Pressure Transient Model Research Articles

Application of pressure small signals extraction and amplification technology in abandoned well pattern for geothermal energy extraction and H2 storage: Numerical modeling and economic analysis

Using abandoned reservoirs for geothermal energy development and H2 storage is economical. The impact of complex fractures from long-term oil and gas extraction on geothermal energy and H2 storage is not yet clearly understood. Here, a pressure small signals extraction and amplification (PSEA) technology is developed to improve reservoir monitoring accuracy. This technology is capable of coupling many pressure transient analysis models to invert parameters for multiple scenarios. This work establishes numerical models to simulate the effects of geothermal energy extraction and H2 storage over 5000 days. Results show that this technology improves the accuracy of inverted parameters by 4–14 times. This technology adjusts the production temperature differences in a single injection-production system from 1.4K to 6.5K and the net heat power from 0.25 MW to 1.1 MW, and it can also identify an early low-rate H2 storage phase. The Non-Sorting Genetic Algorithm II calculates that the PSEA technology brings economic benefits of $704,000 and $352,000 for geothermal energy extraction and H2 storage in a single injection-production system. In conclusion, the developed monitoring technology and models improve accuracy in assessing geothermal energy development and H2 storage, preventing failures in residential heating or H2 storage projects.

Multiphase flow analysis of complex wellbore–fracture–cave connections in condensate gas reservoirs

The significant heterogeneity of fracture-caved gas reservoirs and the phase transition behavior with pressure depletion pose great challenges for flow behavior analysis and property estimation. Therefore, the objective of this paper is to develop robust and novel pressure transient analysis models for condensate-gas flow under pressure depletion in fracture-caved gas reservoirs. To characterize the complex connections between wellbore, fracture region, and caves, four conceptual models of wellbore–fracture–cave distributions are determined. The fracture region is considered as a dynamic three-zone (dry gas zone, condensate-gas two-phase zone, and transition zone) to characterize the phase transition during pressure depletion, while a variable storage concept is introduced to describe the phase transition in the wellbore and caves. The results indicate that six typical flow stages can be observed from the type curves: constant wellbore storage flow, variable wellbore storage flow, fracture linear flow (FLS), constant cave storage flow, variable cave storage flow, and transition flow. Moreover, the phase transition behavior in the fracture region is reflected in the changes of one-half slope straight lines during the FLS period, while the phase transition behavior in the wellbore and caves is reflected in the pressure derivative curve as a positive upward bending of the straight line with unit slope at later stage. The property estimation in the fracture-caved gas reservoirs (i.e., length and permeability of the fracture region, the storage coefficient of wellbore and cave) by matching with the actual pressure monitoring data provides a better understanding of the geological evidence.

A novel pressure transient analysis model for fracturing wells in fracture–cavity carbonate reservoirs

Large-scale karst caves are the principal storage spaces for hydrocarbon resources in fracture–cavity carbonate reservoirs. Drilling directly into these caves is considered the ideal mode of development, but many wells do not effectively penetrate karst caves. Therefore, acid fracturing is employed to generate artificial fractures that can connect with these caves. However, there are no appropriate well test methods for fracturing wells in fracture–cavity reservoirs. This study establishes a novel pressure transient analysis model for such wells. A new mathematical model is proposed that couples linear flow in acid fracturing cracks with radial flow in the oil drainage area. The Laplace transform and Stehfest numerical inversion provided analytical solutions for the bottomhole pressure. Typical log–log well testing curves were plotted to analyze oil flow, which occurs in ten stages. During the flow stage in fracturing cracks, the pressure and pressure derivative curves are parallel lines with a slope of 0.5. In the stage of karst cave storage, the pressure derivative curve is a straight line with a slope of 1. A comparison with previous models confirmed the validity of the proposed model. The influence of key parameters on the behavior of typical curves is analyzed. A field case study of the proposed model was carried out. Parameters related to fracturing cracks and karst caves, such as the crack length and cave radius, were successfully estimated. The proposed model has great potential for determining formation parameters of fracture–cavity reservoirs.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies. However, the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis. This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions. The pressure-dependent length shrinkage coefficients, which quantify the length changes of the inner zone and propped fractures, are modified and incorporated into this multi-zone semi-analytical model. With simultaneous numerical iterations and numerical inversions in Laplace and real-time space, the transient solutions to pressure and rate behavior are determined in just a few seconds. The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods: fracture bilinear flow (FR1), dynamic PFs flow (FR2), inner-area linear flow (FR3), dynamic inner boundary flow (FR4), and outer-area dominated linear flow (FR5). The early hump during FR2 period and a positive upward shift during FR4 period are captured on the log-log pressure transient curves, reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary. The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly. The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves. If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected, the flow rate will be overestimated in the later production period.

A numerical pressure transient model of fractured well with complex fractures of tight gas reservoirs considering gas-water two phase by EDFM

Tight gas reservoirs considering gas-water two phase is common and show obvious permeability stress sensitivity and non-Darcy seepage characteristic. However, conventional analytical and semi-analytical solving method cannot simulate wellbore pressure response of tight gas reservoirs considering gas-water two phase. Numerical model can overcome the disadvantage of analytical and semi-analytical method and achieve wellbore pressure response simulation of fractured well with complex fracture. Therefore, a gas-water two phase mathematical model of the fractured well is established and solved by embedded discrete-fracture method (EDFM) and finite volume method. Transmissibility corrections is improved on the basis of the framework of Matlab Reservoir Simulation Toolbox (MRST). Result shows that the seven flow regimes can be found according to the pressure drop derivative curves characteristic. When permeability stress sensitivity and non-Darcy is considered, pressure and derivative curve of middle-late stage shows obvious ‘upwarp’ and non-Darcy make reservoirs pressure uneven distribution. Induced fractures parameters have obvious influence on pressure and derivative curves during early and middle flow regime. In addition, fracture intersection and neighbor well production style has obvious influence on pressure curve.

A three-dimensional numerical pressure transient analysis model for fractured horizontal wells in shale gas reservoirs

Shale gas development has greatly contributed to the world's energy supply. Pressure transient analysis (PTA) has extremely helped the development of shale gas. In this paper, a three-dimensional numerical model for transient pressure analysis of multi-stage fractured horizontal wells (MFHWs) in shale gas reservoirs was proposed, which was based on the embedded discrete fracture model (EDFM). The adsorption effect of shale gas, stress sensitivity of shale reservoir, and high-velocity non-Darcy flow in fractures were considered in this model, and the model was solved by Matlab Reservoir Simulation Tool (MRST). The discrete process of governing equations is described in detail, the typical MFHW pressure transient response curve of a shale gas reservoir was obtained, different flow regimes were divided, and three-dimensional pressure distribution profile of different flow stages were drawn to clearly understand the flow states of shale gas in the reservoir. The effects of different flow mechanisms and fracture properties on the log–log curves of the MFHW pressure transient response were analyzed in detail. The numerical PTA model proposed in this paper not only considers a variety of complex flow mechanisms of shale gas, but also accurately describes the characteristics of complex fracture network of shale reservoirs in three-dimensional conditions through EDFM. In addition, the problems of the incomplete description of shale gas flow stages by conventional analytical methods and semi-analytical methods were avoided through the numerical solution. The pressure response behavior of fluid in shale gas reservoir can be better explained by using this model, which helps to reduce the uncertainty of shale reservoir development.

Study on the Influence of Overflow Well Shut-In Mode on Wellbore Pressure Distribution in Ultradeep Wells

Summary With the deepening of exploration and development of oil and gas resources, more complex oil and gas reservoirs have been found, and oil and gas well drilling has gradually developed to ultradeep (>8000 m). In the oil and gas exploration and development of deep and ultradeep wells, a small-size borehole is usually used to uncover the target layer. In the drilling stage, the annular space gap of slimhole construction is small, the pressure difference is large, and the tripping fluctuation pressure is large; therefore, overflow is easy to occur. Because the upward channeling speed after overflow is fast, the pressure fluctuation caused by shut-in is large, and the requirements for well control are high, making it very important to study the shut-in mode after drilling overflow and the fluctuation of annulus pressure to ensure the safety of ultradeep well drilling. However, the current research on shut-in mode only focuses on changing the length of shut-in time and does not consider the operation steps of closing different components. It is obviously not rigorous to simplify semisoft shut-in and soft shut-in into a hard shut-in process with a long time. In this paper, the pressure wave velocity model and transient flow model of multiphase flow in the annulus are established. The shut-in process of different wellhead components is considered for the first time, the corresponding wellhead opening function is constructed, and the effects of different well shut-in methods on annulus pressure distribution and water hammer effect are studied. Some conclusions can be drawn: The annulus pressure wave velocity aam decreases rapidly with the increase of void fraction and decreases gradually with the increase of solid particle concentration. After hard shut-in, the wellhead pressure increases rapidly and fluctuates periodically. The shorter the shut-in time, the greater is the wellhead pressure. The displacement of drilling fluid has little influence on the pressure peak but has a great influence on the amplitude of pressure fluctuation. When the annulus pressure rises, the casing bulges outward to produce additional tension, while the drillpipe shrinks inward to produce additional pressure. When the annulus pressure drops, the casing shrinks inward to produce additional pressure, while the drillpipe bulges outward to produce additional tension. During soft shut-in, the closing time of the blowout preventer (BOP) has a great impact on the annulus pressure of the wellhead. When the shut-in time is short, the pressure rises instantaneously and fluctuates violently and the cycle is short; during semisoft shut-in, the larger the opening of the throttle valve, the smaller is the fluctuating pressure of the wellhead when the BOP is closed. When the throttle valve is closed after the BOP is closed, then the larger the opening of the throttle valve, the greater will be the fluctuating pressure. With the calculation and discussion of wellbore stress distribution during shut-in of an overflow well in this paper, we hope to provide reference for two groups of people mainly. For one thing, it can offer a new idea, calculation method, and meaningful conclusion to other researchers who are studying in this area. For another, it will help engineers making decisions when overflow occurs.

Pressure Transient Analysis for a Well Drilling into a Large-Size Cave in Fracture-Caved Carbonate Gas Reservoirs

This paper studies the influence of large-size cave on pressure transient characteristics in fracture-caved carbonate gas reservoirs (FCCGR). With the rapid increase of energy demand, the exploration and development of unconventional oil and gas becomes more and more important. In recent years, many FCCGR have been discovered in western China and contribute significantly to Chinese gas reserves. However, with the presence of large-size cave, FCCGR have complex pore structures and strong heterogeneity. Traditional pressure transient analysis models cannot describe the gas flow accurately. This paper develops a novel pressure transient analysis model for FCCGR by coupling the fluctuating pressure and minor energy loss. Based on the solutions, the typical curves are plotted to analyze the pressure transient characteristics. It is found that the flow process can be subdivided into six stages, including the following: (I) wellbore storage, (II) first transition stage, (III) cave storage, (IV) second transition stage, (V) interporosity flow, and (VI) radial flow. The findings indicate that a concave is added, and the wellbore storage occurs earlier due to the existence of cave. Then, the influences of key parameters are studied. The pressure propagation coefficient and cave volume factor influence the stages I, II, III, and IV. When pressure propagation coefficient increases, the wellbore storage becomes larger and cave storage becomes smaller. The first concave moves to upper right. When cave volume factor increases, the wellbore storage occurs earlier and the curves move left in stage I. Interporosity flow factor and storage ratio influence the location and depth of the second concave. Finally, a field gas well is interpreted by using the proposed model, which verifies the reliability and correctness of the model. The findings of this study can help to better understand the influence of large-size cave on pressure transient characteristics. In addition, it can help engineers invert the cave volume, which is of great significance for the development in FCCGR.

Pressure transient behavior modeling of a multi-horizontal well pad with damaged fracture in shale gas

Multi-fractured horizontal wells significantly promoted the development of shale gas, and multi-well pads are applied generally in field application. The interference between adjacent wells attributed to the close well spacing becomes an issue that must be considered. Also, with the proppant accumulation in near-wellbore, fracture damage with low permeability and strong stress sensitivity usually occurs in far from wellbore fracture section. A semi-analytical model of multi-horizontal well pad with damaged fractures is established for the first time with a method that can deal with non-uniform fractures. Based on numerical inversion, the type curve is obtained and eight regimes are identified by the characteristics of the pressure derivative curve. Good agreement with the numerical simulation manifests the correctness of our model. Afterward, the influences of crucial parameters on pressure transient are studied. Considering the influence of adjacent wells, the pressure derivative curve elevates since well interference regime and finally maintains at a value of ∑0.5qwDi during whole system radial flow. Well spacing has an impact on the appearance time of the well interference regime. The pressure transient type curve since well interference regime moves up with higher production rate of adjacent wells. The damaged fracture section influences the early time pressure transient. With the increase of damaged fracture length, the early time pressure drop is enhanced. With consideration of stress sensitivity, ‘hump’ would be identified in the pressure derivative curve. Compared with undamaged fracture section, the ‘hump’ caused by the stress-sensitive damaged fracture section appears earlier due to a sharper conductivity decline. The model reveals the flow mechanism of stress-sensitive partially propped fractures and provides some new insights on pressure transient analysis of multi-horizontal well pad in shale gas.

A novel pressure and rate transient analysis model for fracture-caved carbonate reservoirs

Fracture-caved carbonate reservoirs (FCCRs) have been developed worldwide and contribute significantly to world's hydrocarbon reserves. Numerous models for FCCRs were proposed in the previous works. However, with more and more exploitations, some kinds of FCCRs are observed from the field geological information but not reported in the existing literature. In this paper, a novel model for FCCRs is proposed and its corresponding pressure transient analysis (PTA) and rate transient analysis (RTA) solutions are presented. This model has a wider applicability than the previous models proposed by our research team. First, the geological model is established based on the geological information. Sequentially, the simplified physical model and the mathematical model are developed. Through Laplace transformation, Duhamel's principle, and Stehfest numerical inversion, the solutions of dimensionless bottom-hole pressure and dimensionless flow rate integral are derived. Then, the RTA type curves of two-cave model are plotted to recognize the flow characteristics, which can be divided into five regimes comprehensively. In addition, two concaves are observed on the derivative curve. The RTA type curves of three-cave model are also presented. A comparison between the RTA type curves of two-cave model and three-cave model shows that when one more cave exists in the formation, one more concave will be added to the derivative curve. Furthermore, the differences between the proposed model and previous models are presented through comparing the PTA type curves. Next, the effects of key parameters on the RTA curve behavior of two-cave model are demonstrated. Results indicate that the RTA curves are controlled by the friction and fluctuation coefficients, mobility, storage ratio, region radius, and cave storage constant. The friction and fluctuation coefficients influence the depth of first concave, while the storage ratio, region radius, and cave storage constant dominate the middle flow period, and the mobility has an impact on the boundary dominated flow regime. Finally, the application of proposed model on a field well from Shunbei Oilfield, western China is presented to calibrate its accuracy and reliability. ∙ A novel model for fracture-caved carbonate reservoirs is established. ∙The rate transient characteristics of this model is conducted. ∙Sensitivity studies of some key parameters on the pressure response are conducted. ∙An application of proposed model on a field well is presented.

Approach to shape factor determination in estimating horizontal wells productivity for pressure transient model of Mutalik et al.

Horizontal well productivity (Jh) equation at pseudo-steady state (PSS) of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) has long and widely been known to estimate well performance. One key parameter of that equation is the so-called shape factor (CA) that characterizes the effect of the pressure transient behavior at PSS depending on well and reservoir configuration. For limited well and reservoir configurations, CA tables had been generated decades ago, but at unknown accuracy they are still used widely via tedious correlation or interpolation from those reported CA tables to estimate Jh for different configurations even today. The innovation points in this study are as follows: (1) The pressure transient model of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) (PTM) is improved to generalized pressure transient model (GPTM) and verified by converting several dimensional parameters to dimensionless forms. (2) An efficient algorithm is developed, and accurate CA and Jh are obtained for any well and reservoir configuration. (3) The accuracy of the reported CA tables is quantified, and the consequences are determined when they are used to estimate Jh. (4) New CA tables and their correspondence dimensionless time based on drainage area at PSS ((TDA)PSS) tables are generated for a wider range of well and reservoir configurations. Although horizontal wells usually have been drilled with high dimensionless well length (LD) industrially (i.e., LD > 10), it is still a significant error in Jh by (< 7%) that has been determined when using the reported CA of PTM for rectangular reservoir aspect ratio (xe/ye) = (1) and (2) in the both assumed input data, while for (xe/ye = 5), significant error in Jh starts from (46.43%) to (1037%) for LD = (10) to (100), respectively, in the first assumed input data [variable, dimensionless wellbore radius (rWD)] and expected the same in the second assumed input data (constant rWD).

Evaluation of fracture closure and its contribution to total production for a well with non-planar asymmetrical vertical fracture based on bottom-hole pressure

Hydraulic-fracturing is an important well-stimulation technique, the fracture closure is inevitable during production. The existing pressure transient analysis models either ignore the length of fracture-closure segment that causes the explained fracture half-length to be smaller, or only use the fracture conductivity to evaluate fracture closure. To fully evaluate fracture closure and provide a reference for oilfield engineers determining whether need measures to improve the well performance, meanwhile considering the non-planar asymmetrical fracture is common met in low-permeability reservoirs, this paper proposes to use two parameters (flowrate proportion and conductivity of fracture-closure segment) to comprehensively evaluate fracture closure, and hence develops double-segment non-planar asymmetrical fracture model (DPAFM). Planar asymmetrical fracture model is simplified case of proposed model. The semi-analytical solution is obtained by using finite difference method (FDM) and Gonzalez-Chavez and Cinco-Ley (2006) model is used to verify the solution. The results of this work show that (a) The example of actual well simulation proves the model is more suitable for the actual field data, and the model established is better matched than the saphir software; (b) The proposed model can obtain production proportion and conductivity of fracture-closure segment to comprehensively evaluate fracture closure; (c) There are four typical flow regimes for the DPAFM, including bilinear flow, interference linear flow, formation linear flow, pseudo-radial flow. The interference linear flow regime with ‘V-shape’ characteristic is unique; (d) Conventional explanation thinks the ‘V-shape’ characteristic represents the secondary fracture developed (e.g., OFFN, TLFN and MOFN). However, this paper gives another possibility that the ‘V-shape’ reflects fracture closure. The findings of this study can help for better understanding of illustrating the practicability of proposed methodology in evaluating the fracture closure and reservoir parameters. This research provides guidance for technicians to formulate the next step to increase production plan and helps the oilfield engineers determine whether take measures to improve the well performance. • We present a double-segment non-planar asymmetrical fracture model (DPAFM) considering the effect of conditions inside fracture. • We provide an additional explanation about ‘V-shape’ characteristic on the pressure derivative curve besides the complex fracture geometries. • The field cases illustrate the practicability of proposed methodology in evaluating the reservoir parameters, fracture closure, fracture segment flow rate and fracture propagation.

Analytical modeling of flow regimes during cyclic CO2 injection in hydraulically fractured tight reservoirs for enhanced oil recovery

This paper presents several analytical models for the pressure distribution in hydraulically fractured reservoirs depleted by horizontal wells with the aid of cyclic CO2 injection. The objective is to eliminate uncertainties in predicting reservoir performance after the enhancement by CO2 injection and develop accurate tools for designing CO2 injection projects. This paper's primary purpose is to present novel analytical models for flow regimes and validate them. The proposed models are unique because they are derived without using an approximated approach, they consider multiphase flow and can be utilized for injection applications.Although CO2-injection has been a favorable enhanced oil recovery (EOR) approach in the petroleum industry, some studies reported its negative impact due to the premature decline in production. Additionally, few researchers have linked the cyclic injection with the flow response inside the formation. This paper presents three flow regimes (hydraulic fracture regime, bilinear flow regime, and formation linear-flow regime) that develop during production and injection in unconventional reservoirs. The analytical solutions that encompass the non-approximated trilinear pressure transient model for hydraulically fractured reservoirs are developed. The models are solved by one of the state-of-the-art computational tools. The solutions are used to characterize the analytical models for the three aforementioned flow regimes. Then, the numerical solution is designed to validate the analytical models.The results show a good agreement between analytical and numerical solutions. The hydraulic fracture linear flow regime and bilinear flow regime occur at the early and intermediate well production stage. These flow regimes indicate the end of the CO2 injection into the fractures and the stimulated reservoir volume, respectively. Thus, knowing the period for the CO2 injection and the hydraulic fracture characteristics will facilitate the optimization of the CO2 injection process in tight formations depleted by multiple hydraulic fractures.

Numerical investigation of immiscible Liquid-Liquid displacement in Hele-Shaw cell

In the present work, a numerical simulation has been performed on the immiscible liquid–liquid displacement flow in two- dimensional rectilinear Hele-Shaw cell (HSC) by using ANSYS FLUENT commercial software. The volume of fluid (VOF) model has been used to track the interface of immiscible liquids in the displacement flow process. A finger shape instability records at the oil–water interface when a large viscous liquid oil is displaced by lower viscous liquid water from the oil-saturated Hele-Shaw cell. This finger shape interfacial instability is called viscous fingering. The viscosity ratio (ratio of the viscosity of displacing and displaced liquids) of two-phase flow is less than unity then unstable displacement occurs and results in finger shape instability appears at the interface. The numerical simulation of two-phase flow has been performed by using the pressure base solver and transient model. The present work aims to capture the propagation of a finger shape instability at the oil–water interface and calculate the sweep efficiency by image processing. We observed that water displaces approximately 72.42% of oil from the entire oil-saturated HSC and sweep efficiency gradually increases with time in the displacement process.

Transient Pressure Analysis of Inclined Well in Continuous Triple-Porosity Reservoirs With Dual-Permeability Behavior

Inclined wells has recently been adopted to develop fractured-vuggy carbonate hydrocarbon reservoirs (FVCHRs) composed by matrix, fracture and vug system. Therefore, it is significant for us to describe pressure transient of inclined well for FVCHRs. In this paper, it is assumed that vug and fracture system connect with wellbore, and inter-porosity flow from vug to fracture system appears. Therefore, the pressure transient responses model of inclined well with triple-porosity dual-permeability behavior was built. The model is solved by employing Laplace integral transform and finite cosine Fourier transform. Real-domain solution of the model is obtained by Stehfest inversion algorithm. On the basis model of the published paper, the solution of the simplified model of this paper was validated with horizontal and vertical well of FVCHRs with triple-porosity dual-permeability behavior, and results reach a good agreement. Type curve, according to pressure derivative curve characteristic, can be divided into eight flow regimes, which includes wellbore storage, skin reflect, early vertical radial flow, top and bottom boundary reflection, linear flow, inter-porosity flow from vug to fracture, inter-porosity from matrix to vug and fracture and pseudo-radial flow regimes. The influence of some vital parameters (inclination angle, inter-porosity flow coefficient, well length and permeability ratio etc.) on dimensionless pressure and its derivative curves are discussed in detail. The presented model can be used to understand pressure transient response characteristic of inclined wells in FVCHRs with dual-permeability behavior.

Pressure transient behavior and flow regimes characteristics of vertical commingled well with vertical combined boundary: A field case in XC gas field of northwest Sichuan Basin, China

The multilayered deposition is the main feature of the XC gas reservoir in the northwestern Sichuan Basin. The boundaries among layers of the XC gas reservoir is different. In this paper, we propose an extended pressure transient analysis model for vertical commingle well, considering different boundary radii and boundary types, to capture the Vertical Combined Boundary (VCB) effect on the pressure transient behavior and flow regime characteristics.The analytical solution is yielded by the Laplace transform, Bessel functions, Duhamel's superposition principle, and Stehfest inversion algorithm, and new flow regimes under different boundary combinations are identified by the pressure derivative curve. Taking the dual-layer VCB model as a type example, nine combinations of boundaries are analyzed. Compared with the current vertical commingled well model with the same boundary radii or single boundary types, this model has novel flow regimes controlled by the VCB.The research results indicate that the pressure derivative type curve during the novel flow regimes stage can diagnosis the VCB type. On the one hand, there are quantitative linear relationships between the pressure derivative feature value and interlayer heterogeneity of the VCB model with the same boundary radii. These linear relationships provide a new perspective to quickly capture interlay heterogeneity through the of the pressure derivative feature value. One the other hand, the pressure behavior and flow regimes of the VCB model with different boundary radii obey the successive superposition rule. This rule provides a method to recognize the VCB type with different boundary radii based on that of the VCB with the same boundary radii.Finally, a field case from the northwestern Sichuan Basin gas reservoir is discussed in detail to exhibit the workflow of our model application and validate the capability of our model.

Numerical pressure transient analysis for unfilled-caved carbonate reservoirs based on Stokes-Darcy coupled theory

Caved carbonate reservoirs are very special because of the strong heterogeneity. The pressure transient behavior of the caved carbonate reservoirs is quite different from the conventional homogeneous or dual medium reservoirs because of the presence of large-scale cavities. There are two types of cavities: filled and unfilled, which dominated the production of the reservoirs. Fluid flow in the unfilled cavity should be described by Stokes' equation rather than Darcy's law. It is needed to better understand the role of the unfilled cavities plays in the pressure transient analysis. The objective of this work is to analyze the pressure transient behavior of the unfilled cavities. A coupled Stokes-Darcy pressure transient model is developed and the finite element method is applied in the solutions of the mathematical models. Then, the numerical pressure transient model is used in the analysis of two typical cases: a well drilled into the unfilled cavity (WIC) and a well not drilled into the unfilled cavity (WOC). The type curves of the WIC model indicate that flow in the unfilled cavity is an oscillated pressure-drop rather than a radial flow. The unfilled cavity that the well drilled into would be considered as an enlarged wellbore which is equivalent to a negative skin factor, as a consequence the wellbore storage coefficient will increase. Main characteristics of type curves for WOC model are the valley on the pressure derivative. A cavity with a larger size and smaller distance from the wellbore would give rise to a deeper valley. Comparative results indicate that unfilled cavities described by the Stokes' equation are not the limit of the filled cavities with extremely large mobility, which was predicted by previous work.

Pressure transient behavior of layered commingled reservoir with vertical inhomogeneous closed boundary

The multilayered deposition is the main feature of the tidal flat reservoir in the western Sichuan Basin. The boundary distance among layers of the tidal flat reservoir is different. To understand the influence of vertical inhomogeneous closed boundary (VICB) on pressure transient behavior, an extended n-layer VICB reservoir model is presented.Firstly, the VICB is discretized into n boundary segments representing the characteristics of the individual layer, and the reservoir is divided into n horizontal layers accordingly. The pressure transient model of the n-layer VICB reservoir is established by the seepage equations and boundary conditions of the individual layer. Secondly, solving Bessel equations consisting of 2n boundary conditions by the Cramer's rule to obtain the bottom-hole pressure solution in Laplace space. The wellbore storage and skin effect are taken into account by Duhamel's principle in the Laplace domain. Lastly, the bottom-hole pressure solution in the real-time domain is obtained by the Stehfest numerical inversion algorithm. The comparison result with the bottom-hole pressure of the two-layer reservoir proves the reliability of the n-layer VICB reservoir model.In the n-layer VICB reservoir model, a new VICB radial flow regime is identified which easily mistaken as the outer radial flow of the composite reservoir model. The result of sensitivity analysis shows that the pressure transient behavior of the n-layer VICB reservoir has the “equivalent compound zone effect” and “equivalent boundary radii effect”. There is a quantitative relation between the distribution of VICB and the characteristics value of pressure derivative during the VICB radial flow regime stage.The “equivalent compound zone effect”, “equivalent boundary radii effect” and the quantitative relation provide a simple and fast analytical method for identifying the vertical distribution and distance range of VICB. Finally, a field case from the western Sichuan Basin multilayered gas reservoir is discussed in detail to validate the capabilities of our model.

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.

Increasing confidence in estimating stimulated reservoir volume by integrating RTA and microseismic analysis

Rate Transient Analysis (RTA) and microseismic monitoring are gaining momentum in modelling Stimulated Reservoir Volume (SRV) in Multi-Frac Horizontal Wells (MFHWs) in unconventional reservoirs. From a behavioural perspective, RTA uses history matching and production data analysis to estimate fracture volume and productivity, and microseismic analysis maps frack-ing-induced micro-earthquakes to calibrate the fracture network from a spatiotemporal point of view. Defining the concepts of normalized rate, material balance time and pseudo-time, dynamic drainage volume, together with convolution, deconvolution and analytical models, make RTA a powerful and computationally efficient tool for modelling MFHWs (Blasingame et al., 1991; Agarwal et al., 1998, Mattar and Anderson, 2003). Poe (2005) proposed a rate-transient analysis method for evaluating the performance of wells with limited pressure data using the superposition theory and dimensionless parameters. Soliman and Adams (2010) estimated fracture properties by applying Flow Regime Identification (FRI) plots to early production data, followed by using analytical models derived for each distinct flow regime. Kuchuk et al. (2016) calibrated reservoir models by history-matching the transient flow rate and pressure measurements. Brown (2009), Stalgorova and Mattar (2012a, 2012b), Deng et al. (2015), and Yuan et al. (2015) divided the reservoir into a series of linear flow regions and derived analytical pressure transient models from the pressure diffusion equation, not only to confirm the validity of the identification, characterization and diagnostic analyses but also to provide production forecasts and carry out optimization studies. Clarkson et al. (2015) successfully applied RTA analytical and semi-analytical modelling techniques to a gas condensate MFHW in a Western Canadian Basin, highlighting the fact that building a predictive understanding of drainage volume dynamics is best started with physics-based analytical models rather than multi-phase numerical simulations. This is particularly important in unconventional reservoirs where the complex, small-scale physics and rock-fluid interactions significantly hinder gathering enough measurements to support the numerically added complexities.