A New Solution Methodology to the Material Balance Equation, for Saturated Reservoirs
- Olatunde O. Mosobalaje (Covenant University) | Charles Y. Onuh (Covenant University) | Ifeanyi Seteyeobot (Covenant University)
- Document ID
- Society of Petroleum Engineers
- SPE Nigeria Annual International Conference and Exhibition, 4-6 August, Lagos, Nigeria
- Publication Date
- Document Type
- Conference Paper
- 2015. Society of Petroleum Engineers
- 5 Reservoir Desciption & Dynamics, 5.3.2 Multiphase Flow, 5.3 Reservoir Fluid Dynamics
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The material balance equation (MBE) is a versatile analytical tool in petroleum reservoir engineering. Solution to the MBE is put to a predictive use for predicting reservoir performance, i.e. cumulative oil production, Np as a function of the declining average reservoir pressure, . For under-saturated reservoir (single-phase flow), the MBE presents Np as an explicit function of pressure drawdown ; hence a direct solution of the MBE yields the average pressure, for a given Np value. However, for multiphase flow in saturated reservoirs, the average reservoir pressure does not appear explicitly in the MBE, rather, it is implicitly present in the various pressure-dependent PVT parameters in the MBE (i.e. (Bo, Bg and Rs). Furthermore, the MBE for saturated reservoirs features the cumulative GOR term, Rp, a parameter related to Np; hence solving the MBE for saturated reservoirs typically involves cumbersome iterative schemes.
There exist in the literature various methodologies of solving the MBE with the purpose of predicting estimates of cumulative oil production, Np versus the declining average reservoir pressure, . The methodologies typically involve some multi-step iterations as the equation is solved for Np or Gp at various arbitrarily-chosen pressure nodes.
The need to solve this implicit problem without the rigor of human guesswork is the motivation for this work. This current work therefore presents a simple and computationally-cheap method for solving the MBE for the purpose of predicting estimates of cumulative oil production, Np versus the declining average reservoir pressure, .
In this new solution methodology, the philosophy of solving the MBE is analytically founded on the equality of the Left Hand Side, LHS (fluid withdrawal terms) and the Right Hand Side, RHS (fluid expansion terms) of the MBE for saturated reservoirs, and the pressure that upholds the equality.
This new solution methodology has been applied to two reservoir models and has been found to yield performance predictions that compares excellently well with predictions obtained from numerical solution (simulation) of complex fluid flow equations.
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MOSOBALAJE, O., ORODU, O. D. and TIAB, D. 2014. New Techniques for Estimating Properties of Saturated Reservoirs, using Readily-Available Rate Decline Data. Journal of Petroleum Science and Engineering, Vol 123, pp 96–105. Available Online: http://dx.doi.org/10.1016/j.petrol.2014.06.023