As an enhanced oil recovery method (EOR), chemical flooding has been implemented intensively for some years. Low Salinity WaterFlooding (LSWF) is a method that has become increasingly attractive. The prediction of reservoir behaviour can be made through numerical simulations and greatly helps with field management decisions. Simulations can be costly to run however and also incur numerical errors. Historically, analytical solutions were developed for the flow equations for waterflooding conditions, particularly for non-communicating strata. These have not yet been extended to chemical flooding which we do here, particularly for LSWF. Dispersion effects within layers also affect these solutions and we include these in this work.
Using fractional flow theory, we derive a mathematical solution to the flow equations for a set of layers to predict fluid flow and solute transport. Analytical solutions tell us the location of the lead (formation) waterfront in each layer. Previously, we developed a correction to this to include the effects of numerical and physical dispersion, based on one dimensional models. We used a similar correction to predict the location of the second waterfront in each layer which is induced by the chemical's effect on mobility. In this work we show that in multiple non-communicating layers, material balance can be used to deduce the inter-layer relationships of the various fronts that form. This is based on similar analysis developed for waterflooding although the calculations are more complex because of the development of multiple fronts.
The result is a predictive tool that we compare to numerical simulations and the precision is very good. Layers with contrasting petrophysical properties and wettability are considered. We also investigate the relationship between the fractional flow, effective salinity range, salinity dispersion and salinity retardation.
This work allows us to predict fluids and solute behaviour in reservoirs with non-communicating strata without running a simulator. The recovery factor and vertical sweeping efficiency are also very predictable. This helps us to upscale LSWF by deriving pseudo relative permeability based on our extension of fractional flow and solute transport into such 2D systems.
The objective of this work is to demonstrate that the choice of the conveyance method for Production Logging operations is key in horizontal wells, as it affects the flow dynamics and changes the well inflow performance compared to undisturbed flowing conditions. A case study is presented, showing that critical decisions to develop a field (or not) may have been wrongly influenced by Production Logging results, if the effects of the conveyance on the inflow distribution were not correctly understood.
Synthetic production logs and flowing pressure distributions along the horizontal section were computed, and sensitivities on conveyance method diameter (coiled tubing, tractor and cable), pipe diameter, well length and reservoir properties were also conducted. These results were compared with the normal well flowing conditions to establish the representativeness of the PL measurements. A method for simulating the undisturbed production profile is presented, which uses the results of a Multirate Production Logging and recomputed flowing pressures using nodal analysis.
The presence of the conveyance method alters the well's inflow performance and zonal contributions, due to the modifications of the flow geometry and additional frictional pressure drop. The bottomhole flowing pressure is disturbed, with lower pressures around the heel and higher towards the toe. The drawdown along the horizontal gets modified, acting as a preferential choke for production coming from the toe and increasing the driving force for production from the heel. The severity of the drawdown unbalance is a function of the induced frictional pressure, given by the pipe and conveyance diameter, well length, flow rates, etc. The simulations and sensitivities presented in this paper help to understand how significant the PL measurements are, and when these results become misleading. The case study supports these findings, where the pressure disturbance induced by the conveyance changed the flow distribution dramatically, wrongly indicating than an area of the field was relatively depleted compared to the zone around the heel. The lack of understanding of the impact of the conveyance method can lead to poor developmental decisions.
The paper provides analytical and semi-analytical solutions to predict the temperature transient behavior of a vertical well producing slightly compressible fluid under specified constant-bottom-hole pressure or rate in a two zone, radial composite no-flow reservoir system, where the inner zone could represent the skin zone, whereas the outer zone represents non-skin zone. The solutions are obtained by solving the decoupled isothermal diffusivity equation for pressure and thermal energy balance equation for temperature for the inner and outer zones by using the finite-difference and Laplace transformation. They be used to simulate temperature transient behavior for the general cases of specified variable bottom-hole or rate production represented by piecewise constants in specified time intervals. The convection, conduction, transient adiabatic expansion and Joule-Thomson heating effects are all considered in solving the temperature equation. Graphical analysis procedures for analyzing such temperature transient data jointly with pressure or rate transient data are also discussed. The results show that sandface temperature first decreases due to adiabatic expansion and then increases due to Joule-Thomson heating for both constant rate and constant bottomhole pressure production cases during infinite-acting flow. During boundary dominated flow, sandface temperature decreases linearly with time due to pore-volume expansion of the fluid over the entire no-flow reservoir system. The time rate of decline is governed by the ratio of the adiabatic-expansion coefficient of the fluid to the volumetric heat capacity of the saturated medium and the pore volume. However, these flow regimes are not well-defined for the constant bottomhole production case because the sandface rate decreases continuously during the infinite-acting radial flow and boundary dominated flow periods and distorts the flow regimes which are well defined on the temperature behavior if the well were produced at a constant rate. Sandface temperature data under specified variable rate or bottom-hole pressure show complicated behaviors and require more general automated history matching methods based on simultaneous use of both sandface temperature and rate transient data sets for parameter estimation.
Fluid storage capacity measurements of core-plugs in the laboratory considers pore-volume as a function of effective stress. The latter is equal to (Applied Confining Pressure) − (Effective Stress Coefficient) x (Applied Pore Pressure). However, results are often reported as a function of difference in the applied pressures, because the coefficient is unknown and depends on the sample. This creates confusion during the interpretation of laboratory data and leads to added uncertainties in the analysis of storage capacity.
In this paper we present a new laboratory method that allows simultaneous prediction of the sample pore volume, coefficient of isothermal pore compressibility, and the stress coefficient. These quantities are necessary to predict the fluid storage as a function of effective stress. The method requires two stages of gas (helium) uptake by the sample under confining pressure and pore pressure and measures pressure-volume data. Confining pressure is always kept larger than the equilibrium pore-pressure but their values at each stage are changed arbitrarily. The method considers gas leakage adjustments at high pore pressure. The analysis is simple and includes simultaneous solutions of two algebraic equations including the measured pressure-volume data.
The model is validated by taking the reference pore volume near zero stress. The reference volume predicted matches with that measured independently using the standard helium porosimeter. For sandstone and shale, the pore compressibility is on average 10-5 psi-1 and the effective stress coefficient is slightly higher than 1. The effective stress coefficient in isotropic elastic porous materials is known as the Biot coefficient and the value we predict indicates the relationship between the bulk and grain volume moduli.
Interestingly the effective stress coefficient predicted using shale samples rich in clays and organic matter is slightly higher than for sandstone. This indicates that other features of the sample such as fine-scale texture (laminations, and anisotropy, etc.) could come into play during the fluid storage measurements.
Rate and pressure transient analysis is considered a routine process that has been developed and refined over many years. The underlying assumptions of linearity justify the use of superposition (in time and space), convolution and deconvolution. The reality of non-linearities are handled on a case by case basis depending on their source (fluid, well or reservoir). Shale gas wells are subject to significant non-linearity over their producing life.
We review some of the fundamental equations that govern pressure and rate transient behavior, introduce several new techniques which are suited to the analysis of data from producing wells and apply them to a synthetic example of a shale gas well.
First, we use simple calculus to show how the convolution integral is derived from standard multi-rate superposition. Then, from the convolution integral, we derive an equation that describes the pressure response due to a step-ramp rate (i.e. an instantaneous rate change from initial conditions followed by a linear variation in rate). It results in a combination of the pressure change due to a constant rate and it's integral. Applying superposition to this equation allows any rate variation to be approximated by a sequence of ramps with far fewer points than those required to achieve the same level of accuracy using standard constant step rate superposition.
Second, we re-write multi-rate superposition functions allowing for stepwise linear variable rate which, when applied to flowing data and used to calculate the pressure derivative, can result in a much smoother response and hence an overall improvement in the analysis of rate and pressure transients recorded from producing wells.
Third, we review the use of the Laplace transform and how it can be applied to discrete data with a view to deconvolving rate transient data.
Finally, we demonstrate how data de-trending can remove the impact of long term non-linearities and apply the methods mentioned above to a synthetic dataset based on a typical shale gas well production profile.
We illustrate the advantages of the newly introduced superposition functions compared to conventional analysis methods when applied to the pressure transients of wells flowing at variable rate.
As an example, we have simulated the production of two shale gas wells over twenty years. Both have the same production profile, but one includes pressure dependent permeability. At various intervals during the life of the well, we introduce a relatively short well test which imposes a small variation in rate but does not include a shut-in. We de-trend the rate transients and then apply the techniques described above to analyse the resulting data. The interpretation allows us to identify non-linearities that may be influencing well productivity over time and to obtain a better understanding of the physics of shale gas production.
The mathematics documented in the paper provides a useful overview of how convolution, superposition, deconvolution and Laplace transforms provide the means to analyse pressure and rate transients for linear systems.
Data de-trending removes the impact of long term non-linearities on shorter transient test periods.
We develop and demonstrate some new and improved techniques for rate and pressure transient analysis, and we illustrate how these can provide insight into the non-linearities affecting shale gas production.
Zhang, Na (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University) | Abushaikha, Ahmad Sami (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University)
Modelling fluid flows in fractured reservoirs is crucial to many recent engineering and applied science research. Various numerical methods have been applied, including finite element methods, finite volume methods. These approaches have inherent limitations in accuracy and application. Considering these limitations, in this paper, we present a novel mimetic finite difference (MFD) framework to simulate two phase flow accurately in fracture reservoirs.
A novel MFD method is proposed for simulating multiphase flow through fractured reservoirs by taking advantage of unstructured mesh. Our approach combines MFD and finite volume (FV) methods. Darcy's equation is discreted by MFD method, while the FV method is used to approximate the saturation equation. The resulting system of equations is then imposed with suitable physical coupling conditions along the matrix/ fracture interfaces. This coupling conditions at the interfaces between matrix and fracture flow involve only the centroid pressure of fractures, which brings some simplification in analysis. The proposed approach is applicable for three dimensional systems. Moreover, it is applicable in arbitrary unstructured gridcells with full-tensor permeabilities. Some examples are implemented to show the performance of MFD method. The results showed a big potential of our method to simulate the flow problems with high accuracy and application.
Methane hydrate is formed in a sand pack that undergoes cooling-heating cycles over a range of temperature. Five cycles are designed so that hysteresis can be observed in the sand pack. Each cycle has a different melting temperature which leads to varying intensity of temperature relaxation effect on the hysteresis. Evidence of hysteresis is observed in three separate temperature readings of thermocouples. Formation of hydrates is dependent on the thermal cooling rate of the sand pack, and the melting temperature of the previous cycle. A temperature increase is observed in the whole system, and this increase is driven by temperature peaks indicating significant hydrate formation near the thermocouples. These peaks have important effects on the whole system. By comparing each cycle's temperature peaks, hysteresis is clearly observed at the temperature readings of the short thermocouple. The same hysteresis pattern follows for the location of the temperature peaks. When significant hydrate formation occurs in the sand pack, a steepening of the pressure decline is observed, indicating a rapid loss of free gas in the system. The pattern that is observed in the temperature peaks is also identified in the pressure profiles, thus linking the gas saturation to hydrate formation. The time derivative of pressure corroborates these findings. A new model is proposed for the prediction of secondary hydrate formation time as a function of the melting temperature the porous medium experienced.
In the petroleum industry, well testing is a common practice that consists of wellbore pressure, temperature and flow rates data acquisition to estimate parameters that govern the flow in porous media. Injection-falloff testing is particularly important for offshore reservoirs, especially for the oil reserves that contain high carbon dioxide and sulfur content. In this environment, a conventional well test in an exploratory well should not be run in order to avoid discarding high concentrations of these gases to the atmosphere. Therefore, there is a need for developing techniques for analyzing pressure data from injection-falloff tests. In this work, we have developed an approximate semi-analytical solution for wellbore pressure response during gas injection and falloff well tests in reservoirs containing oil and gas with complex composition by applying the Thompson and Reynolds steady-state theory. For the injection period, we first determine the overall concentrations distributions from a system of hyperbolic conservation equations using the method of characteristics (MOC), assuming a one-dimensional homogeneous reservoir with incompressible fluids and constant molar density, and neglecting capillary, gravity effects, volume changing on mixing and diffusion. During the falloff stage, it is assumed that there is no phase nor concentration movement in the reservoir, which is reasonable as we neglect capillary pressure, diffusion, gravity force and fluid compressibilities. Once we have the concentration profiles in the reservoir, we can calculate the total mobility distributions and then integrate the pressure gradient given by Darcy's law to find the wellbore pressure response. The semi-analytical approximate solution obtained was validated against the commercial numerical simulator STARS from CMG. After validation, the developed model was used as a forward model to estimate absolute permeability and skin factor by history matching noisy data obtained from the numerical simulator mentioned.
Zeng, Jie (The University of Western Australia) | Li, Wai (The University of Western Australia) | Liu, Jishan (The University of Western Australia) | Leong, Yee-Kwong (The University of Western Australia) | Elsworth, Derek (The Pennsylvania State University) | Tian, Jianwei (The University of Western Australia) | Guo, Jianchun (Southwest Petroleum University)
After performing hydraulic fracturing treatments in shale reservoirs, the hydraulic fractures and their adjacent reservoir rocks can be damaged. Typically, the following fracture damage scenarios may occur: (1) choked fractures with near-wellbore damage; (2) partially propped fractures with unpropped or poorly propped sections within the fractures; (3) fracture face damage; and (4) multiple damage cases. The basic equations of fracture skin factors, which are widely used to depict fracture damage, are derived under steady-state conditions. They are not accurate when the damaged length is relatively long and are not applicable for multiple fracture damage and partially propped fractures. In this paper, a new composite linear flow model is established considering all above-mentioned fracture damage mechanisms, complex gas transport mechanisms, and the stimulated reservoir volume (SRV) of shale gas reservoirs.
The matrix model is modified from de Swaan-O's spherical element model considering the slip flow, Knudsen diffusion, surface diffusion, and desorption. Natural fractures are idealized as a thin layer that evenly covers the matrix. The reservoir-fracture flow model is extended from the seven-region linear flow model with four additional sub-regions to handle single and multiple fracture damage mechanisms. Specifically, the inner reservoir region near the primary hydraulic fracture is treated as the SRV where the secondary fracture permeability is higher than that of other unstimulated dual-porosity regions and obeys a power-law decreasing trend due to the attenuate stimulation intensity within the SRV. The flows in different regions are coupled through flux and pressure continuity conditions at their interfaces.
This model is validated by matching with the Marcellus Shale production data. And the degraded model's calculation matches well with that of the seven-region linear flow model validated by KAPPA software. Type curves with five typical flow regimes are generated and sensitivity analyses are conducted. Results indicate that the presence of the SRV diminishes pressure and derivative values in certain flow regimes depending on the SRV properties. Fracture face damage, choked fracture damage, and partially propped fractures all control specific flow regimes but the fracture face damage shows the smallest influence, only dominating the late fracture linear flow regime and the matrix-fracture transient regime. In the multiple fracture damage case, some typical flow regimes can be easily identified except the partially propped fractures. The field application example further ensures the applicability in dealing with real field data.
Rate transient analysis using log-log plots of rate-normalized pressure (RNP) and its derivative (RNP') versus material balance time have proven helpful in providing estimates of shale matrix permeability and SRV drainage volumes in multiple transverse fracture wells (MTFW's) (
We have constructed an analytical model of MTFW's that accurately predicts individual fracture flow performance for both constant and variable rate and constant bottom hole pressure inner boundary conditions. Using this model, we can accurately compute the pressure disturbance and rate change seen at the whole well and for individual fractures to quantify the degree of interference between fractures for any number of parallel, equally-spaced, and equally-sized fractures. This model has been validated by simulation using a commercial simulator. With both this analytical model and a series of numerical simulations, we investigated the fundamental mechanisms of flow in MTFW's and how the estimation of telf may be improved.
Previous authors have represented the progression of flow regimes in MTFW's as a linear flow period that transitions to a pseudo steady state (or apparently boundary-dominated) flow regime. We show that the same flow response is exhibited by a fully-infinite linear system, calling into question the nature of the "stimulated reservoir volume" (SRV) as a bounded reservoir system. In addition, we show telf can be detected and interpreted as the beginning of the onset of this fracture interference using the "limit of detectability" concept.