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.
Fractures can be first-order controls on fluid flow in hydrocarbon reservoirs. Understanding the characteristics of fractures such as their aperture, density, distribution, conductivity, connectivity, etc, is key for reservoir engineering and production analysis.
Well testing plays a key role in the the characterisation of fractured reservoirs, especially. New advances in the Pressure Transient Analysis (PTA) have enabled the interpretation of production data in a way where the resulting geological scenarios are in better agreement with fracture patterns observed in outcrop analogues.
Traditionally, Drill Stem Test (DST) data have been the primay source of information for well testing. However, we hypothesise that wireline conveyed tools designed for Interval Pressure Transient Testing (IPTT) could yield a more throrough description of the near-wellbore heterogeneities, including fractures.
Hence, we investigate the applicability of IPTT for characterising fractured reservoirs using detailed numerical simulations models with accurate wellbore representation to generate synthetic IPTT responses that can obtained through a next-generation wireline testing tool called SATURN. We particularly focus on cases where fractures are present in the near-wellbore region but do not intersect the wellbore. The study included parameters such as fracture densities and conductivities, distance between fractures and wellbore and the vertical extension of the fractures across geological beds.
The impact of the different fracture scenarios on the pressure transient tests was recorded as characteristic signatures on diagnostic plots (pressure derivative curves). We have called these curves "IPTT-Geotypes"; they can be used to assist the interpretation process of IPTT responses. To the best of our knowledge, this is the first time pressure derivative type curves for IPTT in fractured reservoirs are presented in the literature.
A field example of an IPTT case was analysed using the concept of geological well testing. We integrated the information from petrophysical logs and the IPTT-Geotypes to assist the calibration of a reservoir model developed to represent the geological setting of the tested reservoir interval. The results provided a sound interpretation of the reservoir geology and quantitative estimation of the matrix and fracture parameters.
Tamar is a high permeability clastic gas reservoir that behaves like a well-connected tank, in many respects. At the same time, it has a significant level of complexity. The reservoir is comprised of three sand intervals, which are separated vertically by shales and broken into a number of fault blocks. While the degree of aquifer support has been an uncertainty, it is believed that the field demonstrates components of both bottom water and edge water drive. All Tamar wells were equipped with permanent downhole pressure and temperature gauges, and the surveillance of these pressure and rate data over the five-year production history has provided an unusually comprehensive data set.
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.
This paper applies a new constrained multiwell deconvolution algorithm to two field cases: a gas reservoir with two producers, and an oil reservoir with three producers and one injector. Responses given by the constrained multiwell deconvolution are compared with simulations from history-matched reservoir models.
Permanent downhole pressure gauges are routinely installed in most new wells. The resulting large datasets are usually underexploited, however, because it is near impossible to extract information with conventional techniques in the case of well interferences. Multiwell deconvolution (
The published multiwell deconvolution algorithms are extensions of the single-well deconvolution algorithm from von Schroeter
By extracting well and interwell reservoir signatures, multiwell deconvolution allow identification of compartmentalization or unanticipated heterogeneities very early in field life, making it possible to adjust the field development plan and the locations of future wells. In addition, it can accelerate the history-matching process by doing it on constant rate pressure responses rather than on complex production histories. An added advantage is that the comparison between the model derivatives and the actual deconvolved derivatives enables identification of mismatch causes.
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.
Scapolo, Matteo (KIDOVA France & Imperial College London) | Garcia, Michel H. (KIDOVA France) | Mathieu, Jean-Baptiste (KIDOVA France) | Siffert, Deborah (KIDOVA France) | Gosselin, Olivier R. (Imperial College London) | Ackerer, Philippe (LHyGeS)
Using geostatistical modelling to populate reservoir properties is nowadays the most common approach in the industry and it has received a great deal of attention. A geostatistical reservoir model defines a space of spatial uncertainty, which can be explored by generating many equiprobable reservoir property realisations that are as many possible reservoir models complying with static data. Among them, the relevant models are those that also match the dynamic data, which complete the available data for reservoir model calibration. Finding the relevant reservoir models in the space of spatial uncertainty is a time-consuming process that requires simulating the dynamic (flow) response of many reservoir models. Having a fast and reliable simulation method is then highly desirable to speed up the process of reservoir model calibration. In this context, a new approach has been developed and tested. The method allows easy and fast comparison between interpreted well-test results and equivalent (average) reservoir model properties in terms of transmissivity (k.h) and permeability. The comparison can be used to validate or reject a reservoir model, and to obtain indications on how to modify it to fit the well-test data. This paper presents the method and the results obtained to evaluate its performances and to validate it.
Well-test-interpreted permeabilities (or transmissivities) are nothing but weighted average permeabilities that are to be calculated from permeabilities defined over closed surfaces properly defined around the well, the weights depending on the flow geometry. The proposed method is based on steady-state flow simulation that is carried out by making the tested well a source term (producing or injecting well) at the centre of a simulation domain (reservoir model region). The latter must be extended enough to contain, or at least overlap, the stabilisation area of the well test in which average transmissivities are to be estimated. The method relies on three key aspects: defining a simulation domain (extension and shape) that is consistent with the actual well-test drainage area, defining relevant boundary conditions to reproduce flow paths that are consistent with those generated by the actual well test, using the new effective-gradient based averaging method to compute average permeabilities over closed surfaces properly defined.
The method is tested on various synthetic and partly real field cases, for which the transient well-test responses are first simulated and interpreted, then compared with the transmissivities, predicted using the new method. Sensitivity analysis is also carried out on calculation parameters (flow simulation domain, flow rates…) to check the robustness of the method and identify improvement avenues. All these results tend to confirm the effectiveness of the method, which can combine speed and accuracy. This method is intended to be used as an objective function to perform automatic or assisted reservoir model calibration on interpreted well-test data. It is expected to be particularly useful to calibrate naturally fractured reservoir models for which permeability tensors are to be calculated from uncertain locally defined fracture property statistics.
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.
Aslanyan, Artur (Nafta College) | Grishko, Fedor (Salym Petroleum Development N.V.) | Krichevsky, Vladimir (Sofoil) | Gulyaev, Danila (Sofoil) | Panarina, Ekaterina (Sofoil) | Buyanov, Anton (Polykod)
A waterflood study has been performed on a heterogeneous oil deposit with a rising water-cut and production decline after 10 years of commercial production.
Engineers need to predict the production characteristics from hydraulically fractured wells in tight gas fields. Decline curve analysis (DCA) has been widely used over many years in conventional oil and gas fields. It is often applied to tight gas, but there is uncertainty regarding the period of production data needed for accurate prediction.
In this paper decline curve analysis of simulated production data from models of hydraulically fractured wells is used to to develop improved methods for calibrating decline curve parameters from production data. The well models were constructed using data from the Khazzan field in Oman. The impact of layering, permeability and drainage area on well performance is also investigated. The contribution of each layer to recovery and the mechanisms controlling that contribution is explored.
The investigation shows that increasing the amount of production data used to fit a hyperbolic decline curve does not improve predictions of recovery unless that data comes from many years (20 years for a 1mD reservoir) of production. This is because there is a long period of transient flow in tight gas reservoirs that biases the fitting and results in incorrect predictions of late time performance. Better predictions can be made by estimating the time at which boundary dominated flow is first observed (tb), omitting the preceding transient data and fitting the decline curve to a shorter interval of data starting at tb. For single layer cases, tb can be estimated analytically using the permeability, porosity, compressibility and length scale of the drainage volume associated with the well. Alternatively, tb can be determined from the production data allowing improved prediction of performance from 2-layer reservoirs provided that a) there is high cross-flow or b) there is no cross-flow and the lower permeability layer either does not experience BDF during the field life time or it is established quickly.