In this work we present the "Transient Hyperbolic" relation for the analysis and interpretation of time-rate performance data from wells in shale gas/liquids-rich shale plays. This model assumes a transient "b(t)" function which has constant early-time and constant late-time values, with an exponentially decaying transition function. This "b(t)" function is derived from the Gompertz logistic function.
Our goal in developing this formulation is to represent the early-time (or clean-up) portion of the production profile (often a hyperbolic function), the transition to the terminal hyperbolic behavior, and finally, the terminal hyperbolic behavior — where the terminal hyperbolic is usually representative of the "non-interfering" vertical fractures in a multi-fractured horizontal well (MFHW). We could further modify this relation to have a terminal exponential decline (thought to represent the performance of the stimulated-reservoir-volume (or SRV)), but that is not a primary purpose of this work — our primary purpose is to demonstrate the "Transient Hyperbolic" nature of the flow behavior from a multi-fractured horizontal well in a shale gas/liquids-rich shale play.
The technical contributions of this work are:
Limited attempts have been made to model shale gas reservoirs on a compositional basis. Multiple distinct physical phenomena influence the behavior of reservoir fluids in shale, resulting in measurable compositional changes in the produced gas over time. These phenomena include differential desorption, fractionation via phase change, and preferential diffusion. To address these phenomena, we have developed a compositional numerical model which describes the coupled processes of diffusion and desorption. We have also developed a tool for generating simulation grids capturing fracture geometries of realistic complexity. By combining the physics of flow in complex fractures with diffusion through nanopores, we show how gas composition changes during production. We identify and illustrate signature trends in the flowing gas composition according to our model. In addition, we present a workflow for the integration of measured gas composition data into traditional production data analysis. We prove that the onset of various transient flow regimes that are unique to shale gas reservoir systems can be identified in the model-based flowing composition data. For example, the transition from fracture-drainage to matrix-drainage can be identified by a characteristic trend in flowing gas composition. Some reservoir properties can be determined through analysis of the compositional shift in the flowing gas. This work expands the current understanding of well performance for shale gas to include physical phenomena that lead to compositional changes for realistic fracture configurations. This work can be used to optimize fracture and completion design, improve well performance analysis and provide more accurate reserves estimation. In this work we develop a numerical model which captures multicomponent desorption, diffusion, and phase behavior in ultra-tight rocks, we present a grid generation technique which captures the complexity of shale system fractures, and we validation of our interpretations of diagnostic trends.
This paper presents an integrated technique for evaluating the productionperformance of gas wells with finite-conductivity vertical fractures.Ourmethodology combines conventional pressure transient test analysis with newmaterial balance decline type curves developed specifically for gas wells withfinite-conductivity, vertical fractures.We utilize short-term pressurebuildup test analysis to enhance the production data analysis, particularly forinterpretation of early-time transient flow behavior.We illustrate—withseveral field cases—that both techniques can be integrated to provide not onlya more consistent and systematic analysis methodology, but also a more accurateassessment of stimulation effectiveness.
This paper presents results from a laboratory study comparing capillary pressure measurement techniques for tight gas sands. Included in our evaluation are the more traditional high-speed centrifuge and high-pressure mercury injection methods as well as the less conventional high-pressure porous plate and vapor desorption techniques. The results of our study show significant differences between the mercury injection data and composite capillary pressure curves constructed with data from the other three methods. Consequently, we have concluded that high-pressure mercury injection can be used to quantify pore size distribution, but often inaccurately characterizes capillary pressures, particularly at the irreducible water saturation. Moreover, our study suggests that a composite capillary pressure curve constructed from a combination of the vapor desorption data for the low water saturation range and high-speed centrifuge or high-pressure porous plate data for the high saturation range provides the most accurate capillary pressures for tight gas sands.
This paper presents results from a laboratory study comparing Klinkenberg-corrected permeability measurements in tight gas sands using both a conventional steady-state technique and two commercially-available unsteady-state permeameters. We also investigated the effects of various rate and pressure testing conditions on steady-state flow measurements. Our study shows the unsteady-state technique consistently overestimates the steady-state permeabilities, even when the steady-state measurements are corrected for gas slippage and inertial effects. The differences are most significant for permeabilities less than about 0.01 md. We validated the steady-state Klinkenberg-corrected permeabilities with liquid permeabilities measured using both brine and kerosene. Although gas slippage effects are more pronounced with helium than with nitrogen, we also confirmed the steady-state results using two different gases. Moreover, we show results are similar for both constant backpressure and constant mass flow rate test conditions. Finally, our study illustrates the importance of using a finite backpressure to reduce non-Darcy flow effects, particularly for ultra low-permeability samples.
Many oil and gas production come from naturally fractured reservoirs. The reservoir properties and production performance of this reservoir show a unique behavior, which are different from the homogeneous reservoir. Hence, evaluation and forecasting production of these reservoirs require special models and approaches.
This paper attempts to utilize production data inversion method to obtain parameters such as permeability, skin factor, initial fluid-in-place and production potential in a naturally fractured reservoir. The model can then be used to forecast production from this type of reservoir.
The method uses type curve approach that incorporate concepts of both transient and boundary dominated flow models. Application of this method to oil field data is presented as well as comparison with results obtained from other methods (such as well test analysis and volumetric calculation).
The results of this research provide engineers a tool to evaluate and monitor production/reservoir performance of naturally fractured reservoirs regularly by analyzing production data (which are always recorded) without additional testing.
In this paper we present the development of a rigorous approach for the solution of non-linear partial differential equations by use of the Laplace transformation - in particular, the convolution theorem for Laplace transforms. While the rigor of this new approach is general, our paper is devoted to the development, verification, and application of this method for the case of real gas flow in porous media. This paper focuses on verification of real gas flow solutions using the results of numerical simulation.
The major results of this work are:
Development of a general analytical approach in the Laplace domain for solving non-linear partial differential equations.
Verification and application of this new approach for the flow of a real gas in porous media.
We observe excellent agreement between the numerical and analytical results for the case of a single well produced at a constant rate in a closed reservoir. We conclude that this approach could be adopted as a method of verification for numerical simulation, as well as for analytical modelling of the gas flow case - in particular, for modelling future performance directly and accurately, without numerical simulation or some weak approximation (p or p2 approximations, etc.).
In addition to the specific problem considered in this work, the flow of a real gas in porous media, we believe that it may be possible to extend this work for the development of analytical solutions for multiphase flow.
This paper presents the methodology and results of a reservoir characterization study of Clear Fork carbonates in the TXL South Unit Field located in Ector County, Texas. The principal objective of our study was to evaluate a targeted infill drilling strategy for future field development. Our study incorporated an integrated approach for which the primary evaluation tool was decline type curve analysis of well production data. The well performance analysis was both supplemented and complemented with petrophysical and geological studies, each representing different reservoir scales. On the basis of our study, we identified areas of the field with the highest reservoir quality and largest oil-in-place volume, thus identifying the areas of the field best suited for infill drilling.
This work provides a concept for modelling well performance behavior in a gas condensate reservoir using an empirical model for the gas mobility function. This model is given by:
This concept model represents the minimum gas permeability (or mobility) near the wellbore and the maximum (or original) gas permeability (or mobility) in the "dry gas" portion of the reservoir, as well as the transition regime. This model was constructed based on observations derived from numerical simulation results where the saturation, effective permeability, and gas mobility are presented as functions of distance in the reservoir.
The utility of this concept is that it can be used to develop a pressure solution for the behavior of the gas phase produced from a gas condensate reservoir. This new solution is vali-dated against numerical simulation and has been presented graphically for use in well test analysis (in the form of "type curves"). The advantage of this solution over the conventional radial composite reservoir solutions is that the evolution of the condensate zone can be represented and evaluated as it occurs in time. The obvious limitation is the simplified form of the kg profile as a function of radius and time, as well as the depen-dence/appropriateness of the "a" coefficient.
Application of this new pressure solution to well test analysis is proposed - and comparisons to the radial composite (and other reservoir models) are also presented. Our goal is to demonstrate that the proposed solution has potential utility in the analysis and interpretation of reservoir performance data (most likely, pressure drawdown and pressure buildup test data).
We recognize that the simplicity of this approach may have practical limitations - for example, we consider a radially-varying mobility profile, but we also assume a constant diffusivity - this is a potential shortcoming that should be considered in future work.
The primary objective of this work is:
To develop an analytical representation of the pressure behavior in time and space for a reservoir system with a varying mobility profile (see Fig. 1 for the mobility profile observed from numerical simulation for a radial gas condensate reservoir system).
The secondary objectives of this work are:
To utilize this new model as a mechanism to develop graphical solutions for the pressure derivative in time and radial distance so that the new solution can be compared to other solutions (e.g., the 2-zone radial composite reservoir model and various cases of the sealing fault model (time derivative) - as well as the pressure and pressure derivative (radial derivative) as a function of radial distance derived from numerical simulation).
To use this new model to develop solutions which include wellbore storage and skin effects for modeling the pressure drop and pressure drop derivative functions in time.
To propose applications in the analysis of well test data acquired from pressure drawdown or pressure buildup tests.
Statement of Problem
This work is focused on the concept of using a functional form to represent a prescribed mobility profile (i.e., k/µ) and to incorporate this empirically-derived model into the rigorous diffusivity equation for the liquid case. The goal is to use this concept and the resulting flow model to represent the gas condensate case. We are treating this case as a "liquid equivalent" problem where non-idealities (e.g., pressure-dependent PVT functions) are addressed using the conven-tional pseudofunctions (i.e., pseudopressure and pseudotime).
This work provides the development, validation, and appli-cation of new decline type curves for a well with a finite conductivity vertical fracture centered in a bounded, circular reservoir. This work fills a significant void in the modern inventory of decline type curves. In particular, this work is directly applicable to production data analysis for cases taken from low permeability gas reservoirs.
Using an appropriate analytical solution for this case, we pre-pared "decline" type curves for FcD values from 0.1 to 1000 - individual type curves are generated for each FcD value using a range of reD values from 2 to 1000. The following "type curves" are provided:
"Fetkovich" format rate-time decline type curves (con-stant pressure case): qDd versus tDd
"Fetkovich-McCray" format rate-time decline type curves (equivalent constant rate case): qDd versus
"Fetkovich-McCray" format rate-cumulative decline type curves: qDd versus NpDd
We provide an example demonstration of the methodology for decline type curve analysis using a field case of continuously measured production rate and surface pressure data obtained from a low permeability gas reservoir.
These solutions/type curves provide an analysis/interpretation mechanism that has not previously been available in the petroleum literature. Compared to field data, we find that the traditional type curve solutions for an infinite conductivity vertical fracture are typically inadequate - and, the new solutions for a well with a finite conductivity vertical fracture clearly show much more representative behavior. This validation suggests that the proposed type curves will have broad utility in the petroleum literature - particularly for applications in low permeability gas reservoirs.
The following objectives are proposed for this work:
To develop and validate a series of decline type curves for a well with a finite conductivity vertical fracture centered in a bounded, circular reservoir.
To provide a methodology for using decline type curves to analyze and interpret production or injection well performance for a well with a finite conductivity vertical fracture.
To demonstrate these new type curves using continuously measured production data (rates and pressures).
In considering these objectives we note that we are strongly motivated to provide these tools in light of the current high level of activity in the analysis and interpretation of reservoir performance data acquired from low permeability gas reservoirs. We recognize that current methods based on the case of a vertical well with an infinite conductivity vertical fracture are overly-ideal for low permeability reservoirs and we must reconcile the need for a new decline type curve for a finite conductivity vertical fracture. This rationale is the moti-vation for this work.