Well Design and Construction

The Provost Dina 'X' Pool is a turbidite sand with a pay zone of up to 20 m at a depth of 200 mSS. The field contains approximately 1.2 million m3 of oil and there is a bottom water aquifer with partial pressure support in parts of the field. Most of the vertical wells in the field shut-in due to high water cuts after a relatively short period of production. Therefore, a numerical simulation study of the whole field was undertaken in order to improve recovery by infill drilling as well as by investigating different operating strategies. This paper describes the integrated team approach taken with input from the geological, production and reservoir engineering specialists to construct a reservoir model. The model has been successfully history matched and used, in turn, for predicting the performance of the field under existing conditions as well as a variety of infill drilling and operating scenarios. Results indicate that significant water coning, which would be observed with new vertical wells in certain areas of the pool, can be reduced through horizontal infill wells. Despite the potential technical success of horizontal infill wells, they were not economically feasible in this particular reservoir and vertical infill wells were the preferred choice. It is shown that a combination of carefully planned vertical infill wells and a pressure maintenance program is able to boost the ultimate recovery by 34% while keeping the development costs to a minimum. Results of various operating strategies are presented and the optimum field development scenario implemented in the field is outlined. The initial actual reservoir behaviour is discussed in the light of the results from the simulation study. Introduction The Provost Dina 'X' pool was discovered in 1988 at an initial pressure of 6450 kPa. The reservoir is located in east central Alberta, south of the town of Consort. The formation is a turbidite sand with a limited bottom water aquifer support. The production from the pool began with the discovery well 05-15-35-06 W4M and, to date, a total of 11 wells have delineated a reservoir area of slightly more than 32 ha. (see Figure 1). Historically, most of the vertical wells in the field experience high water cuts after a relatively short period of production. Thus, a significant portion of the reserves cannot be produced because of water coning. Infill drilling can compete favourably with BOR processes for the recovery of the bypassed oil for much less investment and operating cost. As the existing vertical wells have to be operated above the critical water coning rates to be economic, horizontal wells become another option for infill drilling. The field experience indicates that horizontal wells can reduce the water coning tendency while increasing the oil production. However, further improvement to oil production rate of horizontal wells is still limited by the encroachment of the water cone when the bottom water exists. Therefore a simulation study was undertaken to investigate the feasibility of increasing reserves by infill drilling with horizontal and vertical wells. Model Construction The black oil simulation module (SimBest II) of The Petroleum WorkBench reservoir management package of Scientific Software-Intercomp was used to conduct this simulation study. SimBest II is a three-dimensional, fully implicit reservoir simulator which is capable of handling as many as three fluid phases and five components in a dual and/or single porosity mode. P. 555

Stable cones created by a horizontal well drilled with maximum clearance from the unwanted fluid are studied (Muskat9 type approach, using pertinent viscous flow potential), yielding practical values for the critical rate per unit length of a horizontal well, and for the critical cone elevation, depending on both vertical and horizontal permeabilities, oil thickness, both fluid gravities, and oil viscosity. Critical rate weakly decreases when vertical permeability decreases. The same type of analysis is repeated for a vertical well completed over a very short interval (modelized as a point source) also with maximum clearance from the gas cap or water table, yielding values of critical rate and cone height for the vertical well. In this case the critical rate slightly increases when vertical permeability decreases. The outcome of a comparison between both types of wells shows that a critical cone comes closer to the horizontal well than to the vertical well. Also horizontal wells generally allow higher critical rates than vertical wells, however this advantage lessens with increased anisotropy. Very simple formulas are provided to evaluate what gain in critical rate may be obtained from a horizontal well.

The purpose of this paper is to report on the field test results of the Texaco Canada Petroleum Inc. (TEXCAN) and the Alberta Department of Energy (ADOE, formally AOSTRA), Electrical Horizontal Well Project in the Lloydminster heavy oil area. Two vertical wells (15D-25-56-2W4 and 13C-30-56-1W4) and one horizontal well (16D-25-56-2W4) were connected electrically and heated. This paper presents an overview of electrically heating a horizontal well with vertical wells, the design of the electrical heating system, operational experience, test data, and a discussion on the successes and problems of the project. Three wells were electrically heated; two deviated vertical wells and one horizontal well. The pilot project experienced premature equipment failure and sand production problems. Although a significant production response was achieved at the vertical wells, ongoing operations were not achieved because of sanding problems. The sand problem required daily workovers on the wells to maintain operations. As a result of these problems, and the limited current that can be supplied from just two vertical wells, the thermal response at the horizontal well was 3 - 5 °C and no production response was observed. The project was a technical success in that electrical current from two vertical wells was returned to the power conditioning units via the horizontal well and a thermal response was observed at all the wells. At the vertical wells, there was at times a greater than three times productivity response during electrical heating operations. Introduction Horizontal Wells and Heavy Oil Horizontal wells, typically 500 m in length and longer, are common in the exploitation of heavy oil reservoirs around the world. Horizontal wells offer prospects of improved performance over vertical wells, primarily due to the larger contact area between the formation and the wellbore. Also, the technology for drilling a horizontal well is as advanced as for drilling a vertical well. The cost of drilling a horizontal well is about the same as the cost to drill two to three vertical wells. There are production disadvantages and problems that are unique to a horizontal well application in heavy oil reservoirs. The production rate declines very rapidly during the first several months of production. It is also possible that the entire length of the horizontal well may not be productive. In some production systems, the limiting factor in producing the oil is the mechanical limitation of the pumping equipment, which is exceeded because of the very high viscosity of the oil. Finally, there may be skin effects, such as the visco-skin(1) that may further reduce the productivity of the well. This skin effect and other thermally alterable skin effects (for example, asphaltene precipitation) can block flow into the well, thereby decreasing the effective length and productivity of the well. Increasing the effective length of the well and removing any skin effects can improve the productivity of the well. Electrical Heating Electrical heating of vertical wells has been attempted on several occasions with encouraging results(2-10). Until now, there have been no electrical heating tests that use horizontal wells.

A compositional equation-of-state simulator has been used to make comparisons of CO2 process performance with several combinations of horizontal and vertical wells and various alternative reservoir descriptions. This is the first time that the performance of CO2 flooding using horizontal wells has been reported. We have used the reservoir and fluid properties of an actual West Texas carbonate reservoir that is currently being waterflooded. The phase behavior and properties of the CO2 used in these simulations are typical of those of multiple-contact- miscible field conditions of West Texas. A layered-type reservoir description was initially used to investigate the effect of water- altemating-gas (WAG) ratio with various combinations of well types. We then investigated the effect of vertical permeability, length, and position of the horizontal injector using the same reservoir description and a horizontal injector-vertical producer combination. Similar investigations using an unconditioned stochastic permeability field having a Dykstra Parsons coefficient (VDP) of 0.81 were made. Our final three-phase flow simulation was performed using a stochastic permeability field conditioned with core data. Since three nonaqueous phases can occur at low temperatures typical of West Texas floods resulting in up to four-phase flow with mobile water, we investigated the impact of four-phase flow in one of these simulations. This is the first time that three-dimensional, four-phase flow reservoir simulations have been reported with either vertical or horizontal wells.

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated–saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace–finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

The Gulf of Thailand (GoT) is south of Bangkok. The pay interval typically covers 3000 to 5000 vertical feet. It is composed of a series of stacked fluvial point bars sands that have limited areal extent. In addition, normal faulting breaks them up further. Because all 40 acre wells will be drilled at some point, the justification for drilling a horizontal well is based on incremental recovery over vertical wells. In 2010, a team was assembled to look at establishing a common method to evaluate horizontal wells. Production results from horizontal wells were compared to vertical wells. Concept models were used to evaluate different factors in horizontal well recovery. Where available, history matched simulation models were used to compare horizontal to vertical wells. In addition, the team looked at factors in horizontal well performance. The team collected information on all wells drilled. The team looked for relationships to EUR and recovery factor. Then, the team took a more in depth study of the best horizontals and the worst horizontals. The overall recovery factor averages 20% for horizontal wells and 12.5% for an equivalent vertical well. The average incremental is 7.5%. There are three sources for this difference. The first is improved areal sweep efficiency of a horizontal well. The second is lower abandonment pressure with deep gas lift valves than with a vertical well. In looking at the best and worst performing horizontal wells, the poorer wells were in small reservoirs, often drilled very close to contacts and some were drilled into depleted reservoirs. The best wells were drilled in large very continuous reservoirs and often had strong reservoir drive (either water drive or gas cap expansion). Description The Gulf of Thailand (GoT) is south of Bangkok. Figure 1 is a map of the Gulf of Thailand. The pay interval typically covers 3000 to5000 vertical feet. It is composed of a series of stacked fluvial point bars sands that have limited areal extent. In addition, normal faulting breaks them up further. The overall development strategy is to drill wells on equal spacing (40 acres) on the high side of the faults to encounter as many sands as possible. Figure 2 illustrates the stratagraphic and structural complexity. Chevron has drilled over 80 horizontal wells in the GoT with an average of about 5–10 every year. The targets are oil reservoirs that are at least 25 feet thick. By nature of the depositional and structural setting, these are relatively small reservoirs, usually with OOIP between 0.7 to 6.0 MMBO. The sands can have both a GOC and an OWC. Because all 40 acre wells will be drilled at some point, the justification for drilling a horizontal well is based on incremental recovery over vertical wells. Because the horizontal well design and execution plans are typically developed during the same drilling programs of vertical wells, a quick and reliable method of horizontal well evaluation is needed. In 2010, as part of the Reservoir Management Framework, a team was assembled to look at establishing a common method to evaluate horizontal wells. As part of this initiative, the team looked at factors in horizontal well performance. The study also included a comparison to vertical wells. The team used a multi faceted approach. Production results from horizontal wells were compared to vertical wells. Concept models were used to evaluate different factors in horizontal well recovery. Where available, history matched simulation models were used to compare horizontal to vertical wells.

Properties of gas condensate reservoirs are particularly difficult to study due to the composition and phase changes of light components that occur during the reservoir depletion. At the first stage of their discovery, these reservoirs behave like gas reservoirs during depletion. Once the dew point pressure is reached at reservoir conditions of pressure and temperature a retrograde condensation phase develops in the reservoir. Liquid condensation in the formation can result in severe loss of well deliverability and therefore of gas and condensate recovery, which will certainly lead to a loss of income. In this study, the performance of horizontal wells and vertical wells in Gas condensate reservoirs is investigated under various depletion schemes. The expected low horizontal well drawdown pressure, compared to vertical well for the same flow rate, considerably reduces retrograde condensation. A reservoir simulator is used to compare liquid saturation profiles in the case of horizontal and vertical wells in Gas condensate reservoirs. The influence of the horizontal well length section and reservoir thickness on horizontal well productivity, and condensate recovery were also simulated. Another factor investigated in this study is the effect of drilling a horizontal well in a Gas condensate reservoir that has already been developed by vertical wells. To illustrate the productivity increase due to the use of horizontal wells in gas condensate reservoirs, Djebel Bissa field data are presented and discussed using a compositional single well model (VIP simulator). The main results of this investigation are: Because pressure drawdown is smaller for a horizontal well than that for a vertical well, the problems related to the liquid deposit can be reduced by the use of horizontal wells. Layers of value of kh contains the most liquid accumulations.

Length and profile shape of horizontal section of the production well is one of the main issues in the justification of horizontal well completion. Justified choice of horizontal well completion and profile design is based on the main objectives: provide high initial rate, maximize the cumulated gas and condensate production, reduce the risk of well drilling and completion, extend a period with water free production, hence resulted in the maximum NPV. The main factors that influence the choice of horizontal well profile are the geological structure of the productive formation, its reservoir properties, the location of formation fluid contacts, formation anisotropy, the ratio of vertical and horizontal heterogeneity. In this paper we investigate the influence of mentioned geological factors on the choice of horizontal well profile. Various profiles of horizontal wells- directional, horizontal and U-shaped have been considered for gas condensate reservoirs. The analysis was conducted on the basis of hydrodynamic modeling Eclipse 300 using a function of multi-segment well. After choice of the optimal length for the horizontal section of the well, a simulation was performed. Also there was a comparison of the performance for directional and U-shaped horizontal wells with the same length. During comparing the well performance well productivity, cumulative gas and condensate production, inflow profiles, the conditions of liquid removing from well bottom of were evaluated. Sensitivity evaluation of the optimal profile selecting to the reservoir permeability and its anisotropy was performed. It helps to take into account the effect of uncertainty on the performance of the well. Selecting a profile of the horizontal section of the well is one of the main issues in the design and affects not only the final gas and condensate recovery, but also helps to clarify the geological structure formation during logging, and enable the development of all productive layers, reduce the risk of complications during the operation. Structural features of horizontal wells unlike allow to obtain vertical flow rates several times superior performance of vertical wells. And the increase in horizontal wells is provided not by increasing the drawdown, and by increasing the filter surface. Productivity is limited in the vertical wells of the reservoir reveals the thickness, whereas the thickness of a predetermined value for the formation and drawdown -the geometrical parameters of the liner and, consequently, horizontal wells depends on the length of the horizontal wellbore. The horizontal wellbore completion may be regarded as an effective method for production of hydrocarbons, and as a method of stimulation. Engineering and technology horizontal drilling, completion fluid, their performance, conduct work under stimulation to them, economic indicators drilling and operation of horizontal wells devoted several thousand research. At the same time question the justification of the optimal design and the length of the gas and gas condensate wells are virtually unexplored. Studies on this topic have been done by Z.S. Aliyev, V. Sheremet and V.A. Chernykh. Z.S. Aliyev in one of his works says that the only way to study the optimal design of horizontal gas wells drilled in inhomogeneously layered strata, is a numerical solution to this problem through the creation of geological and mathematical models of fragments of such deposits and the joint solution of unsteady, multidimensional, multiphase and multicomponent filtering the horizontal trunk with the equation of motion with a variable flow rate of the mixture along the length of the barrel. In this paper we provide a rationale for completing horizontal wells for specific geological conditions of the N-th gas condensate field located in the east of the autonomous area.

Amoco Sharjah Oil Company (ASOC) is conducting a horizontal/multi-lateral drilling program in the lower Cretaceous carbonate formation of its Sajaa retrograde/condensate field which lies at a true vertical depth of approximately -12,000 ft subsea. This program has included two single laterals and three dual lateral wells (two herringbone and a stacked-style). Three wells (one single and two dual laterals) were re-entries into original vertical development wells. Production rates from these wells are three to five times the calculated rate from vertical wells. Coil tubing production logging and stimulation operations were conducted in two of the wells of measured depth >15,600 ft (horizontal lateral length of 3,500 ft). Selective re-entry in the dual lateral with coil tubing was not successful. An acid wash stimulation improved the production rate by 30% in the single lateral well that was treated. The production log was capable of providing gross production rates of each lateral. A multilateral re-entry system has been installed in the current stacked-style dual lateral for future selective re-entry by coil tubing. Introduction Amoco Sharjah Oil Company discovered the Sajaa retrograde condensate field in December, 1980 and production began in 1982. The onshore Sajaa field is located in Sharjah, United Arab Emirates. The majority of the reserves have been developed from the Shuaiba and Kharaib carbonate formations in the lower Cretaceous Thamama group. The Shuaiba formation's top is at approximately -12,000 ft subsea and the Kharaib's top is 250 ft below the Shuaiba top. The Shuaiba is capped by the Nahr Umr shale formation. By November 1995 the field had been developed with 28 vertical development wells. A study concluded that a horizontal well in the Shuaiba should be significantly more productive than a vertical well because of wellbore contact increase. This led to the recommendation of the Sajaa field's first horizontal well. This paper reviews the drilling, completion and stimulation of the Sajaa horizontal wells; two single laterals and three dual laterals. The major drilling problem is geosteering in the Shuaiba formation because it has minimal logging characteristics, changing dip angles and unpredictable faults. The operations are complicated by the vertical depth of - 12,000 ft tvd and bottom hole temperatures of 295 F. The laterals are not lined, but the desire to selectively re-enter the dual laterals has led to several alterations in the completion philosophy. Completion designs have to be adapted to new wells and dual laterals which are initiated from original vertical wells. Coil tubing was used to run a production log in one of the dual laterals which allowed gross production measurement of each lateral. Selective re-entry into each lateral was not successful and the failed coil tubing acid stimulation required a work-over. The laterals were successfully re-entered with tubing and stimulated. Coil tubing was used to perform a 15% HCl acid wash of a single lateral increasing production by 30%. Horizontal Well No. 1 - Single Lateral The location of the first horizontal well was selected because the area had marginal productivity, but contained minimal reservoir uncertainties and dominant Shuaiba productivity. The well was drilled vertically to 10,490 ft then built to 390 at 11,478 ft (11,380 ft tvd) where the 9-5/8" casing was set in the Nahr Umr formation. An 8–1/2" pilot hole was drilled through the target formation to define its characteristics. The porosity zone identified for the lateral was between 11,975 ft and 12,020 ft md (Fig. 1). It was bounded by the Nahr Umr shale (top) and Shuaiba low porosity (bottom). There was concern that the Nahr Umr shale below the 9-–5/8" casing would be less stable at the higher inclinations so it was protected with a 7", 35 ppf liner. P. 349^

The objective of this work was to investigate the viability of converting existing conventional vertical wells to horizontal wells with multiple transverse fractures in targeted reservoirs. These reservoirs can be characterized as two thin, low permeability layers with no crossflow between them. The productivity of these reservoirs was very limited when producing by conventional vertical wells. Reservoir simulation was used to evaluate various combinations of transverse fractures in horizontal wells. These results were compared with simulation results for conventional vertical wells, with and without vertical fractures. Only infinite conductivity fractures were considered. Early transient behavior as well as pseudosteady-state behavior were simulated. The results show that horizontal wells with transverse fractures appear to make production of the targeted reservoirs economically feasible. It has been shown that the productivity index of horizontal wells with transverse fractures is mainly affected by the distance between the outermost fractures and not by the number of fractures nor the spacing between them. Between fractures perforations has been shown to have negligible effects on increasing the productivity of horizontal wells with transverse fractures in these reservoirs. Decline type curves are presented, for horizontal wells with transverse fractures, for future performance prediction and reserves estimates.

Enhanced Oil Recovery pilot testing aims at reducing uncertainty ranges for parameters and determining operating conditions which improve the economics of full-field deployment. In the 8.TH and 9.TH reservoirs of the Matzen field, different well configurations were tested, vertical versus horizontal injection and production wells. The use of vertical or horizontal wells depends on costs and reservoir performance which is challenging to assess. Water cut, polymer back-production and pressures are used to understand reservoir behaviour and incremental oil production, however, these data do not reveal insights about changes in reservoir connectivity owing to polymer injection. Here, we used consecutive tracer tests prior and during polymer injection as well as water composition to elucidate the impact of various well configurations on sweep efficiency improvements. The results show that vertical well configuration for polymer injection and production leads to substantial acceleration along flow paths but less swept volume. Polymer injection does not only change the flow paths as can be seen from the different allocation factors before and after polymer injection but also the connected flow paths as indicated by a change in the skewness of the breakthrough tracer curves. For horizontal wells, the data shows that in addition to acceleration, the connected pore volume after polymer injection is substantially increased. This indicates that the sweep efficiency is improved for horizontal well configurations after polymer injection. The methodology leads to a quantitative assessment of the reservoir effects using different well configurations. These effects depend on the reservoir architecture impacting the changes in sweep efficiency by polymer injection. Consecutive tracer tests are an important source of information to determine which well configuration to be used in full-field implementation of polymer Enhanced Oil Recovery.

The success, safety and stability of treatment methods of bottomhole formation zone depend on adequate bottomhole pressure. The latter is not directly controllable, but it can be changed by adjusting injection pressure. Using the Paccaloni method for any given measured injection rate, the downhole injection pressure can be estimated. In this paper, the Paccaloni method was developed, and the pressure drop changes in the skin zone for horizontal and vertical wells were estimated for planning acid treatment of the bottomhole formation zones in vertical, deviated and horizontal wells. To model pressure and velocity distributions in the bottomhole zone for the case of water injection in a vertical and horizontal wells COMSOL Mathphysics modules were used.

This paper presents comparative analysis between the pressure behavior of a horizontal well and a vertical well both subject to edge water drive. Green and source function were used to evaluate the performance of horizontal well and vertical well, eventually, compared based dimensionless pressures and pressure derivatives computed by varying the reservoir geometry. Results presented as type curves show that the rate of decline of the pressure derivative curve is more sharper and sensitive in vertical well than horizontal well of the same geometry indicating a shorter period of clean oil production in vertical well than the horizontal well. The period of radial flow as shown by the horizontal flattened part of the type curve indicate that for all reservoir geometry, the horizontal well will be able to sustain longer period of the radial flow than vertical well given infinite conductivity condition. http://dx.doi.org/10.4314/njt.v36i2.19

Although the technology of highly inclined and horizontal wells has recently progressed significantly, a reliable and practical formula to estimate the productivity of the well with respect to any angle of slant and anisotropy of permeability is still missing. This paper provides a method of estimation which fills the gap. The well pressure decline curves are generated by a semi-analytical in-house simulator. They lead to a geometrical pseudo skin factor which is matched for slanted wells with an analytically-derived equation. For horizontal wells, comparison is made with several existing formulae. An unrestrictive approach of anisotropy is possible through a spatial transformation from real medium into equivalent isotropic medium : this is achieved by modifying the length, azimuth, inclination and radius of the well. Equations of the pseudo skin factor are modified according to this transformation. Calculations reveal that a slanted well is less affected by anisotropy than a horizontal well : with a low vertical permeability, it can be more advantageous than a horizontal well of the same length. Graphic charts are displayed to easy the choice between horizontal and highly inclined wells.

A novel procedure is proposed for a quick and accurate evaluation of bottomhole wellbore pressure. The procedure has led to simple correlations for both horizontal and vertical wells which can be applied to calculate the bottomhole wellbore pressure and productivity index for the entire producing period. The correlations proposed here provide an excellent approximation of the semi-analytical solution at a much reduced computational time. Successful validation of the equations for different well locations and different reservoir geometries has also been achieved. Approach Bottomhole wellbore pressure and productivity index are two important quantities for both horizontal and vertical wells. For a horizontal or vertical well in a homogeneous but anisotropic reservoir, analytical equations can be obtained for bottomhole wellbore pressure drawdown once pseudo-steady state is reached. Practically, simple equations to evaluate the bottomhole wellbore pressure drawdown in early and transient time are as important as those for late time when the pseudo-steady state flow occurs. Although either the integral transformations (IT) (such as Laplace and Fourier) and separation of variables (SOV) method or the instantaneous point source/sink superposition and the Newman's product method may be used to determine the wellbore pressure drawdown, they take nontrivial (and usually long) computational time to get results, as a consequence they are impractical for routine reservoir engineering applications, such as well performance modeling. Therefore, a novel procedure is proposed here to develop simple yet accurate correlations to evaluate bottomhole wellbore pressure and well productivity index. The idea is very simple and the procedure consists of the following three steps: Step 1. Use the instantaneous point source/sink solution (IPSS) approach to compute wellbore pressure drawdown at different times; Step 2. Design appropriate functional forms which reflect characteristics of the wellbore pressure variation with time; Step 3. Apply a nonlinear regression method to determine the relevant correlation coefficients. Results Correlations for Horizontal Wells. Two functional forms of the wellbore pressure drawdown of horizontal wells, which are valid for the entire time period (from early time to transient and then to late-time long after pseudo-steady state is reached) have been tried for correlating the wellbore pressure drawdown data for different horizontal wells: Form I: (1) Form II: (2) where (3) The values of correlation coefficients, a, b, A and B, for different horizontal wellbore lengths, well locations and reservoir dimension ratios are given in Ref. 2. It was found that both functional forms can provide accurate predictions of the wellbore pressure for the entire time range. P. 287^