Boundary-dominated Flow Period Research Articles

Rate transient analysis of wells exhibiting two-phase (gas+water) flowing by use of pseudopressure-based approach

The primary focus of rate transient analysis (RTA) is put on the estimation of the reserves of gas/water reservoirs. RTA based on the single-phase assumption is limited to gas/water two-phase flow in the development of the material-balance time function. This work aims to propose a practical approach for analyzing production data from wells exhibiting gas/water two-phase flow during both infinite-acting flow (IAF) and boundary-dominated flow (BDF) periods. In this work, we present a comprehensive pseudopressure-based solution associated with the constitutive saturation/pressure (Sw/p) relationship. The pseudovariables, namely pseudopressure and β-factor, have the ability of handling the two-phase nonlinearities in the governing flow equations of gas and water phases and generating the required benchmark analytical solutions for liquid flow equation. By integrating the liquid-type solutions with the principle of Duhamel convolution, a set of gas/water-phase productivity equations are recast for wells producing at different operating conditions, including constant bottomhole-pressure, constant rate and steplike change in bottomhole-pressure/rate. The presented solutions provide a theoretical framework for developing two-phase RTA based on two-phase material-balance pseudotime (MBPT). The RTA method is validated against synthetic cases generated from numerical simulation, and the dependability of two-phase MBPT is also corroborated in detail. A field case example is analyzed to demonstrate the practical applicability of this method. The RTA method provided herein accounts for all flowing phases in the reservoir, and serve as an alternative to numerical model history matching for estimating original gas in place (OGIP) and original water in place (OWIP).

Decline-curve analysis with decline rate for improving reserves estimation in gas reservoirs

Over decades, the rate decline analysis has been the industry's bedrock for reserve estimation. The Arps method has gained credibility since its introduction in 1945, particularly in oil reservoirs. However, gas reservoirs present challenges due to handling increasingly deeper geologic horizons with higher pressure and low-permeability formations, rock compaction, and overpressured reservoirs, among other challenges. This study shows a novel decline-curve analysis involving the decline rate rather than the flow rate. The proposed methodology applies to production data from a gas reservoir with varying operating conditions during the boundary-dominated flow (BDF) period. The method does not involve any pseudo-functions.The proposed method is independent of the variation of flow rate and pressure. The PVT data (viscosity, compressibility, z-factor) aids the construction of a type-curve involving the viscosity-compressibility ratio with the recovery factor without any reservoir-specific information. The decline rate with adjustment for changing operating conditions leads to a single decline-curve plot involving the viscosity-compressibility ratio (λ) and dimensionless pressure (pD) without any correlating parameter. Two synthetic examples verified the proposed approach, and two field datasets validated it. Overall, the proposed method strengthens the reserve estimation with an independent process for meeting corporate and regulatory requirements in conventional and tight-gas reservoirs.

Assessing reservoir connectivity with pressure/rate surveillance data

Estimating reservoir connectivity is critical for assessing infill-drilling prospects and initiating fluid injection in enhanced oil recovery operations. Several methods have appeared in the literature over decades to meet these business needs, given that all tools, including seismic imaging, have limitations. Besides imaging, geochemical fingerprinting constitutes a powerful tool to gauge the compartmentalization question. However, real-time pressure/rate surveillance data allows assessing interwell connectivity vis-à-vis the overall drainage volume. This study presents a simplified approach to using the reciprocal-productivity index (RPI) vs. the total-material-balance time ( t ¯ T M B ) plot. This tool exhibits the same slope for those wells in the same compartment beyond the start of the boundary-dominated flow (BDF) period. The wells showing different slopes imply that they are in separate drainage volumes. The early-time transient period remains muted to minimize confusion on this Cartesian plot. We validated the proposed tool's efficacy with 2D and 3D models with increased degrees of reservoir complexity, followed by the verification phase with four field examples. The use of other analytical tools complemented our findings.

A multi-fractured well performance model for unconventional reservoirs

Due to the ultra-low permeability of unconventional reservoirs, transient state prevails for a considerable period. Despite this, fracture interference can cause an apparent no-flow boundary. Consequently, the Duong's model, which was developed for transient-state period, yields unreliable estimates during the late-time period. In this paper, the Duong's model is modified to account for boundary effects caused by fracture interference and/or unstimulated reservoir regions that serve as no-flow boundaries. Specifically, an empirical correction function, which assumes an exponential decline, has been used as a “modifier” to extend the Duong's model to boundary-dominated flow period. The correction function ensures that during boundary-dominated flow period, an exponential-decline behaviour dominates. The proposed rate-decline model encompasses a gamma function, which converges at large times. Results show that a fractured-well production behaviour is characterised by a decaying power-law during early-time period and tends to exponential decline during late-time period. The results also suggest that although the conventional Duong's model gives good estimates during the transient-state period, it yields optimistic estimates during the boundary-dominated flow period. The proposed model gives a good match and estimates not only in the transient-state period, but also in the boundary-dominated flow period. A major advantage of the proposed model is that it converges to estimated ultimate recovery at large times without imposing any rate and time limits. A good agreement of the estimated ultimate recovery with analytical and semi-analytical models was obtained. Also, results suggest that the proposed model gives conservative estimates. The proposed model will be useful for analysing and predicting both the early- and late-time production performance of a multi-fractured well producing from an unconventional reservoir.

Using Agarwal analytical approach with superposition rate and time solutions to analyze multi and single well systems

There are many RTA (Rate Transient Analysis) methods available to analyze wells producing from unconventional formations. The approach of Agarwal (2010) is one of the RTA techniques which have gained an increasing interest due to its simplicity, flexibility, and wide range of applications. In this study, the approach of Agarwal (2010) was adopted to analyze not only single well systems but also multi-well systems by using three different equations. These equations were then integrated with the principle of superposition rate rather than conventional superposition time. By using two field cases, the accuracy of the proposed approaches was validated with current analytical methods and reservoir simulation. The first case represents a multi-well system in which the wells producing with a fixed flowing pressure were put on production at the same time. The operating conditions were then relaxed in the second case by allowing the wells to have different production starting times and varying production profiles.Additionally, this work examined in details the ability of the superposition rate function in converting various production behaviors to their equivalent constant rate solutions. This research clearly shows the advantage of the superposition rate solution over the traditional superposition time function (material balance time) in maintaining the data order in time. Such an advantage makes it easier for the analyst to observe the production changes in well performance in real normal time.Several case studies were used to show how Agarwal (2010) can be utilized to extract different information from boundary-dominated flow period which are useful in the evaluation of reservoir compartmentalization and the effectiveness of infill drilling campaigns. In addition to that, the application of Agarwal (2010) in terms of frac hits evaluation and refracturing operations encountered during the transient flow period was also examined.

Injection data analysis using material balance time for CO2 storage capacity estimation in deep closed saline aquifers

Estimating the ultimate storage capacity of deep saline aquifers is important to address the formation potential to store the envisioned large volumes of CO2. Injection data (i.e. injection rate, bottomhole pressure, and cumulative injected volume of CO2) are routinely recorded during storage operations. These data contain valuable information on the subsurface (e.g. the reservoir pore volume and the formation storage capacity) that can be extracted. In this paper, we present a two-step graphical technique to infer the pore volume and the ultimate storage capacity of closed saline aquifers by analyzing the available injection data. First, the pore volume is inferred through adapting the concept of the material balance time. Material balance time is an approximate superposition time function developed to interpret production data from oil and gas wells operating at variable pressure/rate conditions during the boundary-dominated flow period. Using material balance techniques, the ultimate storage capacity is then estimated through linear extrapolation of the average pressure trend to the maximum allowable pressure the formation can withstand. The average pressure is not available in practice, but is can be obtained from the injection data. Two approaches are presented in this study to calculate the average pressure; namely the rigorous and the approximate approaches. Unlike the rigorous approach, the approximate approach does not require a prior knowledge of some reservoir properties (e.g. relative permeability, absolute permeability, formation porosity and thickness) to calculate the average pressure. To investigate its potential and reliability in analyzing CO2 injection data, the proposed technique is applied to four synthetic cases representing different well operating conditions. Results indicate that the approximate approach consistently overestimates the actual (simulated) storage capacity as compared to the rigorous approach. The agreement - between the inferred and the simulated reservoir pore volume, and between the analytical and numerical estimates of storage capacity - validates the potential application of the technique to CO2 storage in closed saline aquifers. The technique is further substantiated through application to a field data set utilized from a commercial-scale geological storage (CGS) project. Field data interpretation shows that the proposed technique can be utilized to identify the degree of hydraulic continuity and reservoir compartmentalization within a target formation by interpreting the corresponding pressure and rate responses.

Modifying rock compressibility to analyze the production data of non-volumetric gas and gas condensate reservoirs

Production data analysis, particularly the flowing material balance method, has been used for many years as an efficient, practical, and significant method to obtain important reservoir parameters. Many studies have been done to develop the flowing material balance method in different types of reservoirs which in most of them, the main limitation is that the reservoir has been considered to be volumetric. Therefore, despite being widely used, this method has not been well developed for non-volumetric water drive reservoirs. In the present work, an extremely simple yet very accurate method was introduced to obtain an excellent estimation of average pressure and gas in place of non-volumetric dry gas and gas condensate reservoirs. In our proposed method, a modified rock compressibility parameter was presented to modify current flowing material balance equations which have been developed for volumetric dry gas and gas condensate reservoirs previously. Using the proposed compressibility, the modified flowing material balance equations can be used for non-volumetric dry gas and gas condensate reservoirs producing with constant bottomhole pressure during the boundary-dominated flow period. Moreover, the iterative procedures to estimate average pressure and gas in place of these kinds of reservoirs were presented in detailed steps. Also, the validity of the proposed flowing material balance equations was performed using a commercial numerical reservoir simulator. The obtained results prove the efficiency of the proposed method. Furthermore, due to the high amount of uncertainty in aquifer parameters, an uncertainty analysis has been performed on aquifer parameters using Monte-Carlo simulation. The results of the study indicated that the determination of appropriate aquifer parameters has a significant impact on the estimation of reservoir parameters which can be obtained using a combination of uncertainty analysis and the proposed flowing material balance technique.

A production-based model for a fractured well in unconventional reservoirs

Due to the depletion of conventional reservoirs and the high demand of energy, unconventional reservoirs will be relied on to supply the world's energy for the foreseeable future. Unfortunately, because of their complex storage and flow mechanisms, modelling and analysis of unconventional reservoirs have been very challenging. Although semi-analytical and numerical models have been proposed, these models rely on somewhat simplifying assumptions and require several input parameters. In this paper, a production-based model is proposed to analyze and predict a fractured-well performance in unconventional reservoirs (specifically, tight and shale reservoirs). The model assumes a power law with a stretched exponential cut-off. While the power-law term governs the transient-state period, the stretched exponential term, which is a superposition of exponential decays, governs the boundary-dominated flow period. As a result, the model is capable of matching both the transient state and boundary-dominated flow portions of the data. The model has been validated with a numerical data and applied to several field data. Results of the model have been compared with other existing models. The findings show that the proposed model yields relatively good estimates, and matches both the transient and boundary-dominated flow periods. The proposed model may contribute to the ongoing efforts to improve the analysis and forecasting of fractured-well performance in unconventional reservoirs.

A new production analysis method for shale gas well based on the evaluation of decline parameters in advance

Production forecasting for multi-fractured horizontal well (MFHW) in shale gas reservoir is of vital importance to the evaluation of development potential.In this paper, we develop a new method to predict production of the MFHW under constant bottom-hole Pressure (BHP) condition. Based on the analytical model, well's life cycle is divided into two stages, in which the decline models are established, respectively. According to these models, the decline exponent is a function of fluid properties, the pressure drawdown strategy and heterogeneous completion. It can be directly calculated without production data matching. Influence of desorption on decline exponent, calculation of “initial pressure” during boundary dominated flow (BDF) period, are discussed. A workflow is established to perform production forecasting for a MFHW with complex fracture configuration and constant BHP in shale reservoir. A preliminary scheme is also developed to extend the workflow to variable BHP condition. Results indicate that a special hyperbolic model in which decline exponent changes as pressure drops, can be employed to forecast production during BDF. A constant decline exponent may result in an underestimation/overestimation well production, especially, in the BDF period. This new method can be used to explore how each factor impacts well productivity rigorously. Compared with conventional methods, it is of higher accuracy when making production forecast, especially for wells with short history.

To Interpret Rate Transient Analysis for the Determination of Reservoir Properties

Rate-time decline curve analysis is a major technique which is mostly used in petroleum engineering. Many methods are used for the determination of the decrease in the production rate within a given period of time. The main disadvantage of Arp’s decline type curve analysis is that it is only used for boundary dominated flow period; it is not used for transient flow period. The analysis of the Fetkovich is to determine the log-log type curve for both the transient flow period (early time period or infinite) and boundary-dominated flow period (late time period). Arps developed the type curve which shows the production rate decline with time for the finite reservoir or late time period. The exponential or constant flow decline, hyperbolic decline, and harmonic decline according to the value of decline curve exponent (b) is given by Arps. After that Fetkovich improved on earlier work done by Arps in predicting decline production rate of wells over a given period of time. The main objective of this study was to plotting the rate transient analysis curve. I will plot the Fetkovich type curve (combined early and late times region). The graph will be plotted between the dimensionless decline flow rate (qDd) and the dimensionless decline time” (tDd). This will be the objective of the study.

Use of a New Analytical Model To Match Production Data and Identify Opportunities To Maximize Well Productivity in the Tuscaloosa Marine Shale Reservoir

Summary The low productivity of the oil wells in the Tuscaloosa Marine Shale (TMS) Trend, located in Louisiana and Mississippi, is a mystery. Production data from 55 wells in the TMS Trend were analyzed to identify possible means of enhancing well productivity. The −1/2 slope in a log–log plot for reservoir linear flow (RLF) was observed for some wells, but not all, and the −1 slope for boundary–dominated flow (BDF) has not been seen in the past 5 years of production. The behavior of the TMS wells is attributed to the ultralow permeability of the TMS matrix and the decline of fracture conductivity, both of which delay the BDF. On the basis of the concept of the distance of investigation, derived from the radius–of–investigation concept, the matrix permeability of the seven TMS wells was estimated to be between 34 and 65 nd, with an average of 51 nd. A new mathematical model for production decline of multifractured horizontal wells was developed taking into consideration the time–dependent fracture conductivity during the BDF period. This model fits TMS–well production data, with an average error of 6.12% and an R2 value of 0.96. Assuming constant matrix permeability, fitting the new model to the production data in the BDF period gives a rate of fracture–conductivity decline of between 0.20 and 0.74% per month. The new mathematical model reveals opportunities to optimize well completion to enhance well productivity in the TMS Trend. For a given amount of fracture proppant allocated to a well, the shortest possible fracture spacing should be used to maximize well productivity. If the number of fractures is fixed as a constraint of well completion design, well productivity is inversely proportional to the square root of fracture spacing (i.e., if the fracture spacing is shortened by fourfold, well productivity is expected to double). If the horizontal wellbore length is fixed as a constraint of well completion, well productivity is inversely proportional to fracture spacing (i.e., if the fracture spacing is shortened by 50%, well productivity is expected to double).

An Analytical Model for Capturing the Decline of Fracture Conductivity in the Tuscaloosa Marine Shale Trend from Production Data

Fracture conductivity decline is a concern in the Tuscaloosa Marine Shale (TMS) wells due to the high content of clay in the shale. An analytical well productivity model was developed in this study considering the pressure-dependent conductivity of hydraulic fractures. The log-log diagnostic approach was used to identify the boundary-dominated flow regime rather than the linear flow regime. Case studies of seven TMS wells indicated that the proposed model allows approximation of the field data with good accuracy. Production data analyses with the model revealed that the pressure-dependent fracture conductivity in the TMS in the Mississippi section declines following a logarithmic mode, with dimensionless coefficient χ varying between 0.116 and 0.130. The pressure-dependent decline of fracture conductivity in the transient flow period is more significant than that in the boundary-dominated flow period.

Analysis of production prediction in shale reservoirs: Influence of water film in inorganic matter

To commercially develop shale gas reservoirs, multi-fractured horizontal wells are widely employed in the industry. A number of analytical models have been proposed to evaluate and forecast production from fractured horizontal wells. However, the water film adsorbed in inorganic pores of shale matrix is often neglected and its effect on gas production has never been focused on. Moreover, the effect on gas production caused by the characteristic of a well not located in the center of drainage area has not been drawn much attention. In this work, on a basis of enhanced-fracture-region (EFR) model, a new model is put forward to conduct production prediction of multi-fractured horizontal wells from shale gas reservoirs. This novel approach incorporates critical gas transport mechanisms in shale, and considers the characteristic of a well not located in the center of drainage area. Specifically, this model takes the bulk-gas transport regimes, water film effect, stress dependence and real gas effect into account, which matches well with the real shale reservoirs. The analytical solution of the proposed model is deduced by employing the Laplace transformation approach, and then introducing the numerical algorithm put forward by Stehfest to invert to the real time domain. This presented model is verified by both numerical simulation cases and actual field applications. In addition, a sensitivity study is performed to illustrate various parameters on flow-regime and production curves. Results illustrate that both the size of stimulated zone and distance from the well to the outer boundary contribute to the well performance. A larger size of the stimulated zone increases the duration of the first linear flow period, whereas will shorten the duration of the third boundary dominated flow period. A larger distance from the well to the outer boundary leads to stronger gas production. The real gas has non-obvious effect on gas production. Both the stress dependence and humidity have negative effects on production curves, which are induced by the decrease of the effective pore radius. Specifically, compared with the gas production without considering water film effect, when the humidity value is 0.1, gas production can achieve an average decrease of 18.57%. When the humidity value is 0.3, gas production can reach an average decrease of 26.10%.

Adaptability of Power Law Exponential Decline Model for Hydraulically Fractured Unconventional Reservoirs during and After Linear Flow

Reserve estimation of unconventional formations is a new challenge to reservoir engineers due to the geological uncertainty and complex flow patterns evolving in the multi-fractured horizontal wells (MFHWs). Some predicting models have been presented and widely used in MFHWs exhibiting a long-term linear flow, such as stretched-exponential production-decline (SEPD), power law exponential decline (PLE) and Duong’s model. Plenty of successful field applications of these models seem to have demonstrated their availability and correctness especially in the transient linear flow period. Due to the limitation of reservoir boundaries or size of stimulated volume, any fractured tight reservoir will eventually exhibit a boundary-dominated-flow (BDF). The models above which show “goodness of fit” in linear flow may not be used or will cause great error when used to predict production in BDF period. This paper compared the newly developed PLE model with the traditional Arps’ hyperbolic decline model in terms of production historic match, decline rate and decline exponent during and after linear flow. The analysis result demonstrated that PLE model actually cannot match production decline characteristics as previously thought when only linear flow appears and it is a model which should be used in the transition period rather than linear flow period as applied in the past few years. The wrong usage of the model will cause great error to reserve estimation. The modified steps to predict production in different flow pattern are given in this work. The outcome of this work should help the industry to forecast production and ultimate reserve more accurately in tight oil and shale gas reservoirs.

Temperature transient analysis for bounded oil reservoir under depletion drive

The significant pressure and temperature signals at wellbores associated with hydrocarbon production can be very useful for reservoir characterization and production analysis purposes. Temperature transient analysis is emerging partly due to the advancement of the downhole temperature monitoring system. Among different flow regimes encountered during the production of a vertical well, the long-lasting boundary dominated flow is crucial since most oil in conventional reservoirs are recovered during this period. The production induced temperature response behaves transient for boundary dominated pressure response and can be analyzed for reservoir property estimation. In this work, we derive a novel temperature transient analytical solution to model sandface temperature signal under boundary dominated flow. Our approach to obtaining the analytical solution from the governing energy balance equation uses Laplace transform with the input of pseudo-steady state pressure equation. This solution can be integrated with previous temperature transient analytical solutions to model the temperature signal from a depletion drived production well. The temperature modeling results acquired from this analytical solution are validated against those from numerical simulation in multiple cases and present distinct behavior under boundary dominated flow. Compared to the heating Joule-Thomson effect in the transient period near the production well, a cooling effect is observed throughout the reservoir after pressure transient reaches the reservoir outer boundary. The magnitude of this cooling effect is proportional to production time. This finding shows the potential of using temperature data at observation wells away from the production well during boundary dominated flow. Further parametric analyses are conducted on eight reservoir, production, and fluid properties to investigate their impacts on the temperature modeling results. These parameters are categorized based on their sensitivities on periods of transient and boundary dominated flow, in which total compressibility and production drainage area are sensitive to the temperature signals under boundary dominated flow only. Unlike the drawdown test, we find that the buildup temperature behavior under boundary dominated flow is identical to that during the transient period. After presenting the forward temperature modeling results, we extend existing reservoir characterization procedures to incorporate the boundary dominated flow. Drainage area and the distance to the closest boundary from the production well can be estimated from the measured temperature data acquired at both production and observation wells. Decent accuracies of the estimations are achieved for the examples presented in this work. The effects of thermal conduction and heat loss may not introduce significant errors in both forward and inverse thermal modeling for the long-lasting boundary dominated flow period.The temperature transient analytical solution under radial boundary dominated flow introduced in this paper considerably extends the scope for temperature transient analysis. This solution enables observation well temperature transient analysis, which seems promising for field application during the boundary dominated flow period. The analytical solution presented herein helps to advance the temperature transient analysis over the whole well production period and forms a basis for future studies on variable rate temperature transient analysis (rate-temperature transient analysis).

Treatment of Rate-Transient Analysis During Boundary-Dominated Flow

Summary Significant advances have been made in the development of analytical models for performing rate-transient analysis (RTA) for single-phase oil and gas reservoirs. The primary complication associated with the adaptation of these solutions to wells exhibiting multiphase flow is the single-phase assumption in the development of the material-balance time function. Despite some efforts in modifying existing dry-gas formulations for use with gas/condensate reservoirs, that approach is not practical for analyzing multiphase flow from oil wells with multiphase-flow characteristics. In this work, we present a simple yet semianalytical model that provides a solution for analyzing production data from wells exhibiting multiphase flow during boundary-dominated flow periods. The solution is obtained by combining the material-balance equation and the productivity index (PI) for all flowing phases. Appropriately defined total pseudopressure and total pseudotime are introduced to handle the associated multiphase nonlinearities in the governing flow equations of oil, gas, and water phases simultaneously. A generalized flowing-material-balance (FMB) equation is derived from the total pseudovariables to estimate original fluid in place and drainage area (given volumetric input). The presented model provides a theoretical framework for analyzing production data considering a wide variety of reservoir-fluid systems. The new method is validated against numerical simulation, covering a wide range of fluid properties and operating conditions. In all simulated cases, the new method matches simulation input acceptably. Two field examples are also analyzed to demonstrate the practical applicability of this approach. This work serves as a practical and simple engineering tool for production-data analysis on wells exhibiting single and multiphase flow during boundary-dominated flow.

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.

Multiphase Linear Flow in Tight Oil Reservoirs

Summary The main objective of this work is to gain a general understanding of the performance of tight oil reservoirs during transient linear two-phase flow producing at constant flowing pressure. To achieve this, we provide a theoretical basis to explain the effect of different parameters on the behavior of solution-gas-drive unconventional reservoirs. It is shown that, with the Boltzmann transformation, the highly nonlinear partial-differential equations (PDEs) governing two-phase flow through porous media can be converted to two nonlinear ordinary-differential equations (ODEs). The resulting ODEs simplify the calculation of the reservoir performance and avoid the tedious calculation inherent in solving the original PDEs. Thus, the proposed model facilitates sensitivity studies and rapid evaluation of different hypotheses. Moreover, successful conversion of the highly nonlinear PDEs (in terms of distance and time) to the ODEs (in terms of the Boltzmann variable) implies that the saturation and pressure are unique functions of the Boltzmann variable, and as a result, saturation is a unique function of pressure. This transformation enables us to explain (a) the constant gas/oil ratio (GOR) that has been observed in some hydraulically fractured tight oil reservoirs and (b) the straight-line plot of 1/qo and 1/qg vs. t during constant-pressure two-phase production. An approximate analytical model is also developed. It is shown that the proposed approximate solution can be converted to a form similar to the well-known equations for single-phase flow, which enhances our understanding of two-phase-flow behavior. Extensive sensitivity studies are performed to examine the utility of the proposed model in predicting the performance of tight oil reservoirs. The applicability of the conclusions to the boundary-dominated flow period is investigated. On the basis of numerous simulation studies, it is shown that the impact of various parameters on boundary-dominated flow can be predicted with the transient solution, without the need for running multiple numerical simulations.

History Matching and Forecasting Tight Gas Condensate and Oil Wells by Use of an Approximate Semianalytical Model Derived From the Dynamic-Drainage-Area Concept

SummaryRecently, low-permeability (tight) gas condensate and oil reservoirs have been the focus of exploitation by operators in North America. Multifractured horizontal wells (MFHWs) producing from these reservoirs commonly exhibit long periods of transient flow, during which two-phase flow of oil and gas begins because of well flowing pressures dropping to less than saturation pressure. History matching and forecasting of such wells can be rigorously performed by use of numerical simulation, but this approach requires significant data and time to set up. Analytical methods, although requiring fewer data and less time to apply, have historically been developed only for single-phase-flow scenarios. In this work, a novel and rigorous analytical method is developed for history matching and forecasting MFHWs experiencing multiphase flow during the transient and boundary-dominated flow periods.The distance-of-investigation (DOI) concept has been used for many years in pressure-transient analysis to estimate distances of reservoir boundaries to wells, among other applications. In the current work, the DOI concept is used to estimate dynamic drainage area (DDA) to forecast tight gas condensate and oil wells; a linear flow geometry is assumed. During transient flow, the DDA is calculated at each timestep by use of the linear-flow DOI formulation; a multiphase version of the linear-flow productivity-index (PI) equation and material-balance equations for gas, condensate, and oil are solved iteratively for pressure, saturation, and fluid-production rate. The PI equations for gas and oil use pseudopressure, which is evaluated with saturation/pressure relationships derived from pressure/volume/temperature data. For boundary-dominated flow, when the drainage area is static, the inflow equations are again coupled with material balance for both phases.The new method is validated against numerical simulation, covering a wide range of fluid properties and operating conditions. The new method matches the simulation acceptably for all cases studied. Field examples of MFHWs are also analyzed to demonstrate the practical applicability of the approach. The three liquid-rich shale examples analyzed were also chosen to represent a wide range of fluid properties. In all cases, acceptable history matches are achieved.The new analytical forecasting/history-matching procedure developed in this work provides a practical alternative to numerical simulation for tight gas condensate and oil experiencing two-phase flow during the transient-flow period. The method, which does not rely on Laplace-space solutions, is conceptually simple to understand, easy to implement, and avoids the inconvenience of Laplace-space inversion.

On the analysis of production data: Practical approaches for hydraulically fractured wells in unconventional reservoirs

Abstract This work presents new solutions to modeling the production performance of hydraulically fractured wells in unconventional reservoirs, where intensive hydraulic fracturing creates a stimulated reservoir volume (SRV) with an induced permeability field within. We found previously that the permeability field induced in the SRV (single porosity) can be effectively represented by an exponential or linear dependence of permeability on the distance measured from the main hydraulic fracture plane. However, many researchers consider dual porosity as a necessary ingredient in modeling unconventional reservoirs. In this work, we extend the induced permeability field model to the dual porosity idealization, considering transient fluid transfer from matrix to natural fractures and distance-dependent properties of the medium of secondary porosity (affected by the intensive stimulation). We show that the combined effect of creating a main fracture and altering the properties of the medium of secondary porosity leads to a production behavior that can be characterized and understood provided that effects related to skin and varying flowing bottomhole pressure are correctly accounted for. In addition to the standard diagnostic tools for decline-curve or rate-transient analysis, we use the ratio between the production time and material balance time, a dimensionless group that enables identifying the characteristic signatures of flow regimes. We provide practical criteria to identify various scenarios affecting the data during the pre-linear and pre-bilinear flow regimes in the reservoir (short times). Then we show that transient, late transient and boundary dominated flow periods can also be diagnosed using the dimensionless group, providing a useful addition to existing procedures involving conventional plots. In connection to the new model, this work also discusses a novel approach to handle non-constant bottomhole pressure, the cause of significant distortion in production data at early times. In particular, we consider the effect of a bottomhole pressure exponentially approaching a stabilized value. We show that the deviation from the idealized constant bottomhole pressure case depends on the flow regime in the reservoir, fluid and reservoir properties, skin factor, and the mean lifetime (the time when 63% of the total change has happened) of the decaying part of the flowing pressure. The results reveal that half-, three-fourths-, and unit-slope straight lines (on log–log plot of production rate versus time) develop at short times during the increasing trend of production rate. These new flow regimes enable to gain useful information about the SRV from the early stage of the production history – if the quality of data allows such a detailed analysis. We present a field example involving multi-fractured horizontal wells producing from a shale-gas reservoir, to illustrate, in a practical manner, how to apply the new approach when interpreting production history of wells in unconventional reservoirs.