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Boundary-Dominated Flow

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Luis F. Ayala – One of the best experts on this subject based on the ideXlab platform.

  • Application of Superposition Principle to Variable Rate/Pressure Production Analysis of Multi-Fractured Horizontal Wells in Unconventional Gas Reservoirs
    Journal of Natural Gas Science and Engineering, 2019
    Co-Authors: Miao Zhang, Luis F. Ayala


    Abstract Application of superposition principle to non-linear gas governing equations has been an elusive goal in early-transient production data analysis and has been so far limited to the use of empirical and approximate methods best applicable to Boundary-Dominated Flow conditions. This paper presents a novel and rigorous semi-analytical model that is applicable for the analysis of production data from multi-fractured horizontal gas wells (MFHWs) producing under early-transient variable rate/pressure production conditions. Nonlinear, pressure-dependent hydraulic diffusivity retained in pseudo-pressure-based gas diffusivity equation is straightforwardly and rigorously captured without approximation. The resulting formulation of superposition applied in nonlinear gas system is written in terms of the classical solution for the governing linear partial differential equation (PDE) plus an analytical adjustment factor that quantifies the nonlinearity of the system. Numerical examples and field cases are presented to test the validity and showcase the capabilities of proposed approach. Comparisons against available empirical and approximate models are also provided for these cases.

  • Analysis of Multiphase Reservoir Production From Oil/Water Systems Using Rescaled Exponential Decline Models
    Journal of Energy Resources Technology-transactions of The Asme, 2019
    Co-Authors: Luis F. Ayala


    In this study, we present an analytical approach based on rescaled exponential models that are able to analyze production data from oil/water systems producing under Boundary-Dominated Flow conditions. The model is derived by coupling two-phase oil/water material balances with multiphase well deliverability equations. Nonlinearities introduced by relative permeability in multiphase oil/water systems are accounted for via depletion-dependent parameters applied to each of the Flowing phases. This study shows that So–Sw–p relationships based on Muskat’s standard assumptions can be successfully deployed to correlate saturation and pressure changes in these two-phase systems without the need for user-provided surface production ratios or well-stream composition information. The validity of the proposed model is verified by closely matching predictions against finely gridded numerical models for cases constrained by both constant and variable bottomhole pressure production. In addition, a straight-line analysis protocol is structured to estimate the original oil and water in place on the basis of available production data using rescaled exponential models. Finally, we explore conditions for validity of the assumptions used in the proposed model, including the So–Sw–p formulation, by conducting extensive sensitivity analysis on input parameters.

  • Use of rescaled exponential models for Boundary-Dominated liquid-rich gas Flow analysis under variable bottomhole pressure conditions
    Journal of Natural Gas Science and Engineering, 2017
    Co-Authors: Madhu Singh, Miao Zhang, Hamid Emami-meybodi, Luis F. Ayala


    Abstract The analysis of production data from natural gas reservoirs can serve as one of the most powerful tools to estimate remaining reserves and provide a forecast of its future performance. While fundamentals of decline for dry gas reservoirs are well described in literature, those for liquid-rich gas reservoirs are yet to be well-understood. Any predictive model used to analyze these reservoirs must account for the inherent changes in reservoir fluid composition during their producing life due to condensate dropout within the reservoir, once reservoir pressure falls below dew point pressure. This study presents a mathematical model capable of predicting non-linear Flow behavior in multiphase gas-condensate reservoirs using rescaled exponential models applicable to Boundary-Dominated Flow regimes under variable bottomhole pressure conditions. We develop a set of analytical solutions for surface oil and total hydrocarbon Flowrates, for wells producing under variable bottomhole pressure. We model hydrocarbon production from gas-condensate reservoirs by employing a material balance over produced condensate and total hydrocarbons. In this material balance approach, we use equivalent fluid molar densities in multiphase systems, resulting in analytical equations for the different Flowing phases. The developed set of analytical solutions aims at providing an accurate estimate of reservoir behavior and available reserves, which can be used to inform critical economic decisions for further development of the reservoir. The proposed rescaled models minimize assumptions and stay true to the physics of multiphase Flow. We demonstrate that the developed analytical model closely predicts the numerical simulation results for the hydrocarbon Flowrates as well as the estimated reserves where a wide range of gas-condensate reservoirs, from lean to liquid-rich, is considered.

Salam Al-rbeawi – One of the best experts on this subject based on the ideXlab platform.

  • Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model
    Petroleum, 2019
    Co-Authors: Salam Al-rbeawi, Jalal F. Owayed


    Abstract This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs. This approach demonstrates the impact of variable Sand face Flow rate on reservoir performance. A new model for P/R deconvolution is used to convert pressure pulse from variable Flow rate to single and constant rate response. The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume. Multi-linear Flow regimes approach is used to describe pressure behavior in the reservoirs while decline Flow rate behavior is described by newly proposed model in this study. This model depicts, instead of van Everdingen model, indirectly the declining rate with time by using pressure responses with production time. Decline Flow rate behavior simulated by linear and bi-linear Flow models are also studied and compared with the one obtained by the new model. Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable Flow rate considering different reservoir configurations and operating conditions. The results are interpreted and analyzed for better understanding pressure behaviors, Flow regime types, and productivity index trends for continuously changing Flow rate especially at early production time. Estimating stimulated reservoir volume ( V s r v ) is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state Flow when late time boundary dominated Flow regime is reached. The outcomes of this study can be summarized as: 1) Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline Flow rate model that indirectly simulates variable Flow rate with time. 2) Generating analytical models for dimensionless pressure and Flow rate for constant and variable Flow rate using the concept of P/R convolution and deconvolution. 3) Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior. 4) Studying the applicability of linear and bi-linear Flow models in converting variable Flow rate pressure response to single and constant Flow rate pressure response. 5) Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume. The most interesting points are: 1) The main difference in wellbore pressure behavior between variable and constant Flow rate can be seen at early production time, however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure. 2) A unit slope line Flow regime could be developed for varied Flow rate pressure response at very early production time similar to the wellbore storage dominated Flow regime. 3) Productivity index calculated by the proposed models for variable Flow rate is greater than the index for constant Flow rate. 4) The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant Flow rate. 5) The decline rate models for linear and bi-linear Flow are not applicable in pressure deconvolution technique.

  • Transient and Pseudo-Steady-State InFlow Performance Relationships for Multiphase Flow in Fractured Unconventional Reservoirs
    Transport in Porous Media, 2019
    Co-Authors: Salam Al-rbeawi


    The objective of this paper is developing new methodology for constructing the inFlow performance relationships (IPRs) of unconventional reservoirs experiencing multiphase Flow. The motivation is eliminating the uncertainties of using single-phase Flow IPRs and approaching realistic representation and simulation to reservoir pressure–Flow rate relationships throughout the entire life of production. Several analytical models for the pressure drop and decline rate as wells productivity index of two wellbore conditions, constant Sandface Flow rate and constant wellbore pressure, are presented in this study. Several deterministic models are also proposed in this study for multiphase reservoir total mobility and compressibility using multi-regression analysis of PVT data and relative permeability curves of different reservoir fluids. These deterministic models are coupled with the analytical models of pressure drop, decline rate, and productivity index to construct the pressure–Flow rate relationships (IPRs) during transient and pseudo-steady-state production time. Transient IPRs are generated for early-time hydraulic fracture linear Flow regime and intermediate-time bilinear and trilinear Flow regimes, while steady-state IPRs are generated for pseudo-steady-state Flow regime in case of constant Sandface Flow rate and Boundary-Dominated Flow regime in case of constant wellbore pressure. The outcomes of this study are as follows: (1) introducing the impact of multiphase Flow to the IPRs of unconventional reservoirs; (2) developing deterministic models for reservoir total mobility and compressibility using multi-regression analysis of PVT data and relative permeability curves; (3) developing analytical models for different Flow regimes that could be developed during the entire production life of reservoirs; (4) predicting transient and steady-state IPRs of multiphase Flow for different wellbore conditions. The study has pointed out: (1) Multiphase Flow conditions have significant impact on reservoir IPRs. (2) Multiphase reservoir total mobility and compressibility exhibit significant change with reservoir pressure. (3) Constant Sandface Flow rate may demonstrate IPR better than constant wellbore pressure. (4) Late production time is not affected by multiphase Flow conditions similar to transient state Flow at early and intermediate production time.

  • Deep insights to transient pressure behavior and stabilized productivity index of multilateral wells in laterally and spatially anisotropic reservoirs
    Journal of Natural Gas Science and Engineering, 2018
    Co-Authors: Salam Al-rbeawi


    Abstract The objective of this paper is focusing deep insights on stabilized productivity index (PI) and transient pressure behaviors and Flow regimes of multilateral wells. It introduces an integrated approach for the performance of reservoirs depleted by multilateral wells extending in arbitrary trajectories. The study introduces new practical solutions for estimating stabilized pseudo-steady state (PSS) productivity index and starting time of PSS as well as transient PI behavior of multilateral wells in single and dual porous media with laterally and spatially anisotropic characteristics. Several analytical models are used in this study for describing pressure and pressure derivative behavior of multilateral wells considering different reservoir configurations and types and different wellbore lengths and directions. These models are developed for laterally and spatially anisotropic reservoirs consisting of single homogenous and dual heterogeneous porous media (Naturally fractured reservoirs) and depleted by multilateral wells extending from single vertical wellbore at different horizons and directions. The models are modified to identify the staring time of PSS Flow or the time when boundary dominated Flow regime is developed. They are also applied to estimate the time variant transient PI and time invariant stabilized PSS PI for constant single lateral Flow rate or constant vertical wellbore commingled Flow rate. The outcomes of this study are summarized in: 1) Developing new analytical solutions for pressure distribution in porous media drained by multilateral wells. 2) Developing new integrated approach for estimating stabilized PSS productivity index. 3) Understanding pressure, pressure derivative, and PI behavior of finite acting reservoir depleted by multilateral horizontal wells during transient and PSS production. 4) Investigating the impacts of different reservoir configurations and types, wellbore lengths and directions, permeability anisotropy characteristics, and single and dual porous media petrophysical properties on stabilized PSS productivity index. The novel points in this study are: 1) The optimum reservoir configuration that gives the maximum stabilized PI is the rectangular shape reservoir with reservoir length to width ratio of ( 2 − 4 ) . 2) The lateral with long wellbore and the slightly deviated from the horizontal directions gives the greatest stabilized productivity index. Stabilized PI is impacted by the length and direction of each multilateral as well as lateral wellbore location in the vertical plane. 3) Lateral reservoir anisotropy exhibits bad PI compared to the spatial anisotropy. 4) PI of conventional dual porous media reservoirs is greater than the index of unconventional reservoirs at early and late production time, but the index at intermediate production time demonstrates the greater value for unconventional reservoirs.

Thomas Alwin Blasingame – One of the best experts on this subject based on the ideXlab platform.

  • Beyond Decline Curves: Life-Cycle Reserves Appraisal Using an Integrated Work-Flow Process for Tight Gas Sands
    SPE Annual Technical Conference and Exhibition, 2007
    Co-Authors: Jay Alan Rushing, Kent Edward Newsham, Albert Duane Perego, Joseph Thomas Comisky, Thomas Alwin Blasingame


    Decline curve analysis is often either the only or the primary tool used for reserve evaluations in tight gas sands. However, the Flow and storage properties characteristic of lowpermeability sands often preclude accurate assessments using only or primarily decline curve analysis, especially early in the productive life. The most accurate reserve estimates incorporate multiple data sources and the appropriate evaluation techniques. Therefore, this paper presents a reserves appraisal work-Flow process that complements traditional decline curve analyses with comprehensive and systematic data acquisition and evaluation programs that integrate both static and dynamic data. Our approach—which has been developed specifically to incorporate the production characteristics of tight gas sands— is an adaptive process that allows continuous but reasonable reserve adjustments over the entire field development and production life cycle. Implementing this process will prevent unrealistic (either too low or high) reserve bookings. Although it is applicable during any field development phase, our work-Flow process is most beneficial during early stages before true Boundary-Dominated Flow conditions have been reached and when reserve evaluation errors are most likely.

  • Estimating Reserves in Tight Gas Sands at HP/HT Reservoir Conditions: Use and Misuse of an Arps Decline Curve Methodology
    SPE Annual Technical Conference and Exhibition, 2007
    Co-Authors: Jay Alan Rushing, Albert Duane Perego, Richard Burl Sullivan, Thomas Alwin Blasingame


    This paper presents the results of a simulation study designed to evaluate the applicability of an Arps decline curve methodology for assessing reserves in hydraulically-fractured wells completed in tight gas sands at high-pressure/high-temperature (HP/HT) reservoir conditions. We simulated various reservoir and hydraulic-fracture properties to determine their impact on the production decline behavior as quantified by the Arps decline curve exponent, b. We then evaluated the simulated production with Arps’ rate-time equations at specific time periods during the well’s productive life and compared estimated reserves to the true value. To satisfy requirements for using Arps’ models, all simulations were conducted using a specified constant bottomhole Flowing pressure condition in the wellbore. Our study indicates that the largest error source is incorrect application of Arps’ decline curves during either transient Flow or the transitional period between the end of transient and onset of Boundary-Dominated Flow. During both of these periods (principally the transient period), we observed bexponents greater than one and corresponding reserve estimate errors exceeding 100 percent. The b-exponents generally approached values between 0.5 and 1.0 as Flow conditions approached true Boundary-Dominated Flow. Agreement between Arps’ suggested b-exponent range and our results using simulated performance data also indicates that, if applied under the correct conditions, the Arps rate-time models are appropriate for assessing reserves in tight gas sands at HP/HT reservoir conditions. Introduction Tight gas sands constitute a significant percentage of the domestic natural gas resource base and offer tremendous potential for future reserve and production growth. According to a recent study by the Gas Technology Institute (GTI), tight gas sands in the US comprise 69 percent of gas production from all unconventional natural gas resources and account for 19 percent of total gas production from both conventional and unconventional sources. The same study estimates total domestic producible tight gas sand resources exceed 600 Tcf, while economically recoverable gas reserves are 185 Tcf. Most of the resources assessed in the 2001 GTI study were at depths less than 15,000 ft, yet the natural gas industry continues to extend exploration and development activities to much greater depths. In some geologic basins, those depths are approaching 20,000 to 25,000 ft. Many of these deep natural gas resources are not only characterized by lowpermeability, low-porosity reservoir properties, but these reservoirs also exhibit abnormally high initial pore pressure and temperature gradients — i.e. high-pressure/hightemperature (HP/HT) reservoir conditions. Similar to conventional natural gas resources, tight gas sand reserves are routinely assessed with Arps’ decline curve techniques. The original Arps paper suggested the decline curve exponent, b, should fall between 0 and 1.0 on a semilog plot. However, we often observe values much greater than 1.0, particularly in tight gas sands at HP/HT reservoir conditions. Deviations in observed b-exponents from the expected range suggest Arps’ rate-time relationships may not be valid for modeling the decline behavior of tight gas sands at HP/HT conditions. More importantly, inappropriate use of the Arps models may cause significant reserve estimate errors in these unconventional natural gas resources. Since these depths and extreme reservoir conditions require wells that are very expensive to drill, complete and operate; it is imperative that we understand both the well productivity and production decline behavior. We also need to determine the applicability of the Arps rate-time equations for assessing reserves. To address these concerns, we have conducted a series of single-well simulation studies to develop a better understanding of both the shortand long-term production decline behavior and to identify those parameters affecting the production decline. In this study we simulated a range of reservoir and hydraulic fracture properties, including: Vertical heterogeneity from layering, permeability contrast among layers, horizontal permeability anisotropy, and stressdependent reservoir properties; 2 J.A. Rushing, A.D. Perego, R.B. Sullivan, and T.A. Blasingame SPE 109625 Variable effective fracture conductivities and lengths, unequal fracture wing lengths, two-phase and non-Darcy Flow, and stress-dependent fracture properties; and Reservoir temperatures ranging from 300 to 400F and initial pore pressure gradients ranging from 0.60 to 0.90 psi/ft. We evaluated the simulated production with the Arps ratetime equations. Reserve estimates were obtained at various time periods during the well’s productive life by extrapolating the best-fit Arps model through the simulated production. Our assumed economic conditions for estimating reserves were either a rate of 50 Mscf/d or a producing time period of 50 years, whichever came first. Reserve estimate errors were computed by comparing those estimated reserves to the “true” value. For this paper, we define the “true” estimated ultimate recovery (EUR) to be the 50-year cumulative production volume. For reference, we also summarize the Arps rate-time equations in Table 1, given below: Table 1 — Summary of the Arps’ rate-time relations (Ref. 1)

  • Estimation of Reserves Using the Reciprocal Rate Method
    Rocky Mountain Oil & Gas Technology Symposium, 2007
    Co-Authors: Thomas Alwin Blasingame, Parker D. Reese


    In this work we develop, validate, and apply the “reciprocal rate method” to estimate oil reserves using only rate-time production data. This approach requires the development of Boundary-Dominated Flow, and can be used to validate reserve extrapolations from numerical/analytical reservoir models. The methodology does presume that Flowing well bottomhole pressures are approximately constant — but we will demonstrate that the method is tolerant of substantial changes in the Flowing bottomhole pressure.