Pressure Type Curves Research Articles

Transient analysis of horizontal wells with multiple fractures in sour gas reservoirs

Due to the decrease of reservoir pressure, the elemental sulfur deposits in sour gas reservoirs, leading to the reduction in the reservoir porosity and permeability. It can also impact the transient pressure and rate behavior of gas wells, which is always reflected in pressure and flow rate type curves. However, few studies focus on transient analysis of multi-fractured horizontal wells affected by sulfur deposition. Therefore, the objective of this work is to develop a comprehensive model to analyze the transient pressure and flow rate of multi-fractured horizontal wells in sour gas reservoirs. Pseudo-time function and pseudo-pressure function are derived and the point source method is applied in this model. Then the proposed model is validated against analytical solutions and real production data. Furthermore, sensitivity analysis for pressure and rate type curves was conducted. Results show that the pressure type curves can be divided into six stages. The reservoir with higher H2S concentration will result in more sulfur deposition, which requires larger pressure difference to maintain a constant rate in the late time. Fracture properties impact flow rate in the early production time, and increasing fracture conductivity and fracture number is helpful to reduce the generation of sulfur deposition. For a smaller reservoir, larger pressure difference is essential to stabilize constant production rate, which means more sulfur deposition will be produced in the reservoir. During the development of sour gas reservoir, it is important to control flow rate to reduce pressure depletion for decrease amount of sulfur deposition. This paper reveals the impacts of sulfur deposition on type curves and provides a comprehensive transient analysis for multi-fractured horizontal wells in the development of sour gas reservoirs.

In-situ characterization of nonlinear flow behavior of fluid in ultra-low permeability oil reservoirs

Correlating velocity-gradient relation is crucial for understanding flow behavior of fluid in low-permeability oil reservoirs. Instead of experimental approaches, this paper utilized downhole pressure data analysis for in-situ characterization of nonlinear flow behavior at low velocity. We introduced a dynamic permeability concept, which connects flow equation and nonlinear flow behavior. We then employed pseudo-linear function, piecewise function and continuous function to characterize the nonlinear flow behavior. The transient pressure type curves response ascended in the late-time flow period with consideration of nonlinear flow effect, suggesting that nonlinear flow equations can affect the characteristic of the type curves. The coefficients of approximation function are considered to be model parameters and are determined by downhole pressure analysis. Through our workflow, we can obtain a velocity-gradient relation, describing the nonlinear flow behavior of in-situ fluid. The practicality and efficiency of our new method are illustrated by comprehensive case studies. The in-situ flow behavior in reservoir scale can be characterized by normalizing multiple velocity-gradient curves derived from individual well analysis. Compared with core-flooding experiments, the proposed method is more convenient and economic to characterize flow behaviors in low-permeability oil reservoirs.

Pressure and rate transient modeling of multi fractured horizontal wells in shale gas condensate reservoirs

Gas condensate production using technology of multi-stage hydraulically fracturing in shale gas condensate reservoirs' horizontal wells is a new topic of unconventional resources studies. Thus, shale gas condensate as a new source of energy can be considered as an important issue for development and further studies. In this work, a semi-analytical solution of gas and oil two-phase flow is presented for pressure transient analysis (PTA) and rate transient analysis (RTA) of a shale gas condensate reservoir's production data. Fluid flow assumption here is flow in a pseudo triple-porosity porous media, which are matrix, natural fractures and adsorbed gas. Adsorbed gas is a form of gas in porous rock pores like free gas, but unlike that, it is not free to flow initially and requires pressure drop to desorb from micro- (or even nano-) pores of rock to flow in matrix and then in fracture. In this study, desorption of the adsorbed gas is modeled with Langmuir isotherm theory. Based on the results, type curves of two-phase pseudo-pressure and also two-phase rate decline are plotted. These type curves are analyzed with different sensitivities to Langmuir volume, interporosity flow parameters, horizontal well length, number of multiple-fractures and Corey model relative permeability exponents. Τhe strength of this work is to plot type curves of pressure and rate transient analysis of multi-stage hydraulically fractured well (MHFW) in shale gas condensate reservoir in terms of rich gas production of the well.

An Analytical Flow Model for Heterogeneous Multi-Fractured Systems in Shale Gas Reservoirs

The use of multiple hydraulically fractured horizontal wells has been proven to be an efficient and effective way to enable shale gas production. Meanwhile, analytical models represent a rapid evaluation method that has been developed to investigate the pressure-transient behaviors in shale gas reservoirs. Furthermore, fractal-anomalous diffusion, which describes a sub-diffusion process by a non-linear relationship with time and cannot be represented by Darcy’s law, has been noticed in heterogeneous porous media. In order to describe the pressure-transient behaviors in shale gas reservoirs more accurately, an improved analytical model based on the fractal-anomalous diffusion is established. Various diffusions in the shale matrix, pressure-dependent permeability, fractal geometry features, and anomalous diffusion in the stimulated reservoir volume region are considered. Type curves of pressure and pressure derivatives are plotted, and the effects of anomalous diffusion and mass fractal dimension are investigated in a sensitivity analysis. The impact of anomalous diffusion is recognized as two opposite aspects in the early linear flow regime and after that period, when it changes from 1 to 0.75. The smaller mass fractal dimension, which changes from 2 to 1.8, results in more pressure and a drop in the pressure derivative.

Mathematical model of fractured horizontal well in shale gas reservoir with rectangular stimulated reservoir volume

Production performance analysis of shale gas development has posed a great challenge for scientific researchers owing to the complex percolation mechanisms and massive hydraulic fracturing. The unique accumulation and transporting mechanisms in multiscaled shale pores, such as adsorption, desorption, diffusion, and slippage, lead to gas seepage behaviors deviating from Darcy flow. Compared to previous studies, this paper presents a comprehensive mathematical model incorporating all the above percolation mechanisms for multistage fractured horizontal wells, in which rectangular stimulated reservoir volume (SRV) is taken into account. A numerical solution for such a complex model is obtained by extending the boundary element method to application. The verification of our method is confirmed by comparison to semi-analytical results of a simplified model. From the well testing type curves, nine flow regimes were identified, most of which are not observed in conventional linear flow models. The effects of sensitive parameters, such as fracture number, size and permeability of the SRV, and formation permeability, on pressure type curves were investigated. The comprehensive model in this paper provides another method to guide the development of shale gas reservoirs, including interpretation of formation properties, guiding fracturing design, and conducting post-fracture evaluation.

Well Test Analysis for Fractured and Vuggy Carbonate Reservoirs of Well Drilling in Large Scale Cave

A well test analysis model for fractured and vuggy carbonate reservoir of wells drilling in large scale cave considering wellbore storage and skin factor is established in this paper. The Laplace transformation and Stehfest numerical inversion are applied to obtain the results of wellbore pressure. Through the sensitivity analysis of different parameters for the well test typical curves, it is found that the change of the well test curves is in accordance with the theoretical analysis. With the increase of skin factor, the hump of well test typical curves is steeper. The storage ratio influences the depth and width of the concave in the pressure derivative curves. The cross flow coefficient mainly affects the position of the concave occurrence in the pressure derivative curves. The dimensionless reservoir radius mainly affects the middle and late stages of the log-log pressure type curves, and the later well test curves will be upturned for sealed boundary. The duration of the early stage of the log-log curves will become longer when drilling in large scale cave. The effective well radius is increased to a certain extent, which is in full agreement with the conclusions in this paper. The size of the caves has the same effect on the well test typical curves as wellbore storage coefficient. Due to acidification, fracturing, and other reasons, the boundary of the cave will collapse. Therefore, considering the wellbore storage coefficient and skin effect is very important during well testing. However, the existing models for well testing of fractured and vuggy carbonate reservoir often ignore the wellbore storage coefficient and skin effect. For fractured and vuggy carbonate reservoirs of well drilling in large scale cave, the existing models are not applicable. Since the previous models are mostly based on the triple-porosity medium and the equivalent continuum. The well test model for well drilling in large scale cave of fracture-cavity carbonate reservoirs with wellbore storage coefficient and skin factor in this work has significant application value for oil field.

Pressure transient analysis for off-centered fractured vertical wells in arbitrarily shaped gas reservoirs with the BEM

Because transient pressure analysis is important for postfracture evaluation and reservoir characteristic assessment, and hydraulic fracturing has been widely applied in recent oil/gas development, physical and mathematical models are important for petroleum engineers. Although there numerous reports relate to fractured wells in the centers of reservoirs, research on off-centered fractured wells is rare, and it is difficult to obtain a semianalytical solution with conventional methods. In this paper, a mathematical model of an off-centered, infinite-conductivity fractured well in an arbitrarily shaped gas reservoir is established. The boundary element method (BEM) is implemented to analyze the well transient pressure response. Two validation cases of center wells with circular and rectangular outer boundaries are used to verify the correctness of our method. The pressure response of an off-centered fractured well differs from that of the conventional case at the early stage of the boundary reflection flow period. Furthermore, if the well is close enough to the boundary, the pressure derivative curves will show another step before the boundary-dominated flow period. In the end, the model is extended to dual- and triple-porosity reservoirs. The pressure type curves and their sensitivity analyses are also determined. From this study, it is clear that the BEM can be an effective and precise method to cope with the fluid flow problems in such a complex situation.

Solution and type curves for the seepage model of the water-bearing coalbed with leakage recharge

To analyze the effects of the leakage recharge of the aquifer on the initial dewatering of coalbed methane wells, the mathematical seepage model of water in the coalbed considering the aquifer leakage was established by using the leakage coefficient according to the unsteady seepage theory. The model was solved after Laplace transform and the Stehfest numerical reverse inversion was used to obtain the solution in right space. Then, the log-log type curves of pressure and pressure derivative were created with new combinations of parameters. Based on the natural seepage mechanism, the influence of aquifer leakage on curve shape was judged. It is found that the radial flow ends earlier as the leakage coefficient increases. Moreover, it was proposed to obtain reservoir permeability, skin factor, and leakage coefficient by using type curve matching. The type curves are useful for quantitatively evaluating the level of leakage, thereby guiding the adjustment of the following production system for CBM wells. Curvas de solución y tipo para el modelo de filtración de capas carboníferas acuíferas con recarga de fugasResumenEste estudio estableció el modelo matemático de filtración de agua en una capa carbonífera al estimar la salida acuífera con el uso del coeficiente de fuga, de acuerdo con la teoría de filtración inestable, para analizar los efectos en la recarga de pérdida de fluidos de un acuífero en el drenado inicial para pozos de gas metano. El modelo se resolvió tras usar la transformación Laplace y la inversión numérica Stehfest para encontrar la respuesta en el lugar indicado. Luego, se creó la representación algorítmica de la presión y la presión derivativa con nuevas combinaciones de parámetros. Se evaluó la influencia de la pérdida de fluido del acuífero en la forma de la curva con base al mecanismo físico de filtración. Se estableció que el flujo radial finaliza antes de que el coeficiente de pérdida de fluido se incremente. Además, se propone el uso de la curva tipo correspondiente para obtener la permeabilidad del reservorio, el factor de daño y el coeficiente de pérdida de fluido. Las curvas tipo son útiles para evaluar cuantitativamente el nivel de la pérdida de fluido, y de esta manera guiar el ajuste de un sistema de producción consecuente para pozos de gas metano de carbón.

Five-region flow model for MFHWs in dual porous shale gas reservoirs

The multiple fractured horizontal well (MFHW) has becoming an effective technique to develop ultra-low permeability unconventional shale gas reservoir. The complex fracture network induced around the well and hydraulic fractures during the fracturing process as well as the multiple seepage mechanism of shale gas, such as gas ad-/desorption, diffusion, percolation et al., make the well testing model of MFHW rather complex. By dividing the stimulated reservoir into five regions with different formation properties and taking into account the multiple seepage mechanisms in shale formations, this paper proposed a five-region linear flow model to analyze the well transient pressure responses of MFHWs. By using Laplace transformation method, the analytical solution of the presented model in Laplace space is obtained and the transient pressure type curves are also plotted. In addition, the gas flow periods are analyzed based on analysis of type curves and the effects of the following parameters on type curves are discussed, such as the size of SRV region, gas diffusion coefficient and interporosity factors, et al. the results obtained in this paper can be used to better understand the gas flow mechanisms and pressure response dynamics of MFHW in shale gas reservoirs.

Variable-Permeability Well-Testing Models and Pressure Response in Low-Permeability Reservoirs with non-Darcy Flow

<p>This paper proposes the concept of variable-permeability effect and sets up the one-dimensional and two-dimensional non-Darcy well testing models. The finite difference algorithm is employed to solve the differential equations of the variable-permeability model, and the non-convergence of the numerical solutions is solved by using the geometric mean of permeability. The type curves of pressure and pressure derivative with variable-permeability effect are obtained, and sensitivity analysis is conducted. The results show that the type curves upturn in the middle and late sections, and the curves turn more upward with the severer of the variable-permeability effect. The severer the non-Darcy effect is, the less obviously the curve upturns caused by boundary effect. Furthermore, the boundary effect is increased by increasing the number of impermeable boundaries or decreasing the distance between the well and boundary.</p>

Capturing the effects of secondary fractures on production data using flow regime equations and specialised plots: An uncertainty analysis approach

Abstract Many fractured horizontal wells are completed in tight oil/gas or shale gas reservoirs which have significant networks of interconnected secondary fractures. However, the existing linear transient dual- and triple-porosity models do not properly account for secondary fractures. While the dual-porosity model assumes negligible secondary fractures, the linear sequential triple-porosity model assumes negligible fluid transfer between the rock matrix and hydraulic fractures. Hence, the application of these models for production data analysis of fractured horizontal wells could result in unreasonable reservoir/fracture parameter estimates and hydrocarbon forecast. For this reason, the quadrilinear flow model (QFM) was developed to account for matrix–hydraulic fracture communication. Although QFM properly accounts for the contribution of secondary fractures during reservoir depletion, reservoir parameter estimation from its type-curve matching procedure has a high degree of uncertainty. This paper proposes simplified QFM flow regime equations to reduce the uncertainty associated with reservoir parameter estimation. This study carefully analyses the general QFM solution by observing the flow regions from dimensionless rate and pressure type-curves. This solution is simplified by eliminating dimensionless parameters with negligible contribution to fluid depletion within the duration of each flow region. The resulting simplified analysis equations are analytically inverted from Laplace space to time space. The simplification process yields (i) analysis equations for different flow-regions of the specialised rate-normalised pressure and pressure derivative plots and (ii) explains the possible physics behind the flow-regions. The effect of secondary fracture networks on reservoir depletion can be investigated by applying QFM analysis equations on specialised rate-normalised pressure and pressure derivative production data plots. The choice of these plots is based on operational well constraints and observable flow regions. The QFM analysis equations are applied to interpret production data of two multifractured horizontal wells completed in the Cardium and Bakken Formations. The results estimate effective half-length of hydraulic fractures, investigate the presence/absence of secondary fractures and propose a workflow for handling the uncertainty in reservoir parameter estimation when applying the specialised analysis equations.

A well test model for stress-sensitive and heterogeneous reservoirs with non-uniform thicknesses

In view of the anisotropy, heterogeneity and stress-sensitive permeability in low permeability reservoirs, an analytical well test model was established by introducing the concept of permeability modulus. This model considered the permeability stress-sensitivity, wellbore storage effect, and the skin effect. The perturbation technique and Laplace transformation were used to solve the mathematical model analytically in Laplace space, and the bottom-hole pressure type curves were plotted and analyzed in real space by using the Stehfest numerical inversion.

Numerical study on transient flow in the deep naturally fractured reservoir with high pressure

According to the experimental results and the characteristics of the pressure-sensitive fractured formation, a transient flow model is developed for the deep naturally-fractured reservoirs with different outer boundary conditions. The finite element equations for the model are derived. After generating the unstructured grids in the solution regions, the finite element method is used to calculate the pressure type curves for the pressure-sensitive fractured reservoir with different outer boundaries, such as the infinite boundary, circle boundary and combined linear boundaries, and the characteristics of the type curves are comparatively analyzed. The effects on the pressure curves caused by pressure sensitivity module and the effective radius combined parameter are determined, and the method for calculating the pressure-sensitive reservoir parameters is introduced. By analyzing the real field case in the high temperature and pressure reservoir, the perfect results show that the transient flow model for the pressure-sensitive fractured reservoir in this paper is correct.