Flowing-material-balance (FMB) analysis is a practical method for determining original hydrocarbon volumes in place. It is attractive because it enables performing material-balance calculations without shutting in wells to obtain estimates of reservoir pressure. However, with some exceptions, its application is limited to single-phase oil and/or gas reservoirs over limited pressure ranges during depletion. In unconventional reservoirs, reservoir and/or production complexities may further restrict FMB use. Among these complexities are significant production/injection of water, production resulting in higher gas/oil ratios (GORs) and pressure drawdowns, geomechanical effects, and multiwell-production effects. As a result, application of the conventional FMB to unconventional reservoirs may lead to significant errors in hydrocarbons-in-place estimation. This paper first discusses the application of conventional FMB to the analysis of single-phase or multiphase flow in single or multiwell scenarios, and then provides a new, comprehensive version of the FMB to address the previously mentioned complications. For the new FMB, pseudopressure is used to account for two-phase oil/gas flow. In addition, by use of a general material-balance equation, water production/injection and multiwell effects are included in the analysis. The new FMB-analysis approach is validated by comparing results with numerical simulation of multifractured horizontal wells (MFHWs). These comparisons demonstrate that, not only gas production, but also water production/injection can have a significant effect on the calculated original-in-place hydrocarbon volumes. The new FMB-analysis approach provided herein successfully accounts for all flowing phases in the reservoir, and is demonstrated to be applicable for multiwell scenarios. The methodology presented in this paper maintains the simplicity of FMB, yet accounts for multiphase flow and multiwell complications. The developed FMB and the presented approach can be used by reservoir engineers to reasonably determine the original volumes of hydrocarbons in place in both conventional and unconventional reservoirs.
Unconventional fractured gas wells occasionally exhibit bilinear flow during early production. When this flow regime is observed, important fracture properties can be estimated such as conductivity and/or spacing. However, the application of present-day rate-transientanalysis (RTA) methods to bilinear flow results in up to 18% error. This error is rate-dependent, and occurs because of nonlinearities in the gas-diffusivity equation. This paper presents a new correction factor that handles the rate dependency of bilinear flow, and enables more-accurate reservoir characterization.
The diffusivity equation of gas in porous media has some nonlinearities that cannot be addressed by only using the real-gas pseudopressure. Even though neglecting these nonlinearities results in a model that is sufficiently accurate for the radial-flow case, errors arise in the boundary-dominated-flow (BDF) (Fraim and Wattenbarger 1987), the linear-flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012), and, as shown in this article, the bilinear-flow cases. Currently, no research studies provide an accurate bilinear-flow analytical model for gas reservoirs. To bridge this gap and to provide rate-transient analysts with a practical tool, this work presents a correction factor that can be incorporated into the existing bilinear-flow models. The correction factor was developed following an approach similar to that of Ibrahim and Wattenbarger (2006). The first step was to simulate a number of reservoir and well conditions. Second, fracture properties were back calculated with the current the bilinear-flow models. Finally, errors between the back calculated and the simulated properties were correlated to dimensionless drawdown. After these steps, a correction factor was obtained that applied to various bilinear-flow cases.
The obtained numerical results indicate that errors in bilinear-flow models are correlated with rate, or more precisely, dimensionless drawdown [a similar behavior is observed in the analytical model of linear flow, as demonstrated by Ibrahim and Wattenbarger (2006)]. This correlation can be used to reduce error to less than ±3%. Because the simulated cases cover an extensive range of unconventional reservoir conditions, the empirical correction is robust and applicable to a wide variety of reservoir conditions. Most importantly, the correction is practical and can be readily incorporated into existing bilinear-flow models. The application of the new correction is demonstrated in this article with synthetic and field examples.
Jia, Pin (China University of Petroleum, Beijing) | Cheng, Linsong (China University of Petroleum, Beijing) | Clarkson, Christopher R. (University of Calgary) | Qanbari, Farhad (University of Calgary) | Huang, Shijun (China University of Petroleum, Beijing) | Cao, Renyi (China University of Petroleum, Beijing)
In a multiwell pad, the chance of interwell communication increases because of the creation of primary and secondary fractures during hydraulic-fracture stimulation. The flow behavior associated with communicating wells is significantly different from that of a single isolated well, because of interplay of flow caused by the interconnected fractures, complex connections, and multiple production conditions. The main purpose of this paper is to develop a rigorous and efficient flow model and quantify flow characteristics of multiple pad wells communicating through primary and secondary fractures.
In the model, matrix and primary- and secondary-fracture flows are captured. Fractures are explicitly represented by discrete segments. The Laplace-transform finite-difference (LTFD) method is used to numerically model fracture flow, with sufficient flexibility to consider arbitrary fracture geometries and fracture-conductivity distributions. The analytical matrix-flow model, derived with the line-source function in the Laplace domain, is dynamically coupled with the fracture-flow model, by imposing the continuity of pressure and flux on the fracture surface. Thus, a hybrid model in the Laplace domain is constructed. The main advantage of the solution occurring in Laplace domain is that computations can be performed at predetermined, discrete times, and with grids only for fractures. Thus, stability and convergence problems caused by time discretization are avoided, and the burden of gridding and computation is decreased without loss of important fracture characteristics.
The model is validated through comparison with a fully numerical simulator and a semi-analytical model. Detailed flow-regime analysis reveals that pressure interference caused by communication significantly alters the flow signature compared with single (isolated) wells. Before interference, the communicating wells behave as single isolated wells, and will exhibit a fracture linear-flow period and possibly even a matrix linear-flow period. After interference, the flow behavior of the system will vary largely with different production strategies. When the communicating wells all operate under the constant-rate condition, the transient responses of the wells will gradually merge to develop another matrix linear-flow period. If the wells are operated under the constant-bottomhole-pressure (BHP) conditions, the response deviation caused by interference will increase with production; therefore, one of the wells will undergo a rate loss. The results of a sensitivity analysis for a two-well system demonstrate that the time to well interference is primarily determined by secondary-fracture conductivity, number of connections, and communicating-well operating conditions. With larger contrasts in these properties, interference time is accelerated. However, for different production strategies, the effects on the flow behavior after interference are variable.
Recently, 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 boundarydominated 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.
There is now an array of analytical, semianalytical, and empirical forecasting methods that can be used to history match and forecast multifractured horizontal wells (MFHWs) completed in low-permeability (tight) reservoirs. Recent developments in analytical modelling have extended model application to cases in which the fracture geometry associated with MFHWs is complex. However, analytical modelling is still primarily limited to single-phase-flow problems, which is very restrictive, and potentially inaccurate, for tight oil and liquid-rich gas reservoirs flowing at less than saturation pressure.
In this work, a semianalytical method is presented for history matching and forecasting MFHWs with simple and complex fracture geometry completed in tight, black-oil reservoirs and flowing at less than the bubblepoint pressure. The linear-to-boundary (LTB) model, commonly used to model flow in the inner (stimulated) region of an MFHW, is altered to account for two-phase flow of oil and gas. The enhanced-fracture-region (EFR) case, in which both stimulated and nonstimulated regions contribute to flow, is approximated (empirically) by superposition of two modified LTB models (one representing the inner fractured region and the other the outer, nonstimulated region), and similarly altered to account for two-phase flow. An important observation is that, for MFHWs flowing at less than bubblepoint at constant flowing bottomhole pressure during transient linear flow, the slope of the square-root-of-time plot for both oil and gas phases is constant [i.e., gas/oil ratio (GOR) is constant]. The slope and intercept of the square-root-of-time plot for the primary phase (e.g., oil in the cases studied) can therefore be used to generate a forecast during the transient linear-flow period for oil and for gas (by assuming constant GOR). For boundary-dominated flow, a robust method for forecasting gas and oil was developed using material balance for both phases combined with a modified productivity-index equation that accounts for multiphase flow. A fully implicit approach has been used to solve the flow equations for oil and gas.
The new modified LTB and EFR models simplify forecasting considerably for low-permeability black-oil reservoirs exhibiting multiphase flow behaviour, relative to numerical simulation, although they are not as rigorous. The new models can, however, be tied directly to the results of rate-transient analysis and are flexible enough to be applied to common conceptual models used in the literature for forecasting MFHWs under certain conditions.
The new modified LTB model has been compared with both simulated and field examples. The initial results demonstrate that transient- and boundary-dominated-flow periods for oil and gas are reasonably matched with the new approach, although slight mismatches may occur, particularly during early boundary-dominated flow. The limits of the new forecasting method will continue to be explored in future work.
Behmanesh, Hamid (University of Calgary) | Clarkson, Christopher R. (University of Calgary) | Tabatabaie, S. Hamed (University of Calgary) | Heidari Sureshjani, Mohammadhossein (IOR Research Institute)
Long-term transient linear flow of hydraulically fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed by use of the square-root-of-time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, in which the average pressure in the distance of investigation (DOI) is calculated with an appropriate material-balance equation. The DOI calculation is therefore a key component in the determination of the linear-flow parameter (product of fracture half-length and square root of permeability, xf√k) and the calculation of contacted fluid in place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions.
In this work, we have derived the DOI equations analytically for transient linear flow under constant-flowing-pressure and -rate conditions. For the first time, rigorous methodologies have been used for this purpose. Two different approaches were used: the maximum rate of pressure response (impulse concept) and the transient/boundary-dominated flow intersection method. The two approaches resulted in constants in the DOI equation that are much different from previously derived versions for the constant-flowing-pressure case. The accuracy of the new equations was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. Single-phase oil and gas cases were analyzed; pseudovariable alteration for pressure-dependent porosity and permeability was required in the analysis.
The calculated linear-flow parameters, determined from our new DOI formulations for the constant-flowing-bottomhole-pressure (FBHP) case, and the input values to numerical simulation, are in good agreement. Of the two new DOI-calculation methods provided, the maximum rate of pressure response (unit impulse method) provides more accurate results. Finally, a field case was analyzed to determine the impact of DOI formulations on derivations of the linear-flow parameter from field data.
Linear-flow analysis on the basis of the DOI calculations presented in this work is significantly improved over previous formulations for constant FBHP.
Analytical methods for analyzing and forecasting production from multifractured horizontal wells completed in unconventional reservoirs are in their infancy. Among the difficulties in modeling such systems is the incorporation of fracture-network complexity as a result of the hydraulic-fracturing process. Along with a primary propped-hydraulic-fracture network, a secondary fracture network, which may or may not contain proppant, may be activated during the stimulation process, creating a “branched fracture” network. These secondary fractures can be the result of reactivation of healed natural fractures, for example. In the current work, we develop a fully analytical enhanced fracture-region (EFR) model for analyzing and forecasting multifractured horizontal wells with complex fracture geometry that is more-general, -rigorous, and -flexible than those previously developed. Specifically, our new model allows nonsymmetric placement of a well within its area of drainage, to reflect unequal horizontal-lateral spacing; this is a very real scenario observed in the field, particularly for the external laterals on a pad. The solutions also can be reduced to be applicable for homogeneous systems without branch fractures. In addition to the general EFR solution, we have provided local solutions that can be used to analyze individual flow regimes in sequence. We provide practical examples of the application (and sometimes misapplication) of local solutions by use of simulated and field cases. One important observation is that a negative intercept obtained from a straight line drawn through data on a square-root-of-time plot (commonly used to analyze transient linear flow) may indicate EFR behavior, but this straight line should not be interpreted as linear flow because it represents transitional flow from one linear-flow period to another. Our general EFR solution therefore provides a powerful tool to improve both forecasting and flow-regime interpretation for hydraulic-fracture/reservoir characterization.
The rapid pace of exploitation of unconventional gas and light oil plays in North America has necessitated the development of new production-forecasting methodologies to aid in reserves assessment, capital planning, and field optimization. The generation of defendable forecasts is challenged not only by reservoir complexities but also by the use of multifractured horizontal wells (MFHWs) for development. In this work, a semianalytical method (SAM) is developed to provide a solid theoretical basis for forecasting. The technique is analytical in that it uses the methods of Agarwal (2010) to calculate contacted oil in place and contacted gas in place (COIP/ CGIP) from production rates, flowing pressures, and fluid properties. The rate-normalized pressure (RNP) derivative (RNP) is a key component of the calculation; pseudopressure is used for gas cases. The technique is also empirical in that an empirical function is fitted to the resulting COIP/CGIP curve vs. time. Although the method is flexible enough that any equation can be used to represent the COIP/CGIP curve, and hence, the sequence of flow regimes exhibited by MFHWs, the equation must be capable of being integrated to allow the extraction of RNP. The stabilized COIP/CGIP during boundary-dominated flow (BDF) must be specified for forecasting -- thereafter, the method uses a materialbalance simulator to model BDF. Hence, if the well is still in transient flow, a range in forecasts may be generated, depending on the assumed stabilized COIP/CGIP. The new SAM addresses some of the current limitations of empirical and fully analytical (modeling) approaches. Empirical methods, which have been adapted to account for long transient and transitional flow periods associated with ultralow-permeability reservoirs, lack a theoretical basis, and therefore input parameters may be difficult to constrain. However, empirical methods are simple to apply and require a minimum amount of data for forecasting. Analytical models, while representing the physics better, nonetheless require additional reservoir and hydraulic-fracture data that may not be available on every well in the field. The SAM proposed herein is intended to bridge the gap between empirical and modeling-based approaches -- it is more rigorous than purely empirical methods, while requiring a lesser amount of data than fully analytical techniques. The new method is tested against simulated and field cases (tight oil and shale gas). Although a simple power-law function is used in the current work to represent the COIP/OGIP curve, which appears adequate for the cases studied, one should note that wells exhibiting long transitional flow periods (e.g., elliptical/ radial) will likely require a different functional form.
Ghanizadeh, Amin (University of Calgary) | Aquino, Samuel (University of Calgary) | Clarkson, Christopher R. (University of Calgary) | Haeri-Ardakani, Omid (Geological Survey of Canada) | Sanei, Hamed (Geological Survey of Canada)
The results from an ongoing laboratory study investigating petrophysical and geomechanical characteristics of the Montney and Bakken formations in Canada are presented. The primary objectives are to 1) fully characterize the pore network (porosity, pore size distribution) and fluid transport (permeability) properties of these formations in areas with limited datasets; 2) investigate the interrelationship between petrophysical and geomechanical characteristics of these fine-grained tight reservoirs; and 3) analyze the effects of different geological factors on porosity, pore size distribution and permeability. The techniques used for characterization include: Rock-Eval pyrolysis (Tmax, TOC); bitumen reflectance; petrography (grain size); helium pycnometry; low-pressure gas (N2) adsorption (surface area, pore size distribution); pressure-decay profile permeability, pulse-decay and crushed-rock gas (N2, He) permeability; fracture permeability and mechanical hardness tests.
Rock-Eval analysis and microscopic observations indicate that most samples are organic-lean (average TOC content: 0.3%), ranging from fine-grained siltstone to very fine-grained sandstone (grain size: 31.8-53.7 μm). The measured pulse-decay and crushed-rock permeability values increase significantly with increasing porosity (2.1-14.1%), ranging between 1.1·10-6 and 7.3·10-2 mD. For the plugs analyzed (“as-received”), profile (probe) permeability values (9.1·10-4 - 6.7·10-3 mD) are consistently higher than pulse-decay (1.6·10-5 - 9·10-4 mD) and crushed-rock (1.1·10-6 - 5.4·10-5 mD) permeability values. Corrected profile (probe) permeability values for “in-situ” effective stress (5.3·10-5 - 1·10-3 mD) are, however, comparable with the pulse-decay (1.6·10-5 - 9·10-4 mD) permeability values. Unpropped fracture permeability, determined using an innovative procedure in this work, can be significantly (up to eight orders of magnitude) higher than matrix permeability under similar effective stress conditions. The grain size and mechanical hardness data are correlated to permeability. The dominant pore throat diameter controlling fluid flow is estimated for all samples using Winland-style correlations; these values agree with those obtained from low-pressure N2 adsorption analysis.
Applying multiple innovative analysis techniques on a large number of samples (26 m of slabbed core, 22 core plugs and their accompanying cuttings), this study provides a roadmap to fully characterize the fluid storage and transport properties of fine-grained tight oil and liquid-rich gas reservoirs. We demonstrate that pore structure, large- and fine-scale (cm-size) permeability heterogeneity, and mechanical characteristics of tight oil and liquid-rich gas reservoirs can be suitably-characterized using the methods we have used with application to flow-unit identification and mechanical stratigraphy determination. We further present useful correlations between petrophysical and geomechanical properties for the reservoirs studied.
Rate- and pressure-transient analysis of unconventional gas and oil reservoirs is a challenge because of the complex reservoir characteristics that dictate flow. Transient linear flow is usually an important flow regime for these reservoirs and is often associated with linear flow to induced hydraulic fractures. One of the complications in the analysis of this flow regime is stress sensitivity of porosity and permeability. This work provides a new method for analysis of transient linear flow in stress-sensitive tight oil reservoirs. A correction factor is used to correct the results of the conventional method for analysis of transient linear flow in tight oil reservoirs. A new method is developed for calculating the correction factor by use of an analytical solution to the flow equation. The correction factor is used for production-data analysis of two examples for constant-pressure and constant-rate production. The results indicate that the correction factor becomes more important for higher values of permeability modulus and pressure drawdown. Further, we demonstrate that the correction factor can eliminate the considerable error of the conventional analysis method in estimating initial reservoir permeability or hydraulic fracture half-length.