Predictable Control of Reservoir Pressure Through Voidage Replacement
Authors: Shiralkar G.S. , Stephenson R.E. 
Published: March 2010

Abstract
Effective reservoir management often requires operating a reservoir under conditions of controlled pressure, e.g., a solvent flood at pressures above the MMP. Sometimes regulatory agencies require pressure maintenance. This paper presents the theoretical basis, implementation and application of a method to predictably control average reservoir pressure for black oil and compositional systems.
Pressure maintenance results if "volumes in equal volumes out." However, fluid volumes can change dramatically across the reservoir, due to phase change and expansion. Evaluation of "volumes in" and "volumes out" becomes unclear, and current definitions of "voidage replacement ratio " (VRR) are thus subjective in nature.
Concepts of partial molar volumes are used to convert the impact of local mass fluxes into equivalent changes in region average pressure. Thus, a pressure equation is-derived for a region's average pressure that accounts for effects of phase change and nonideal mixing within a heterogeneous region.
This region pressure equation includes but goes beyond current ideas of VRR into direct and predictable control of region pressure. Thus, we can repressure a reservoir at a required rate (kPa/year) or simply maintain pressure at a predetermined level (kPa) by the realistic balancing of injection and withdrawal rates. Remarkable accuracy of pressure maintenance in particular (less than 35 kPa (5 psi) deviation from target over many years) is demonstrated through simulations of both water and solvent floods.
Since pressure control is direct and predictable, multiple simulations with tedious trial and error are avoided. Finally, the algorithm is inexpensive and easy to implement in existing generalized compositional models.

Introduction
Operation of a reservoir with control over pressure has numerous applications, ranging from primary to waterflood to solvent injection. While pressure maintenance is often desirable, at other times it may suffice to allow pressure to decline in a controlled manner. A concept often encountered within the petroleum industry is that of the voidage replacement ratio (VRR)(1) defined for a fixed portion (region) of the reservoir as:
Equation (1) (Available in full paper)
However, since fluids change volume within the reservoir, evaluation of these reservoir volumes is ambiguous. Ultimately, the idea behind voidage replacement is one of reservoir pressure control through injection in order to balance the effects of fluid production. With this in mind, a region "pressure equation" has been developed to allow direct and predictable control over the pore volume weighted average of reservoir pressure within a reservoir region. Two separate though related, problems are addressed - how to calculate the levels of injection/production necessary to reach and maintain a desired pressure in the reservoir, and how to reach/maintain that level reliably. The algorithm is best suited for implementation in a reservoir simulator.

Theoretical Discussion of Pressure Equation
In all cases, the average region pressure refers to the pore-volume weighted average pressure.
The physical interpretation of the pressure equation is explored below in the context of generalized compositional simulation. The concepts of multiphase partial mass or molar volumes and multiphase fluid compressibility that arise with the volume balance method are used to obtain a regional "pressure equation. "