University of Regina

Summary Cold heavy oil production with sand (CHOPS) technique has successfully improved oil recovery from heavy oil reservoirs due to high permeability channels resulted from sand failure and foamy oil flow enhancing heavy oil movability. However, impacts of the sand failure and the foamy oil flow on multiphase fluid flow features are still not properly understood. In this paper, an effective and systematic framework has been proposed to characterize the multiphase fluid flow and determine the three-phase relative permeability of CHOPS processes. A recently developed sand failure criterion and a relative permeability model have been integrated with a reservoir simulator to simulate the CHOPS process. The unknown parameters involved in the systematic framework are intelligently determined by an iterative ensemble smoother (IES) algorithm, which also enables sensitivity analysis on CHOPS production profiles. Subsequently, the proposed framework is tested through a laboratory CHOPS experiment. It has also been found that using two sets of three-phase relative permeability is capable of representing the segment-type nature of the multiphase flow and reproducing the transition stage on the production profiles. Furthermore, the comparison between two sets of three-phase relative permeability indicates that the sand failure phenomenon yields a reduced residual oil saturation and an increased oil/gas relative permeability. In addition, the sensitivity analysis demonstrates that the segment-type nature of production profiles results from the variation of key impact factors dominating the multiphase fluid flow in CHOPS processes. Overall, the proposed systematic framework can not only reproduce the physical phenomena of sand failure and foamy oil, but also provide a convenient tool to characterize the multiphase flow in CHOPS processes.

Summary

Accurate prediction of density of an oil/gas mixture by using the ideal mixing (IM) rule is a great challenge, and its progress is still far from satisfactory. The method proposed by Standing and Katz (1942) for determining methane and ethane apparent densities is limited to only black oils and volatile oils. The methods recently proposed by Saryazdi (2012) and Saryazdi et al. (2013) to determine effective densities of methane through n-heptane (C₁ through n-C₇) and CO₂ have shown some success, respectively, though limitations remain and the extent of their applications is still constrained. In this study, we developed a tangent-line approach for the effective density of C₁ through n-C₈, CO₂, N₂, toluene, cyclohexane, and dimethyl ether (DME). This method is more general and flexible than the extrapolation method proposed by Saryazdi (2012). A comprehensive database is established to first develop new correlations with one set of data and then compare them with the other. We successfully extended using the IM rule with effective density (IM-E) to condensate/bitumen systems, solvent/bitumen fraction systems, and solvent/bitumen systems with substantial extraction [i.e., emergence of a solvent-rich liquid phase (denoted as the L₁ phase)] by properly treating the densities of condensate, bitumen fractions, extracts, and residues. This study focuses on heavy-oil/bitumen-associated systems, and the observed patterns and trends for different systems will be presented and explained in Part II of this study (Chen and Yang In Press).

In this paper, pragmatic and robust techniques have been developed to simultaneously interpret absolute permeability and relative permeability together with capillary pressure in a naturally fractured carbonate formation from wireline formation testing (WFT) measurements. By using two sets of pressure and flow rate field data collected by dual-packer tool, two high-resolution cylindrical near-wellbore numerical models are developed for each dataset on the basis of single- and dual- porosity concepts. Then, simulations and history matchings are performed for both the measured pressure drawdown and buildup profiles, while absolute permeability is determined and relative permeability is interpreted with and without considering capillary pressure. Compared to the experimentally measured relative permeability curves for the same formation collected from literature, relative permeability interpreted with consideration of capillary pressure has a better match than those without considering capillary pressure. Also, relative permeability obtained from dual porosity models has similar characteristics to those from single porosity models especially in the region away from the endpoints, though the computational expenses with dual porosity models are much larger. Absolute permeabilities in the vertical and the horizontal directions of the upper layer are determined to be 201.0 md and 86.4 md, respectively, while those of the lower layer are found to be 342.9 md and 1.8 md, respectively. Such a large vertical permeability of the lower layer reflects the contribution of the extensively distributed natural fractures in the vertical direction.

Recently, substantial technical progress has been made to solve complex tasks in the field of artificial intelligence (AI) by incorporating deep neural networks into reinforcement learning (RL). In this paper, four state-of-the-art deep RL algorithms are applied to optimize the net present value (NPV) of waterflooding (WF) under geological uncertainties by adjusting the water injection rate. They include the deep Q-network (DQN), double DQN (DDQN), dueling DDQN, and deep deterministic policy gradient (DDPG). A set of fifty reservoir realizations are generated by using a geostatistical technique to account for the geological uncertainties. It is found that the deep RL algorithms can optimize the WF in a 3-D 3-phase (oil-water-gas) reservoir under geological uncertainties. More specifically, both DQN and particle swarm optimization (PSO) converge to the same highest NPV, whereas the other three deep RL algorithms can find some local optimum NPVs due to the exploration-exploitation problem. DDPG converges faster than PSO and requires the least numerical simulation runs among all deep RL algorithms. The optimum water injection rate determined in the consideration of geological uncertainties not only increases the expected NPV but also reduces its standard deviation. The optimum WF starting time is found to be in the middle of the primary production. In this way, the solution-gas drive is continued and the water-cut is decreased. The production performances are compared under three different water injection scenarios: no-control, reactive-control, and optimum-control. The optimum-control scenario achieves a low water-cut and a stable oil production rate.

Recently, substantial technical progress has been made to solve complex tasks in the field of artificial intelligence (AI) by incorporating deep neural networks into reinforcement learning (RL). In this paper, four state-of-the-art deep RL algorithms are applied to optimize the net present value (NPV) of waterflooding (WF) under geological uncertainties by adjusting the water injection rate. They include the deep Q-network (DQN), double DQN (DDQN), dueling DDQN, and deep deterministic policy gradient (DDPG). A set of fifty reservoir realizations are generated by using a geostatistical technique to account for the geological uncertainties. It is found that the deep RL algorithms can optimize the WF in a 3-D 3-phase (oil-water-gas) reservoir under geological uncertainties. More specifically, both DQN and particle swarm optimization (PSO) converge to the same highest NPV, whereas the other three deep RL algorithms can find some local optimum NPVs due to the exploration-exploitation problem. DDPG converges faster than PSO and requires the least numerical simulation runs among all deep RL algorithms. The optimum water injection rate determined in the consideration of geological uncertainties not only increases the expected NPV but also reduces its standard deviation. The optimum WF starting time is found to be in the middle of the primary production. In this way, the solution-gas drive is continued and the water-cut is decreased. The production performances are compared under three different water injection scenarios: no-control, reactive-control, and optimum-control. The optimum-control scenario achieves a low water-cut and a stable oil production rate.

Summary In this paper, we formulated an analytical material-balance model (MBM) to predict cumulative heavy-oil and gas-production data, as well as the average reservoir pressures, during the primary production and subsequent cyclic solvent injection (CSI) in a heavy-oil reservoir. The theoretical MBM considers the nonequilibrium foamy-oil phase behavior and foamy-oil flow by invoking two kinetic equations with nucleation and decay coefficients. In addition, we conducted four laboratory sandpack tests of the primary production and subsequent CSI to validate the new production model. It was found that the predicted cumulative heavy-oil production data and average reservoir pressures agreed reasonably well with the measured data during the primary production and subsequent CSI. However, there were large discrepancies between the predicted and measured cumulative gas-production data in the CSI owing to its strong gas channeling, which is a major technical issue to be studied further. Moreover, dissolved CH 4 in the heavy oil became dispersed CH 4 bubbles more quickly when the nucleation coefficient was larger at a higher pressure-drawdown rate or in less-viscous heavy oil. The foamy heavy oil with dispersed CH 4 bubbles was more stable when the decay coefficient was smaller at a higher pressure-drawdown rate or in more-viscous heavy oil. It was also found that the foamy-oil isothermal compressibility increased by 10 to 1,000 times and that the dispersed-gas percentage in the foamy oil could reach as high as 14 vol% during the primary production.

Summary In this study, theoretical models have been formulated, validated, and applied to evaluate the transient pressure behavior of a horizontal well with multiple fractures in a tight formation by taking stress-sensitive fracture conductivity into account. On the basis of the superposition principle in the Laplace domain, we propose a coupled matrix/fracture-flow model with consideration of the stress-sensitivity effect in fractures, which strengthens the nonlinearity of the governing equations. More specifically, a new slab-source function in the Laplace domain was developed to describe the transient pressure responses caused by fluid flow from the matrix to the fracture, and a new solution was derived to describe the fluid flow in the fracture under the stress-sensitivity effect. Subsequently, a semianalytical method was applied by discretizing each hydraulic fracture into small segments, and a linearization scheme and an iteration method are adopted to deal with the nonlinear problem in the Laplace domain. Meanwhile, a modified superposition principle was proposed and applied to generate the pressure distributions for buildup tests with consideration of stress-sensitive fracture conductivity. Furthermore, pressure responses and their corresponding derivative type curves were generated to examine the effect of stress-sensitive conductivity. For pressure-drawdown tests, it is found that gradual increases in both pressure drop and pressure derivative occur over time because of the partial closure of the fractures. The stress-sensitivity effect in fractures becomes more evident with a smaller fracture conductivity and a larger fracture-permeability modulus. From the pressure-buildup curves, a one-fourth-slope line characteristic of the bilinear-flow period and constant derivatives of 0.5 representing a pseudoradial-flow regime can be clearly observed. Only fracture conductivity near the wellbore at the shut-in time can be estimated from the buildup pressures obtained in this work, whereas pressure-buildup analysis derived from the traditional superposition principle will result in an erroneous evaluation of the stress-sensitive fracture conductivity. It is also found that the effect of permeability hysteresis in the fractures has a negligible impact on the pressure-buildup responses.

Summary Cold heavy-oil production with sand (CHOPS) has been one of the major recovery processes for developing unconsolidated heavy-oil reservoirs by taking advantage of sand production and foamy-oil flow. However, effective characterization and accurate prediction of sand production is still a challenge. In this work, a pressure-gradient-based sand-failure criterion is proposed for quantifying sand production and characterizing wormhole propagation. The proposed sand-failure criterion was initially developed at the pore-scale level, while a pseudointeraction force between two neighboring sand grains was proposed to implicitly represent the potential contributions of cementation and geomechanical stresses to the fluidization of sand. The criterion was then extended to a grid scale within a wormhole because the pressure gradient is constant at either a pore scale or a grid scale. With the bottomhole pressure being an input constraint, the proposed sand-failure criterion was validated with good agreement by reproducing production profiles and wormhole propagation from laboratory experiments and a CHOPS well in the Cold Lake Oil Sands Area. This was a confirmation that the proposed sandfailure criterion can be used to characterize the sand production in a CHOPS process. Introduction In a heavy-oil reservoir, the sand flux along with the oil flowing into wells has been proved to surprisingly stimulate oil production (Smith 1988). With the advance of progressing-cavity pumps that enable the mixture of oil and sand to flow effectively, CHOPS has been extensively applied to the primary development of unconsolidated heavy-oil reservoirs in western Canada (Huang et al. 1998; Tremblay et al. 1999; Han et al. 2007; Sharifi Haddad and Gates 2015). The CHOPS wells can be found in Lloydminster Field, Provost Field in the Cold Lake Oil Sands Area, Lindbergh Field, Elk Point Field, Frog Lake Field, and in China and Kuwait (Huang et al. 1998; Dusseault 2002; Meza Diaz et al. 2003; Du et al. 2009; Sanyal and Al-Sammak 2011). The typical characteristics of production profiles for CHOPS wells were mainly summarized from field experiences. Most of the sand is commonly produced during the first several months of a CHOPS well life, and the oil-production peak is usually later than the sand-production peak because of the coupling influences of sand production together with pressure depletion (Huang et al. 1998).

Summary

Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into mathematical models to take into account the stress-sensitivity effect. In this way, the resulting nonlinearity of the mathematical models is weakened by using Pedrosa’s transform formulation. Then a semianalytical method is applied to solve the coupled nonlinear mathematical models by discretizing each HF into small segments. Furthermore, the pressure response and its corresponding derivative type curve are generated to examine the combined effects of non-Darcy flow and stress sensitivity. In particular, stress sensitivity in HF and natural-fracture (NF) subsystems can be respectively analyzed, while the assumption of an equal stress-sensitivity coefficient in the two subsystems is no longer required. It is found that non-Darcy flow mainly affects the early stage bilinear and linear flow regime, leading to an increase in pressure drop and pressure derivative. The stress-sensitivity effect is found to play a significant role in those flow regimes beyond the compound-linear flow regime. The existence of non-Darcy flow makes the effect of stress sensitivity more remarkable, especially for the low-conductivity cases, while the stress sensitivity in fractures has a negligible influence on the early time period, which is dominated by non-Darcy flow behavior. Other parameters such as storage ratio and crossflow coefficient are also analyzed and discussed. It is found from field applications that the coupled model tends to obtain the most-reasonable matching results, and for that model there is an excellent agreement between the measured and simulated pressure response.

Summary Analytical models have evolved in their capacity to represent the transient response of multifractured horizontal wells producing from unconventional reservoirs. Their use for analyzing flow scenarios that transcend their scope is thus prone to errors. Our solution is based on the Laplace-transform boundary-element-method (BEM) implementation of the Green's function solution of the diffusivity equation. We represent the reservoir as a 2D composite system, with the outer boundaries and the interface between reservoir regions discretized appropriately. The first example showcases a multifractured horizontal well traversed by identical, evenly spaced, fully penetrating, vertical hydraulic fractures within a stimulated reservoir volume (SRV). Besides showing that all the verification and example cases are in excellent agreement with numerical solution, we demonstrate the utility of our solution for modeling variable-rate flow commonly observed in practical field-production scenarios, showing its potential for history matching and forecasting the performance of multifractured horizontal wells. Introduction With the proliferation of activities on shale and tight-sand resource plays, the need to understand their flow dynamics and characterize them, for recovery optimization, is central to reservoir management. These plays have micro-to nanodarcy permeabilities; hence, they cannot sustain commercial production unless they are engineered with unconventional stimulation methods, of which the multifractured horizontal well is the method commonly used. Hydraulic fracturing is known to generate a dendritic secondary fracture network in addition to the propped primary fractures. For horizontal wells, this completion technology creates a complex flow system (e.g., as shown in Figure 1) that poses a formidable challenge regarding representation in analytical models. Several analytical models have been developed to aid understanding flow behavior of multifractured horizontal wells.