical solution method of Green and Source function is deployed to determine the performance of a horizontal well located between two parallel sealing faults, assuming simple rectangular reservoir geometry. Also, the dimensionless pressure and derivative approach is applied for all computations as it prevents the problem of unit conversions, reduces longer expressions and it helps to handle numerical values. The pressure expression derived from this work reveals that a maximum of two flow periods occur for the stated reservoir model. It was found out that an inverse relationship exists between dimensionless pressure and dimensionless length while pressure increased with thickness. Also high vertical permeability shortens the effect of the early radial flow period experienced by the horizontal well, thereby increasing productivity index. Finally, it was discovered that increased perforation length reduces the production potential of the horizontal well.
 Keywords: Dimensionless pressure, pressure derivatives, heterogeneity, pressure performance, reservoir and wellbore characterization.

Geothermal wells with water hammer during injection fall-off test: Numerical pressure transient analysis

Extended pressure fall-off test data of low permeability wells can display oscillations that cannot be easily interpreted by using the existing analytical pressure transient analysis (PTA) methods. Additionally, water hammer effects resulting from wellhead valve shutting off are observed immediately after valve closure.Numerical PTA applied to well MOL-GT-03, Belgium, using 1-D radial model with fractional dimension grid gave a good match with field data clearly indicating low reservoir permeability and the fractured nature of the reservoir. In addition, the water hammer effect was investigated by solving the wave equation to help identifying the extent of the well reach providing an estimate to the reservoir boundary.

Numerical analysis on the mechanism of hydraulic fracture behavior in heterogeneous reservoir under the stress perturbation

Hydraulic fracturing is the key technology employed to alter the permeability of tight reservoirs. In this article, the discrete element fluid–solid coupling method is improved, and sinusoidal stress waves are applied at the boundary of a heterogeneous reservoir to simulate perturbation. The influence of stress wave frequency on the mode of crack propagation in the hydraulic fracturing process and the internal stress changes in specimens under different in situ stress ratios are investigated. The simulation results suggest that (1) under a constant injection rate, an increased frequency is associated with a gradual increase in the breakdown pressures, an increase in the time required for cracking breakdown, and faster propagation of cracks propagating; and (2) the hydraulic fracture propagation direction obviously deflects towards the stress wave propagation direction, and the failure mode becomes more complicated under the combined action of the ground stress and the stress wave; and (3) the maximum principal stress inside the specimen is compressive stress, and the curves of the maximum principal stress and maximum shear stress are periodic vibration, with the characteristics of a large amplitude at a low frequency and a small amplitude at a high frequency. The initiation of cracks near the injection hole results from a reduction in the maximum principal stress and an increase in the maximum shear stress. The analysis indicates that the stress wave has a non-negligible influence on hydraulic fracturing and provides a better guideline for understanding the mechanical nature of hydraulic fracturing under the influence of stress perturbation.

Synchrosqueezing Matching Pursuit Time–Frequency Analysis

Time–frequency analysis of the nonstationary signals is one of the hot researches in geophysics, environmental science, geology, and other fields. Matching pursuit (MP) has been widely used to reveal the characteristics in time–frequency domain, which helps to study the changes and differences of subtle geological structures. Compared with traditional time–frequency analysis methods, MP has higher time–frequency resolution. The synchrosqueezing transforms (SSTs) have been proven to be an effective methodology to improve the time–frequency resolution by squeezing and redistributing the time–frequency coefficients in the frequency direction. Considering the superiority of the SSTs, this letter proposes a novel time–frequency analysis method called synchrosqueezing MP to enhance the energy aggregation of the time–frequency plane. The proposed method can squeeze the time–frequency distribution into near the center time and frequency of the selected wavelet by a 2-D Gaussian function. We used synthetic and field seismic data to demonstrate the feasibility of our method. The results prove the superiority of our method in describing reservoir boundaries.

Estimation of Effective Permeability, Fracture Spacing, Drainage Area, and Incremental Production from Field Data in Gas Shales with Nonnegligible Sorption

SummaryIn a previous work, we introduced a three-parameter scaling solution that models the long-term recovery of dry gas from a hydrofractured horizontal well far from other wells and the boundaries of a shale reservoir with negligible sorption. Here, we extend this theory to account for the contribution of sorbed gas and apply the extended theory to the production histories of 8,942 dry-gas wells in the Marcellus Shale. Our approach is to integrate unstructured big data and physics-based modeling. We consider three adsorption cases that correspond to the minimum, median, and maximum of a set of measured Langmuir isotherms. We obtain data-driven, independent estimates of unstimulated shale permeability, spacing between hydrofractures, well-drainage area, optimal spacing between infill wells, and incremental gas recovery over a typical well life. All these estimates decrease to varying extents with increasing sorption. We find that the average well with median adsorption has a permeability of 250 nd, fracture spacing of 16 m, 30-year drainage length of 79 m, and a 30-year incremental recovery of 67%.

Analytical investigation of gas production from methane hydrates and the associated heat and mass transfer upon thermal stimulation employing a coaxial wellbore

In this study, an analytical approach has been developed to couple the wellbore heating process by hot water circulation and the associated methane hydrate dissociation in the reservoir. A coaxial wellbore is assumed as the heat source where both conduction and convection heat transfers are considered. It consists of an inner tube and an outer structure of casing, gravel, and cement layers. In the reservoir, a similarity solution employing a moving boundary separating the dissociated and undissociated zones is employed to build the analytical solution. Two different operating schemes for water supply into wellbore heat source have been studied: i) from the inner tube; and ii) from the annulus section of the wellbore. Temperature distribution along the wellbore, temperature and pressure distributions in the reservoir, hydrate dissociation rate, and energy efficiency considering various initial and boundary conditions and reservoir properties are evaluated. The two different operating schemes have almost the same results with slightly higher gas production in the case of hot water entry into annulus, which is in direct contact with the reservoir. Increasing the inlet water temperature or decreasing the wellbore pressure increases gas production. Applying them simultaneously results in a greater gas production and energy efficiency. Some of the reservoir’s properties, such as porosity, thermal diffusivity, thermal conductivity, and reservoir thickness, have direct relation with the dissociation rate, but the reservoir’s permeability and gas viscosity have almost no impact on the process. The wellbore parameters, such as flow rate of hot water, inlet temperature, and wellbore radius except the inner tube radius, have direct impact on the wellbore mean temperature and the associated results in the dissociation process.

Unlined trench as a falling head permeameter: Analytic and HYDRUS2D modeling versus sandbox experiment

An isosceles triangle in a vertical cross-section of a trench is considered as a boundary from which free water in the trench seeps into a porous bed. A finite, initially impounded water volume vanishes from the channel and soil moisture moves in conjugation with surface water in a transient 2-D saturated-unsaturated regime. If capillarity is ignored and the subjacent soil is assumed to be dry before filling the channel, then a wetting front propagates as a sharp interface mated with drawdown of the channel free water. A Lembke method of consecutive steady states is used to model the interface as a rotating straight-line. A zone of Darcian seepage is a triangle, three sides of which (at each time instance) are a streamline, a constant piezometric head line and isobar. The instantaneous hinge point of the interface demarcates a zone of imbibition from a zone of drainage of this saturated triangle. Mathematically, a Green-Ampt type nonlinear first order ODE is obtained and explicitly integrated by separation of variables and the drawdown time t is explicitly expressed through the water depth H in the trench. In a sandbox with a dune sand, an experimental H(t) is measured in a trench having mild and steep bank slopes. When H(t) > 0 the drawdown rate increases that is attributed to an increase of the effect of capillarity. For this stage, Riesenkampf’s analytical solution for steady 2D tension-saturated flow with a capillary fringe is used. The analytical and experimental results are compared with those obtained by HYDRUS-2D (numerical modeling), involving a reservoir boundary condition introduced for furrow irrigation applications. Model performance parameters including the root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (r2) and Nash-Sutcliffe efficiency (E) showed a good agreement between the measured and simulated values of drawdown time. Results of the t-test between the measured and simulated drawdown time showed insignificant differences at a 5% confidence interval for all the trenches (p > 0.05). HYDRUS simulations quantified the dynamics of a “sinking” saturated “bubble” under the trench: isobars, isotachs, streamlines and loci of the stagnation points are plotted. We illustrate how to use a drawdown curve H(t) for determination of saturated hydraulic conductivity and air-entrance pressure in the Vedernikov-Bouwer model.