Mohammad Sayyafzadeh

An experimental investigation into surface roughness of a hydraulic fracture

The fracture surface roughness is an essential characteristic of the hydraulic fracturing process and has not been fully explored. The surface asperities play a significant role in proppant flow and settlement, fluid leak-off and fracture tip movement. In this study, we performed an experimental investigation to evaluate the fracture surface roughness of a hydraulic fracture generated in the lab tests. The experiments were conducted using a polyaxial cell and a cuboid siltstone block with dimensions of 20 cm × 20 cm × 16.5 cm. The fracturing fluid was injected into a drilled hole in the specimen to initiate and propagate the hydraulic fracture in nearly homogeneous siltstone material. Low injection rates were applied to all lab tests to maintain slow and stable fracture propagation as in the field. The fracture surfaces were digitised by surface mapping techniques utilising high-resolution laser scanning method and analysed using a standard statistical way. Our results showed that the surface topography and roughness parameters are different in various selected segments. However, they follow an increasing trend in radial directions from the initiation point at the wellbore wall toward the specimen borders.

Rock typing and facies identification using fractal theory and conventional petrophysical logs

Rock typing or subdivision of a reservoir either vertically or laterally is an important task in reservoir characterisation and production prediction. Different depositional environments and diagenetic effects create rocks with different grain size distribution and grain sorting. Rock typing and zonation is usually made by analysing log data and core data (mercury injection capillary pressure and permeability measurement). In this paper, we introduce a new technique (approach) for rock typing using fractal theory in which resistivity logs are the only required data. Since resistivity logs are sensitive to rock texture, in this study, deep conventional resistivity logs are used from eight different wells. Fractal theory is applied to our log data to seek any meaningful relationship between the variability of resistivity logs and complexity of rock fabric. Fractal theory has been previously used in many stochastic processes which have common features on multiple scales. The fractal property of a system is usually characterised by a fractal dimension. Therefore, the fractal dimension of all the resistivity logs is obtained. The results of our case studies in the Cooper Basin of Australia show that the fractal dimension of resistivity logs increases from 1.14 to 1.29 for clean to shaly sand respectively, indicating that the fractal dimension increases with complexity of rock texture. The fractal dimension of resistivity logs is indicative of the complexity of pore fabric, and therefore can be used to define rock types.

Low permeability coal seam gas productivity enhancement by cyclic nitrogen injection technique (an adsorption simulation study)

Coal seam gas (CSG) usually contains high levels of methane, which is mostly in the adsorbed state on micropores. For coal that is not highly permeable, stimulation may be required to enhance productivity. In this study, we propose a new technique to increase near wellbore productivity in tight CSG. This technique comprises three stages: injection, soaking and production. Firstly, nitrogen is introduced to the target formation while maintaining high reservoir pressure. Next, the well is shut for a period of time before the gases are flown back to the surface. The technique is based on competitive adsorption of methane and nitrogen during the shut-in period, which yields pressure build-up. Hence, with this combination of desorption, the coal matrix shrinks and permeability eventually increases. The proposed technique was tested by adsorption simulation at core scale. The model was constructed for crushed samples and the extended Langmuir isotherm and micro–macro kinetics models were applied in ASPEN adsorption software. Tight coal was then simulated with different porosity and sorption characteristics. Finally, we used the stress-sensitive permeability model Palmer–Mansoori to predict permeability changes. The results show that permeability is improved based on pressure variations. We observed 10% pressure increments with greater than 150% permeability enhancement. The model indicates the feasibility of the newly proposed technique to produce the ‘unproducible’. However, more experimental and simulation studies at a reservoir scale are needed to fully confirm the technique.

Uncertainty Quantification Using a Multi-objectivised Randomised Maximum Likelihood Method

To propagate uncertainty in reservoir production forecasts, it is typically required to sample a nonlinear and multimodal posterior density function. To do so, different techniques have been proposed and used, such as Markovian algorithms, data assimilation methods and randomised maximum likelihood (RML) method. Through several studies, it has been shown that the RML method provides a reasonable approximation of the posterior distribution, despite the fact that it does not have any rigorous theoretical foundation for nonlinear problems. In order to reduce the computation and also provide an extensive search for multimodal density functions, in this study, the RML method is proposed in a context of a multi-objective genetic algorithm in which each of the equations is considered as a separate objective function. The proposed technique was compared against a Metropolis-Hastings algorithm and an RML with a Levenberg-Marquardt minimiser, using IC-Fault model. The comparison showed that an acceptable set of samples for uncertainty quantification is obtained, and given the fact that the parallelisation of the algorithm is straightforward, it makes the proposed algorithm, efficient in terms of the total processing time.

Uncertainty quantification using a self-supervised surrogate-assisted parallel Metropolis-Hastings algorithm

Parallel tempered algorithm is a Markov-chain Monte Carlo technique, applied to propagate uncertainty in the parameters of interest, using multiple Metropolis-Hastings algorithms. Despite the effectiveness, it is a computationally intensive method, since, at every step, a numerical reservoir simulation should be executed. To reduce the CPU-time of such a process, an online-learning surrogate-assisted algorithm is proposed in which two surrogates (one for high-temperature chains and one for low-temperature chains) are utilised together with the exact function (numerical simulation). After each swap step, both surrogates are re-trained, and their fidelity is estimated. According to the estimated fidelities, the frequency of use, for each surrogate, is defined with a heuristic fuzzy rule. The algorithm stochastically decides between the simulation and surrogates, based on the frequencies. This creates a self-supervised strategy, which can optimise the use of the numerical simulation, through the sampling process. The robustness of the proposed algorithm is analysed using IC-fault model. The outcomes are compared with the results achieved by a typical (unassisted) parallel tempered Metropolis-Hastings algorithm, over a range of chain lengths. The comparison indicates that the proposed algorithm can deliver a significantly better approximation of the probability density function, with the same amount of computation.

A Fast Simulator for Hydrocarbon Reservoirs During Gas Injection

A fast simulator is presented to forecast quickly the performance of oil reservoirs during gas (miscible and immiscible) injection based on transfer functions (TF). In this method, it is assumed a reservoir consists of a combination of TFs. The order and arrangement of TFs are chosen based on the physical conditions of the reservoir that are ascertained by examining several cases. The selected arrangement and orders can be extended. The only required data of this method is production and injection history that are easily accessible. Injection and production rates act as input and output signals to these TFs, respectively. By analyzing input and output signals, matching parameters are calculated for each case study. The outcomes of the method are compared with those obtained by a grid-based simulator. The comparison indicates a good agreement.