In the well testing process, the aims can differ but among the common ones are to determine its initial static reservoir pressure & temperatures as well as the inflow performance characteristics in the well using the mean reservoir pressure and the rate and finally the build-up reservoir pressure for determining the skin as well performing the well test analysis. These test techniques depend on the type of well under the test and the realistic time for allocated. After establishing the reservoir fluid compositions & well capacity in the partial clean-up process, the measurement of the initial reservoir pressure comes next in the initial build-up process. Next the productivity index measurement follows with the aim of establishing the inflow performance curve and boundary implications.

Upon the discovery of a well, the initial pressure will be the static pressure by default. Since it is the measured pressure in the well after closing it for a defined time period (normally 1-3 days). As the production continues this static pressure will approach the mean reservoir pressure where it value is useful in calculating the reserve determination among other useful parameters.

Pressure generally affects the well test analysis, based on a petroleum engineering paper prepared by Cobb, Ramey and Miller (1972). Using the multi-layered analysis and testing techniques in addition to ECLIPSE100 software for simulations, Cobb, Ramey and Miller studied reservoirs and came to the conclusion that pressure transient behavior depended on boundary effects, flow rates and permeability. After their simulation of wellbore pressures for each layer these results did math with those from the ECLIPSE-100 software given the skin-factors and permeability’s.

Rushatmanto et al (2017), argued that determining skin parameters and permeabilities is a classical approach which need to improvement through the use of Pressure Transient Analysis (PTA). The latter uses the time-lapse concept to reduce the uncertainties in the Initial Gas In-Place estimations as well as the accessing of the reservoir dimensions using the boundary conditions. The assessment conducted on Tunu Gas fields located in Kutal Basin, Indonesia meant that the analysis could go on before the initial oil production as opposed to the classical approach which needed the well to be in production for some time period since by then pressure will deplete.

Chen, Z. X. (1989) noted that Initial pressure is of importance in the design of such systems. Other engineers refer to such kind of pressure as Reservoir Pressure determined through pressure data extrapolation from the initial DST buildup. The pressure gives a guide selection for the Horner plot gradient (Second buildup). In the case of the 2nd buildup gradient extrapolation its pressure is less than the reservoir pressure. Even though it some cases it is possible to achieve depletion through identification as well as poor analysis and design. A technique for the Horner plot construction involves effectively producing the rate and time by also tabulating the pressure and time for each buildup time. Cartesian paper plots expand the plot using the buildup log( t +Δt)/ Δt against the pressure. In this case t equals the initial flow time whereas Δt will be starting period for the buildup. The extrapolated curve of the pressure sheds some light in determining the 2nd buildup as illustrated with plot below.

Figure with the Horner Graph

Diffusion does have a correlation with pressure going with Thiberville et al (2020), Dindoruk, Johns and Orr (2020) as well as Muslim, Pramana and Junin (2020). By definition, the unsteady form of diffusion is a state which it time dependent in that the diffusion rate changes with respect to time as per the arguments by Thiberville et al (2020). Thus, the concentration rate with respect to distance remains fairly constant while the varying concentration is never equal to zero. In the entire system with this particular form the diffusion rate will vary with time. Unlike the steady type this one quantifies it using the 2nd and 1st Fick Laws contrast to the latter which only uses the Fick 1st law.

The mathematical expression is that

………………………………………………..equation (a)

Given that D = Diffusivity or Diffusion co-efficient

J = Diffusion Flux (Substance amount per a given area with the defined time.

dc= change in concentration

dx = small distance

dt = small time period

dc/dx = time variation

The skin factor according to Dindoruk, Johns and Orr (2020) uses the radiated pressure among other properties coming from the fluid as shown in the equation (b) below. After assuming the log terms in the equation, skin factor can take the either a value approximately closer to zero or a positive one. In contrast negative skin factor are dangerous since they indicate a possibility of wells not properly stimulated.

……Equation (b)

REFERENCES

Chen, Z. X. (1989). Transient flow of slightly compressible fluids through double-porosity, double-permeability systems—a state-of-the-art review. Transport in Porous Media, 4(2), 147-184.

Cobb, W. M., Ramey Jr, H. J., & Miller, F. G. (1972). Well-test analysis for wells producing commingled zones. Journal of Petroleum Technology, 24(01), 27-37.

Dindoruk, B., Johns, R., & Orr, F. M. (2020, August). Measurement of Minimum Miscibility Pressure: A State-of-the-Art Review. In SPE Improved Oil Recovery Conference. Society of Petroleum Engineers.

Muslim, E., Pramana, A. A., Permadi, A. K., & Junin, R. B. (2020). FUNDAMENTAL OF MINIMUM MISCIBILITY PRESSURE DETERMINATION METHODS. UIR PRESS.

Shah, S. Y., As Syukri, H., Wolf, K. H., Pilus, R. M., & Rossen, W. R. (2020). Foam Generation in Flow Across a Sharp Permeability Transition: Effect of Velocity and Fractional Flow. SPE Journal, 25(01), 451-464.

Rushatmanto, M., Sianturi, J., Suwito, E., & Priskila, L. M. (2017, October). Integration of Time-Lapse Pressure Transient Analysis in Reservoir Characterization and Reducing Uncertainty of Initial Gas-in-Place Estimation: A Case Study in Gas Condensate Reservoir. In SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition. Society of Petroleum Engineers.

Suboyin, A., Rahman, M. M., & Haroun, M. (2020). Hydraulic fracturing design considerations, water management challenges and insights for Middle Eastern shale gas reservoirs. Energy Reports, 6, 745-760.

Thiberville, C., Wang, Y., Waltrich, P., Williams, W., & Kam, S. I. (2020). Modeling of Smart Pigging for Pipeline Leak Detection. SPE Production & Operations.

Wu, Y. S., Pruess, K., & Witherspoon, P. A. (1990). Flow and displacement of Bingham non-Newtonian fluids in porous media.