Single-porosity System Research Articles

Radius of investigation and impact of inter-porosity flow in naturally-fractured reservoirs

The radius of investigation (ROI) is an essential parameter in many reservoir engineering applications. Inconsistencies and ambiguities still exist between different ROI evaluation methods, especially for the dual-porosity (DP) system representing naturally fractured reservoirs. This paper revisited the impact of inter-porosity flow in the DP system and presented ROI equations in the early and late flow periods based on the Laplace space solution of the Warren-Root dual-porosity model. A new comprehensive ROI expression for the DP system is derived which accounts for both storativity ratio () and inter-porosity flow coefficient (). The new method in this paper reveals that the log-log plot of ROI vs. time for DP models exhibits two parallel straight lines linked by a smooth transition curve. The distance of these two straight lines is dependent on and ROI in the intermediate flow period is highly dependent on the value of The new ROI equation for the DP system can degenerate to similar ROI formula for the single-porosity system in early and late flow periods. Comparison analysis of the new method with other approaches is conducted and the validation of the new method is realized by analytical and numerical matching.

Production Calculation Model of Thermal Recovery after Hydraulic Fracturing and Packing in Tight Reservoir

It was deemed important to calculate the thermal recovery production model of tight oil reservoirs after fracturing and packing based on the field data of an oilfield in Bohai Sea, China. The thermal recovery production of a tight oil reservoir after fracturing is demonstrated through theoretical calculation and practical field data on the premise of five hypotheses. Fractures change the fluid flow capacity of the reservoir. Combined with the relevant theories of reservoir thermal production, the dual porosity system in the fractured zone and the single porosity system in the unfractured zone were established. The calculation models of heat loss in the fractured and unfractured zones were derived to determine the thermal recovery heating radius of the reservoir after fracturing and packing. Combined with the pseudo-steady state productivity formula of the composite reservoir, a production calculation model of thermal recovery after fracturing and packing in the tight oil reservoir was established. The results showed that the heating radius of the reservoir after fracturing and packing is smaller than that of the unfractured reservoir, and the additional heat absorption of the fracture system generated by fracturing and packing reduces the thermal recovery effect. The thermal recovery productivity of heavy oil reservoirs is mainly affected by the heating radius. With the increase of fracture density, the heating radius decreases and production decreases. The increase of fracture porosity also leads to the decrease of the heating radius and the production. The calculation result of this model is improved after tight oil reservoir fracturing during the production period, which indicates that the model has a better prediction effect of the production of the tight reservoir after fracturing and packing.

Rigorous Estimation of the Initial Conditions of Flowback Using a Coupled Hydraulic-Fracture/Dynamic-Drainage-Area Leakoff Model Constrained by Laboratory Geomechanical Data

Summary The application of rate-transient-analysis (RTA) concepts to flowback data gathered from multifractured horizontal wells (MFHWs) completed in tight/shale reservoirs has recently been proposed as an independent method for quantitatively evaluating hydraulic-fracture volume/conductivity. However, the initial fluid pressures and saturation in the fracture network and adjacent reservoir matrix are generally unknown at the start of flowback, creating significant uncertainty in the quantitative analysis of flowback data. In this study, we present a semianalytical flow model, coupled with a hydraulic-fracture (fracture) model and constrained with laboratory-based geomechanical data, for evaluating the initial conditions of flowback. In previous work, a semianalytical model based on the dynamic-drainage-area (DDA) concept was used to simulate water-based fluid leakoff from an MFHW into a tight oil reservoir (Montney Formation, western Canada), with minimal mobile water, during and after fracturing operations. The model assumed that each fracturing stage can be represented by a primary hydraulic fracture (PHF) containing the majority of the proppant, and an adjacent nonstimulated reservoir (NSR) or enhanced fracture region (EFR), which is an area of elevated permeability in the reservoir caused by the stimulation treatment. Each region was represented by a single-porosity system. The DDA propagation speed within the PHF during the stimulation treatment was constrained through using a simple analytical fracture model. Although this approach was considered novel, several improvements and additional laboratory constraints were considered necessary to yield more accurate predictions of initial flowback conditions. In the current work, the modeling approach described previously was improved by representing the EFR with a dual-porosity system; fully coupling the fracture model (used for PHF creation and propagation) with the DDA model for fluid-leakoff simulation into the EFR and adding a proppant-transport model; and modeling the shut-in period. Finally, to ensure that model geomechanics were properly constrained, a comprehensive suite of previously gathered laboratory data was used. Laboratory-derived propped (PHF) and unpropped (EFR) fracture-permeability/conductivity data as a function of pore pressure, as well as fracture-compressibility data, were used as constraints for the model. It should be noted that our model assumes that fracture closure has no effect on the pressure/saturation of the PHF/EFR/matrix. The improved model was reapplied to the tight oil field case and yielded more realistic estimates of initial flowback conditions, enabling more confident history matching of flowback data. The results of this study will be important to those petroleum engineers interested in quantitative analysis of flowback data to accurately obtain fracture properties by ensuring proper model creation.

A two-step method to apply Xu\u2013Payne multi-porosity model to estimate pore type from seismic data for carbonate reservoirs

Carbonate reservoirs exhibit strong heterogeneity in the distribution of pore types that can be quantitatively characterized by applying Xu–Payne multi-porosity model. However, there are some prerequisites to this model the porosity and saturation need to be provided. In general, these application conditions are difficult to satisfy for seismic data. In order to overcome this problem, we present a two-step method to estimate the porosity and saturation and pore type of carbonate reservoirs from seismic data. In step one, the pore space of the carbonate reservoir is equivalent to a single-porosity system with an effective pore aspect ratio; then, a 3D rock-physics template (RPT) is established through the Gassmann’s equations and effective medium models; and then, the effective aspect ratio of pore, porosity and fluid saturation are simultaneously estimated from the seismic data based on 3D RPT. In step two, the pore space of the carbonate reservoir is equivalent to a triple-porosity system. Combined with the inverted porosity and saturation in the first step, the porosities of three pore types can be inverted from the seismic elastic properties. The application results indicate that our method can obtain accurate physical properties consistent with logging data and ensure the reliability of characterization of pore type.

Measurement of CO2 diffusion coefficient in the oil-saturated porous media

Molecular diffusion is an important EOR mechanism in naturally fractured reservoirs. However, the laboratory-measured diffusion coefficient in the fractured porous media is still limited; and grid sensitivity analysis is missing in the literature when the single-porosity system is applied to history match the pressure decline curve. We aimed to fill the gaps using Radial Constant Volume Diffusion (RCVD) method experimentally to investigate diffusion coefficients at different pressures in hydrocarbon saturated porous media. A special in-house cell is designed to hold the core sample in the center with the annulus around simulating the fracture. The core is initially saturated with oil while the annulus is filled with CO2 at the same pressure. During the measurements, the system pressure declines as gas diffuses into the oil phase until it reaches chemical equilibrium. The pressure decline curve is history matched to determine the diffusion coefficient. The initial pressure is 597 psi, and the diffusion coefficient is determined in numerical models accordingly. Molecular diffusion coefficients are estimated at different experiment periods to reveal the pressure-dependency. A workflow is proposed to obtain effective diffusion coefficients in dual-porosity models that could be extended to multi-component systems. Besides, flow characteristics in the RCVD system are characterized and capillary pressure effect is investigated in this study.

Production data analysis for dual-porosity gas/liquid systems: A density-based approach

Production data analysis impacts assets value and financial decisions significantly. Naturally fractured reservoirs exist widely around the world. A common method to represent naturally fractured reservoirs is dual-porosity model. Intrinsic characteristics of dual-porosity systems and their unique rate-transient profile require models able to capture well behavior and to achieve production data analysis, which is a proven difficulty for dual-porosity gas system and not completely solved. Moreover, past studies on dual-porosity systems assume constant bottom-hole pressure (BHP) or constant rate production, which impose significant constraint to production data analysis.Recently a density-based approach for analyzing production data was proposed for single-porosity system, which has been proven to successfully describe gas well behavior under boundary-dominated flow (BDF). Using depletion-driven parameters, λ and β, this state-of-the-art approach circumvents pseudo time. It was then extended to variable-pressure-drawdown/variable-rate gas systems and proven successful.In this study, we adopt a rigorously derived interporosity flow equation for gas, which captures viscosity-compressibility change of matrix outflow. Based on that, a density-based, rescaled exponential model for variable pressure drawdown/variable rate production was developed for dual-porosity gas system. Also, we explore straight-line analysis for convenient prediction of OGIP and production rate. The density-based model is tested in a variety of scenarios to showcase its validity.Moreover, based on Warren and Root model, a density-based exponential model for variable pressure drawdown/variable rate in dual-porosity liquid system is proposed and fully verified. A straight-line analysis is proposed to enable explicit OOIP prediction and convenient future production calculation. Moreover, a convenient double-exponential decline model under constant BHP is developed for liquid.To summarize our work, we developed rate-transient analysis method for two types of reservoirs-naturally fractured gas reservoir and naturally fractured oil reservoirs-producing at arbitrary type of production scenario in boundary-dominated-flow stage. The proposed method can evaluate reserve in a convenient and accurate manner. Moreover, the method to predict production using the theory is also provided. An explicit equation correlating dimensionless production rate and dimensionless time is also developed for dual-porosity liquid system producing at constant bottomhole pressure in both early transient stage and boundary-dominated-flow stage.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

A New Method of Optimization Design of Hydraulic Fracture Parameters in Low Porosity and Fractured Gas Reservoir

A new composite reservoir simulation model of lower computation cost was used to optimize hydraulic fracture length and fracture conductivity during performing a hydraulic fracturing. The simulation model is divided into inner part and outer part. The inner part is dual-porosity and dual-permeability system, and the other is single porosity system. The research shows that the natural fracture permeability and density are the most influential parameters; a relative long fracture with high hydraulic fracture conductivity is required for a high production rate due to non-Darcy flow effects. A shorter primary fracture is better in a gas reservoir of high natural density. The composite model represents the flow characteristic more accurately and provides the optimal design of fracturing treatments to obtain an economic gas production.

Salt Precipitation Due to Sc-gas Injection: Single Versus Multi-porosity Rocks

We investigate the consequences of formation dry-out due to the injection of under-saturated supercritical acid gas/CO2 into a Middle Eastern dolomite formation for enhanced oil recovery (EOR) and acid gas (AG)/CO2 disposal purposes. We perform core flood experiments and numerical simulations with the aim to highlight two aspects. Firstly, the risk assessment of injectivity loss associated with the precipitation of salt in the vicinity of an injection well for the respective EOR operation. Secondly, the rock matrix of the formation differs substantially from the simple sandstone of a previous study. The comparison of both rock types gives insight in the qualitatively different impact of salt precipitation on permeability/injectivity in a multi-porosity and a single porosity system, respectively.

Whole Core vs. Plugs: Integrating Log and Core Data to Decrease Uncertainty in Petrophysical Interpretation and Oil-In-Place Calculations

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 137679, “Whole Core vs. Plugs: Integrating Log and Core Data To Decrease Uncertainty in Petrophysical Interpretation and STOIP Calculations,” by S. Serag El Din, SPE, ADCO; M.R. Dernaika, SPE, Weatherford Laboratories; I. Al Hosani, ADCO; L. Hannon, Weatherford Laboratories; S.M. Skjeveland, SPE, University of Stavanger; and M.Z. Kalam, ADCO, prepared for the 2010 Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 1–4 November. The paper has not been peer reviewed. Most carbonate reservoirs are characterized by multiple-porosity systems that impart petrophysical heterogeneity to the gross reservoir interval. The specific types and relative percentages of pores present, and their distribution within the rocks, exert strong control on production and stimulation characteristics of carbonate reservoirs. The effects of heterogeneity on core and log measurements are presented. The challenge is to determine the reliability of applying relatively small-scale properties measured by a log or core to the large-scale reservoir property. Introduction Most sandstone reservoirs are single-porosity systems (i.e., interparticle pores) of relatively uniform (homogeneous) nature. However, most carbonate reservoirs are characterized by multiple-porosity systems. Reservoir heterogeneity results from physical and chemical reorganization processes over time (e.g., compaction, solution, dolomitization, and cementation). Heterogeneity complicates the reservoir-description task, in which reservoir properties (e.g., permeability, porosity, saturation, and rock types) tend to vary as a function of spatial locations in vertical and areal directions. Vertical heterogeneity has shown large effects on sweep efficiencies of waterfloods and conventional gas injection into mixed- to oil-wet carbonate reservoirs. These effects are a result of large variations in permeability between different strata. Permeability and other rock properties can vary along the areal (lateral) direction of the reservoir, which necessitates establishing an accurate and detailed understanding of geological heterogeneities and their effect on petrophysics and reservoir engineering. The effect of rock heterogeneity becomes greater when petrophysical properties are measured at scales ranging from a small trim sample in the laboratory to log measurements in the field. Permeability variation of three orders of magnitude has been reported over a distance of a few centimeters in a carbonate-core plug. In heterogeneous reservoirs, the real challenge is predicting reservoir performance through the acquisition of representative measurements. The challenge would be to reconcile the variability seen in high-resolution (e.g., trim or plug samples) and low-resolution (e.g., wireline logs) measurements and to quantify the technical and physical considerations at the various scales.

ベトナム・ランドン油田フラクチャー型貯留層モデル構築

The Rang Dong oil field is located in the Cuu Long basin, offshore Vietnam. The field was discovered by Japan Vietnam Petroleum Company Ltd. in 1994. The field has naturally fractured basement reservoir, which is producing with 14 producers and 7 injectors as of now. One of the production bottlenecks of the Rang Dong field is gas and water break through. High bubble point pressure oil provides secondary gas cap drive system to the reservoir. But control of the liberated gas production by coning is difficult. Deeper completions to avoid gas break through often result in water break through, although there is no significant pressure support from aquifer. Currently, water injection is applied to the field to control reservoir energy and gas cap development. With this situation, development of reliable model to predict field performance is a key technical requirement to manage the field. This paper describes evolution of the reservoir modeling. Generally, characterization of fractured crystalline rock reservoir is more difficult than sedimentary rock reservoir. After some lessons learnt, new approaches such as 3D seismic reprocessing, highly deviated-horizontal wells, extended well testing were applied to fully evaluate the reservoir. These new approaches made a lot of improvement to understanding of the fracture system and resulting simulation models. Integration of different disciplinary data introduced key concepts such as discrete fractures, productive network and dynamic data matching. The fracture data gathered so far were re-evaluated in the view of connectivity to the productive network. The simulation model consists of discrete mega-fracture framework and associated relatively continuous lower order fractures. The model is calibrated with both static and dynamic data, using such data as seismic, log and well test. This model describes pore space distributions and their connectivity in single porosity system and can re-produce the history of break through and predict the reservoir performances with some practical accuracy in natural depletion condition.

Single and dual-permeability models of chlorotoluron transport in the soil profile

This study presents the transport of chlorotoluron in the soil profile under field conditions. The herbicide Syncuran was applied on a plot (4 m˛) using an application rate of 2.5 kg/ha of active ingredient. Soil samples were taken after 119 days to study the residual chlorotoluron distribution in the soil profile. The single and dual-permeability models in HYDRUS-1D (Šimůnek et al. 2003) were used to simulate water movement and herbicide transport in the soil profile. Soil hydraulic properties and their variability were previously studied by Kutílek et al. (1989). The solute transport parameters, such as the adsorption isotherm and the degradation rate, were determined in the laboratory. Since the solute transport in the field was probably affected by preferential flow, the chlorotoluron distribution in the soil profile calculated using the single-permeability model had a different character than observed chlorotoluron concentrations. The chlorotoluron distribution within depth calculated using the dual-permeability model was closer to the observed behavior of chlorotoluron. While the herbicide did not reach a depth of 8 cm for the single-porosity system, in the case of the dual-permeability model the solute moved to the depth of 60 cm. The dual-permeability model significantly improved correspondence between calculated and observed herbicide concentrations.

Thermomechanical theories for swelling porous media with microstructure

Thermomechanical microstructural dual porosity models for swelling porous media incorporating coupled effects of hydration, heat transfer and mechanical deformation are proposed. These models are obtained by generalizing the three-scale system of Murad and Cushman [56,57] to accommodate heat transfer effects and their influence on swelling. The microscale consists of macromolecular structures (clay platelets, polymers, shales, biological tissues, gels) in a solvent (adsorbed water), both of which are considered as distinct nonoverlaying continua. These continua are homogenized to the meso (intermediate scale) in the spirit of hybrid mixture theory (HMT), so that at the mesoscale they may be thought of as two overlaying continua. Application of HMT leads to a two-scale model which incorporates coupled thermal and physico-chemical effects between the macromolecules and adsorbed solvent. Further, a three-scale model is obtained by homogenizing the particles (clusters consisting of macromolecules and adsorbed solvent) with the bulk solvent (solvent not within but next to the swelling particles). This yields a macroscopic microstructural model of dual porosity type. In the macroscopic swelling medium the mesoscale particles act as distributed sources/sinks of mass, momentum and energy to the macroscale bulk phase system. A modified Green's function method is used to reduce the dual porosity system to a single-porosity system with memory. The resultant theory provides a rigorous derivation of creep phenomena which are due to delayed intra-particle drainage (e.g. secondary consolidation of clay soils). In addition, the model reproduces a class of lumped-parameter models for fluid flow, heat conduction and momentum transfer where the distributed source/sink transfer function is a classical exchange term assumed proportional to the difference between the potentials in the bulk phase and swelling particles.

Compositional Numerical Modelling In Naturally Fractured Reservoirs

Abstract Recent improvements in the. speed. of numerical compositional simulators has made it possible to use a large number of grid blocks to model condensate reservoirs, volatile reservoirs, and gas injection projects. This paper discusses techniques for choosing pseudo components so as to use four to five pseudo components for the simulations. It also discusses the condensate dropout in the reservoir and its effect on the productivity of individual producing wells. The methods for characterizing fracture networks in a naturally fractured reservoir are presented and other parameters which affect hydrocarbon recovery are discussed as part of a parametric study. Introduction In recent years wells have been drilled to greater depths, resulting in the discovery of gas condensate reservoirs and volatile oil reservoirs at relatively high temperatures. A large amount of research has been conducted to investigate productivity from these oil reservoirs. This research has investigated how to tune an equation of state so as to match the actual phase behaviour which is occurring within a reservoir. Studies have reported on the effects of interfacial tension and velocity on gas-oil relative permeability curves. These studies indicate that bench type gas-oil and water-oil relative permeabilities are not applicable to predicting the performance of individual wells in gas condensate reservoirs. Well test data and recent advances in well logging procedures using well-bore imaging techniques have provided tools to better characterize the fracture system which exists in naturally fractured reservoirs. These data have been used in conjunction with stochastic models to describe the fracture network inside of these reservoirs. A parametric study using a number of variables was conducted for this paper. The results from this parametric study are useful in history matching to determine those parameters which, when adjusted, will have the greatest effect on the performance of the reservoir. This study will also suggest modifications which need to be made to numerical simulators so as to better simulate the actual mechanism which are occurring in gas condensate reservoirs. Mechanism of Flow in Naturally Fractured Reservoirs Fluid flow in naturally fractured reservoirs differs significantly from that in a single porosity system. The numerical simulator breaks the reservoir into two different systems: one, a system of matrix blocks which mayor may not have capillary contact and the other, a network of fractures. The simulation assumes that most of the flow to the wells will occur through the fracture network which contains a relatively small fluid volume, but high permeability, and that the bulk of the hydrocarbon fluids are contained within the matrix blocks. As reservoir pressure is depleted, the fluids are expelled from the blocks into the fracture system, which conveys them to the producing wells. Gas condensate reservoirs initially are at pressures at or above the dewpoint. Once the pressure has been depleted below the dewpoint, liquid will condense and two phases will be present. When these two phases are present the liquid will not flow in either the matrix or the fracture system until a critical condensate saturation is obtained.

The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow

Abstract. It is shown that there exists a weak solution to a degenerate and singular elliptic-parabolic partial integro-differential system of equations. These equations model two-phase incompressible flow of immiscible fluids in either an ordinary porous medium or in a naturally fractured porous medium. The full model is of dual-porosity type, though the single porosity case is covered by setting the matrixto-fracture flow terms to zero. This matrix-to-fracture flow is modeled simply in terms of fracture quantities; that is, no distinct matrix equations arise. The equations are considered in a global pressure formulation that is justified by appealing to a physical relation between the degeneracy of the wetting fluid’s mobility and the singularity of the capillary pressure function. In this formulation, the elliptic and parabolic parts of the system are separated; hence, it is natural to consider various boundary conditions, including mixed nonhomogeneous, saturation dependent ones of the first three types. A weak solution is obtained as a limit of solutions to discrete time problems. The proof makes no use of the corresponding regularized system. The hypotheses required for various earlier results on single-porosity systems are weakened so that only physically relevant assumptions are made. In particular, the results cover the cases of a singular capillary pressure function, a pure Neumann boundary condition, and an arbitrary initial condition.