The volume of hydrocarbons contained in tight petroleum reservoirs is immense. Thus, their development is crucial to satisfy the worldwide energy demand. A critical aspect for the development of these formations is the stress dependency of rock properties. As pore pressure changes, porosity, permeability, and compressibility of both matrix and natural fractures in tight reservoirs also change, affecting the wells’ production behavior.
A practical problem in the estimation of stress-dependent properties is that the amount of core data available to perform the corresponding studies in tight formations is generally scarce. Under these circumstances, drill cuttings can be used to obtain this information. These observations lead to the key objective of this paper: to develop a reliable approach for estimating stress-dependent properties through the introduction of an innovative methodology that quantifies changes in properties of tight reservoirs and how to extend this methodology in drill cuttings.
The model developed is based on the relationship between the cube root of normalized permeability and the logarithm of net confining stress defined as confining pressure minus pore pressure applied on the rock. An empirical exponent α is introduced to fit the experimental data from confining tests conducted on both vertical and horizontal core samples. This exponent allows the development of an equation that works independently of the initial net confining stress, which is the main limitation of the models already available in the literature. It is our experience that, in many instances, laboratory tests are run at specific values of net confining stress that do not necessarily match the current stress of the reservoir. The correlation proposed in this paper is valuable because it provides a tool that allows correcting the laboratory results to the appropriate net confining stresses in the reservoir. A statistical analysis is performed to verify the appropriateness of the proposed model for the prediction of rock properties as a function of net confining stress.
It is shown that current formulations are particular cases of the proposed model based on the results obtained for the empirical exponent α. Semilog cross-plots of the cube root of normalized permeability versus the net confining stress using core laboratory data corroborate the robustness of the proposed method. The application of the method with drill cuttings is also demonstrated.
It is concluded that the proposed method provides a more accurate methodology for estimating stress-sensitive properties of rocks in tight formations, which are usually naturally fractured, such as the Nikanassin formation analyzed in this work. Porosity, permeability, and compressibility of tight formations are estimated by following the generalized methodology proposed in this study.
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 23-25 July 2018. The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk.
Ghanizadeh, Amin (University of Calgary) | Clarkson, Chris R. (University of Calgary) | Song, Chengyao (University of Calgary) | Vahedian, Atena (University of Calgary) | DeBuhr, C. (University of Calgary) | Deglint, H. J. (University of Calgary) | Wood, J. M. (Encana Corporation)
A schematic of the liquid permeameter, which was designed and constructed in-house for the measurement of liquid permeability using steady-state and pulse-decay flow techniques, is provided in Figure 1. The liquid flow tests were performed under controlled axial/radial confining pressures in a biaxial core holder.
The fracturing of horizontal wells is a recently developed tool to help enable tight and shale formations to produce economically. Production data analysis of the wells in such formations is frequently performed using analytical and semi-analytical methods. However, in the presence of nonlinearities such as multi-phase flow and geomechanical effects, the numerical simulations are necessary for interpretations and history-matching techniques as they are required for model calibration.
Reservoir history-matching techniques are usually based on the frequentist approach and can provide a single solution that can maximize the Likelihood function. Production forecasts using a single calibrated model cannot honor the uncertainty in the model parameters. Therefore, a Bayesian approach is suggested where we can combine our prior knowledge about the model parameters together with the Likelihood to update our knowledge in light of the data. The Bayesian approach is enriched by applying a Markov chain Monte Carlo process to updated the prior knowledge and approximate the posterior distributions.
In this paper, a one-year production data of a real gas condensate well in a Canadian tight formation (lower Montney Formation) is considered. This is a horizontal well with eight fracture stages. A representative 2D model is constructed which is characterized by 17 parameters which include relative permeability curves, capillary pressure, geomechanical effects, fracture half-length, fracture conductivity, and permeability and water saturation in the stimulated region and the matrix. Careful analysis of available data provide acceptable prior ranges for the model parameters using non-informative uniform distributions. Markov chain Monte Carlo algorithm is implemented using a Gibbs sampler and the posterior distributions are found. The results provide an acceptable set of models that can represent the production history data. Using these distributions, a probabilistic forecast is performed and P10, P50 and P90 are estimated.
This paper highlights the limitations of the current history-matching approaches and provides a novel workflow on how to quantify the uncertainty for the shale and tight formations using numerical simulations to provide reliable probabilistic forecasts.
There have been several benchmarks to test and compare reservoir simulators, but so far, there are not the equivalent exercises for numerical simulators used in the design and interpretation of SCAL laboratory experiments. In this study, we have compared four simulators used for the determination of relative permeability and capillary pressure from SCAL experiments. Several tests are performed in direct simulation (no history matching) with one or two fluids injected, generally called unsteady-state (USS) and steady-state (SS), either without or with capillary pressure corresponding to a mixed wettability (positive and negative Pc in imbibition) sample. In addition, a centrifuge drainage experiment is included in the comparisons.
After discussion, the latest versions of the four simulators use the same boundary conditions and give similar results.
An important point that concerns both inlet and outlet is the notion that in the laboratory the plugs are in equilibrium with fluids in the endpieces at the beginning of most experiments. If out-of-equilibrium conditions (spontaneous imbibition) occur, this phenomenon must be clearly identified because it leads to countercurrent flow at the inlet and/or outlet, and possibly to negative pressure in the water phase. Normally, for SS and USS relative permeability measurements and centrifuge experiments, we assume that fluids are at capillary equilibrium at the beginning of the experiments.
For boundary conditions, two simulators use an extra grid block with Pc = 0 to represent the fluids in the endpieces. One simulator uses directly the boundary condition on the first and last grid block within the plug and the fourth simulator uses a zero-width grid-block set to a fixed saturation condition. We show that the three approaches lead to the same results for pressures and saturation inside the plug.This study does not cover all the types of displacements, and we recommend that providers of SCAL simulators give more details concerning the type of boundary conditions and the way they are coded. Tabular data for Kr, Pc and for the results will be available on the websites of the authors, and on the SCA website.
For an anisotropic medium, the permeability is a second-order tensor. As such, permeability is an entity that is dependent upon the coordinate system used to describe the flow quantitatively, although the flow itself is independent of this system. In particular, this means that when a well is producing fluids from a porous medium, the coordinate system must be specified for descriptive purposes and, consequently, the permeability tensor relative to that coordinate system is determined. It is impossible to simultaneously align a 3D orthonormal coordinate system and a cylindrical well segment defined by a single axis except for special cases. Because the permeability tensor will introduce different formulations depending on the defined coordinate system, its complexity will vary accordingly. The objective of this paper is to define an optimal coordinate system with respect to the simplicity of the flow description into the well with an arbitrary trajectory for the special situation of a laterally isotropic, spatially anisotropic medium. The derivation for this optimization strategy is dependent on a sequence of flow-rate-preserving geometric transformations. The resulting virtual medium has isotropic attributes in the transformed 2D plane. Under this transform, known closed-form models are applicable by use of a single permeability value.
Deglint, H. J. (University of Calgary) | DeBuhr, C. (University of Calgary) | Clarkson, C. R. (University of Calgary) | Krause, F. F. (University of Calgary) | Aquino, S. (University of Calgary) | Vahedian, A. (University of Calgary) | Ghanizadeh, A. (University of Calgary)
Characterization of unconventional light oil (ULO) reservoirs is challenging in part due micro-/nano-scale controls on fluid storage and flow. These microscopic flow controls, such as capillary pressure and relative permeability, are fundamentally controlled by pore-scale topology, interfacial tension, and contact angle. This consequently affects reservoir flow behavior, including oil and gas recovery.
In this study, an environmental SEM, coupled with auxiliary equipment and detectors, is used to investigate the micro and nano wettability characteristics of samples from the Middle Bakken reservoir in Viewfield Saskatchewan, which is an active tight oil development area. Three approaches were identified to evaluate micro wettability of geological materials: condensation and evaporation experiments using distilled water; analysis of cryogenically frozen samples that have imbibed fluid formation fluids; and microinjection of distilled water directly onto the sample. Wherever possible, contact angles were measured by fitting a parameterized Young-Laplace equation to the sessile drop profiles.
Wettability is defined as the propensity of one fluid to spread or adhere to a solid surface in the presence of differing immiscible fluids, and is a general measure of the preference that the rock/oil/brine system has for a particular fluid, namely oil and water (W. G. Anderson 1986). Contact angle measurements on rock/oil/brine systems is a universal measure of the wettability of reservoir rock (Morrow 1990). Because wettability can change at the micro-scale due to changes in mineral matter type and variations in organic matter content, conventional macroscopic methods for measuring wettability may be insufficient for quantifying this variability (W. Anderson 1986).
In this study, microscale variability in wettability is investigated using an FEI Quanta FEG 250 variable-pressure and environmental field emission scanning electron microscope (VP-E-FESEM). The VP-E-FESEM, when coupled with a rich assortment of additional detectors and auxiliary equipment, allows the wettability of native and non-native fluids to be measured and mapped across the sample surface. Three approaches were identified to evaluate micro wettability of geological materials:
Reliable experimental capillary pressure and electrical properties as functions of saturation history are essential as inputs for static and dynamic modeling of a reservoir. The only technique that simultaneously gives both capillary pressure and resistivity index as functions of saturation history, and does not rely on a model with underlying assumptions for calculation, is the porous-plate desaturation method. The main disadvantage with this method is that it is time consuming, caused by the low flux through the porous plate or membrane.
We present drainage capillary pressure curves and resistivity index measured on reservoir rock samples by the porous-plate method at pseudo reservoir conditions. In parallel with this, another plug set has been analyzed by interrupting intermediate capillary displacement pressures before reaching equilibrium, with the objective of establishing Sw-RI relationship much faster. The results show that it is possible to establish identical Sw - RI relationship with a time-saving factor of three for the carbonate rock type under study.
The saturation data were fitted to an exponential-decay model using nonlinear regression in order to derive accurate capillary pressure curves from short-wait porous-plate measurements. A similar model was suggested to describe the resistivity index change and was found to occur at a faster rate than the water saturation change.
The most reliable method that can simultaneously measure capillary pressure (Pc) and resistivity index (RI) as a function of water saturation (Sw) is the method known as the porous plate (PP). However, this method can be quite time consuming due to the ultralow permeability of the porous plate. That is why several methods, such as the membrane technique (Longeron et al., 1994) and the continuous-injection method (Zeelenberg and Schipper, 1991), have been developed to speed up the establishment of these properties. The continuous-injection method measures resistivity index as a function of water saturation. It is identical to the porous-plate technique except that the experiment is performed using an ultralow constant injection instead of using a stepwise constant differential pressure, hence no capillary pressure curves can be directly measured. In the membrane technique experiments, thin micropore membranes can be used to shorten experimental times, minimizing the impact of the membrane permeability.
Precise pore-level knowledge of effective thermal and electrical conductivities guarantees proper thermophysical and petrophysical characterization of the multiphase saturated porous media. High resolution advancing imaging techniques and developing modeling approaches are capable of simulating pore-scale phenomena in micro- and nano-scales. In this paper, a numerical framework is presented to predict relative electrical and thermal conductivity curves of two-phase saturated pore-level structures. Displacement scenarios are first performed applying a geometrical filling process. A set of rules to construct the fluid interfaces under capillary-driven transport are implemented. Subsequently effective thermal and electrical conductivity curves, quantifying the relationship between conductivity and saturation, are determined using steady state diffusion equation. The media under consideration include three-dimensional binary images of oil/water-wet sandstone and carbonate formations and the fluid systems contain steam-oil and water-oil equilibriums. The result packages, including thermal diffusivity and conductivity, electrical conductivity, formation factor, apparent diffusion coefficient, and saturation exponent, are generated and discussed considering rock types and fluid configurations.
This paper presents the formulation and verification of a simple model for predicting the liquid level above steam-assisted gravity drainage (SAGD) production wells. Controlling the proximity of the liquid-vapour interface to the producer is paramount for maximizing the energy efficiency of SAGD, optimizing production, and reducing the risk of liner damage from steam breakthrough; and so a simple model can be used for quick approximation and potentially for decisions on wellbore design and operational control.
The formulation is based on continuity of mass flow and thermal behaviour. Darcy's law is the key phenomenon in formulating an analytical model of the flow through the liquid pool, or steam trap, around the production well, which is referred to in this work as a gravity inflow performance relationship (GIPR). The GIPR relates the liquid level above the producer to the inflow rate, system pressures, and reservoir and fluid properties. To validate our modelling assumptions, the liquid level predicted by the GIPR is compared to data generated from a commercial reservoir simulator for a wide range of operating conditions.
Based on data from 31 reservoir simulations, the GIPR predicts the liquid level with high accuracy. The liquid levels given by the GIPR and reservoir simulator differ by a root-mean-square error of only 0.23 m. The introduction of a correction factor in the GIPR reduces the root-mean-square error to just 0.17 m. Moreover, the GIPR reveals fundamental relationships between the liquid level and SAGD process variables, providing insight into the mechanics of steam trap control. The relationship between the liquid level and the inflow rate yields a criterion for the stability of the liquid-vapour interface above the production well. The criterion elucidates the conditions under which the position of the liquid-vapour interface will be unstable and, thus, the conditions under which steam breakthrough or injector flooding may be expected.
The GIPR provides a simple, efficient, and accurate way to predict the liquid level above SAGD production wells, enabling the optimization of well designs and control strategies to facilitate steam trap control. In addition, the GIPR reveals relationships between variables that are masked with more complex models, providing an enhanced understanding of the SAGD process.