Constant Rate Conditions Research Articles

Pressure Analysis of Onshore and Offshore Shale Gas Reservoirs under Constant-Rate Condition Considering Thin Sandstone Layer and Interlayer Cross-Flow

The extraction of shale gas from onshore and offshore shale gas reservoirs will play an important role in meeting China’s future energy needs, which will not only help alleviate the energy crisis but also contribute to climate change mitigation. As for the target shale formation enriched by thin sandstone layers in typical basins, an analytical calculation method is proposed to perform pressure analysis for multi-layer shale gas reservoirs considering the adsorption–desorption characteristics of shale layer and the interlayer cross-flow. Firstly, the changes in storage capacity and flow resistance are obtained by using the distance of investigation equation. According to the electrical analogy, the equivalent total storage capacity and flow resistance can be calculated considering the sandstone-shale crossflow. Because production from one time step to the other causes depletion of the storage capacity, the reservoir pressure in different time steps can be calculated based on the material balance equation. Numerical models have been constructed based on three typical reservoir lithology combinations (sandstone-shale, shale-sandstone-shale and sandstone-shale-sandstone) to validate the accuracy of the proposed analytical calculation method. Furthermore, three important factors (porosity, the ratio of horizontal/vertical permeability (kh/kv) and the layer thickness) have been selected for the sensitivity analysis to verify the stability. The comparative results indicate that the proposed analytical calculation method is suitable for pressure analysis in shale gas reservoirs containing thin sandstone layers. It will provide theoretical support for the further enhancement of the production of this type of gas reservoirs.

Autogenic evolution of valley‐confined deltas during sea‐level rise: Insights from numerical and physical modelling

AbstractNearshore incised valleys are important conduits for the transport of sediment, nutrients, pollutants and organic carbon from the continents to the sea. Therefore, it is essential to understand the autogenic evolution of deltas confined within incised valleys and how such evolution is affected by relative sea‐level rise. To date, limited research has focused on how deltas constrained by incised valleys or other forms of antecedent topography respond to rising sea level. An existing theory of autostratigraphy envisages scenarios in which two‐dimensional or unconfined three‐dimensional fan deltas can experience three evolutionary stages under constant rates of relative sea‐level rise and sediment supply: progradation, autoretreat and post‐autobreak transgression. In this work, an integrated study of geometric numerical models and physical experiments is undertaken to investigate autostratigraphic delta evolution for a variety of incised‐valley geometries, under conditions of constant rates of relative sea‐level rise and sediment supply. Results indicate that interplays of antecedent topography (valley geometries) and sediment mass balance expressed in resultant deltaic geometries can result in autogenic changes in shoreline dynamics and river avulsion frequency on deltas. The following primary findings arise. (i) Compared to valleys with rectangular and trapezoidal cross‐sectional profiles, valleys with triangular cross‐sections tend to contain deltas that experience faster rates of progradation, autoretreat and post‐autobreak transgression under rising sea level, and exhibit a more prominent convex‐seaward shoreline trajectory. (ii) The shoreline trajectory is also related to delta topset geometry, becoming more convex‐seaward under decreasing topset slopes. (iii) River avulsion frequency on deltas with rising sea level varies markedly across valleys with different geometries, even under the same rate of relative sea‐level rise; this is attributed to the difference in temporal evolution of shoreline migration for different valley geometries and the resultant difference in the delta topset aggradation. This study highlights complexities in responses of sedimentary systems under the confinement of different topographic configurations that have hitherto largely been overlooked in sequence‐stratigraphic models. The findings provide insight into future shoreline behaviour and river avulsion hazard on confined deltas, and for decoding the stratigraphic record.

Develop an empirical flow rate correlation to model wellbore storage phenomenon for wells produced at a constant wellhead pressure

Well-test operation with a constant flow rate for long-time production is not typical in practice. Therefore, reservoirs frequently produce fluids with constant pressure at the wellhead, into a constant pressure separator or pipeline. During the production under this condition, the pressure drop at the wellbore varies as a function of the rate because of changes in the friction flow; therefore, the wellbore formation pressure is not constant. As a consequence, the wellbore storage effect emerges and should be incorporated in the modeling of fluid flow under production at a constant wellhead pressure. All available methods considering the wellbore storage effect can merely be applied for production under the constant rate condition. Moreover, well-test modeling under these circumstances needs a specific function for production rate, which made this type of well-testing less common. Even though there are exact solutions for production under the constant wellbore pressure in the Laplace domain, their inverse transform is quite complex and cannot be applied for modeling the wellbore storage effect. In this study, a new function is introduced as an approximate solution of the diffusivity equation, for a well that produces at a constant wellbore pressure, using multiple steps of the optimization process. Consequently, an efficient correlation is developed for flow rate about or concerning this condition. Next, the effect of the wellbore storage at constant pressure well-test operation was enumerated for the first time, which was commonly neglected in previous studies. This endeavor concentrated on modeling the two types of well-test operation, producing at constant wellhead pressure and, pressure build-up following the production at a constant wellhead pressure (constant pressure Build-up test). The results were also verified with numerical simulation as well as field data further confirming the excellent accuracy of developed solutions.

Predictive model of constant rate expression for dewatering of semi-solid materials

Nonlinear predictive model of constant rate expression is developed for dewatering semi-solid materials and industrial filter cakes. Nonlinear consolidation equation is expressed on the base of a power-law θ-function linearising Darcy law. Analytical solutions of consolidation equation are obtained under the constant rate condition. Presented model permits obtain the local solid and liquid pressure profiles during constant rate solid–liquid expression, as well as the internal distributions of liquid flow rate, local specific cake resistance and void ratio. Proposed analytical model and numerical simulations were used in worked examples for the highly compressible filter cakes of silica and activated sludge, as well as for the moderately compressible filter cake of CaCO3. It is shown that the value of applied expression rate is determinant for the process efficiency. Expression rate should be very low in case of highly compressible filter cakes of silica and activated sludge to avoid very rapid pressure rise and excessively high expression pressure. Obtained results permit verify and confirm Shirato’s hypothesis that internal structure of filter cake compressed under the instantaneous pressure in a constant rate operation is practically the same as that compressed under such a pressure in a constant-pressure operation.

A semi-analytical solution under a variable inner boundary condition for fractured horizontal wells in a rectangular closed reservoir with discrete fracture networks

The paper focuses on establishing a semi-analytical model under a variable inner boundary condition for fractured horizontal wells in a rectangular closed reservoir with discrete fracture networks. In this paper, the inner boundary is a piecewise boundary condition, which varies from Newman boundary condition to Dirichlet boundary condition. Rectangular reservoir model and complex fracture model are established respectively, and hydraulic fractures and natural fractures can cross or not. The governing equation is solved under the first-stage inner boundary condition by using the Laplace transform and Fourier transform methods, and the coupling solution is derived by the condition that the pressure and flux at the discrete fracture networks wall are equal. The control equation under the second-stage inner boundary condition is a completely non-homogeneous equation group, which is solved by variable replacement method. The final pressure and flow solutions under the variable inner boundary conditions are obtained in real space through the Stehfest numerical inversion method. This semi-analytical solution is verified accurately for simple fracture case under constant rate condition and variable inner boundary conditions through numerical simulation. The results show rate decline rate of complex fractures is also very fast, and that of simple fractures is relatively slow through the comparison between complex fracture networks and simple fractures under variable inner boundary conditions. The influence of some important parameters on flow rate and pressure change is analyzed in detail under variable inner boundary conditions, mainly including initial rate, limited pressure, fracture networks permeability and initial reservoir pressure.

Pressure Transient Analysis and Transient Inflow Performance Relationship of Multiple-Fractured Horizontal Wells in Naturally Fractured Reservoirs by a Trilinear Flow Model.

Trilinear flow model is an effective method to reproduce the flow behavior for horizontal wells with multistage hydraulic fracture treatments in unconventional reservoirs. However, models developed so far for transient analysis have rarely considered the inflow performance of wells. This paper introduces a new composite dual-porosity trilinear flow model for the multiple-fractured horizontal well in the naturally fractured reservoirs. The analytical solution is derived under a constant rate condition for analyzing transient pressure behaviors and generating the transient inflow performance relationships (IPRs). The plots of pressure profiles with time could provide insightful information about various flow regimes that develop throughout the entire production cycle. Sensitivity analysis of pressure and pressure derivative response was also performed by varying different parameters (such as hydraulic fracture width and permeability, reservoir configurations, etc.) and by which the impacts of different parameters on the durations of regimes as well as the productivity index can be confirmed. The main outcomes obtained from this study are as follows: (1) the ability to characterize naturally fractured reservoirs using a new composite dual-porosity trilinear flow model; (2) the application of analytical solutions of transient analysis to generate transient IPR curves for different flow regimes; (3) understanding the effect of reservoir configurations, fractures, and matrix characteristics on pressure distribution, flow regime duration, and transient IPR. More specifically, the pressure drop increases and the productivity index decreases with the decrease of the hydraulic fracture conductivity and the increase of matrix permeability and the skin factor. Also, the larger hydraulic fracture spacing and drainage area result in the later onset of the pseudo-steady-state regime. (4) A comprehensive study on transient pressure behaviors and transient inflow performance can provide valuable information to characterize the multifractured complex systems as well as some insights into the production.

A Study of Cake Filtration Parameters Using the Constant Rate Process

The minerals calcium carbonate and talc were filtered under various conditions of filtrate flow rate and suspension concentration, using constant rate conditions with the aid of a peristaltic pump to draw the filtrate. Cake concentrations of between 0.41 and 0.53 v/v for calcium carbonate and 0.19 and 0.26 v/v for talc were recorded. The mean sizes of the two different minerals were very similar, but the average specific resistances obtained from the experiments were 5.9 × 1010 and 7.4 × 1011 m/kg for calcium carbonate and talc, respectively. These results do not agree with what would be predicted from an analytical equation for permeability, such as Kozeny-Carman. In addition, discontinuities were observed in all cases on the curves of filtrate volume with time for the initial stage of filtration. This behaviour is attributed to retarded packing compressibility (RPC) complicating the analysis of the filter medium resistance. RPC is an important component in determining the filter cake resistance and its functionality with cake forming pressure. It is found that there are additional effects that enhance the resistance to permeation in different cake materials, which is not recognised in the standard analytical approaches. These complexities can be related to shape, polydispersity, or agglomeration within the material sample and not to the experimental equipment or procedure. Furthermore, a complete and straightforward methodology is presented in this work for investigating the significance, or otherwise, of medium resistance on the later stages of the filtration.

Pressure transient analysis for multi-wing fractured wells in dual-permeability hydrocarbon reservoirs

Multi-wing and asymmetrical hydraulic fractures around wellbore are usually observed in hydraulic fracturing and refracturing treatments. Therefore, it is significant for us to study pressure transient analysis. In this paper, by employing Laplace transform and finite cosine Fourier transform, a new semi-analytical model was deviated and solved under condition of constant rate for multi-wing fractured wells (MWFWs) of finite conductivity in hydrocarbon reservoirs with dual-permeability behavior in Laplace domain. Stehfest inversion algorithm can be adopted to obtain wellbore pressure of MWFWs in real domain. The solution of the simplified model in this paper was validated with dual porosity dual-permeability and asymmetrical hydraulic fracture, and results reach a good agreement. Type curve, according to pressure derivative characteristic, can be divided into six regimes (bilinear flow, linear flow, radial flow of natural fractures, cross flow and radial flow of system). The influence of some vital parameters (dimensionless conductivity, storage coefficient, crossflow coefficient, permeability ratio et al.) on dimensionless pressure and its derivative curves were analyzed in details. The presented model can be used to understand pressure transient characteristic of MWFWs in hydrocarbon reservoirs with dual-permeability behavior.

On the determination of thermal degradation effects and detection techniques for thermoplastic composites obtained by automatic lamination

Automatic lay-up and in-situ consolidation with thermoplastic composite materials is a technology under research for its expected use in the profitable manufacturing of structural aeronautical parts. This study is devoted to analysing the possible effects of thermal degradation produced by this manufacturing technique.Rheological measurements showed that there is negligible degradation in PEEK for the temperatures reached during the process. Thermogravimetric analysis under linear heating and constant rate conditions show that thermal degradation is a complex process with a number of overlapping steps. A general kinetic equation that describes the degradation of the material with temperature has been proposed and validated. Attenuated total reflectance Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy confirmed that there is no remarkable degradation. The use of a combination of in-situ and ex-situ experimental techniques, including kinetic modelling, not only provides reliable information about degradation but also allows setting optimal processing conditions.

A Laplace-Domain Hybrid Model for Representing Flow Behavior of Multifractured Horizontal Wells Communicating Through Secondary Fractures in Unconventional Reservoirs

Summary In a multiwell pad, the chance of interwell communication increases because of the creation of primary and secondary fractures during hydraulic-fracture stimulation. The flow behavior associated with communicating wells is significantly different from that of a single isolated well, because of interplay of flow caused by the interconnected fractures, complex connections, and multiple production conditions. The main purpose of this paper is to develop a rigorous and efficient flow model and quantify flow characteristics of multiple pad wells communicating through primary and secondary fractures. In the model, matrix and primary- and secondary-fracture flows are captured. Fractures are explicitly represented by discrete segments. The Laplace-transform finite-difference (LTFD) method is used to numerically model fracture flow, with sufficient flexibility to consider arbitrary fracture geometries and fracture-conductivity distributions. The analytical matrix-flow model, derived with the line-source function in the Laplace domain, is dynamically coupled with the fracture-flow model, by imposing the continuity of pressure and flux on the fracture surface. Thus, a hybrid model in the Laplace domain is constructed. The main advantage of the solution occurring in Laplace domain is that computations can be performed at predetermined, discrete times, and with grids only for fractures. Thus, stability and convergence problems caused by time discretization are avoided, and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated through comparison with a fully numerical simulator and a semi-analytical model. Detailed flow-regime analysis reveals that pressure interference caused by communication significantly alters the flow signature compared with single (isolated) wells. Before interference, the communicating wells behave as single isolated wells, and will exhibit a fracture linear-flow period and possibly even a matrix linear-flow period. After interference, the flow behavior of the system will vary largely with different production strategies. When the communicating wells all operate under the constant-rate condition, the transient responses of the wells will gradually merge to develop another matrix linear-flow period. If the wells are operated under the constant-bottomhole-pressure (BHP) conditions, the response deviation caused by interference will increase with production; therefore, one of the wells will undergo a rate loss. The results of a sensitivity analysis for a two-well system demonstrate that the time to well interference is primarily determined by secondary-fracture conductivity, number of connections, and communicating-well operating conditions. With larger contrasts in these properties, interference time is accelerated. However, for different production strategies, the effects on the flow behavior after interference are variable.

A new approach in pressure transient analysis part I: improved diagnosis of flow regimes in oil and gas wells

This paper introduces the statistical method for diagnosing flow regimes for flowing and shut-in conditions. The method utilise the second differencing of pressure change and time that are stationary; then integrate the residual pressure differences using simple statistical tools such as sum of square error SSE, moving average MA and covariance of data to formulate the statistical derivative models. These models are tested with constant pressure, constant rate conditions and in well with high water production. Results from three scenarios investigated demonstrated that the statistical derivatives yielded much clearer reservoir radial flow regimes as the conventional pressure derivatives without data smoothing; therefore give more confident formation permeability estimation. It demonstrated that for high water production well, a good radial stabilisation can be identified. It also showed that in all three scenarios, the drawdown radial fingerprint can be replicated in the build-up pressure responses, hence a good match of the data.

Analytical Model of Waterflood Sweep Efficiency in Vertical Heterogeneous Reservoirs under Constant Pressure

An analytical model has been developed for quantitative evaluation of vertical sweep efficiency based on heterogeneous multilayer reservoirs. By applying the Buckley-Leverett displacement mechanism, a theoretical relationship is deduced to describe dynamic changes of the front of water injection, water saturation of producing well, and swept volume during waterflooding under the condition of constant pressure, which substitutes for the condition of constant rate in the traditional way. Then, this method of calculating sweep efficiency is applied from single layer to multilayers, which can be used to accurately calculate the sweep efficiency of heterogeneous reservoirs and evaluate the degree of waterflooding in multilayer reservoirs. In the case study, the water frontal position, water cut, volumetric sweep efficiency, and oil recovery are compared between commingled injection and zonal injection by applying the derived equations. The results are verified by numerical simulators, respectively. It is shown that zonal injection works better than commingled injection in respect of sweep efficiency and oil recovery and has a longer period of water free production.

Exact analytical solutions for moving boundary problems of one-dimensional flow in semi-infinite porous media with consideration of threshold pressure gradient

By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green's function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal's approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal's approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What's more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.

A New Approach in Pressure Transient Analysis Part I: Improved Diagnosis of Flow Regimes in Oil and Gas Wells

One important limitation of pressure derivatives is diagnosing flow regimes in wells with high water cut and flowing conditions (Drawdown) because the well production are never stable due to surface operating constraint including multiphase metering problem and fluid compressibility, hence most drawdown are not easily interpretable due to noisy data. In some cases where the data are useful, the derivative data are always noisy and difficult to interpret, resulting in the application of deconvolution and various smoothing techniques to obtain a perceived representative model which often time might not. This paper introduces a new statistical method for diagnosing flow regime for both flowing and shut-in conditions. The method utilize the second differencing of pressure and time parameters since pressure change and subsurface flow rate is non-stationary and then integrate the residual pressure differences using simple statistical tools such as sum of square error SSE, moving average MA and covariance of data to formulate the statistical derivative model. The model is tested with constant pressure, constant rate conditions and also in well with high water production Results from three scenarios investigated shows the statistical derivative display distinctive radial flow fingerprint as the conventional pressure derivative with clear reservoir features revealed with high degree of accuracy. It demonstrated that for high water production well, a good radial stabilization can be identified for good permeability estimation without smoothing the data. It also showed that in all three scenarios, the drawdown radial fingerprint can be replicated in the build-up pressure responses, hence a good match of the data. The approach also reduces the derivative noise in the radial flowing period for better interpretation of flow regimes.

Distinctive Flow Regions in Crossform Fracture Model in Shale Gas Reservoir Using Numerical Density Derivative Part 3

The numerical density derivative approach is used to measure fluid densities around the wellbore and to generate pressure equivalent for each phase using simplified pressure-density correlation. While statistical derivative method determines fluid phase permeabilities and also average effective permeability for a given reservoir system with new empirical model. Both methods were only tested in conventional oil and gas reservoir system. This study introduces a new mathematical model for interpreting pressures behavior of a vertical well with cross form fracture in shale gas reservoir using numerical density approach. In this case, the imposed fractures can be longitudinal and transverse but symmetrical to a reference point (the wellbore). The major advantage is that it simplified the complex fracture-matrix flow equation by applying ordinary laplace transform model OLTM to formulate linear, bilinear and trilinear flow model. The model is tested for constant pressure and constant rate conditions with the generated average fluid phase pressure-densities equivalent displaying the distinctive fractures flow fingerprint. It also indicates that the dimensionless rate or pressure derivative response and distinctive flow regions are influenced by mostly fracture’s conductivities, dimensions and reservoir’s boundaries. A new flow region have been added with the first as the linear flow region which is the flow along the vertical plane parallel into the wellbore and the second as the Bilinear or Trilinear flow region which is the flow along the vertical plane parallel to the wellbore, then into the fracture after the pressure pulse reaches the upper and lower impermeable boundaries depending on the ratio of primary and secondary cross form fracture lengths and conductivities. In this paper, it has been demonstrated that for constant rate solution, the smaller the fracture aperture, the reduction in the number of flow regions to be seen.

English

Pumping test was used for the appraisal and evaluation of groundwater potential and design of well. Pumping tests of the calcarious sedimentary rocks of Bhaskar Rao kunta watershed area were carried out for twenty five selected bore wells for quantitative understanding of the groundwater for crop water requirement and groundwater use efficiency. The tests were carried out independently for short duration under constant rate conditions. The acquisition of the drawdown data was interpreted by Jacob straight line method. The results of transmissivity vary from 2.67 to 236.9 m2/day with mean of 37 m2/day, whereas the specific capacity varies from 5.47 to 451.63 m3/d/m with a mean of 76 m3/d/m. Spatial variation of transmissivity values was further analyzed using statistical testing and Krasny’s classification systems; from the results of the statistical testing, 72% of the wells were under covered background transmissivity anomalies; 12% under positive anomalies; 8%, negative anomalies and remaining 8%, positive extreme anomalies. From the results of Krasny’s classification system, 12% of the wells was under  high magnitude (withdrawals of lesser regional importance), 40% of wells was under intermediate magnitude (withdrawals for local water supply), 48% was under low magnitude (smaller withdrawals for local water supply) and 100% of the wells was under covered moderate variations (fairly heterogeneous hydrogeological environment). Spatial variation of transmissivity magnitude and variation was identified as best useful in management practices. Key words:  Transmissivity, magnitude, variation, statistical testing, Krasny’s classification.

Productivity Analysis of Transverse Horizontal Well Commingling in Stripped Gas Reservoir with Bottom Water

Banded gas reservoir with bottom water is a typical gas reservoir. Based on the development characteristics of formation, the further study on commingling production by transverse horizontal well is done, and also combined with seepage theory including the Green function, Duhamel method etc. the dimensionless definitions of relative parameter are given. Whats more, the derivation and formula of production can be achieved respectively under the constant pressure condition and constant production condition. Meanwhile, take commingling production with three banded gas layers for example. Whether the initial pseudo pressure for these layers are equal or not, in both of these cases, the variation curve of gas productivity under the constant pressure and constant rate conditions is described separately. And the law of variation of gas flow backward for some layer when the physical properties of these layers are significantly different.

Enhanced general analytical equation for the kinetics of the thermal degradation of poly(lactic acid) driven by random scission

An enhanced general analytical equation has been developed in order to evaluate the kinetic parameters of the thermal degradation of poly(lactic acid) (PLA) at various linear heating rates and at constant rate conditions. This improvement consisted of replacing the n-order conversion function by a modified form of the Sestak-Berggren equation f(α) = c(1−α)nαm, which led to better adjustment of experimental data, and also adequately represented the conventional mechanisms for solid-state processes. The kinetic parameters so obtained have been compared to those determined by conventional differential and isoconversional methods. Given that the thermal degradation of PLA has been argued to be caused by random chain scission reactions of ester groups, the conversion function (α) = 2(α1/2−α), corresponding to a random scission mechanism, has been tested.

Evaluation of hydrogeological properties of fractured granitic aquifer in a micro watershed of Kandukuru -Southern India

Aquifer performance tests were conducted in a fractured granitic bedrock aquifer to determine the well performance and hydraulic characteristics of bore wells in a micro watershed of Kandukuru from Southern India. The long duration pump tests under constant rate conditions (ranges: 216-363 m3/day) were conducted independently at 6 bore wells to examine the variations in transmissivity. Different analytical methods were employed for the same test data, in order to extract possible variability in hydrogeological parameters. The estimated transmissivity values from different methods are in agreement with at least two of the applied methods. The transmissivity varied from 10.28 to 90.06 m2/day with mean of 33.6 m2/day whereas the specific capacity ranges between 10.40 and 67.31 lpm/m/dd. The values of both these parameters are in concurrence with each other for some tested wells. Application of multiple analytical methods confirmed that Jacob straight line method is an ideal for obtaining agreeable well hydraulic properties of fractured granitic aquifers. The tests have revealed that the sparsely fractured bedrock has feeble multi-dimensional interconnected fracture system. The lamellar hydraulic conductivity is extensive throughout the aquifer. Variations in transmissivity among the closely spaced wells exhibit heterogeneity and anisotropic characteristics. The aquifer has a trend of increasing transmissivity from southeast to northwest. The hydraulic conductivity between few extraction wells is particularly high indicating that they are connected by a highly transmissive fracture. The highly contradictory aquifer parameters within a close range pointed out that the area is subjected to selective structural disturbances. The development of secondary porosity and permeability in the form of fractures system are uneven and superficial. Key words: Aquifer characteristics, fractured granitic terrain, transmissivity, specific capacity, bore well performance.

Laboratory cake filtration testing using constant rate

A precipitated calcium carbonate with Sauter mean diameter of 7.5μm was filtered under conditions of constant rate and constant pressure in a comparative laboratory investigation. The specific cake resistance to filtration was found to vary between 1×109 and 1×1011mkg−1, depending on the applied pressure, and the corresponding filter cake volume concentrations were between 0.42 and 0.54 (v/v). The calculated specific resistance, from the particle size distribution data and the Kozeny–Carman equation is one order of magnitude lower than that measured, even though the solids were extremely robustly characterised. Practical filter testing rather than design based on size distributions is known to be essential. However, the conventional approach is to use constant pressure laboratory tests, the results presented here demonstrate that constant rate filtration is a more reliable method for data acquisition, especially when determining the filter medium resistance, and readily available laboratory equipment is adequate for use.